text
stringlengths
18
50k
id
stringlengths
6
138
metadata
dict
The onset of World War II inflamed rising anti-immigrant sentiment nationwide. The Japanese Exclusion Act, Executive Order 9066, was signed in 1942, requiring the internment of all West Coast Japanese Americans, two-thirds of whom were American citizens. The Mukai family – Kuni, Masa, his wife Chiyeko and their son Milton – fled Vashon, moving to Dead Ox Flats, Oregon where Chiyeko had family. They essentially became voluntary evacuees, moving outside the exclusion zone, and thus were not imprisoned as were the other Japanese families on Vashon. While exiled in Dead Ox Flats, Masa introduced row crops into what was then primarily cattle country. He raised seed for lettuce and other vegetables on 100 acres he purchased. He invented his own harvester to catch flyaway seeds, making a successful living throughout the war. During the war, Maurice Dunsford leased the entire Vashon farm and packing plant from the Mukai family. He operated the plant successfully throughout this period. Phillipe Baccaro, a labor contractor from Canada, sub-leased the house from Dunsford and farmed the land. Together the two of them kept the Mukai enterprises fully operational and profitable throughout the war. « 1926 to 1942 Success | Return and Change: 1946 to Present »
<urn:uuid:8ee35735-3b83-4c34-9050-8f9cd5c25883>
{ "date": "2019-07-16T08:04:58", "dump": "CC-MAIN-2019-30", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524517.31/warc/CC-MAIN-20190716075153-20190716101153-00137.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9738849401473999, "score": 3.578125, "token_count": 276, "url": "https://mukaifarmandgarden.org/history/exile/" }
GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 05 Dec 2019, 12:43 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Four cylindrical cans each with a radius of 2 inches are placed on th Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 59561 Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 18 Feb 2018, 22:54 00:00 Difficulty: 65% (hard) Question Stats: 29% (01:34) correct 71% (01:37) wrong based on 68 sessions ### HideShow timer Statistics Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches? (A) 64 (B) 32 (C) 30 (D) 20 (E) 16 examPAL Representative Joined: 07 Dec 2017 Posts: 1155 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 18 Feb 2018, 23:37 Bunuel wrote: Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches? (A) 64 (B) 32 (C) 30 (D) 20 (E) 16 'the four sides of the box bulge slightly' means that the cans take up a slightly larger area than that of the box. So, we'll look at the extreme of the range - a Logical approach. 4 cans arranged in a box on their base would be arranged in 2 rows of 2 (if they were arranged in 1 row of 4 or another non-symmetrical arrangement then there would be one side that didn't 'bulge'). Since each can has a radius of 2, this means that the cans takes up (2 cans * diameter of 4) = 8 inches. Then, if the cans fit perfectly, the perimeter of the box would be 8*4 =32 inches. But we know that the cans don't quite fit (the sides 'bulge') and therefore our answer is a bit less than 32. Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required. _________________ Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:02 Bunuel wrote: Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches? (A) 64 (B) 32 (C) 30 (D) 20 (E) 16 diameter of can = 4 so if side of the box buiges there is one can at the end of each of the box/facing each side and for it to bulge the box should be able to accommodate 8 inches in length atleast imo 8 is the side of the square and perimeter = 32 (B) looks good but considering bulge of the box i.e takes more area a side of 7.5 can suffice ps - considering the bulge is caused by the exterior of a can went it C at first i thought it'd be B Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:03 DavidTutorexamPAL wrote: Bunuel wrote: Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches? (A) 64 (B) 32 (C) 30 (D) 20 (E) 16 'the four sides of the box bulge slightly' means that the cans take up a slightly larger area than that of the box. So, we'll look at the extreme of the range - a Logical approach. 4 cans arranged in a box on their base would be arranged in 2 rows of 2 (if they were arranged in 1 row of 4 or another non-symmetrical arrangement then there would be one side that didn't 'bulge'). Since each can has a radius of 2, this means that the cans takes up (2 cans * diameter of 4) = 8 inches. Then, if the cans fit perfectly, the perimeter of the box would be 8*4 =32 inches. But we know that the cans don't quite fit (the sides 'bulge') and therefore our answer is a bit less than 32. Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required. I went with C as well initially .. but does the bulge definitetly mean it's going to take more area? Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:06 DavidTutorexamPAL wrote: Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required. even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge examPAL Representative Joined: 07 Dec 2017 Posts: 1155 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:08 Hatakekakashi wrote: I went with C as well initially .. but does the bulge definitetly mean it's going to take more area? I think so... if the sides 'bulge' e.g are pressed outward it is implied that the cans need more space then they have. To be fair this question is more about English than about math, not a standard question IMO _________________ Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:15 1 DavidTutorexamPAL wrote: Hatakekakashi wrote: I went with C as well initially .. but does the bulge definitetly mean it's going to take more area? I think so... if the sides 'bulge' e.g are pressed outward it is implied that the cans need more space then they have. To be fair this question is more about English than about math, not a standard question IMO I understand.. I think the word bulge makes all the difference Regards, HK examPAL Representative Joined: 07 Dec 2017 Posts: 1155 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 00:47 1 Hatakekakashi wrote: DavidTutorexamPAL wrote: Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required. even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge So I did the math and actually you would lose very little height by arranging in a triangle, the answer would still be (C). Basically if you put two cans on the base of the box = the base of the triangle they still need 8 inches of space for width. And if you put the third right above them in the middle then you lose about 0.54 inches in total length giving a length of about 7.46. So a 30-inch-perimeter box with a side of 7.5 inches would still likely bulge on all sides and at any rate is the only relevant answer. Since we're on the topic, consider an arrangement where two cans are in opposite corners and are tangent to each other. The other two cans are on top of them. We have no information on the total height of the box vs. height of the cans so this could work. Then the side of the minimal square is 4 + 2*sqrt(2) and the perimieter is about 27.3 inches This could also be made to bulge on 4 sides quite easily by decreasing the perimeter slightly (but there is no relevant answer). Anyways, for anyone reading please note that the above is not really relevant for your exam, feel free to skip over it _________________ Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 01:51 DavidTutorexamPAL wrote: Hatakekakashi wrote: DavidTutorexamPAL wrote: Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required. even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge So I did the math and actually you would lose very little height by arranging in a triangle, the answer would still be (C). Basically if you put two cans on the base of the box = the base of the triangle they still need 8 inches of space for width. And if you put the third right above them in the middle then you lose about 0.54 inches in total length giving a length of about 7.46. So a 30-inch-perimeter box with a side of 7.5 inches would still likely bulge on all sides and at any rate is the only relevant answer. Since we're on the topic, consider an arrangement where two cans are in opposite corners and are tangent to each other. The other two cans are on top of them. We have no information on the total height of the box vs. height of the cans so this could work. Then the side of the minimal square is 4 + 2*sqrt(2) and the perimieter is about 27.3 inches This could also be made to bulge on 4 sides quite easily by decreasing the perimeter slightly (but there is no relevant answer). Anyways, for anyone reading please note that the above is not really relevant for your exam, feel free to skip over it Thanks for taking your time out to do the math. in any case 30 should be fine then but as you've mentioned that the height of the can is not mentioned and considering the cans resting on the lateral surface i.e like this - instead of | then the answer could also not be determined ( discussion not related to the question) don't you think so? examPAL Representative Joined: 07 Dec 2017 Posts: 1155 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 02:00 Hatakekakashi wrote: Thanks for taking your time out to do the math. in any case 30 should be fine then but as you've mentioned that the height of the can is not mentioned and considering the cans resting on the lateral surface i.e like this - instead of | then the answer could also not be determined ( discussion not related to the question) don't you think so? WRT to the question then the cans are placed on their bases so I don't think they can be placed on their lateral surface. In general I agree with you, without information on the can's height the problem is unsolvable. There are potentially all kinds of different solutions including a mix of 'on the side' and 'on the base' If any of you are incredibly bored, consider this a spare time project to try at home! Take a bunch of cans and play around with them, see how many you can cram into a box. _________________ Current Student Joined: 07 Jan 2016 Posts: 1081 Location: India GMAT 1: 710 Q49 V36 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 19 Feb 2018, 02:08 DavidTutorexamPAL wrote: If any of you are incredibly bored, consider this a spare time project to try at home! Take a bunch of cans and play around with them, see how many you can cram into a box. hahaha :D I weigh 270 pounds so i guess can cram a lot of them Regards, HK Target Test Prep Representative Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2809 Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink] ### Show Tags 21 Feb 2018, 14:21 Bunuel wrote: Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches? (A) 64 (B) 32 (C) 30 (D) 20 (E) 16 The 4 cans will be placed on the square base of the box in the 2-by-2 formation. Since the total length of the diameters of 2 cans is 4 + 4 = 8, the cans would fit in a square with perimeter 8 x 4 = 32 without any bulging. Since all the sides of the box bulge slightly, the perimeter of the base of the box should be slightly less than 32. A possible value is 30. _________________ # Jeffrey Miller Jeff@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Four cylindrical cans each with a radius of 2 inches are placed on th   [#permalink] 21 Feb 2018, 14:21 Display posts from previous: Sort by
crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00538.warc.gz
null
Enter the Step 2 score, mean Step 2 score, and standard deviation of Step 2 scores into the calculator to determine the percentile rank. ## Step 2 Percentile Formula The following formula is used to calculate the Step 2 Percentile. P = (S - M) / SD Variables: • P is the percentile rank • S is the Step 2 score • M is the mean Step 2 score • SD is the standard deviation of Step 2 scores To calculate the Step 2 Percentile, subtract the mean Step 2 score from the individual’s Step 2 score. Then, divide the result by the standard deviation of Step 2 scores. The result is the percentile rank, which indicates the percentage of scores in its frequency distribution that are equal to or lower than it. ## What is a Step 2 Percentile? A Step 2 Percentile is a scoring system used in medical education, specifically for the United States Medical Licensing Examination (USMLE) Step 2 Clinical Knowledge (CK) test. It ranks a student’s score against others who took the same exam, providing a percentile that shows how a student’s score compares to others. For example, if a student is in the 90th percentile, it means they scored higher than 90% of test takers. This percentile is often used by residency programs to compare applicants. ## How to Calculate Step 2 Percentile? The following steps outline how to calculate the Step 2 Percentile using the formula: P = (S – M) / SD 1. First, determine the Step 2 score (S). 2. Next, determine the mean Step 2 score (M). 3. Next, determine the standard deviation of Step 2 scores (SD). 4. Next, use the formula P = (S – M) / SD to calculate the percentile rank (P). 5. Finally, calculate the Step 2 Percentile. 6. After inserting the variables and calculating the result, check your answer with the calculator above. Example Problem : Use the following variables as an example problem to test your knowledge. Step 2 score (S) = 85 Mean Step 2 score (M) = 75 Standard deviation of Step 2 scores (SD) = 10
crawl-data/CC-MAIN-2023-50/segments/1700679100518.73/warc/CC-MAIN-20231203225036-20231204015036-00322.warc.gz
null
Guess what. A few years ago, NASA found that our solar system has a tail. No, we haven’t heard that it is wagging and a far as we know the only one that has caught it is NASA’s Interstellar Boundary Explorer space probe. This was in 2009. This tail is a stream of charged particles originating in the Sun. They stream backwards from the Sun’s path of travel through galactic space. The effect is a long tail pointing back from where the Sun (and its planets) has come. The spacecraft, launched in 2008, is mapping the turbulent boundary far beyond Pluto, between interstellar space and the the heliosphere. An article in Sky and Telescope explained that charged particles and magnetic field lines flowing from the Sun as the “solar wind” make up an enormous bubble encasing the solar system, called the heliosphere. Interaction between these particles and the hydrogen atoms in deep space are detected by the craft. The mapping revealed the tail looking “downwind” in the direction of where the constellations Orion and Taurus meet on the winter evening sky. The Sun, along with the Earth and other planets is heading roughly towards the bright star Vega in the constellation Hercules, well seen in the summer evening sky. Hurtling forward with its great tail, the solar system is moving at approximately 136.7 miles a second. At this rate we travel an entire light year in 1,400 years. Note, the distance to the nearest other star system, Alpha Centauri, is 4.3 light years. The Milky Way Galaxy is big indeed. It takes the Sun as much as 240 million years to orbit once around the galaxy, with all the other stars moving as well. The tail isn’t something you would easily see “from out there”- no more than you could see the wind blowing. A tail of charged particles, however, has been photographed streaming back from another star, a famous variable star named Mira. It was pictured in ultraviolet light by NASA’s Galaxy Evolution Explorer space telescope. Mira’s tail is 13 light years long. The tail looks a lot like a comet tail. The solar wind is also responsible for pushing back the fine dust and gas from a melting comet as it passes by the Sun, creating a long vaporous tail. NASA reports that nearly a dozen competing theories have been introduced to explain this phenomenon. Tails of course are well known to backyard astronomers. I’ve had plenty of cats come by in the dark while I’m trying to look through the telescope. The constellations also sport quite a few tails- depending on how you connect the stars. Those with tails include Leo the Lion, Draco the Dragon, Canis Major the Big Dog, Hydra the Sea Serpent, Cygnus the Swan and even Ursa Major the Big Bear. Ever see a bear with a long tail? The Big Dipper is part of the Bear constellation, and some see the Dipper’s “handle” as the tail! Enough of this “tail.” For more information on the IBEX space mission, visit: http://www.nasa.gov/ibex . Full Moon is on Sept. 6. Keep looking up! — Peter Becker is Managing Editor at The News Eagle in Hawley, PA. Notes are welcome at firstname.lastname@example.org. Please mention in what newspaper or web site you read this column.
<urn:uuid:880d2e05-66e7-49af-b645-4bd02bc952db>
{ "date": "2018-12-17T16:19:53", "dump": "CC-MAIN-2018-51", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376828697.80/warc/CC-MAIN-20181217161704-20181217183704-00096.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9438671469688416, "score": 4, "token_count": 730, "url": "https://www.kiowacountysignal.com/lifestyle/20170901/looking-up-night-sky-is-full-of-tails" }
Using thermal imaging, the scientists observed that bees had physically moved the absorbed heat in their bodies to previously cooler areas of the hive." New York, July 26 - To protect their young ones from heat, honey bees can absorb heat from the brood walls just like a sponge and later transfer it to a cooler place to get rid of the heat from their bodies, says a study. Moving heat from hot to cool areas is reminiscent of the bio-heat transfer via the cardiovascular system of mammals, said Philip Starks, a biologist at Tufts University in the US. This is the first study to show that worker bees dissipate excess heat within a hive in process similar to how humans and other mammals cool themselves through their blood vessels and skin. This study shows how workers effectively dissipate the heat absorbed via heat-shielding, a mechanism used to thwart localised heat stressors, Starks added. Previous research has shown that workers bees, among other duties, control the thermostat essential to the hive's survival. When temperatures dip, worker bees create heat by contracting their thoracic muscles, similar to shivering in mammals. To protect the vulnerable brood when it is hot, workers fan the comb, spread fluid to induce evaporative cooling, or - when the heat stress is localised - absorb heat by pressing themselves against the brood nest wall (a behaviour known as heat-shielding). But until this study, scientists did not know how the bees got rid of the heat after they had absorbed it. For the study, researchers collected data on seven active honey bee hives that were framed by clear Plexiglas walls and using a theatre light, the researchers raised the internal temperature of the hives for 15 minutes. Using thermal imaging, the scientists observed that bees had physically moved the absorbed heat in their bodies to previously cooler areas of the hive. The study appeared in the journal Naturwissenschaften, The Science of Nature.
<urn:uuid:a252dcb0-6e04-4b63-812c-25aedaa19ccf>
{ "date": "2015-09-04T14:34:07", "dump": "CC-MAIN-2015-35", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645353863.81/warc/CC-MAIN-20150827031553-00348-ip-10-171-96-226.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9418038725852966, "score": 3.546875, "token_count": 401, "url": "http://www.nerve.in/news:2535002391204" }
E.1.1 Define the terms stimulus, response and reflex in the context of animal behaviour. Stimulus: a change in the environment (Internal or external) that is detected by a receptor and elicits a response. Response: a reaction to a stimulus Reflex: a rapid, unconscious response E.1.2 Explain the role of receptors, sensory neurons, relay neurons, motor neurons, synapses and effectors in the response of animals to stimuli. Receptors: They transform the stimuli into a nerve impulse. They are often modified nerve endings. Sensory neurons: It is a part of the peripheral nerve system, and is a type of neuron. Connects the receptors to the CNS. The impulse travels along the axon of the sensory neuron. The cell body is located in the dorsal root ganglion. Relay neurons: They are inside the grey matter of the spinal cord, and it's involved in the reflex arc of the CNS. It forms a synapse with the sensory neurone, and then with the cell body of a motor neurone. Motor neurons: a neurone of the peripheral nerve system. Carries the nerve impulse from the CNS to the effector. Its cell body is also inside the grey matter. The Axon leaves through the ventral root of the spinal cord, and travels through the body to the effector. It forms a synapse with an effector, such as a muscle. Synapses: a junction between two nerve cells or a nerve cell and an effector. E.1.3 Draw and label a diagram of a reflex arc for a pain withdrawal reflex, including the spinal cord and its spinal nerves, the receptor cell, sensory neuron, relay neuron, motor neuron and effector. Prey Preference in the Garter Snake of California Hypothesis: the difference in diet selection is behavioral and genetically inherited. Experiment: in an experiment pregnant snakes from two coastal regions have been collected. Inland and Coastal animals are isolated from each other. The hatchlings are offered Banana slug food over a 10 day period. Conclusion: Coastal Garter Snake eat more Banana slugs than Inland Garter Snakes. Behavior differences are genetically based. Two populations have diverged due to a difference in behaviour. The experimental conclusion was followed up with an investigation looking for the heritable aspect of the 'slug smelling' difference between coastal and inland Garter snakes. The difference between the coastal and inland Garter snake is genetic, the gene allows snake to detect the molecule that is slugs 'smell'. In other words, the sense of smell of the snakes is different. The evolution of 'slug smelling' in coastal species is an adaption made in the colonisation of the regions (10,00 years). Those individuals with the 'slug smelling' gene found more or better food 'non smellers', through better more successful reproduction this gene becomes more frequent in the population.
<urn:uuid:1cecb106-f4f6-4e6a-85d7-67dccc9ae022>
{ "date": "2014-10-25T01:22:45", "dump": "CC-MAIN-2014-42", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646849.7/warc/CC-MAIN-20141024030046-00044-ip-10-16-133-185.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.921590268611908, "score": 4.1875, "token_count": 613, "url": "http://eclair910.blogspot.com/p/option-e-neurobiology-and-behaviour.html" }
GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 17 Oct 2019, 19:13 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # There are a total of 10 sandwiches in a picnic hamper, 5 of which are Author Message TAGS: ### Hide Tags Senior RC Moderator Joined: 02 Nov 2016 Posts: 4106 GPA: 3.39 There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink] ### Show Tags 04 Mar 2019, 14:42 1 00:00 Difficulty: 25% (medium) Question Stats: 83% (01:24) correct 17% (01:40) wrong based on 35 sessions ### HideShow timer Statistics There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed? A. $$\frac{3}{10}$$ B. $$\frac{2}{45}$$ C. $$\frac{3}{80}$$ D. $$\frac{1}{27}$$ E. $$\frac{1}{120}$$ _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 3074 Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink] ### Show Tags 04 Mar 2019, 23:03 1 Solution Given: • There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. • 3 sandwiches are removed at random. To find: • The probability that all 3 roast beef sandwiches are removed. Approach and Working: • The number of ways we can remove 3 sandwiches from a total of 10 sandwiches = $$^{10}C_3$$ = 120 • The number of ways we can remove 3 roast beef sandwiches from a total of 3 roast beef sandwiches = $$^3C_3$$ = 1 • Therefore, the required probability = $$\frac{1}{120}$$ Hence, the correct answer is option E. _________________ GMAT Club Legend Joined: 18 Aug 2017 Posts: 5014 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink] ### Show Tags 06 Mar 2019, 02:17 total sandwiches = 10 so beef being removed = 3/10 * 2/9 * 1/8 1/120 IMO E There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed? A. $$\frac{3}{10}$$ B. $$\frac{2}{45}$$ C. $$\frac{3}{80}$$ D. $$\frac{1}{27}$$ E. $$\frac{1}{120}$$ Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8086 Location: United States (CA) Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink] ### Show Tags 08 Mar 2019, 08:02 There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed? A. $$\frac{3}{10}$$ B. $$\frac{2}{45}$$ C. $$\frac{3}{80}$$ D. $$\frac{1}{27}$$ E. $$\frac{1}{120}$$ The probability that 3 beef sandwiches are removed is (3C3)/(10C3) = 1/[(10 x 9 x 8)/3!] = 1/120. _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are   [#permalink] 08 Mar 2019, 08:02 Display posts from previous: Sort by
crawl-data/CC-MAIN-2019-43/segments/1570986677412.35/warc/CC-MAIN-20191018005539-20191018033039-00136.warc.gz
null
Teaching Ideas # 10 Ways to use Building Bricks in the Classroom Kids love building bricks! It brings an element of fun to any learning concept! We have put together some of our most favorite classroom activities using building bricks. Nifty tip: rather than writing on the bricks with permanent marker, stick masking tape on each piece so that you can re-use them for other activities! ## Letters, Sounds and Words ### 1. Lowercase and Uppercase Students have to match up the lower case and upper case letters of the alphabet. ### 2. Sight Word Tower Students need to say the sight word correctly before they add a building brick to their tower. They keep going until they get stuck on a word! Who can build the highest sight word tower? Check out our huge range of sight word flashcards. ### 3. Sentence Structure Activity Students pick from a range of nouns, verbs and adjective building bricks to create their very own sentence. ### 4. CVC Words! Using our CVC Flashcards, students find the matching building brick to create the word! ## Numbers, Measurement and Classifying ### 5. Greater Than or Less Than? A great activity to help consolidate the concept of greater than or less than. Use our Greater/Less Than Crocodile Posters and 0-20 Number and Word Flashcards – Circles. Students pick two numbers, build a tower with each number and then place the greater than or less than crocodile in the middle. ### 6. Fractions A great way to demonstrate fractions with a familiar article. I used the Fraction Wall Poster to create the image below. I colored the tops of the building bricks with a black permanent marker to show the different fractions. Use this idea as a great matching game or as a simple display for students to refer to! ### 7. Estimate and Measurement Students estimate how many pieces will cover certain articles such as an exercise book. After they have estimated, they then work out the answer. Students can estimate how many building bricks it will take to be the same height as the jar, then see how close their estimation was… ### 8. Counting Using masking tape, write the numbers 1-20 on a set of building bricks. You may wish to make it slightly harder for older students, such as skip counting, or larger numbers. Students then put the bricks in order by creating a tower! ### 9. Sorting and Classifying Using our Venn Diagram Template, students sort and classify a pile of building bricks. A great way to discuss the similarities and differences and how to use a Venn Diagram. ### 10. Build a Clock Face Use the building bricks to create a clock face. A great way to consolidate the five minutes between each number on the clock face! Have your students create their very own clock using the building bricks and a big piece of paper.
crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00349.warc.gz
null
Egypt Under Nasser, War with Israel Arab summit, Egyptian government, War of Attrition, Sinai Peninsula, Suez Canal In June 1967 Israel, unable to secure military assistance from the United States or any European nations, launched surprise air attacks against its Arab enemies, virtually destroying the air forces of the UAR, Jordan, Syria, and Iraq. In the ensuing Six-Day War, Israel captured the Gaza Strip and the Sinai Peninsula from the UAR. Nasser retaliated by breaking diplomatic relations with the United States, which he accused of aiding Israel, and again closing the Suez Canal. Jordan and Syria likewise suffered defeat and lost territory to the Israelis. In the wake of its defeat, the UAR sought more weapons and military advisers from the USSR. It also began to make peace with Saudi Arabia, on whom it had to rely for economic assistance. Under the terms of a peace plan for Yemen, Egyptian troops were at last withdrawn from Yemen in December 1967. As Saudi influence increased, the Egyptian government began, imperceptibly at first, moving from Arab socialism toward a more Islamic orientation. In November 1967 the UN Security Council passed Resolution 242, a peace proposal that called for Israelís withdrawal from lands taken in the recent fighting. In 1968 UAR and Israeli forces began firing regularly at each other across the Suez Canal, leading Nasser in March 1969 to declare a War of Attrition against Israel. Israel responded with air and land attacks on the UAR. Nasser, in turn, requested more Soviet military assistance. In 1970 U.S. secretary of state William Rogers proposed a peace plan that would have extended Resolution 242 by requiring Israel to give back almost all the land it had taken in 1967 in return for peace treaties with its Arab neighbors. Israel rejected the plan, while Nasser decided to join Jordan in accepting the plan. Palestinian commandos who opposed the plan challenged Jordanís King Hussein. Nasser called another Arab summit in Cairo and managed to reconcile the two sides. He died of a heart attack within hours after the meeting ended. Nasserís death and funeral led to an outpouring of grief throughout the Arab world. Article key phrases:
<urn:uuid:9d89bae2-6597-4b12-8500-6244730beb62>
{ "date": "2019-03-26T05:56:30", "dump": "CC-MAIN-2019-13", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204857.82/warc/CC-MAIN-20190326054828-20190326080828-00216.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9468264579772949, "score": 3.65625, "token_count": 441, "url": "http://countriesquest.com/africa/egypt/history/egypt_under_nasser/war_with_israel.htm" }
Word 2013 Table Tricks and Tips In Word 2013, text pours into a table on a cell-by-cell basis. You can type a word, sentence, or even a paragraph. All that text stays in the cell, though the cell changes size to accommodate larger quantities of text. You can format a table’s cell just like any paragraph in Word, even adding margins and tabs. All the standard text and paragraph formats apply to cells in a table just as they do to regular text, but your first duty is to get text into a table’s cell. If you have large quantities of text in a single cell, you probably don’t need a table to present your information. Even though you can format first-line indents for text in a cell, such formatting can be a pain to manipulate. Show the Ruler when you work with formatting a table. Navigate a table Text appears in whichever cell the toothpick cursor is blinking. Though you can simply click the mouse in a cell to type text, you can use keyboard shortcuts to move around the table: Press the Tab key to move from cell to cell. To move back, press Shift+Tab. When you press the Tab key at the last cell in a row, the toothpick cursor moves down to the first cell in the next line. Pressing the Tab key in the table's last, lower-right cell automatically adds another row to the table. To produce a tab character within a cell, press Ctrl+Tab. When you press the Enter key in a cell, you create a new paragraph in a cell, which probably isn’t what you want. The Shift+Enter key combination can be used break up long lines of text in a cell. Select in a table You can select the text itself, or you can select a cell, row, or column. Here are some suggestions: Triple-click the mouse in a cell to select all text in that cell. Select a single cell by positioning the mouse in the cell's lower-left corner. The mouse pointer changes to a northeastward-pointing arrow, as shown in the margin. Click to select the cell, which includes the cell’s text but primarily the cell itself. Move the mouse into the left margin and click to select a row of cells. Move the mouse above a column, and click to select that column. When the mouse is in the "sweet spot," the pointer changes to a downward-pointing arrow. Selecting stuff in a table can also be accomplished from the Table group on the Table Tools Layout tab. Use the Select menu to select the entire table, a row, a column, or a single cell. Clicking the table’s handle selects the entire table. The handle is visible whenever the mouse points at the table or when the insertion pointer is placed inside the table. Math in a table The main difference between Word and Excel is that Word’s math commands aren’t as sophisticated as the ones you find in Excel. Some would consider that a blessing. Follow these steps: Create a table that contains values you want to add. The values can be in a row or column. The last cell in that row or column must be empty. It’s into this cell that you paste the SUM formula. Click the mouse in the cell where you want to place the formula. Click the Table Tools Layout tab. Click the Formula button in the Data group. The Formula dialog box appears. Choose SUM from the Paste Function menu. Click the OK button. The values in the row or column are totaled and the result displayed in the table. When you change the values in the table, you need to refresh or update the formula. To do so, right-click on the total in the table. From the pop-up menu, choose the command Update Field. If you don’t see the Update Field command, you clicked on the wrong text. Convert text into a table If you started working on your document before you discovered the Table command, you probably have fake tables created by using tabbed text. If so, you can easily convert that text into a bona fide table by following these simple steps: Select the text you want to convert into a table. It helps if the text is arranged into columns, with each column separated by a tab character. If not, things get screwy but still workable. From the Insert tab, choose Table→Convert Text to Table. The Convert Text to Table dialog box appears. Ensure that Tabs is selected in the Convert Text to Table dialog box. Confirm that your text-to-table transition is set up properly by consulting the Number of Columns item in the Convert Text to Table dialog box. If the number of columns seems correct, the conversion most likely is a good one. When the number of columns is off, you have a rogue tab somewhere in your text. You probably need to make adjustments, reset column widths, and so on and so forth. These tasks may be a pain, but they're better than retyping all that text. Turn a table into plain text To boost your text from the confines of a table’s cruel and cold cells, obey these steps: Click the mouse inside the table you want to convert. Don’t select anything — just click the mouse. Click the Table Tools Layout tab. From the Table group, choose Select→Select Table. From the Data group, choose Convert to Text. The Convert to Text dialog box appears. As with converting text to a table, some cleanup is involved. Mostly, it’s resetting the tabs — nothing complex or bothersome.
<urn:uuid:0db30a05-fc19-4089-8fac-e47ca3e2b9d5>
{ "date": "2015-04-27T04:24:29", "dump": "CC-MAIN-2015-18", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246657041.90/warc/CC-MAIN-20150417045737-00142-ip-10-235-10-82.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8486335873603821, "score": 3.578125, "token_count": 1209, "url": "http://www.dummies.com/how-to/content/word-2013-table-tricks-and-tips.navId-815728.html" }
Most of us in the Midwest at least take trees for granted. They are so common and seem to grow so easily that we fail to consider how carefully they have to be designed to survive. The leaves of trees are especially complex. Not only is their chemistry that turns sunlight and common chemicals into usable complex compounds highly sophisticated, but their physical makeup and shape are also carefully engineered. Leaves have to be arranged on a tree so that there is an efficient interception of the sun's rays. If you have ever stood beneath a tree and looked at its shadow, you know that very little sunlight is wasted. In addition to absorbing sunlight and carrying on photosynthesis, leaves have to be able to endure a great deal of physical abuse. In severe wind, a leaf has to have minimal drag. If the drag of leaves is high, a tree will be toppled by even moderate winds. To have a low drag, the shape is critical. A highly streamlined object with a gentle rounding upstream and an elongated point going downstream will experience less than 10% of the drag of a sphere or a cylinder of equal volume. The complex shapes of most leaves do not conform to this simple shape we have just described. Steven Vogel, writing in Natural History magazine (September, 1993, pages 59-62), has found that when exposed to wind, leaves reconfigure themselves into cones or roll themselves up so that they are stable in high winds. It is obvious that a rolled-up leaf or a cone-shaped object is less likely to catch wind than an open object which can act like a sail. Groups of leaves can naturally fold into a communal cone, once again minimizing the drag that they put on the tree. There are enormous engineering problems involved in the catching maximum sunlight, having enough volume to carry on sufficient photosynthesis to supply the needs of the plant, and having a way to avoid providing sufficient surface area to push over the tree. The design of leaves that allows all of these characteristics to be present is incredible. A leaf's stem must resist bending in an up/down direction in order to catch sunlight. To provide the rolling up of leaves or the formation of cones, the stem must permit twisting. This is done by grooves in the stem which are positioned in such a way to decrease torsional stiffness without decreasing flexural stiffness. The common leaf speaks eloquently of the incredible complexity of all living things. We suggest that the assumption that chance can explain all of these things takes more faith than does the admission that intelligent design was the cause. Back to Contents Does God Exist?, Sep/Oct 1996
<urn:uuid:ecee066a-ae84-4875-9e15-5c090077c386>
{ "date": "2016-06-25T05:07:02", "dump": "CC-MAIN-2016-26", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783392099.27/warc/CC-MAIN-20160624154952-00046-ip-10-164-35-72.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.964755117893219, "score": 4.09375, "token_count": 531, "url": "http://www.doesgodexist.org/SepOct96/Leaves.html" }
Any timekeeping device will contain at least three different parts: a drive mechanism, an escapement device (way of measuring time), and a method of display. A windup alarm clock, for example, uses a tension spring as a drive mechanism, an escapement wheel, and the gear driven mechanical hands moving across the clock face as a display of the time. Generations of timepieces through history have worked to improve accuracy. Early mechanical clocks used falling weights as drive devices and a verge and foliot as an escapement device. The verge was a gear tensioned by a weight and the foliot was a ratchet type device that oscillated back and forth on the verge in a hold release pattern creating the familiar tick tock sound of clocks. Escapement wheels in mechanical clocks of today use much the same concept. The discovery of the pendulum by Galileo provided an even more accurate method of timekeeping as the frequency of the pendulum�s swing is not affected in time by its amplitude. In other words, even as the pendulum�s swing weakened in amplitude, the frequency between cycles remained constant. Having a timepiece that was portable also had its challenges. Pendulum clocks don�t work well in motion. Spring driven clocks give portability, but run faster when newly wound and progressively slower as the spring relaxes. Electric clocks were an improvement, but with still relatively low frequency escapement at 60 cycles per second, were not extremely accurate. Enter the Quartz Clock. Quartz timepieces use the nature of the quartz crystal to provide a very accurate resonator which gives a constant electronic signal for timekeeping purposes. Quartz crystals are piezoelectric, which means that they generate an electrical charge when mechanical pressure is applied to them. They also vibrate if an electrical charge is applied to them. The frequency of this vibration is a function of the cut and shape of the crystal. Quartz crystals can be cut at a consistent size and shape to vibrate at thousands of times per second, making them extremely stable resonators for keeping very accurate time. Although the piezoelectric effect of quartz crystals had been understood since the 1880s, the first application of this quartz property in the use of a time piece didn�t occur until 1927. It was in that year that the original quartz clock was invented by W.A. Marrison and J.W. Horton. Their quartz clock was a very large device as compared with today�s quartz wristwatches which also use microchip and liquid crystal display technology. Further reading: How quartz watches work, by Horology.com Stephen Portz, Technology Teacher, Space Coast Middle School, FL The basic principle behind all watches and clocks is a device that oscillates at a fixed frequency. Early mechanical watches and clocks used a pendulum or springs with some form of regulator to keep the frequency fixed. Time is simply measured by counting these oscillations. A simple device might oscillate at 1Hz (once per second), therefore 1 second would elapse for each oscillation. Quartz watches began to appear in the early 1970s. They use a crystal of quartz (silicon dioxide) shaped like a small bar. This is a 'piezoelectric' material - when bent or compressed it generates a small electric field (and vice versa). The crystal is formed to have a natural oscillation at around 32,000Hz. These oscillations generate small electrical signals which are 'divided down' by the circuit within the watch to the required frequency (usually seconds) and translated into pulses which are sent to the watch display or a motor to move the seconds hand. The advantage of quartz watches is their simplicity and accuracy - crystals maintain their frequency over broad operating conditions and are cheap to make. Higher accuracy devices generally use a material with even higher frequencies (again the frequency must be as stable as possible). Atomic clocks count the oscillations between the nucleus and the electrons in an atom (typically cesium) which oscillate at around 9 billion Hz. There is a good website with more details of quartz watch operations at http://www.howstuffworks.com/quartz-watch2.htm Jules Seeley, M.S., Physics graduate; Strategy Consultant, London 'My scientific work is motivated by an irresistible longing to understand the secrets of nature and by no other feelings.'
<urn:uuid:16539367-c2b6-4fd4-8a47-6ab8ce72497c>
{ "date": "2019-01-24T05:05:08", "dump": "CC-MAIN-2019-04", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584518983.95/warc/CC-MAIN-20190124035411-20190124061411-00258.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9551658630371094, "score": 3.875, "token_count": 913, "url": "https://www.physlink.com/Education/AskExperts/ae559.cfm" }
Swiss Mennonites in the Netherlands During the 16th and early 17th centuries there was hardly any contact between the Dutch and the Swiss Mennonites. About 1640, when the Dutch Mennonites became aware of the bad conditions of the Mennonites in Zürich, Switzerland (see Hattavier), and soon after, of the persecutions in the canton of Bern, they tried both directly through one of their members, Adolph de Vreede, who visited Bern, and especially by the intervention of the Netherlands States-General (see François Fagel) to support their Swiss brethren and to ameliorate their lot. This intervention, however, had only slight effect, and particularly in the canton of Bern conditions gradually grew worse. Bernese authorities had resolved to remove all the Mennonites from their territory because of their refusal to do military service and to unite with the state church. On 18 March 1710, a shipload of Bernese Mennonites who were to be forcibly transported to the English colonies in North America were released by order of the Dutch government when they arrived at Nijmegen in the Netherlands. Nearly all of them returned to the Palatinate, Germany. A small number of Swiss Mennonites seem to have immigrated to the Netherlands as early as 1660, settling in the province of Groningen; Swiss Brethren from the Palatinate are also reported to have settled near the city of Groningen. The Dutch Mennonites, whose delegates had set up a committee for the relief of foreign Mennonites in February 1660 (see Fonds voor Buitenlandsche Nooden) and who upon the initiative of Jan van Ranst of Rotterdam had made a proposal in 1671 to help the oppressed Mennonites in Switzerland by bringing them all to the Netherlands and settling them there at the expense of the Dutch Mennonites, began a major relief undertaking in 1711, when many Mennonites had to leave Switzerland. Johann Ludwig Runckel, the "resident" (that is, ambassador) of the Netherlands in Switzerland, made contact with the Dutch government and the Dutch Mennonites and after much negotiation with the Bernese authorities organized the immigration to the Netherlands. Runckel faced many difficulties. The Bernese Mennonites had just rejected the invitation of King Frederick I to settle in Prussia because they did not like to leave their native country, in spite of all persecution and misery. Also the controversy between the Amish and Reist groups was unfavorable to the success of the emigration, for often the Reist group refused to sail in the same ships with the Amish. Besides all this, many Mennonites in the canton of Bern had gone into hiding, although a mandate of amnesty had been proclaimed by the government of Bern. Finally 363 persons, including some non-Mennonites, were more or less voluntarily loaded into four ships and sailed from Basel on 18 July 1711. At Breisach, Germany, thirteen Mennonites left the ships. The others arrived at Amsterdam on 3 August, where they were warmly welcomed by the Dutch Mennonites, who attended to their many wants. Provided with many things (including an amazing quantity of hooks and eyes!), they were divided into four groups, and sailed on 20 August from Amsterdam to Harlingen in Friesland (21 persons), to Groningen (126), to Kampen (87), and to Deventer (116). A few remained in Amsterdam. Some of these immigrants were penniless; others had brought their money, even considerable amounts. Some were craftsmen, others farmers. The craftsmen were directed to Groningen and Deventer; the farmers obtained farms near Kampen, Groningen, and Sappemeer. Both the craftsmen and the farmers received ample support from the Dutch Committee. At Groningen, Elder Alle Derks was very active in behalf of the refugees; at Deventer Steven Cremer aided them. The Swiss emigrant group which was conducted to Harlingen were followers of Hans Reist (all the others were Amish). Only a few stayed at Harlingen; most obtained farms near Gorredijk in Friesland, but they did not feel at home here; in May 1712, with the aid of the Dutch Committee they were settled amidst their coreligionists near Kampen. But because of objection to the Amish views most of them moved to the Palatinate in the next year. In the following years most of the group which was located at Deventer moved to Kampen or to Groningen and Sappemeer, some immigrated to the Palatinate, and a few soon joined the Deventer Old Flemish Mennonite church. There was no Swiss Mennonite congregation at Deventer as there was at Kampen and at Groningen and Sappemeer. The Kampen group used the Swiss-German language for two or three decades, and then adopted the Dutch in its services. Elders of this group were Daniel Ricken 1712-1736, Peter Teune 1736-1763, Jacob Stähly 1736-1757, Hans Hupster 1769-1792, and finally a Dutch Mennonite, Jan Hans Hoosen 1805-1822. In 1822 their congregation merged with the Dutch Mennonite church at Kampen. That there were serious difficulties in the Swiss Amish group (which congregation is not clear) in the Netherlands, so serious as to cause a suspension of all communion, baptism, marriages, and ordinations for at least six years, is revealed by a letter written by Johannes Nafziger, an Amish bishop of Essingen near Landau in the Palatinate in 1781. Nafziger tells of three successive committees of Amish ministers from the Palatinate and Alsace sent to Holland in 1766, 1767(?), and 1770 to settle the dispute and supervise the congregation there, which they successfully did. The letter is published in Mennonite Quarterly Review II (1928) 198-204. The Groningen-Sappemeer group, which was augmented in the following years by the arrival of some new emigrants from Bern, worshiped both in the town of Groningen and near Sappemeer. Their first elder was Hans Anken, who seems to have served both in Groningen and Sappemeer as did his successors until about 1760. About 1720 a schism arose among these Swiss Brethren, dividing them into the Oude Zwitsers (Old Swiss) and Nieuwe Zwitsers (New Swiss). The cause of this schism is said to have been the purchase of a house by Elder Anken, which a part of his congregation, composed of very plain people, considered too sumptuous and too worldly. The Oude Zwitsers were the more conservative group, not only in dress, but also in maintaining their native tongue. Their church services also differed from those of the New Swiss, who soon adapted themselves to the Dutch way of living and worshiping, using the Dutch language by about 1750. In the Old Swiss services, after the preacher had finished his sermon other brethren spoke to express their agreement with the sermon or to add a few words from the Bible. They knelt for (silent) prayer and practiced foot washing in their communion services. They had no special confession of faith; the German Ausbund was their hymnal. Both at Groningen (about 1720 in a house "Achter de Muur") and in Sappemeer (in a house on the Kleinemeer) the Swiss Brethren had meetinghouses, which were used in turn both by the Old and the New Swiss. Gradually the ties between the members living in and near Groningen and those in Sappemeer relaxed. In Groningen the Old and New Swiss merged about 1780. Here the Swiss congregation bought the former Waterlander meetinghouse in the Pelsterstraat in 1815. After the death of their last preacher, Christiaan Jacobs Leutscher, who served 1812-died 1824, the Swiss congregation merged with the Dutch Mennonite congregation of Groningen. At Sappemeer the Oude Zwitsers and Nieuwe Zwitsers seem to have merged about 1790. In the meantime some Old Swiss had joined the Sappemeer Old Flemish church, where as many New Swiss joined the Waterlander congregation. The (united) Swiss congregation of Sappemeer merged with the main Dutch congregation before 1802. Preachers and elders of the Groningen-Sappemeer Swiss groups (as far as the lists are complete and reliable) were as follows: New Swiss: Hans Anken, elder 1712-?, Michael Ruysser (Riszer) 1711-1759, elder after the death of Anken, Peter Leenders 1711-1757, Jan van Ko(o)men, died 1743, Anthony Kratzer 1740-1779, elder 1760, Christiaan Ancken 1754-1770, Jan Leenders 1754-1759(?), Rudolf Leutscher 1755-1761. Then the Groningen New Swiss group was led by Balster Franssen (Wolkammer) 1762-1782, Hendrik Cornelis 1768-1808, elder 1794, Rudolf (or Roelof) Jans 1781-died 1790, Izaak Jannes Leutscher (1740-1826) 1799, elder 1811, David Jacob de Goed 1811-1813, and Christiaan Jacobs Leutscher (1812-1824). The last leaders of the Sappemeer group were Isaak van Kalkar (Calcar) 1772-1796, Alle Cornelis 1791-1800, and Ties Hansen Top 1791-1797. Old Swiss: Abraham Loover (Lauffer), died 1774, living near Groningen, elder 1726, Claus Gerber 1739-1761, Peter Riegen (Ricken) 1740-1772. Jacob Stehle (Stähly), the elder of the Kampen Swiss Mennonite group, also seems to have served the Groningen-Sappemeer group 1736-1757. David Righen (died 1796), preacher 1767, elder 1774, was the last elder of this group. The Swiss Mennonites in the Netherlands, who at first lived and worshiped rather separately from their Dutch coreligionists both because of their language and their particular views and practices, gradually adjusted themselves to the Dutch Mennonite practices. But not all. A number of them, particularly members of the Kraster (Krätzer), Rijkens (Rich, Ricken), and Stuckje (Stucky) families, joined the Reformed Church in the late 18th and the 19th centuries. Dassel, H. Sr. Menno's Volk in Groningen, Groningen: 21 f., 39-42. De Boer, M. G. “Vom Thunersee zum Zapemeer.” Berner Zeitschrift für geschichte und Heimatkunde (1947) I, reprinted. Doopsgezinde Bijdragen (1869): 7-11; (1881): 103 f.; (1908): 85-105; (1909): 127-55. Gratz, Delbert L. Bernese Anabaptists and their American descendants. Goshen, IN: Mennonite Historical Society, 1953. Reprinted Elverson, Pennsylvania: Old Springfield Shoppe, 1994: 56-66. Hoop Scheffer, Jacob Gijsbert de. Inventaris der Archiefstukken berustende bij de Vereenigde Doopsgezinde Gemeente to Amsterdam, 2 vols. Amsterdam: Uitgegeven en ten geschenke aangeboden door den Kerkeraad dier Gemeente, 1883-1884: v. I, Nos. 1009 f., 1060, 1065, 1151, 1196, 1210-12, 1216, 1225, 1392, 1746 f., 1757-83, 1866-68, 1891; v. II, Nos. 50b, 866. Huizinga, J. Stamboek of Geslachtsregister der Nakomelingen van Samuel Peter (Meihuizen) en Barbara Fry. Groningen: 1890: I, 1-143. Müller, Ernst. Geschichte der Bernischen Täufer. Frauenfeld: Huber, 1895. Reprinted Nieuwkoop: B. de Graaf, 1972: 158 f., 164-94, 257-328. Naamlijst der tegenwoordig in dienst zijnde predikanten der Mennoniten in de vereenigde Nederlanden. Amsterdam, 1731, 1743, 1755, 1757, 1766, 1769, 1775, 1780, 1782, 1784, 1786, 1787, 1789, 1791, 1793, 1802, 1804, 1806, 1808, 1810, 1815, 1829. |Author(s)||Nanne van der Zijpp| Cite This Article Zijpp, Nanne van der. "Swiss Mennonites in the Netherlands." Global Anabaptist Mennonite Encyclopedia Online. 1959. Web. 23 Nov 2017. http://gameo.org/index.php?title=Swiss_Mennonites_in_the_Netherlands&oldid=143735. Zijpp, Nanne van der. (1959). Swiss Mennonites in the Netherlands. Global Anabaptist Mennonite Encyclopedia Online. Retrieved 23 November 2017, from http://gameo.org/index.php?title=Swiss_Mennonites_in_the_Netherlands&oldid=143735. Adapted by permission of Herald Press, Harrisonburg, Virginia, from Mennonite Encyclopedia, Vol. 4, pp. 672-673. All rights reserved. ©1996-2017 by the Global Anabaptist Mennonite Encyclopedia Online. All rights reserved.
<urn:uuid:343a4c81-b806-4829-b394-42ff2183d0bb>
{ "date": "2017-11-23T18:40:16", "dump": "CC-MAIN-2017-47", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806856.86/warc/CC-MAIN-20171123180631-20171123200631-00456.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9303199648857117, "score": 3.5, "token_count": 3076, "url": "http://gameo.org/index.php?title=Swiss_Mennonites_in_the_Netherlands" }
Information Possibly Outdated The information presented on this page was originally released on April 1, 2010. It may not be outdated, but please search our site for more current information. If you plan to quote or reference this information in a publication, please check with the Extension specialist or author before proceeding. Robots help teach math, science and engineering MISSISSIPPI STATE – Nearly 200 Mississippi 4-H youth are learning science, technology and engineering skills as they work with robots and meet monthly via videoconferencing to learn new skills and take on new challenges. Mariah Smith, an instructor with the Mississippi State University Extension Service, is coordinating the program for Mississippi 4-H. She said the youth learn basic science, technology and engineering concepts behind robots and make simple robotic elements out of non-traditional parts. “We have 29 counties with robotics clubs, and once a month, we hold a videoconference to deliver content for them to work on,” Smith said. “Each month has a specific focus, and we develop the lesson plans for that month. The topic relates to an aspect of the robot that can help youth see the concept in action. We take the 4-H motto of ‘learning by doing’ to a new level.” One meeting focused on the use of wheels and axles and studied torque. Their supply list for the activity included drinking straws, a pack of gum, Life Savers and lollipops. “We made a candy car and learned how to convert degrees and rotations to inches,” Smith said. “Our wheels were the Life Savers, and we taught them that as the wheel makes a complete turn, they could measure the rotation of the wheel and determine that one rotation was equal to the number of inches the car travelled. Converting rotations to inches or degrees is critical when programming a robot.” Other activities the clubs have done include building an electric circuit board and making it work in a game, and building a small motor out of a battery, copper wire, a magnet and paper clips. Wes Pumphrey, a student worker in MSU’s computer services department, is majoring in computer engineering and is involved in the 4-H robotics program. He breaks complex concepts into small, simple segments for the youth to grasp. “I find robots fascinating and am looking for ways to convey basic engineering subjects to the younger youth of Mississippi,” Pumphrey said. “I challenge the kids of 4-H by creating small activities or experiments that, when put together and into practice, will educate them in these fields.” The robotics clubs build on skills the youth will need in the robotics competitions at 4-H Club Congress or Project Achievement Days. Clubs meet once a month for a lecture and demonstration via the Extension Service videoconferencing network available in each county. “This is quite possibly the best way to communicate to all 82 counties in the state simultaneously,” Pumphrey said. “I am able to perform the activities as live action, and then I can answer any questions as the kids experiment for themselves.” Smith said clubs and individuals earn points each month by completing the task presented in the monthly meeting and through an online blog. 4-H youth wishing to participate in the robotics competition will receive a robotics kit on loan from the MSU Extension Service Computer Applications and Services Department. “We’re teaching them the concepts behind robotics through fun and easily accessible activities. Once they understand the concepts, they can transfer that knowledge to their robots,” Smith said. “They are getting hands-on experience so that when they get their robots, they will be ready to work with them.” Youth may also earn extra points by completing the HotBot challenges, which are activities that reinforce what they learned in the club meeting. The individual and group HotBot winners will receive an all-expense-paid robotics day camp in their county this summer, Smith said. “The HotBot challenges are geared toward bringing different disciplines together,” Smith said. “We ask participants to do things like build a simple motor, build a bot out of recycled materials or come up with their own song based on a robotics theme.” Those completing the HotBot challenges are required to document their activities, taking pictures and videotaping their work so Smith and her staff can evaluate performance and award HotBot points. Boys and girls ages 8-18 are members of the 4-H robotics clubs, and Smith said a big emphasis of the clubs is to interest young people in science, technology and engineering. Contact the local county Extension office for more information on the 4-H robotics program.
<urn:uuid:fa4070e0-aba7-4501-8e3f-1a9d88ba0484>
{ "date": "2021-06-21T04:36:33", "dump": "CC-MAIN-2021-25", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488262046.80/warc/CC-MAIN-20210621025359-20210621055359-00536.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9438985586166382, "score": 3.671875, "token_count": 986, "url": "https://extension.msstate.edu/news/feature-story/2010/robots-help-teach-math-science-and-engineering?page=116" }
# Numeral systems ## Numeral system b - numeral system base dn - the n-th digit n - can start from negative number if the number has a fraction part. N+1 - the number of digits ## Binary Numeral System - Base-2 Binary numbers uses only 0 and 1 digits. B denotes binary prefix. #### Examples: 101012 = 10101B = 1×24+0×23+1×22+0×21+1×20 = 16+4+1= 21 101112 = 10111B = 1×24+0×23+1×22+1×21+1×20 = 16+4+2+1= 23 1000112 = 100011B = 1×25+0×24+0×23+0×22+1×21+1×20 =32+2+1= 35 ## Octal Numeral System - Base-8 Octal numbers uses digits from 0..7. #### Examples: 278 = 2×81+7×80 = 16+7 = 23 308 = 3×81+0×80 = 24 43078 = 4×83+3×82+0×81+7×80= 2247 ## Decimal Numeral System - Base-10 Decimal numbers uses digits from 0..9. These are the regular numbers that we use. #### Example: 253810 = 2×103+5×102+3×101+8×100 ## Hexadecimal Numeral System - Base-16 Hex numbers uses digits from 0..9 and A..F. H denotes hex prefix. #### Examples: 2816 = 28H = 2×161+8×160 = 40 2F16 = 2FH = 2×161+15×160 = 47 BC1216 = BC12H = 11×163+12×162+1×161+2×160= 48146 ## Numeral systems conversion table Decimal Base-10 Binary Base-2 Octal Base-8 Base-16 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F 16 10000 20 10 17 10001 21 11 18 10010 22 12 19 10011 23 13 20 10100 24 14 21 10101 25 15 22 10110 26 16 23 10111 27 17 24 11000 30 18 25 11001 31 19 26 11010 32 1A 27 11011 33 1B 28 11100 34 1C 29 11101 35 1D 30 11110 36 1E 31 11111 37 1F 32 100000 40 20 Currently, we have around 5612 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.
crawl-data/CC-MAIN-2022-33/segments/1659882572221.38/warc/CC-MAIN-20220816060335-20220816090335-00196.warc.gz
null
Main Page | See live article | Alphabetical index # Quotient group Given a mathematical group G and a normal subgroup N of G, the factor group, or quotient group, of G over N can be thought of as arising from G by "collapsing" the subgroup N to the identity element. It is written as G/N. ## Definition Formally, G/N is the set of all left cosets of N in G, i.e. Note since N has to be normal, then the right cosets will do also. Generally, if two subsets S and T of G are given, we define their product as: This operation on subsets of G is associative, and if N is normal, then it turns the set G/N into a group: (aN)(bN) = (aN)(Nb) = a((NN)b) = a(Nb) = a(bN) = (ab)N -- which establishes closure. From the same calculation, it follows that eN=N is the identity element of G/N and that a-1N is the inverse of aN. ## Examples Consider the group of integers Z (using addition as operation) and the subgroup 2Z consisting of all even integers. This is a normal subgroup because Z is abelian. There are only two cosets, the even and the odd numbers, and Z / 2Z is therefore isomorphic to the cyclic group with two elements. As another abelian example, consider the group of real numbers R (again with addition) and the subgroup Z of integers. The cosets of Z in R are of the form a + Z\', with 0 ≤ a < 1 a real number. Adding such cosets is done by adding the corresponding real numbers, and subtracting 1 if the result is greater than or equal to 1. The factor group R/Z is isomorphic to S1, the group of complex numbers of absolute value 1 using multiplication as operation. An isomorphism is given by f(a + Z') = exp(ai) (see Euler's identity). If G is the group of invertible 3-by-3 real matrices, and N is the subgroup of 3-by-3 real matrices with determinant 1, then N is normal in G (since it is the kernel of the group homomorphism det), and G/N is isomorphic to the multiplicative group of non-zero real numbers. ## Properties Trivially, G/G is isomorphic to the group of order 1, and G/{e} is isomorphic to G. When G/N is finite, its order is equal to [G:N], the index of N in G. If G is finite, this is also equal to the order of G divided by the order of N; this may explain the notation. There is a "natural" surjective group homomorphism π : GG/N, sending each element g of G to the coset of N to which g belongs, that is: π(g) = gN. The application π is sometimes called canonical projection. Its kernel is N. There is a bijective correspondence between the subgroups of G that contain N and the subgroups of G/N; if H is a subgroup of G containing N, then the corresponding subgroup of G/N is π(H). This correspondence holds for normal subgroups of G and G/N as well, and is formalized in the lattice theorem. Several important properties of factor groups are recorded in the fundamental theorem on homomorphisms and the isomorphism theorems. If G is abelian, nilpotent or solvable, then so is G/N. If G is cyclic or finitely generated, then so is G/N. Every group is isomorphic to a group of the form F/N, where F is a free group and N is a normal subgroup of F.
crawl-data/CC-MAIN-2024-30/segments/1720763514908.1/warc/CC-MAIN-20240719135636-20240719165636-00108.warc.gz
null
How Supplements are Regulated in the US Nature of the US Government The US Constitution’s fourth article states that the United States shall be ruled by federalism. Federalism is the division of government between different groups: local, state, and federal. In the US, the federal government’s powers are limited to only those things stated within the Constitution. Anything outside of the powers expressly stated by the Constitution are state powers. Of importance to us are the federal constitutional powers to regulate interstate commerce. Interstate commerce is the trade between states. If a product is produced in one state and sold in more places than just that one state, it falls under federal jurisdiction. If a product is produced and sold in only one state, it would be under state jurisdiction. The Constitution went in effect in 1789, long before the Internet, cars, planes, and other modern technologies. Because of modern technology, interstate commerce occurs much more often than in 1789. The proliferation of interstate commerce forced the federal government to increase in size. The Creation of Agencies Federal agencies are legal for the constitution allows the legislative branch to enact laws. If the legislative branch enacted a law that allowed the federal government, the executive branch, to start an agency whose sole purpose is to carry out a certain federal power, the new federal agency would be legal and constitutional. Once the federal agency steps outside of federal powers (for example, into state powers), it would be unconstitutional. Role of Federal Trade Commission Originally, the FTC were created for the protection of competition (“The Federal Trade Commission Turns 100” 2010). The 1914 Act created the FTC because the Sherman Antitrust Act failed to properly protect competition as legislature originally intended. The Sherman Antitrust Act’s implementation by the judicial system used the “Rule of Reason” which was criticized for being very vague, uncertain, and subjective (Cornell 1987). The 1914 Act, which created the FTC, was an attempt to better protect competition. It was not until 1938, with the passage of the Wheeler-Lea Act, also called the Federal Trade Commission Act of 1938, that consumer protection was an item of concern for the FTC (Udell 1977). Consumer protection against false advertising is one of the main functions of the FTC today. Implications of Wheeler-Lea Act Wheeler-Lea allowed the FTC to have greater regulatory powers. Before Wheeler-Lea, the FTC had powers regulating advertising if the advertisement resulted in an unfair advantage that can hinder competition. After Wheeler-Lea, the FTC had powers to regulate any advertising that was misleading for the purpose of protecting consumers (“The Federal Trade Commission Act of 1938” 1939). The act also removed the necessity for the FTC to prove that consumers were harmed by the advertisement (“The Federal Trade Commission Turns 100” 2010). By removing the necessity of harm, any advertisement that was deemed to be misleading can be penalized even if no one was actually mislead or harmed. The Wheeler-Lea Act allows the FTC to amend misleading advertising by: issuing a cease and desist, restraining the advertisement, and issuing criminal penalties (Handler 1939). Before the act, the FTC only had powers to issue reports and regulate commerce (“The Federal Trade Commission Turns 100” 2010). Although it has the power to issue criminal penalties, the burden of proof for a criminal case, beyond a reasonable doubt, is very hard to prove and therefore such penalties are rare (Cornell 1987). FTC Improvement Act of 1975 The judicial branch found that the legislative powers of the FTC were far too small given the tasks the FTC must accomplish. The FTC Improvement Act of 1975 expanded the FTC’s powers by: expanding the FTC’s authority, clarifying the FTC’s rulemaking ability, allowing the FTC to have consumer participation, allowing the FTC to issue fines, and increase the scope of cease and desist orders (Udell and Fischer 1977). Originally, the FTC was enacted under the constitutional powers of protecting interstate commerce. The 1975 Act expanded the FTC’s powers by broadening its scope from anything within interstate commerce to anything within or affecting interstate commerce. This means that the FTC can go after intrastate business if that business has been found to affect interstate commerce (Udell and Fischer 1977). This broadening of scope is fundamental in the present day FTC powers. Allowing the FTC to have consumer participation, issue fines, and increase cease and desist scopes allows the FTC to have a far greater reach with much faster swiftness. For example, if the FTC issued a fine for company A for a set of behaviors, company B’s similar behavior would also be fined as well even if the FTC did not go through the bureaucratic process of showing how company B’s behavior is misleading (Udell and Fischer 1977). Role of Food and Drug AssociationThe FDA was enacted in 1906 to protect consumers for mislabeled or misbranded foods, drugs, and drinks (“Significant Dates in U.S. Food and Drug Law History” 2013). Supplements are considered an in between category: they are foods that have drug-like properties. With concerns to supplement’s the FDA’s main purpose is to ensure that supplements are safe for consumption. The FDA does this by testing all supplement ingredients for safety before they reach market (“Dietary Supplements” 2013). How Government Actions Work As we have seen, although it was not the FTC’s original purpose, the FTC can go after a supplement company if it makes claims that are misleading to consumers. This can include weight loss claims that are misleading, the use of doctor actors who are not physicians, and other deceptive practices. The 1975 Act allows the FTC to make specific industry rules as well. The FDA’s role in supplement regulations is that it ensures that supplements are safe for human consumption. The FDA makes available a list of supplements that have been found to be tainted (see https://www.accessdata.fda.gov/scripts/sda/sdNavigation.cfm?sd=tainted_supplements_cder). For the most part, the FDA is concerned with the quality and ingredients of a product whereas the FTC is concerned with the claims being made. - Handler, Milton. “The Control of False Advertising under the Wheeler-Lea Act.” Law and Contemporary Problems 6.1 (Winter 1939): 91-110. JSTOR. Web. 2/04/2013. - “Dietary Supplements.” Dietary Supplements. FDA.gov, 29 Apr. 2013. Web. 02 Mar. 2013. https://www.fda.gov/Food/DietarySupplements/default.htm. - “The Federal Trade Commission Act of 1938.” Columbia Law Review 39.2 (February 1939): 256-273. JSTOR. Web. 2/04/2013. - Cornell, Arthur. “Federal Trade Commission Permanent Injunction Actions Against Unfair and Deceptive Practices: The Proper Case and the Proper Proof.” St. John’s Law Review 4.61 (Summer 1987): 504-558. JSTOR. Web. 2/04/2013. - “The Federal Trade Commission Turns 100.” Federal Trade Commission. FTC.gov, 18 Nov. 2010. Web. 02 Mar. 2013. https://ftc.gov/ftc/turns100/index.shtm. - Udell, Gerald and Fischer, Philip. “The FTC Improvement Act.” Journal of Marketing 41.2 (Apr. 1977): 81-86. JSTOR. Web. 2/04/2013. - “Significant Dates in U.S. Food and Drug Law History.” Significant Dates in U.S. Food and Drug Law History. FDA.gov, 11 June 2012. Web. 02 Mar. 2013. https://www.fda.gov/aboutfda/whatwedo/history/milestones/ucm128305.htm.
<urn:uuid:dc2ade20-0bc8-4d46-a241-74fe9f118fa7>
{ "date": "2023-01-27T07:45:05", "dump": "CC-MAIN-2023-06", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00417.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9331265091896057, "score": 3.90625, "token_count": 1687, "url": "https://blog.priceplow.com/supplement-regulation?print=print" }
# Need done by tomorrow | Statistics homework help Assignment – Show the set up of each problem and the formula used when working these problems. Question 1 In a poll of 500 voters in a campaign to eliminate non-returnable beverage containers, 225 of the voters were opposed. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed the container control bill. Question 2 A random sample of 94 contractors had an average yearly income of \$97,000 with a standard deviation of \$8,000. If       we want to determine a 95% confidence interval for the average yearly       income, what is the value of t? What       are the degrees of freedom for this problem, and how was it calculated? Develop       a 95% confidence interval for the average yearly income of all pilots. Question 3 In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 14 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds. Determine       a 97% confidence interval estimate for the mean weight of the carry-on       luggage. Determine       a 95% confidence interval estimate for the mean weight of the carry-on       luggage. Question 4 A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.8 to 12.2 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.45, determine the size of the sample. Project For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here. Hint from Dr. Klotz – use the information beginning in section 8.4 for #1 Using the ROI data set: For       each of the 2 majors consider the ‘School Type’ column.  Assuming       the requirements are met, construct a 90% confidence interval for the       proportion of the schools that are ‘Private’.  Be sure to interpret       your results. What        are the two possible data values in this column? Given        which data value you are looking for, which one is the        “success?”  Which one is the “failure?” What        proportion of the values is the success?  This is your p. How        many values are there in all?  This is your n. From        the chart on page 340, what is your z-sub-alpha-over-two? Show        how these values have been inputted into the formula and what the result        was. Explain        how to get the interval.  What do you do with the answer from #6? State        and interpret the interval. Repeat        these steps for the second major. For       each of the 2 majors construct a 95% confidence interval for the mean of       the column ‘Annual % ROI’.  Be sure to interpret your results.         Here’s some direction – this time, the data values are numbers       rather than public/private.  The formula has to be different because       there is no “success/failure” option, but rather       numbers. What        is the mean of the data set? What        is the standard deviation of the data set? What        is your z-sub-alpha-over-two? What        formula will you use, and why? Show        your work as you calculate. What        do you have to do with your answer in #5 to get the interval? State and interpret the interval ## Order a similar paper and get 15% discount on your first order with us 98% Success Rate “Hello, I deliver nursing papers on time following instructions from the client. My primary goal is customer satisfaction. Welcome for plagiarism free papers” Stern Frea 98% Success Rate Hi! I am an English Language and Literature graduate; I have written many academic essays, including argumentative essays, research papers, and literary analysis. Dr. Ishid Elsa 98% Success Rate "Hi, count on me to deliver quality papers that meet your expectations. I write well researched papers in the fields of nursing and medicine". Dr. Paul P. Klug 99% Success Rate "A top writer with proven reliability and experience. I have a 99% success rate, overall rating of 10. Hire me for quality custom written nursing papers. Thank you" ## Tell Us Your Requirements Fill out order details and instructions, then upload any files or additional materials if needed. Then, confirm your order by clicking “Place an Order.” ## Make your payment Your payment is processed by a secure system. We accept Mastercard, Visa, Amex, and Discover. We don’t share any informati.on with third parties ## The Writing Process You can communicate with your writer. Clarify or track order with our customer support team. Upload all the necessary files for the writer to use. Check your paper on your client profile. If it meets your requirements, approve and download. If any changes are needed, request a revision to be done. ## Recent Questions ### Implementation of a Progressive Care Unit Implementation of a Progressive Care Unit ### Implementation of a Progressive Care Unit for Patients with Moderate Injury Severity Admitted to the Emergency Department Implementation of a Progressive Care Unit for Patients with Moderate Injury Severity Admitted to the Emergency Department ### Intervention Plan Design Intervention Plan Design ### Problem Statement (PICOT) Problem Statement (PICOT) ### 6.4 Assignment: Final Capstone Project Paper (Phase 7 of Final Capstone Project) 6.4 Assignment: Final Capstone Project Paper (Phase 7 of Final Capstone Project)
crawl-data/CC-MAIN-2024-18/segments/1712296817239.30/warc/CC-MAIN-20240418191007-20240418221007-00271.warc.gz
null
# Find Missing Number 1. Given a set of positive numbers less than equal to N, where one number is missing. Find the missing number efficiently. 2. Given a set of positive numbers less than equal to N, where two numbers are missing. Find the missing numbers efficiently. 3. Given a sequence of positive numbers less than equal to N, where one number is repeated and another is missing. Find the repeated and the missing numbers efficiently. 4. Given a sequence of integers (positive and negative). Find the first missing positive number in the sequence. Solutions should not use no more than O(n) time and constant space. For example, 1. A=[2,1,5,8,6,7,3,10,9] and N=10 then, 4 is missing. 2. A=[2,1,5,8,6,7,3,9] and N=10 then, 4 and 10 are missing. 3. A=[2,1,5,8,3,6,7,3,10] and N=10 then, 3 is repeating and 9 is missing. 2. A=[1,2,0] then first missing positive is 3, A=[3,4,-1,1], the first missing positive is 2. Single Number Missing A trivial approach would be to sort the array and loop through zero to N-1 to check whether index i contains number i+1. This will take constant space but takes O(nlgn) time. We can do a counting sort to sort the array but still it’ll take in O(n+k) time and O(k) space. But we need to do it O(n) time and constant space, how? Its rather simple to do it if we apply some elementary mathematics. We know that the input set contains positive numbers less than equal to N. If there were no missing in the sequence then summation of all the numbers would yield a sum of N*(N+1)/2 , which is the value of summation of numbers 1 to N. But if one number is missing then the summation of the given numbers, S will be less than expected sum N*(N+1)/2 and the difference (N*(N+1)/2 – S) is the missing number. This is O(n) time and O(1) space algorithm. ```public int missingNumber(int[] nums) { int n = nums.length; int expectedSum = n*(n+1)/2; int actualSum = 0; for(int i=0; i<n; i++){ actualSum+= nums[i]; } return (expectedSum-actualSum); } ``` Two Missing Numbers We can solve it using math same as above. Let’s say p and q are the missing numbers among 1 to N. Then summation of given input numbers, ```S = N*(N+1)/2 - p -q =>p+q = N*(N+1)/2 -S ``` Also, we know that multiplication of numbers 1 to N is N! – ```P = N!/pq =>pq = N!/P ``` Then we can solve these two equations to find the missing number p and q. However this approach has a serious limitation because the product of a large amount of numbers can overflow the buffer. We could have used long but still multiplication operation is not cheap. Can we avoid multiplication? As the numbers are positive and between the range [1,N] we could use the element of the array as index into the array to mark them as exists. Then the positions for missing element will be unmarked. But it’ll change the array itself. How do we make sure that marking one position we are not losing information at the position we are marking. For example, A=[2,1,5,8,6,7,3,9] then if we mark A[A[0]-1] i.e. A[1] with special value, lets say 0 marking 2 as not missing, then A becomes A’=[2,0,5,8,6,7,3,9], then we are losing information and A[A[1]-1] i.e. A[0] will never get marked to inform us that 1 is not missing. We can actually overcome the overwriting issue by just negating the number at index A[abs(A[i])-1] for each i. So, we are not losing value but just changing the sign and indexing based on absolute value. After we mark for all the numbers we can now have a second pass on the array and check for unmarked i.e. positive elements. At the same time we can revert the negated elements back to positive thus getting back to original array. Below is the implementation of this idea. ```public static void find2Missing(int[] a, int n){ for(int i = 0; i < a.length; i++){ if(a[Math.abs(a[i])-1] > 0){ a[Math.abs(a[i])-1] = -a[Math.abs(a[i])-1]; } } for(int i = 0; i < a.length; i++){ if(a[i] > 0){ System.out.println("missing: "+i+1); } else{ a[i] = -a[i]; } } } ``` The above solution has a limitation that we assume the input array is not immutable. What if we can’t update the input array (i.e.e immutable) and still we need to find the missing values in O(n) time and constant space? We need some brain teaser here. If we had no missing numbers then xor of all numbers from 1 to n i.e. xor1=1^2^..^n, and xor of all numbers in the array i.e. xor2=A[0]^A[1]^…^A[n-1], they should give us the same result. Hence xor of these two xor results should yield a 0 (as equal by xor). Now, if two of the numbers are missing then in xor1 all elements would cancel each other except the missing p and q. All the bits that are set in xor1 will be set in either p or q. So if we take any set bit of xor1 and divide the elements of the array in two sets – one set of elements with same bit set and other set with same bit not set. By doing so, we will get x in one set and y in another set. Now if we do XOR of all the elements in first set, we will get x, and by doing same in other set we will get y. Which set bit to chose? We can actually chose any but it is easier to the right most set bit because we can directly get the mask as easy as xor&~(xor-1). Below is the implementation of this idea – ```//O(n) time, O(1) space public static void findMissing2(int a[], int n){ int mask = 0; //O(n) for(int i = 1; i<=n; i++){ } //O(n) for(int i = 0; i < a.length; i++){ } //get the right most set bit int mis1=0, mis2=0; for(int i = 0; i<a.length; i++){ mis1 ^= a[i]; } else{ mis2 ^= a[i]; } } for(int i = 1; i<=n; i++){ mis1 ^= i; } else{ mis2 ^= i; } } System.out.println("missing numbers : "+mis1+", "+mis2); } ``` One Missing, One Repeated What if we have one single number getting repeated twice and one missing? Note that, missing one element and repeating one element is equivalent phenomena with respect to xor arithmetic. Because during xor1 these repeating element will nullify each other and made the element missing in the xor. That is we can use the same procedure described above to find one missing and one repeated element. First missing Positive For example, A=[1,2,0] then first missing positive is 3, A=[3,6,4,-1,1], the first missing positive is 2. Can we use some of the above techniques we discussed? Note that, there might be more than one missing numbers as well as negative numbers and zeros. If all numbers were positive then we could have used the 2nd method for finding two missing number where we used the element as index to negate the value for marking them as non-missing. However, in this problem we may have non-positive numbers i.e. zeros and negatives. So, we can’t simply apply the algorithm. But if we think carefully then we notice that we actually don’t have to care about zeros and negative numbers because we only care about smallest positive numbers. That is if we can put aside the non-positive numbers and only considers the positives then we can simply apply the “element as index to mark non-missing by negating the value” method to find the missing positives. How do we put aside non-positive elements? We can actually do a partition as we do in quicksort to create a partition where all positive elements will be put on left of the partition and all zeros and negatives on the right hand. If we find such a partition index q, then A[0..q-1] will contain all positives. Now, we just have to scan the positive partition of array the i.e. from 0 to q-1 and mark A[abs(A[i])-1] as marked i.e negating the value. After marking phase we sweep through the partition again to find first index i where we find a positive element. Then i+1 is the smallest i.e. first missing positive. If we do not find such an index then there is no missing numbers between 1 to q (why?). In that case we return next positive number q+1 (why?). Below is the implementation of this algorithm which assumes we can update the original array. It runs in O(n) time and constant space. ```public static int firstMissingPositive(int[] nums) { if(nums.length == 0){ return 1; } int p = 0; int r = nums.length - 1; int q = p-1; for(int j = 0; j<=r; j++){ if(nums[j] > 0){ swap(nums, ++q, j); } } q++; for(int i = 0; i < q; i++){ int index = Math.abs(nums[i])-1; if(index<q){ nums[index] = -Math.abs(nums[index]); } } for(int i = 0; i < q; i++){ if(nums[i] > 0){ return i+1; } } return q+1; } ```
crawl-data/CC-MAIN-2018-09/segments/1518891811243.29/warc/CC-MAIN-20180218003946-20180218023946-00427.warc.gz
null
Galileo’s highly-accurate clocks are at the heart of the system. Each satellite emits a signal containing the time it was transmitted and the satellite’s orbital position. Because the speed of light is known, the time it takes for the signal to reach a ground-based receiver can be used to calculate the distance from the satellite. Galileo’s timing needs to be accurate to the scale of nanoseconds – one billionth of a second – so this distance can be derived to a very high degree of certainty. Combine inputs from several satellites simultaneously and the receiver’s place in the world is pinpointed: Galileo’s aim is to deliver accuracy in the metre range once the full system is completed. All clocks are based on regular oscillations – traditionally the swing of a pendulum, tick of clockwork or pulse of quartz crystal. Highly accurate atomic clocks rely on switches between energy states of an atom’s electron shell, induced by light, laser or maser energy – if you force atoms to jump from one particular energy state to another, it will radiate an associated microwave signal at an extremely stable frequency. The passive hydrogen maser clock is the master clock on board each satellite. It is an atomic clock which uses the ultra stable 1.4 GHz transition in a hydrogen atom to measure time to within 0.45 nanoseconds over 12 hours. A rubidium clock will be used as a second, technologically independent time source. It is accurate to within 1.8 nanoseconds over 12 hours. Prototype versions of these clocks have already been flown on ESA’s GIOVE missions. Designing atomic clocks for space The very first atomic clock, developed in England in 1955, was the size of a room. For satellite navigation, the challenge was coming up with a design that was compact and robust enough to fly in space. Based on ESA research and development dating back to the early 1990s, two separate atomic clock technologies have been developed and qualified in Europe, then proved suitable for the harsh environment of space by the two GIOVE missions. Passive hydrogen maser clock Galileo’s desk-sized passive hydrogen maser clock is made of an atomic resonator and its associated control electronics. A small storage bottle supplies molecular hydrogen to a gas discharge bulb. Here molecules of hydrogen are split into individual hydrogen atoms. After dissociation, the atoms enter a resonance cavity after passing through a magnetic state selector, used to admit only atoms of the desired energy level. Within the resonance cavity, the atoms are confined inside a quartz storage bulb. Within it, the hydrogen atoms tend to return to their 'fundamental' energy state, emitting a microwave frequency as they do so. This frequency is detected by an interrogation circuit which tunes an external signal to the 'natural' transition of the hydrogen atoms, amplifying the microwave signal. The resonant frequency of the microwave cavity is approximately 1.420 GHz. The clock's electronics includes circuitry for the control of the frequency plus the thermal control system to maintain the resonant cavity at the correct temperature. The atomic resonator is very sensitive to its external environment. Great care is required to keep environmental disturbances – such as heat, magnetism and radiation – minimal so that the full performance potential of these sophisticated clocks can be achieved. The smaller, simpler rubidium clock follows the same basic principle, with gaseous rubidium atoms released into a vapour cell inside an atomic resonator. Within it, they are stimulated by the light of a rubidium discharge lamp; a photodiode records the light levels passing through the cell. The excited atoms return to their lower state, after which they are switched to an intermediate level using microwave energy at a precise frequency. At this intermediate state, their light absorption is maximised.The photodiode is attached to control systems that tune the microwave to maintain maximum light absorption. The rubidium discharge lamp returns the rubidium to their higher state, from which they decay, restarting the process. Galileo System Time Both Galileo’s atomic clocks are very stable over a few hours. If they were left to run indefinitely, though, their timekeeping would drift, so they need to be synchronised regularly with a network of even more stable ground-based reference clocks. These include clocks based on the caesium frequency standard, which show a far better long-term stability than rubidium or passive hydrogen maser clocks. These clocks on the ground – gathered together within parallel Precise Timing Facilities in the Fucino and Oberpfaffhofen Galileo Control Centres – also generate a worldwide time reference called Galileo System Time (GST), the standard for Europe’s system, accurate to 28 billionths of a second. In parallel, a system for generating navigation signals has been developed, with a navigation signal generator, a navigation antenna and associated equipment.
<urn:uuid:2c1a1674-4918-4bdb-b2c3-67ac3728f918>
{ "date": "2019-11-13T12:52:22", "dump": "CC-MAIN-2019-47", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667260.46/warc/CC-MAIN-20191113113242-20191113141242-00098.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9231634140014648, "score": 4, "token_count": 1022, "url": "https://www.esa.int/Applications/Navigation/Galileo/Galileo_s_clocks" }
Education & Training Patient Health Library Neuroscience CenterSearch Health Information (Disorders of Head Size) Cephalic disorders affect the central nervous system as it develops. They may also affect the brain and the growth of the skull. These disorders can cause a variety of developmental delays, physical handicaps, and threats to a child’s life. Cephalic disorders, which may also be called neurodevelopmental disorders, begin early in a baby’s development during pregnancy. One of the most noticeable signs of a cephalic disorder is a head of an unusual size or shape. Problems caused by cephalic disorders are most likely when the head is much smaller or larger than the average for a child’s age. Facts about cephalic disorders The effect of any given disorder on a specific child may be mild or severe, depending on the parts of the brain and central nervous system affected. Many people with cephalic disorders live relatively normal lives, but some cephalic disorders are so severe that a baby will die within weeks or months of birth. Types of cephalic disorders Here are several types of cephalic disorders: Anencephaly. This disorder occurs when the top of the neural tube doesn’t close during the development of the fetus. This results in a baby developing without the forebrain. The baby may be born without any skull covering the remaining brain. Babies with this defect often die within days of birth. Holoprosencephaly. During development in the womb, the brain grows into one single lobe instead of two. There are varying grades of severity ranging from severe abnormalities with limited function, to very mild abnormalities with the ability to lead a relatively normal life. Many babies with the severe form of this disorder die before or soon after birth. Others may live but may have severely deformed faces. Hydranencephaly. Babies born with this disorder have pockets of cerebrospinal fluid in the place of the two separate lobes of the brain. They may appear normal at birth, but within a few months become irritable and do not develop along a normal timeline. Hydrocephalus. Not really a cephalic disorder, hydrocephalus can cause a large head size because of the buildup of cerebrospinal fluid in the ventricles of the brain. Because the skull plates in neonates and infants have not yet fused, there is little to prevent the head from enlarging significantly with increased internal pressure. Hydrocephalus is caused by either production of too much fluid, poor resorption of the fluid produced, or an obstruction along the normal pathway of fluid flow in the brain. These children usually require placement of a shunt to drain the excess fluid. Lissencephaly. This disorder occurs because brain cells called neurons do not go to the right location to help the baby’s brain develop. This results in an unusual brain formation and an extremely small head, as well as other physical deformities in the face, hands, and other body parts. Microcephaly. This is a disorder in which the head is much smaller than average. Many children with smaller than average heads have normal intelligence and develop correctly. But this condition may be associated with cerebral palsy, Down syndrome, poor motor skills, lack of balance and coordination, and difficulty thinking and learning as expected for the child’s age. Other birth defects, such as lissencephaly or porencephaly, also have microcephaly as a symptom. Macrencephaly. Also called megalencephaly, this is a disorder in which the head is much larger than average. It occurs more often in boys than girls. The large head size may be caused by a brain that grows unusually large and heavy. It often causes seizures, developmental delays, partial paralysis, and other motor difficulties. Children with this disorder may have an unbalanced face. It is also related to the cephalic disorder called porencephaly. Porencephaly. During development, a pocket of cerebrospinal fluid forms in the baby’s brain, causing this cephalic disorder. This is thought to be related to an infection, either in utero or the neonatal period. Some children with this disorder have normal intelligence and few if any developmental problems, but others die within a few years of life. Schizencephaly. This rare cephalic disorder results from clefts forming in one or both hemispheres of the brain. Impairment is related to the number and location of the clefts. Some people with this disorder lead relatively normal lives, but others may have severe developmental delays or seizures. Symptoms vary depending on the type of cephalic disorder, but may include: Unusually large or small head Difficulty swallowing or eating Poor muscle tone Deformed fingers or toes Delays in the development of physical abilities or language In order to make a diagnosis, the doctor may consider symptoms and medical history, and perform a physical examination of the skull and body. The doctor may also order tests: CT scan or MRI scans Head size is often considered during diagnosis. A doctor will use a measuring tape to measure the circumference of the head. That is the distance around the head. The tape is usually placed just above the eyebrows and around the widest part of the head. This number is compared with standard growth charts. Head size can change as a baby grows into a toddler or young child. Measurement of head size may be done at every well check or office visit in order to find out whether the head is changing shape. This usually continues until age 3, unless there is a reason to keep track past that age. When to call a doctor Some cephalic disorders are clearly present from birth. Others are not. Call your doctor if you have concerns about your child’s ability to meet milestones as expected, such as starting to roll over, crawl, walk, or speak at the expected age. Also call if you are concerned about the shape of your child’s face or head. Treatment for cephalic disorders depends on the type of disorder. Treatments may include: Physical therapy for motion Speech therapy for language Medication, such as anti-seizure drugs, for symptoms Shunts to drain excess fluid off the brain Surgery to correct a deformed skull or face The true cause of cephalic disorders is not fully known. Experts believe that genes may be a factor. At the same time, events during a woman’s pregnancy, such as having an infection or being exposed to toxic chemicals, may also play a role. Women have the best chance of preventing cephalic disorders by trying to be as healthy as possible throughout their pregnancy. This means avoiding illicit drugs, alcohol, and cigarettes, and eating a varied, healthy diet. Getting enough folic acid has been shown to reduce the risk for certain birth defects, including some cephalic disorders. Many women, however, take good care of themselves during pregnancy and still give birth to a child with a cephalic disorder. Online ResourcesNational Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/anencephaly/anencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/cephalic_disorders/cephalic_disorders.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/holoprosencephaly/holoprosencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/hydranencephaly/hydranencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/lissencephaly/lissencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/megalencephaly/megalencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/porencephaly/porencephaly.htm National Institute of Neurological Disorders and Stroke http://www.ninds.nih.gov/disorders/schizencephaly/schizencephaly.htm
<urn:uuid:e31e14fe-5d60-4a21-8b6e-2f21fcb86a8a>
{ "date": "2014-03-12T09:36:18", "dump": "CC-MAIN-2014-10", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021587780/warc/CC-MAIN-20140305121307-00008-ip-10-183-142-35.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9335227608680725, "score": 3.8125, "token_count": 1807, "url": "http://www.montefiore.org/body.cfm?id=1767&action=detail&AEProductID=Staywell_39091&AEArticleID=74_134" }
Canada reintroduces bison to its oldest national park CALGARY, Alberta—Rangers have successfully reintroduced a herd of plains bison to Canada's oldest national park, officials said on Monday, Feb. 6, more than 130 years after the iconic North American animal last grazed the eastern slopes of the Canadian Rockies. Parks Canada moved 16 bison from a protected herd in central Alberta into an enclosed pasture in Banff National Park in the west of the province last week. The herd will stay under observation in an enclosure in the remote Panther Valley until summer 2018, when the animals will be released into the full 459 square miles re-introduction zone in the park's eastern valleys. Parks Canada said bison were once dominant grazers and a "keystone species," and bringing them back to Banff will restore their missing role in the ecosystem. Bison also have great spiritual meaning for Canada's aboriginal groups, having once provided an important source of food, clothing and shelter. The re-introduction coincides with the 150th anniversary of Canada's confederation. "This is a historic moment and a perfect way to mark Canada's 150," Environment and Climate Change Minister Catherine McKenna said in a statement. "Not only are bison a keystone species and an icon of Canada's history, they are an integral part of the lives of indigenous peoples." Vast bison herds up to 30 million animals strong once migrated freely across the plains of North America, including the montane and sub-alpine meadows where the front ranges of the Rocky Mountains meet western Canada's rolling prairies. The animal was nearly hunted to extinction by humans, and rangers estimate bison have not grazed in the valleys of Banff National Park since before the park was established in 1885.
<urn:uuid:322f31bf-ec8d-4b9e-ae66-8ad5b65797aa>
{ "date": "2019-05-25T13:57:41", "dump": "CC-MAIN-2019-22", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258058.61/warc/CC-MAIN-20190525124751-20190525150751-00058.warc.gz", "int_score": 4, "language": "en", "language_score": 0.935724675655365, "score": 3.578125, "token_count": 371, "url": "https://www.agweek.com/news/4212899-canada-reintroduces-bison-its-oldest-national-park" }
By the paragraph above, we know how waves are formed in the ocean. However, it would be advantageous to know that there are many types of waves and they are categorized on the basis of their formation and behavior. Below is the list of them : Breaking Wave: An ocean wave is said to be a breaking wave when it collapses on the top of itself. They are further of two types. - Plunging Breaker Wave: This type of wave reaches a steeper beach and curls. Their motion is quite fast. - Spilling Breaker Wave: This type of wave reaches a sloping beach hence dispersing its energy over a large surface area. Deep Water Wave or Swell Wave: Deep Water wave a.k.a swell wave is made when numerous waves of different lengths merge into one wave. These are long, strong and travel over large distances.
<urn:uuid:388e9ac0-6464-4209-9db9-971779247f07>
{ "date": "2020-01-25T07:51:58", "dump": "CC-MAIN-2020-05", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251671078.88/warc/CC-MAIN-20200125071430-20200125100430-00217.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9568454027175903, "score": 3.640625, "token_count": 176, "url": "https://engineeringinsider.org/waves-formation-ocean-water/2/" }
# Data Structure Questions and Answers-Pancake Sort ## Data Structure Questions and Answers-Pancake Sort Question 1 What is the time complexity for a given pancake sort given it undergoes "n" flip operations? A O(n) B O(n2) C O(n3) D O(2n) Question 1 Explanation: Most sorting algorithms try to sort making the least number of comparisons but in pancake sort we try to sort using as few reversals as possible. Because the total number of flip operations performed in a pancake sort is O(n), the overall time complexity is O(n2). Question 2 Which operation is most essential to the process of pancake sort? A Flip the given data B Find the largest of given data C Finding the least of given data D Inserting something into the given data Question 2 Explanation: When we use pancake sort, we sort the array to find the largest, and then flip the array at that point to bring that value to the bottom of the pancake stack. The size of the array that we are dealing with is then reduced and the process continues. Flip operation is the most important function in the pancake sort technique. Question 3 There is one small error in the following flip routine. Find out which line it is on. 1 void flip(int arr[], int i) 2 { 3 int t, init = 0; 4 while (init < i) 5 { 6 t = arr[init]; 7 arr[i] = arr[init] ; 8 arr[i] = t; 9 init++; 10 i--; 11 } 12 } A Line 3 B Line 5 C Line 7 D Line 9 Question 3 Explanation: After initialization of the array titled arr; for each while loop iteration of increasing init, we should make arr[init]=arr[i]. This makes sure that the changes will be made in order to flip the order of the array that was to be flipped. Here in line 7 it has been written in reverse and is incorrect. Question 4 How many flips does the simplest of pancake sorting techniques require? A 3n-3 flips B 2n-4 flips C 2n-3 flips D 3n-2 flips
crawl-data/CC-MAIN-2020-50/segments/1606141727782.88/warc/CC-MAIN-20201203124807-20201203154807-00600.warc.gz
null
# Question: What Does Product Mean? ## Whats does product mean? Definition: A product is the item offered for sale. A product can be a service or an item. It can be physical or in virtual or cyber form. Every product is made at a cost and each is sold at a price. The price that can be charged depends on the market, the quality, the marketing and the segment that is targeted.. ## What are the 4 operations? The four operations are addition, subtraction, multiplication and division. ## How do you calculate product? Cost-based pricing involves calculating the total costs it takes to make your product, then adding a percentage markup to determine the final price. For example, let’s say you’ve designed a product with the following costs: Material costs = \$20. Labor costs = \$10. ## What are the 7 types of product? Types of Product – Goods, Services, Experiences, Convenience, Shopping, Specialty Goods, Industrial Goods and Consumer Goods. ## How do you find a product? In mathematics, a product is a number or a quantity obtained by multiplying two or more numbers together. For example: 4 × 7 = 28 Here, the number 28 is called the product of 4 and 7. As another example, the product of 6 and 4 is 24, because 6 times 4 is 24. ## What is the product of a number? The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5 and so on. ## Does product mean add or subtract? Adding two (or more) numbers means to find their sum (or total). Subtracting one number from another number is to find the difference between them. Multiplication means times (or repeated addition). A product is the result of the multiplication of two (or more) numbers. ## What are the 4 fundamental operations? the four basic operations are addition, subtraction, multiplication and division. ## Is product and sum the same? SUM – The sum is the result of adding two or more numbers. … PRODUCT – The product of two or more numbers is the result of multiplying these numbers. ## What is the product of a number and 7? When you see the word PRODUCT, think about multiplication. The product of 7 and a number e is written 7e. NOTE: The term 7e really means 7 times e. ## Is product number the same as serial number? A serial number is a unique number or string of characters that identifies a product. While any product may have a serial number, they are especially common for electronics, such as computers, mobile devices, and audio and video equipment. ## What is the product of 1? 1. The product of any number times 1 is that number. You learned this in the multiplicative identity property example above. ## Does product mean multiply? The product meaning in math is the result of multiplying two or more numbers together. … Multiplying two numbers by a multiplier and then adding them is the same as multiplying their sum by the multiplier. ## What defines a good product? Above all else, great products have a clearly defined sense of purpose, deliver value in a singularly focused way, and do so as well or better than any other product in the marketplace. … Lesser-known products are more than capable of doing the same. ## What is the product of any number and 1? The product of any number and 1 is equal to that number. The number 1 is often called the multiplicative identity. The numbers 1, 2, 3, 4 and so on. Also called counting numbers. ## What is the product of 5 12? In other words, we find the product of 5 and 12 by simply calculating 5 times 12 which equals 60. ## What is the product of 100? The product of first 100 whole numbers will be 0. It is because 0 is also a whole number and any thing multiplied by 0 will give out answer to be 0,no matter how long the series is. ## What does the product means in math? The term “product” refers to the result of one or more multiplications. For example, the mathematical statement would be read ” times equals ,” where. is the product. ## What is product give example? Most goods are tangible products. For example, a soccer ball is a tangible product. Soccer Ball: A soccer ball is an example of a tangible product, specifically a tangible good. An intangible product is a product that can only be perceived indirectly such as an insurance policy. ## What is a product of 10? The result of multiplying 10 with 10 is called the product. Thus, the product of 10 and 10 is as follows: 100. In other words, we find the product of 10 and 10 by simply calculating 10 times 10 which equals 100. Pretty easy huh? ## What is the product of three numbers? Multiplying three numbers. How to multiply three numbers: Multiply the first number by the second number. Multiply the product of the first multiplication by the third number.
crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00075.warc.gz
null
# Exponentiation In mathematics, exponentiation (power) is an arithmetic operation on numbers. It can be thought of as repeated multiplication, just as multiplication can be thought of as repeated addition. In general, given two numbers $${\displaystyle x}$$ and $${\displaystyle y}$$, the exponentiation of $${\displaystyle x}$$ and $${\displaystyle y}$$ can be written as $${\displaystyle x^{y}}$$, and read as "$${\displaystyle x}$$ raised to the power of $${\displaystyle y}$$", or "$${\displaystyle x}$$ to the $${\displaystyle y}$$th power".[1][2] Other methods of mathematical notation have been used in the past. When the upper index cannot be written, people can write powers using the ^ or ** signs, so that 2^4 or 2**4 means $${\displaystyle 2^{4}}$$. Here, the number $${\displaystyle x}$$ is called base, and the number $${\displaystyle y}$$ is called exponent. For example, in $${\displaystyle 2^{4}}$$, 2 is the base and 4 is the exponent. To calculate $${\displaystyle 2^{4}}$$, one simply multiply 4 copies of 2. So $${\displaystyle 2^{4}=2\cdot 2\cdot 2\cdot 2}$$, and the result is $${\displaystyle 2\cdot 2\cdot 2\cdot 2=16}$$. The equation could be read out loud as "2 raised to the power of 4 equals 16." More examples of exponentiation are: • $${\displaystyle 5^{3}=5\cdot {}5\cdot {}5=125}$$ • $${\displaystyle x^{2}=x\cdot {}x}$$ • $${\displaystyle 1^{x}=1}$$ for every number x If the exponent is equal to 2, then the power is called square, because the area of a square is calculated using $${\displaystyle a^{2}}$$. So $${\displaystyle x^{2}}$$ is the square of $${\displaystyle x}$$ Similarly, if the exponent is equal to 3, then the power is called cube, because the volume of a cube is calculated using $${\displaystyle a^{3}}$$. So $${\displaystyle x^{3}}$$ is the cube of $${\displaystyle x}$$ If the exponent is equal to -1, then the power is simply the reciprocal of the base. So $${\displaystyle x^{-1}={\frac {1}{x}}}$$ If the exponent is an integer less than 0, then the power is the reciprocal raised to the opposite exponent. For example: $${\displaystyle 2^{-3}=\left({\frac {1}{2}}\right)^{3}={\frac {1}{8}}}$$ If the exponent is equal to $${\displaystyle {\tfrac {1}{2}}}$$, then the result of exponentiation is the square root of the base, with $${\displaystyle x^{\frac {1}{2}}={\sqrt {x}}.}$$ For example: $${\displaystyle 4^{\frac {1}{2}}={\sqrt {4}}=2}$$ Similarly, if the exponent is $${\displaystyle {\tfrac {1}{n}}}$$, then the result is the nth root, where: $${\displaystyle a^{\frac {1}{n}}={\sqrt[{n}]{a}}}$$ If the exponent is a rational number $${\displaystyle {\tfrac {p}{q}}}$$, then the result is the qth root of the base raised to the power of p: $${\displaystyle a^{\frac {p}{q}}={\sqrt[{q}]{a^{p}}}}$$ In some cases, the exponent may not even be rational. To raise a base a to an irrational xth power, we use an infinite sequence of rational numbers (xn), whose limit is x: $${\displaystyle x=\lim _{n\to \infty }x_{n}}$$ like this: $${\displaystyle a^{x}=\lim _{n\to \infty }a^{x_{n}}}$$ There are some rules which make the calculation of exponents easier:[3] • $${\displaystyle \left(a\cdot b\right)^{n}=a^{n}\cdot {}b^{n}}$$ • $${\displaystyle \left({\frac {a}{b}}\right)^{n}={\frac {a^{n}}{b^{n}}},\quad b\neq 0}$$ • $${\displaystyle a^{r}\cdot {}a^{s}=a^{r+s}}$$ • $${\displaystyle {\frac {a^{r}}{a^{s}}}=a^{r-s},\quad a\neq 0}$$ • $${\displaystyle a^{-n}={\frac {1}{a^{n}}},\quad a\neq 0}$$ • $${\displaystyle \left(a^{r}\right)^{s}=a^{r\cdot s}}$$ • $${\displaystyle a^{0}=1}$$ It is possible to calculate exponentiation of matrices. In this case, the matrix must be square. For example, $${\displaystyle I^{2}=I\cdot I=I}$$. ## Commutativity Both addition and multiplication are commutative. For example, 2+3 is the same as 3+2, and 2 · 3 is the same as 3 · 2. Although exponentiation is repeated multiplication, it is not commutative. For example, 2³=8, but 3²=9. ## Inverse Operations Addition has one inverse operation: subtraction. Also, multiplication has one inverse operation: division. But exponentiation has two inverse operations: The root and the logarithm. This is the case because the exponentiation is not commutative. You can see this in this example: • If you have x+2=3, then you can use subtraction to find out that x=3−2. This is the same if you have 2+x=3: You also get x=3−2. This is because x+2 is the same as 2+x. • If you have x · 2=3, then you can use division to find out that x=$${\textstyle {\frac {3}{2}}}$$. This is the same if you have 2 · x=3: You also get x=$${\textstyle {\frac {3}{2}}}$$. This is because x · 2 is the same as 2 · x • If you have x²=3, then you use the (square) root to find out x: you get the result that x = $${\textstyle {\sqrt[{2}]{3}}}$$. However, if you have 2x=3, then you can not use the root to find out x. Rather, you have to use the (binary) logarithm to find out x: you get the result that x=log2(3). ## References 1. "Compendium of Mathematical Symbols" . Math Vault. 2020-03-01. Retrieved 2020-08-28. 2. Weisstein, Eric W. "Power" . mathworld.wolfram.com. Retrieved 2020-08-28. 3. Nykamp, Duane. "Basic rules for exponentiation" . Math Insight. Retrieved August 27, 2020. Categories: Mathematics | Hyperoperations Information as of: 28.10.2020 07:42:01 CET Source: Wikipedia (Authors [History])    License : CC-by-sa-3.0 Changes: All pictures and most design elements which are related to those, were removed. Some Icons were replaced by FontAwesome-Icons. Some templates were removed (like “article needs expansion) or assigned (like “hatnotes”). CSS classes were either removed or harmonized. Wikipedia specific links which do not lead to an article or category (like “Redlinks”, “links to the edit page”, “links to portals”) were removed. Every external link has an additional FontAwesome-Icon. Beside some small changes of design, media-container, maps, navigation-boxes, spoken versions and Geo-microformats were removed. Please note: Because the given content is automatically taken from Wikipedia at the given point of time, a manual verification was and is not possible. Therefore LinkFang.org does not guarantee the accuracy and actuality of the acquired content. If there is an Information which is wrong at the moment or has an inaccurate display please feel free to contact us: email.
crawl-data/CC-MAIN-2020-50/segments/1606141188146.22/warc/CC-MAIN-20201126113736-20201126143736-00075.warc.gz
null
Universal Design for Learning Elements of Good Teaching - Universal Design Definition: - Universal design is an approach to designing course instruction, materials, and content to benefit people of all learning styles without adaptation or retrofitting. Universal design provides equal access to learning, not simply equal access to information. Universal Design allows the student to control the method of accessing information while the teacher monitors the learning process and initiates any beneficial methods. Although this design enables the student to be self-sufficient, the teacher is responsible for imparting knowledge and facilitating the learning process. It should be noted that Universal Design does not remove academic challenges; it removes barriers to access. Simply stated, Universal Design is just good teaching. - Students who speak English as a second language. - International students. - Older students. - Students with disabilities. - A teacher whose teaching style is inconsistent with the student’s preferred learning style. - All students. - Identify the essential course content. - Clearly express the essential content and any feedback given to the student. - Integrate natural supports for learning (i.e. using resources already found in the environment such as study buddy). - Use a variety of instructional methods when presenting material. - Allow for multiple methods of demonstrating understanding of essential course content. - Use technology to increase accessibility. - Invite students to meet/contact the course instructor with any questions/concerns. "Compiled from North Carolina State University's Principles of Universal Design and Chickering and Gamson's Seven Principles for Good Practice in Undergraduate Education. By Curriculum Transformation and Disability, University of Minnesota, Funded by the U.S. Department of Education. Project #P333A990015." - Course content offers various methods of Representation. Universally designed course content provides alternative representations of essential concepts. Various methods of representation can allow the student to learn the information in their preferred means. Example: Placing course notes on the web allows students to gain the information by lecture and text. Additionally, a student with a visual impairment could tape record the lecture to capture the notes in alternate format. - Course content offers various methods of Engagement. Universally designed course content maintains varied skill levels, preferences, and interests by allowing for options. By having flexible teaching strategies and course content, students can choose methods that support their interest and skill levels. Example: When teaching a foreign language, students could choose from a variety of on-line options that would allow them to practice fluency and comprehension at a reading level that is appropriate for them. - Course content offers various methods of Expression. Universally designed course content allows for alternate methods of expression. This allows the student multiple means of demonstrating mastery of the material. Example: Allowing the students to demonstrate knowledge on a subject by doing an oral presentation or writing a paper or taking a test. Students with a speech impediment may be unable to present the information orally while students with a fine motor disability may have difficulty taking a written exam. This information is available in alternative format upon request. Please call the Office for Disability Services at 292-3307. - Put course content on-line allowing students to “pick up” material that might have been missed in lecture. - Use peer mentoring, group discussions, and cooperative learning situations rather than strictly lecture. - Using guided notes enables students to listen for essential concepts without copying notes off of overhead. - Update course materials based on current events and student demands. - Provide comprehensive syllabus with clearly identified course requirements, accommodation statement and due dates. - Fluctuate instructional methods, provide illustrations, handouts, auditory and visual aids. - Clarify any feedback or instructions, ask for questions, and repeat or give additional examples. - Relate a new topic to one already learned or a real-life example. - Allow a student to tape record lectures or provide him/her with a copy of your notes. - Allow the student to demonstrate knowledge of the subject through alternate means. - Permit and encourage the use of adaptive technology. - Develop study guides. - Give more frequent exams that are shorter in length. Universal Design. Available: http://www.cast.org Curriculum Transformation and Disability. Funded by the US Department of Education. Project #P333A990015. Ways to Incorporate Universal Instructional Design. Common Teaching Methods. Available here. Do-It. University of Washington. Funded by the National Science Foundation, The US Department of Education, and the State of Washington. Grant # 9725110. Available: http://www.washinton.edu/doit/. University of Arkansas at Little Rock. College of Education. Available: www.ualr.edu/~coedept/curlinks/sped.html This publication is funded by the US Department of Education under grant #P333A990046. For additional copies or more information, please contact: Margo Izzo, Ph.D., Phone: 614-292-9218, Email: firstname.lastname@example.org NOTE: This information is available in alternate format upon request. Please call the Office for Disability Services at 614-292-3307. The Partnership Grant Home | OSU Home Page Upcoming TELR Events Training and Professional Development Opportunities Fast Facts for Faculty and Related Publications Partnership Grant Contact
<urn:uuid:c420eb0a-e173-4914-89a5-14b669a326c5>
{ "date": "2013-05-19T18:43:21", "dump": "CC-MAIN-2013-20", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697974692/warc/CC-MAIN-20130516095254-00002-ip-10-60-113-184.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8657016754150391, "score": 4.125, "token_count": 1139, "url": "http://ada.osu.edu/resources/fastfacts/Universal_Design.htm" }
# When does Equality for this Classical Inequality Hold? When $$a, b \in \mathbf{R}$$ and $$p \geq 1$$, it is known that we have $$|a + b|^p \leq 2^{p - 1}(|a|^p + |b|^p).$$ I am trying to see the sufficient and necessary condition of the equality of this inequality to hold. My attempt is the following: We wish to show that $$|a + b|^p = 2^{p - 1}(|a|^p + |b|^p)$$ We start by noticing that this inequality turns into the triangle inequality when $$p = 1$$ and the equality for triangle inequality holds if and only if we have $$a = cb$$ for $$c \in \mathbf{R}$$. Now suppose this condition is true, we shall show if extra conditions are needed for general $$p \geq 1$$. Now with the condition $$a = cb$$ for $$c \in \mathbf{R}$$, we have $$|a + b|^p = |cb + b|^p = |(c + 1)b|^p = |c + 1|^p |b|^p$$ On the other hand, we have $$2^{p - 1}(|a|^p + |b|^p) = 2^{p - 1}(|c|^p|b|^p + |b|^p) = 2^{p - 1}((|c|^p + 1)|b|^p) = 2^{p - 1}(|c|^p + 1)|b|^p.$$ That is, we need to have $$2^{p - 1}(|c|^p + 1) = |c+ 1|^p.$$ Therefore, we have if $$a = cb$$ for some $$c \in \mathbf{R}$$ such that $$2^{p - 1}(|c|^p + 1) = (c + 1)^p$$, then $$|a + b|^p = 2^{p - 1}(|a|^p + |b|^p)$$. However, I am not sure if this is a good enough condition to characterize the equality. • Duplicate of your question: math.stackexchange.com/questions/143173/… Apr 28 at 3:29 • @KylerS Thank you for your comment. However, if I read it correctly, I do not think the post answers my questions as to the conditions when the equality of this inequality holds. Apr 28 at 3:46 • I understand - maybe you can use Newton's generalized binomial theorem (for real p) and some facts about binomial coefficients and determine when? Apr 28 at 4:53 For $$p>1$$ the function $$t \to t^{p}$$ is striclty convex function on $$[0,\infty)$$. Hence, $$|\frac {a+b} 2|^{p}\leq (\frac {|a|+|b|}2)^{p} <\frac {|a|^{p}+|b|^{p}}2$$ (which is same as $$|a + b|^p < 2^{p - 1}(|a|^p + |b|^p).$$) unless $$a=b$$. So equality holds only when $$a=b$$. For $$a\ge b\ge 0,$$ with $$a,b$$ not both $$0$$: Let $$a,b$$ vary but with the restriction that $$a+b=2m$$ is constant. Let $$f=2^{p-1}(a^p+b^p)-(2m)^p.$$ Since $$db/da=-1$$ we have $$df/da=p2^{p-1}(a^{p-1}-b^{p-1}),$$ which is positive excspt when $$a=b.$$ Hence $$f$$ achieves a minimum only when $$a=b=m,$$ when $$f=0.$$
crawl-data/CC-MAIN-2022-33/segments/1659882573172.64/warc/CC-MAIN-20220818063910-20220818093910-00472.warc.gz
null
## Conversion formula The conversion factor from years to seconds is 31536000, which means that 1 year is equal to 31536000 seconds: 1 yr = 31536000 s To convert 4.4 years into seconds we have to multiply 4.4 by the conversion factor in order to get the time amount from years to seconds. We can also form a simple proportion to calculate the result: 1 yr → 31536000 s 4.4 yr → T(s) Solve the above proportion to obtain the time T in seconds: T(s) = 4.4 yr × 31536000 s T(s) = 138758400 s The final result is: 4.4 yr → 138758400 s We conclude that 4.4 years is equivalent to 138758400 seconds: 4.4 years = 138758400 seconds ## Alternative conversion We can also convert by utilizing the inverse value of the conversion factor. In this case 1 second is equal to 7.206770905401E-9 × 4.4 years. Another way is saying that 4.4 years is equal to 1 ÷ 7.206770905401E-9 seconds. ## Approximate result For practical purposes we can round our final result to an approximate numerical value. We can say that four point four years is approximately one hundred thirty-eight million seven hundred fifty-eight thousand four hundred seconds: 4.4 yr ≅ 138758400 s An alternative is also that one second is approximately zero times four point four years. ## Conversion table ### years to seconds chart For quick reference purposes, below is the conversion table you can use to convert from years to seconds years (yr) seconds (s) 5.4 years 170294400 seconds 6.4 years 201830400 seconds 7.4 years 233366400 seconds 8.4 years 264902400 seconds 9.4 years 296438400 seconds 10.4 years 327974400 seconds 11.4 years 359510400 seconds 12.4 years 391046400 seconds 13.4 years 422582400 seconds 14.4 years 454118400 seconds
crawl-data/CC-MAIN-2021-25/segments/1623487625967.33/warc/CC-MAIN-20210616155529-20210616185529-00022.warc.gz
null
- Scientists found a new DNA structure, named i-motif, in human cells. - They have built an accurate fragment of an antibody molecule to recognize i-motif’s structure. - It’s a four-stranded knot of DNA, where C letters (cytosine) on the same DNA strand bind to each other. For the first time, researchers at the Garvan Institute of Medical Research, Australia, have detected a new structure of DNA, named i-motif, in human cells. It’s described as “twisted knot” of DNA – a form that has never been directly observed in the nuclei of human cells. DNA (Deoxyribonucleic Acid) is made up of nucleotide molecules, which contain adenine (A), cytosine (C), guanine(G) and thymine (T). The order of these four determines genetic code, which provides accurate instruction for how human bodies are formed and how they work. Human DNA has approximately 3 billion bases, of which 99% are same in all people. DNA has a “double helix” structure, which was first uncovered by Francis Crick and James Watson in 1953. Now scientists have observed something different than this old structure. In laboratory tests, they identified new short stretches of DNA that can play a crucial role in when and how the code of DNA is ‘read’. How I-motif is Different Than Double Helix DNA? It’s a four-stranded knot of DNA, where C letters (cytosine) on the same DNA strand bind to each other. Whereas in double helix DNA, C binds to G (guanine), and opposite strand letters recognize each other. The two parallel duplexes make a quadruplex structure. I-motif is stable in acidic environment, but starts to become unstable in neutral or basic solutions. Also, it’s rich in uncommon C-C (cytosine-cytosine) bonds. Scientists have already observed this i-motif DNA structure — in a research done in 2014 — but under artificial environments in the lab. This time, they’ve identified it in an actual human cell. Because of i-motif’s pH dependent folding, its DNA sequences have been used as pH switches for nanotech applications. Initially, i-motif was thought to be unstable at physiological pH. However, new studies have made it clear that this isn’t always the case. The stability of i-motif depends on parameters like sequence and surrounding scenarios. How Did They Identified It? Schematic of i-motif and G4 structures | Credit: Garvan Institute of Medical Research Scientists built an accurate fragment of an antibody molecule to recognize i-motif’s structure. Also, i-motifs could be attached to this newly developed fragment with high affinity. Before this, the lack of i-motif-specific antibody hampered our understanding of its functionalities. However, the fragment did not recognize DNA in 4-stranded structure, called G quadruplex structure, nor did it identify DNA in helical shape. It helped scientists to precisely locate the i-motif in human cell lines. They detected several green spots inside the nucleus, by applying fluorescence methods. These spots show the precise location of i-motifs. What’s even more interesting is, they saw spots were appearing and disappearing at irregular intervals. This means that i-motifs were forming and dissolving over time. They mostly formed (while DNA is being ‘read’) at the late G1 phase – a specific location in the cell. Also, they were detected in the endpoints of chromosomes, called telomeres (key to aging) and in a few promoter areas that decide whether genes are switched off or on. The results provide a core foundation for future researches scrutinizing the key function of this genomic DNA structure, and for validation as a therapeutic target in pathological scenarios like cancer.
<urn:uuid:d5cf187c-95a3-4264-b238-e443c3fccc4e>
{ "date": "2019-07-20T16:40:43", "dump": "CC-MAIN-2019-30", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00137.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9391844868659973, "score": 3.640625, "token_count": 854, "url": "https://www.rankred.com/i-motif-new-dna-structure-in-human-cells/" }
One of the common questions people have in preparing learning materials is also the one they tend to skip over when no immediate yes/no is to be had. Why accessibility matters to all teachers Creating content comes with responsibility – The Australian legislation pertaining to equal rights of access for all is the Disability Discrimination Act (DDA) 1992. The Blind Citizens of Australia site has an online copy-and-paste email format for lodging an inaccessible web site complaint under the DDA to the Human Rights and Equal Opportunities Commission (HREOC). The applicability of the DDA legislation to internet websites was tested and proven back in 2000, with the case of Bruce Lindsay Maguire v Sydney Organising Committee for the Olympic Games which Maguire won. The ‘industry standard’ guidelines for web accessibility is conformance and validation to W3C accessibility checklist guidelines. How to create accessible content PAC is a recommended set of criteria from World Wide Web Consortium (W3C): PDF Techniques for WCAG 2.0 - Document is marked as tagged - Document Title available - Document Language defined - Accessible Security Settings - Tab follows Tag-Structure - Consistent Heading Structure - Bookmarks available - Accessible Font Encodings - Content completely tagged - Logical Reading Order - Alternative Text available - Correct Syntax of Tags / Rolls - Sufficient contrast for Text - Spaces existent There are several common problems with documents, most often in PDF documents which are the most widely used form of electronic distribution to students. Abobe has an excellent guide for authors which is free to download. In addition, there is a pre-flight checklist which can be used before your course materials are presented to students. Why bother? Well, besides the legal and ethical requirements – many teachers have no idea whom will finally enroll on their course. Using a inner-self probability strategy is a bad way to address these responsibilities. - If the document contains scanned text, apply Optical Character Recognition (OCR) - Add author, title and subject and set the language in the document properties - Tag the document to provide structure for remediation and support for bookmarks - All documents should be structured so that an accessibility statement is the first text to be read aloud, to ensure the reader does not have to try and find it. - Verify accessibility (see tool below) - Verify and correct the Reading Order - Add descriptive text to images or mark them as background - Optimize the file size and set compatibility - Redact all personal and private information - Add bookmarks - Verify accessibility (use software or contact someone who knows how) - Does the linking page contain a link to download Adobe Reader - Form fields, if used, are accessible. - Descriptions must reflect the nature of the input and tab order must be set in a logical sequence. - Security settings, if used, do not interfere with screen readers. Test your PDF Documents You can download this free tool to run over your documents, which will give you a report.
<urn:uuid:96f4817b-808f-4755-a103-095aba157f1c>
{ "date": "2016-10-27T08:50:51", "dump": "CC-MAIN-2016-44", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721174.97/warc/CC-MAIN-20161020183841-00263-ip-10-171-6-4.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8640053272247314, "score": 3.53125, "token_count": 639, "url": "https://deangroom.wordpress.com/2012/11/13/accessbility-why-to-do-it-how-to-do-it/" }
Greater access to women's education in the Islamic world has had dramatic effects on both gender relations and women's social and economic standing. Family lives have also changed, as women are marrying later and having fewer children, and thanks to the increased confidence that education has given women, they are turning to political participation as a way to reform societal inequalities throughout the Islamic world. Setbacks and Changes Muslim women are often disadvantaged in their access to education and employment -- 17 of the world's 20 countries with the greatest gender inequality are in the Islamic world. In Iran, for example, women possess fewer work-related skills than men, on average, and due to a prejudicial justice system, they are beholden to the dictates of their husbands and male family members. Since these factors often limit women to the domestic sphere, many have chosen to immigrate to the West to seek education and employment. In Iran, for example, this option has always existed for many upper-class women, but increasingly, middle- and lower-class women from small towns are leaving in search of educational and work opportunities. As a result, Muslim women's university participation is rapidly rising both abroad and in Islamic countries including Iran, where female students outnumbered males 110 to 100 as of 2005. Learning to Love Oneself Some Western scholars have hypothesized that Muslim women's increasing access to education would result in them becoming dislocated from their religion and culture. "The Guardian" reported in 2006, however, that evidence from interviews with female Muslim students show that religiosity is increasing as a source of self-identification. "The Guardian" also reports that evidence indicates that racial prejudice associated with Islamophobia is a potential barrier to education and employment. By emphasizing religion in their self-identities, "The Guardian" reports, female Muslim students have emancipated themselves from feelings of racial discrimination, thus giving them greater confidence. Muslim women's increased access to education has had significant impact on gender relations in the Islamic world. Access to higher education has created opportunities for social relations between men and women that were previously nonexistent in parts of the Islamic world. In addition to greater confidence among female students, which has helped them to raise their social status to equal that of men in many respects, there have been dramatic changes in the home lives of educated Muslim women, such as an increase in their average age of marriage to the late 20s and a decrease in the number of children that they have. Women in Work and Politics Muslim women's attitudes toward their employment prospects have become more positive as their access to education increases. Education, "The Guardian" reports, has helped to equip Muslim women with the knowledge of the available resources for job seekers that globalized economic integration, including Western-based Women's Rights NGOs, has provided. In addition to secondary education, the Islamic world has also seen the introduction of literacy programs and other grassroots educational efforts for women. Besides employment opportunities, these educational efforts have also served to increase Muslim women's political participation. With greater awareness of the unequal treatment that they face from their families and society, Muslim women are turning to political avenues in increasing numbers as a means to social and cultural reform. - Political Psychology: Young Muslim Women in France: Cultural and Psychological Adjustments - Legatum Institute: Women and Education in the Islamic Republic of Iran: Repressive Policies, Unexpected Outcomes - The Guardian: Muslim Women and Higher Education: Identities, Experiences and Prospects: A Summary Report - World Economic Forum: Global Gender Gap Report 2012 - Brookings Institute: Are Iranian Women Overeducated? - The Journal of Developing Areas: Education and Fertility: A Panel Data Analysis for Middle Eastern Countries - Journal of Business Ethics: Women, Management and Globalization in the Middle East
<urn:uuid:92beb769-68f3-498f-b4d5-93da34bc4bb6>
{ "date": "2020-07-02T16:38:38", "dump": "CC-MAIN-2020-29", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655879532.0/warc/CC-MAIN-20200702142549-20200702172549-00256.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9728138446807861, "score": 3.703125, "token_count": 765, "url": "https://classroom.synonym.com/effects-educated-women-islam-8455.html" }
Brain-compatible activities to inspire active learning in the third-grade classroom! This valuable guide gives teachers the tools they need to plan lessons correlated to the way the brain learns best and to ensure success for all students regardless of their learning style or special challenges! Drawing on classroom-tested, research-based strategies from Worksheets Don't Grow Dendrites: 20 Instructional Strategies That Engage the Brain , this practical resource offers a variety of content-specific activities that incorporate graphic organizers and other visuals that reinforce student learning. Based on national academic standards, these activities feature graphic organizers and visuals such as bar graphs, timelines, concept maps, sequence charts, cause-and-effect charts, segmenting mats, labeled diagrams, and more. Each activity includes step-by-step directions, skills objectives, materials lists, and a myriad of creative reproducibles that help students organize and record their learning. This resource offers a multitude of brain-compatible activities that cover topics such as: multiplication, division, area, seeds, planets, animal groups, immigration, communities, inventions, story planning and writing, fitness games, art, music, and much more. Make a real difference in your students' energy, motivation, and achievement by applying these proven strategies to help them master curriculum objectives! About the Author: Marcia L. Tate is the executive director of professional development for the DeKalb County School System, Decatur, Georgia. During her 28-year career with the district, Tate has been a classroom teacher, reading specialist, language arts coordinator, and staff development director. As an educational consultant, she has presented to over 50,000 administrators, teachers, parents, and business and community leaders throughout the United States.
<urn:uuid:1706ccb1-b3f7-4aea-b523-e4cfa8af1c24>
{ "date": "2021-03-06T14:14:44", "dump": "CC-MAIN-2021-10", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178375096.65/warc/CC-MAIN-20210306131539-20210306161539-00138.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9257985353469849, "score": 4.03125, "token_count": 348, "url": "https://ca.corwin.com/en-gb/nam/book/engage-brain-graphic-organizers-and-other-visual-strategies-grade-three" }
A new study claims that the big Antarctic ice melt scenarios just aren't plausible. Have doomsday predictions on the sea level rise caused by melting in Antarctica been way off? A new study indicates that while Antarctica will contribute to sea level rises due to global warming in this upcoming century, the nightmare scenarios that many have been predicting just don’t seem at all likely to happen, according to a BBC report. Using computer models, a research team led by Catherine Ritz, who hails from the Université Grenoble Alpes, France, and Tamsin Edwards, from the Open University, UK, published a paper in the journal Nature that looks at how the polar south would respond if greenhouse gases rise at their current rates. They found that the most likely outcome is a rice of 10 centimeters by 2100, far from the more devastating impact of a rise of 30 centimeters or more that some research has claimed. They put the odds of that happening at just one in 20. Their computer models take into account the shape of the bedrock of the continent and how the ice moves on it. Satellites have spotted some thinning and retreat of glaciers on the western half of the continent, which are said to be in an “irreversible” decline. They ran 3,000 simulations using their model and then compare them to what’s actually happening in the Amundsen Sea, throwing out versions that appear to be moving too quickly or too slowly. It was through this method they came to the conclusion that a 10 centimeter rise was most likely, which actually agrees with predictions by the Intergovernmental Panel on Climate Change (IPCC) in 2013. However, it disagrees with IPCC on the likelihood of a catastrophic rise of up to a meter, something the team found to be not plausible. “The bed of Antarctica is so important for what the ice sheet is doing, and there are parts of it that are just too bumpy and rough or are not sloping in a way that will allow for anything to happen too quickly,” Edwards said according to the BBC report. “That’s not to say that if things kept going for a few hundred or a thousand years you couldn’t get that kind of dramatic collapse – but we don’t think on the timeframe of a couple of hundred years that the ice can respond that fast.”
<urn:uuid:b9c77402-f0fd-4f71-ba9c-d689738d7732>
{ "date": "2018-07-21T15:46:19", "dump": "CC-MAIN-2018-30", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592636.68/warc/CC-MAIN-20180721145209-20180721165209-00337.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9538107514381409, "score": 3.5625, "token_count": 490, "url": "https://www.morningticker.com/2015/11/are-global-warming-advocates-grossly-exaggerating-sea-level-rise/" }
Molecular nanotechnology or "nanotech" as it is popularly called is the technology of manipulating materials at the molecular level or the "nanoscale (a nanometer spans only three or four atoms.)" And while that may appear futuristic, it is not: Design rules of silicon chips have already dropped below 100 nanometers. Nobel laureate Richard Feynman first publicized the idea of nanotechnology in a talk that he gave on December 29th, 1959, at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech) entitled, "There's Plenty of Room at the Bottom." There he described an "ultimate vision," the possibility of vertically integrating manufacturing right down to the individual atom. By starting at the "bottom," in Feynman's words, atomically precise manufacturing methods could be the ultimate in miniaturization. "There is nothing that I can see in the physical laws that says the computer elements cannot be made enormously smaller than they are now. . .the wires should be 10 or 100 atoms in diameter, and the circuits should be a few thousand should be 10 or 100 atoms in diameter, and the circuits should be a few thousand angstroms [100 nm] across," said Feynman, in his 1959 talk. He went on to encourage designers to think small, because, in his opinion, all it would take to get there would be ingenuity. "The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom. It is not an attempt to violate any laws; it is something, in principle, that can be done; but in practice, it has not been done because we are too big," said Feynman. Feynman's overall concept was that when engineers begin to precisely manipulate matter at the atomic level, we would finally achieve what the alchemists sought in the Middle Ages we would be able to take whatever raw atoms are available and rearrange their neutrons, protons and electrons into whatever we want with nothing left over. During his 1959 talk, Feynman went on to offer a $1,000 prize for the first electric motor small enough to be contained inside a 1/64 inch cube. Today, the Foresight Institute has picked up the baton with an annual "Feynman Prize in Nanotechnology ($5,000) and the Feynman Grand Prize ($250,000). Feynman's dream sparked the imagination of a generation of dreamers including a faction whose thinking extended into science fiction. Their dreams exceeded those of the ancient alchemists in proposing that individual atoms of inexpensive raw materials garden variety dirt could be rearranged into complex, fully formed electromechanical devices or just about anything that is "manufactured." Science fiction authors began speculating on how virtually any kind of mechanical, chemical or complex electromagnetic device could be constructed with "nano-robots" automatic "assemblers" working atom-by-atom. At least some of this dreaming became feasible in 1982 when manipulation of individual atoms become possible thanks to the invention of a breakthrough tool called the scanning tunneling microscope (STM), which won its inventors, IBM researchers Gerd Binnig and Heinrich Rohrer, the 1986 Nobel Prize. The same year the duo followed up by co-inventing yet another tool, the atomic force microscope (AFM). More than anything else, scanning probe microscopy (including both atomic force microscopy and scanning tunneling microscopy) gave birth to nanotechnology. A probe only a single-atom wide, enabled engineers to "push" atoms into "designer" molecules. IBM's Zurich Research Laboratory has subsequently demonstrated that the tips could be used to store bits by impressing 10 nm marks in a soft polymer sheet, thereby packing a terabit per square inch the so-called Millipede memory chip (see "IBM stores terabits of memory on a single chip," EE Times, June 24, 2002, http://www.eetimes.com/story/OEG20020624S0030). Soon after scanning probe microscopy made possible that manipulation of atoms, Eric Drexler, now chairman of the Foresight Institute, released his 1986 book Engines of Creation, which popularized the term "nanotechnology" and fleshed out its "ultimate vision." Drexler predicted that nanoscale assemblers would automatically assemble molecular building blocks into nearly any type of manufactured good watch to watchtower. The term "nanotechnology" itself was coined in 1974 by Tokyo Science University professor Norio Taniguchi, author of "Nanotechnology: Integrated Processing Systems for Ultra-Precision and Ultra-Fine Products" (Oxford Science Publications), but he used the term to signify machining traditional silicon to tolerances of less than a micron. Taniguchi's original concept submicron machining of silicon has already produced a number of tiny mechanical devices that today are called microelectromechanical systems (MEMS). MEMS are the most highly developed application of nanotechnology today from air-bag sensors in automobiles to thin-film heads for disk drives. Meanwhile, the world's first company dedicated to Drexler's ultimate vision Zyvex Corp. (Richardson, Texas, www.zyvex.com) hopes to create nano-assemblers by downsizing MEMS to the nanoscale through the nanoelectro-mechanical systems (NEMS) project for the Advanced Technology Program at the National Institute of Standards and Technology (NIST), along with Standard MEMS Inc. and university collaborators Rensselaer Polytechnic Institute Center for Automation Technologies, the University of Texas at Dallas, and the University of North Texas. Similar research is proceeding separately at big corporations like IBM, Hewlett-Packard, Motorola and Raytheon. The federal government has enlisted the help of universities and smaller companies with its National Nanotechnology Initiative funded with over $500 million, and with separate programs inside its own research facilities at national labs and the National Aeronautics and Space Administration (NASA, www.nasa.gov). The New York City-based NanoBusiness Alliance (A HREF = "http://www.nanobusiness.org">http://www.nanobusiness.org) claims that over $1 billion will be spent in nanotechnology research and development in 2003. Venture capitalists have been investing for several years. Draper Fisher Jurvetson, for instance, has already invested $40 million to start up 12 new nanotechnology ventures, like NanoOpto Corp. (specializing in subwavelength optical NEMS and nano-imprint lithography, http://www.nanoopto.com). The Texas Nanotechnology Initiative (http://www.texasnano.org) also tracks venture investments, estimating that $1 billion will be invested in researching electronic applications of nanotechnology over the next five years. Nanotechnology research today uses three types of well-understood molecular building blocks proteins, polymers and carbon nanotubes. (Carbon nanotubes are rolled hexagonal graphite sheets grown from carbon 60, also known as Buckminsterfullerene, a geodesic-dome-shaped molecule, which, together with other fullerenes such as C70, now constitutes the third elemental form of carbon, after graphite and diamond). Proteins, which are building blocks of DNA, have recently been harnessed with atomic precision by biochemists with the help of gene copying machines used by genome researchers. These mainly one-dimensional structures can be accurately grown in repetitive patterns according to rules designed into to their "seeds" similar to crystal growth patterns. Researchers like professor Carlos Bustamante at Howard Hughes Medical Institute, professor Andreas Engel at the University of Basel (Switzerland) and professor Steve Block at Stanford University have all made progress at rearranging proteins into atomically precise "designer" molecules that could serve as a nanoassembler's building blocks, in the long term, or in the near term as components in hybrid systems. Even IBM got into the protein act in 2000 (see EE Times, Sept. 13, 2000, http://www.eetimes.com/story/OEG20000913S0061) when it used the "lock and key" molecular recognition mechanism built into protein molecules, in an early biological application of nanotechnology. A MEMS "comb" had each tooth pretreated with a specific molecular "key," making it deflect in the presence of a single type of molecule. By measuring the deflection, IBM was able to detect DNA strands with only a single missing bond on a long protein chain, a feat impossible in real-time using conventional equipment. The second category of possible building blocks for delivering on nanotechnology's ultimate vision is polymers. Several different researcher groups have demonstrated that Brownian motion the random "mixing" of molecules in a liquid or gas can exhibit auto-assembly if the parts are pretreated a la IBM's lock-and-key application. For instance, Sandia National Labs, a pioneer in MEMS technology, has demonstrated that small molecules with the edges pretreated so that they can only bond together with the correct other parts, auto-assemble into atomically precise molecular building blocks (see "Experiments refine self-organizing principles" EE Times, Oct. 23, 2001, http://www.eetimes.com/story/OEG20010917S0076). Carbon nanotubes are the most promising of all building blocks for nanotechnology for the short term certainly the next five years. Besides being stronger than steel, carbon nanotubes exhibit many fascinating electronic properties, such as: ballistic transport of electrons at room temperature, the ability to serve as the channel of a silicon transistor, and the ability to behave like either a p-type and n-type semiconductor without having to doped (see "Nanotechnology creates 1-terabit memory," EE Times, http://www.eetimes.com/story/OEG20020611S0018). IBM recently demonstrated a transistor using a single carbon nanotube a prototype that could be packing terabits of information on memory chips within five years. Right now, however, the most successful electronic application of nanotechnology has been the carbon nanotubes themselves. Measuring only 1 to 2 nanometers in diameter, they are being fitted to scanning probe microscopes for even easier manipulation of individual atoms. They are also being prepared as additives for just about everything from rubber-as-strong-as-steel to emitters for microscopic vacuum tubes (see "Vacuum tubes born again in nanotube MEMS", EE Times, June 17, 2002, page 51). Companies like Carbon Nanotechnologies Inc. and Applied Nanotechnologies Inc. are growing nanotubes to the specifications of a diverse set of future applications. Carbon Nanotechnologies, for instance, co-founded by Carbon 60 discoverer Richard Smalley, is developing carbon nanotubes called "buckytubes" single-walled carbon nanotubes produced by a proprietary process. Smalley, Harold Kroto and Robert Curl won the 1996 Nobel Prize for their discovery of carbon 60 fullerenes (buckyballs). Applied Nanotechnologies, on the other hand, develops applications for carbon nanotubes to improve existing devices, such as field-emitter cathodes for microwave amplifiers, gas discharge tubes as well as pocket-sized X-ray- and e-beam-machines. Many nanotube-based devices have been demonstrated in the laboratory that, while falling short of self-replication or auto-assembly, nevertheless may become very important to chip makers. University researchers have paved the way, starting with Richard Smalley's own research group at Rice University. Many other groups have made important contributions too, such as Cees Dekker's Molecular Biophysics Group at Delft University of Technology (Lorentzweg, The Netherlands) and professor Paul McEuen's group at Cornell University, both of which paved the way early-on by characterizing carbon nanotubes. Likewise, professor Sumio Iijima at the Japan Science & Technology Corp. (Kawaguchi City, Japan) has been coordinating that country's characterization of nanotubes and related electronic applications of nanotechnology. Stateside, Harvard University professor Charles Lieber's research group has demonstrated how to grow silicon nanowire building blocks as electronic components that can be assembled into molecular-sized circuits. Big corporate internal research groups are also getting into the act, including IBM, HP and Bells Labs, Lucent Technologies Over the next five years, carbon nanotubes will likely be integrated into hundreds of applications. Carbon Nanotechnologies has already licensed its carbon-nanotube manufacturing process to DuPont for its flat-panel display group, which will use them as thick-film emitters resulting in a display that is lighter, thinner and more energy-efficient than today's. Dow Chemical is likewise gearing up to offer what they call "affordable and well-performing nanomaterials" to its existing customer base, such as Ford Motor Co. Traditional semiconductor makers are also getting in the act, from Motorola Inc. to NEC and Samsung. For instance, Motorola's Physical Science and Research Laboratories are characterizing nanotubes, to each end of which they have successfully added single-molecule electrodes, in the hopes of shrinking and accelerating the performance of future sensors. Soon the mother of all nanotube applications flash memory replacement will likely bear fruit at IBM, packing billions of transistors into the space now housing only millions and, once again, extending Moore's Law. Why now? Intel co-founder Gordon Moore's so-called "law" is actually a prediction that every 18 months semiconductor fabricators will be able to cram twice the number of transistors on a microchip. However, lithographically patterned semiconductor technology is running up against physical and economic constraints in its quest for smaller dimensions the state of the art is only a few hundred nanometers and faster performance. Not the least of the concerns is the soaring costs of all this downsizing. Nanopatterning the extension of photolithographic techniques into the nanoscale domain will assist in reducing chip sizes further, extending the lifetime of traditional transistors. But more importantly, nanopatterning will assist in the placement of nanotubes into otherwise conventional silicon transistors. Many groups are demonstrating methods to nanopattern traditional silicon to below 100 nanometers. For instance, Stephen Chou's team at Princeton University has demonstrated a laser-assisted direct imprint technique that may be able to shrink feature sizes to 10 nm (Chou fires his laser through a printing mask made from quartz to directly melt the surface of the silicon for "etch-less" nanopatterning of silicon chips.) Even with nanopatterning, there remain many hurdles such as heat dissipation and interference between the tiny components. HP's Quantum Science Research Lab claims that it will take a decade of intensive research to wear down the nitty gritty engineering problems that crop up at these small scales. HP fellow and director of the company's Quantum Science Research Laboratories, R. Stanley Williams, recently revealed a nanotechnology patent, shared with HP's Phillip Kuekes and UCLA scientist James Heath, that enables a crossbar grid of nanoscale wires, separated by a single molecule thickness of rotaxane, to form switches between selected intersections by electrically activating the rotaxane molecule between them. Even with the extension of chip-making techniques into the nanometer domain, nanotechnology proponents claim further size reductions may need a new approach from the bottom up (atom-by-atom) rather than from the top down as in conventional lithograhphy. The "top-down" approach currently practiced in chip-making forces us to spend more and more on higher and higher precision machinery to make smaller and smaller photolithographic lines for the ever shrinking size of chip features. It's a trend in common with all manufacturing processes today that attempt to make smaller devices today's manufacturing processes are subtractive processes that start with large assemblies of molecules. It is likely that nanotech approaches that start by aggregating individual atoms or molecules could address all such manufacturing needs. Indeed, in a nanotechnologist's ideal world every engineer's design would be married to a perfectly vertical manufacturing technology that harvests its own raw atoms, makes them into perfect molecules for a specific applications, assembles these perfect molecular building blocks into smart materials, assembles the materials into subsystems, and assembles the subsystems into finished devices. But the problem with that kind of thinking is that without the availability of extremely small and extremely fast assemblers, such vertical integration simply isn't possible. Manipulating materials atom by atom manually would take eons even to build even the simplest systems. But proponents of this vision take heart from the fact that Nature routinely exhibits encoding mechanisms that could, theoretically, be used to "program" smart materials into automatically assembling themselves. Nature auto-assembles all its molecules into subsystems and the subsystems into finished devices, whether it is "growing" crystals from atoms or growing full-blown biological systems from a single fertilized egg cell. Nanotech's ultimate vision conjures up armies of man-made nano-assemblers spinning out plastic as strong as steel, much the way wood is spun out by the "assemblers" in a tree. To scale up to the task size, these self-replicating molecular assemblers would make copies of themselves from molecular building blocks until they had enough of themselves to perform the task at hand, be it assembling a microchip or a highway. Much science fiction is made of the amazing scales of economy that could be reaped by this approach, and an active search is on in scientific circles for molecular designs that can serve as the "tools" and "dies" for such nanoscale construction projects. Critics are not so optimistic. Besides the usual doomsday predictions of self-assembling nano-robots running amok, at least one well-placed critic challenges the feasibility of realizing the ultimate vision. Nobel laureate Richard Smalley is no doomsayer, since he co-founded one of the most promising nanotech companies (Carbon Nanotechnologies). Nevertheless, Smalley's poignant criticism is that molecular auto-assembly, as proposed by Feynman and Drexler, is just too ambitious. In particular, Smalley says that the "fat-" and "sticky-finger" problems will prevent the success of the necessary auto-assembly steps. Others claim that such fine-scale materials will be too brittle, lacking the strength for macroscopic projects. Still others charge that the second law of thermodynamics will foil the ultimate vision (nanoscale friction generates too much heat, essentially making it impossible to scale up from nano-sized to macroscopic devices). The 'beginning' of life On the positive side, most of the advantages of nanotechnology will be reaped along the way to the ultimate vision. Why? Because nanotechnology is at the "beginning" of its lifetime, whereas silicon technologies are at the end of their lifetimes. Nanotechnology can only ascend reaping geometrically increasing benefits as each succeeding layer of knowledge builds on the one before. In contrast, top-down manufacturing methods, such as semiconductor manufacturing processes, are increasingly expensive as they attempt to scale down. Nanotechnology benefits will be able to bootstrap the advantages of bottom-up discoveries as they are uncovered. First, engineers will learn how to add auto-assembling techniques to existing silicon chips, which will help in learning how to coax these smart materials into auto-assembling subsystems, and eventually auto-assembling subsystems into devices at least in theory. In nanotech-land, chemistry meets silicon micromachining techniques through a melding of the appropriate natural laws. The mechanisms that bond atoms together into useful molecules are well-understood, as are the principles governing the growth of crystals. Together these chemistries can control how raw materials are transformed how sand is processed into microchips. Unfortunately, today all the reagents and catalysts and other chemicals needed to promote the desired reactions inevitably lead to byproducts, many of which are unwanted. Nanotechnology ups the ante by downsizing chemistry from mixing vats containing billions of atoms, to individual atoms bonding together into smart molecular building blocks. Using molecular modeling software, engineers of the future will design molecular building blocks that fit perfectly with each other. Byproducts would be completely eliminated ultimately. Early applications, however, will be successful because they have just one nanoscale aspect transistors using nanotubes as the channel, for example. Auto-assembly would be a useful property no matter the scale, but is not used today for economical reasons-it is usually more economical to build a machine that makes a part, rather than design a "smart" part that can make itself. But even if nanotechnology's ultimate vision of large-scale molecular self-assembly is never realized, the field itself will yield a variety of benefits through an understanding of how materials can be manipulated at the nanoscale. Along the long-range development cycle to the ultimate vision of molecular self-replication and auto-assembly, there will be many milestones. In fact, there are so many advantages to acquiring precise control of materials at the atomic-level that the original goal of self-replication and auto-assembly could be easily obscured. Materials specialists have long used nanoscale additives to make certain goods more durable: Carbon black, which consists of nano-sized particles, has been strengthening the sidewalls of automobile tires for 100 years. Such nanomaterials from 3M, Monsanto and others will reap nano-related benefits long before we have any sort of nano-assemblers. In recognition of these benefits one investment house in Tel Aviv the Millennium Materials Technologies Fund has decided to focus on funding only nanotech materials makers. Many U.S. businesses are following suit. For instance, Applied Science Inc. (Cedarville, Ohio) has patented a multiwalled carbon nanotube material, called Pyrograf, and is marketing it as an additive that makes polymers stronger and conductive. Its customers include General Motors Corp. and Goodyear who are constantly on the look out for weight- and cost-reduction techniques in automobiles., The semiconductor industry is evaluating the material for everything from semiconductor handling trays to a thermal backing for next-generation microchips. A number of composite materials use nanotechnological approaches. Magnetoresistive heads for hard disk drives use layers of composite material measuring just a few nanometers thick. Molecular control maintains the purity of these layers. which are combined to form macroscopic systems the recording head itself. Other nanotech materials exploit various aspects of submicron-sized particles, such as the use of "quantum dots" as biological markers. Companies like Quantum Dot Corp. are capitalizing on work dating back to the 1980s performed separately by researcher Louis Brus at Bell Laboratories and researcher/collaborators Alexander Efros and A.I. Ekimov of the Yoffe Institute in St. Petersburg (Russia) which harnesses silicon nanoparticles. Quantum Dot and others are extending that work by fabricating silicon nanospheres that are smaller than the Bohr's radius of silicon (the natural distance between electron-hole pairs in silicon). Stimulating these nanoparticles with low-energy radiation while their electron-hole pairs are confined enables them to store more energy than their usual quantum states would allow, resulting in emissions that are shifted to visible wavelengths. Quantum Dot's patented "Qdot nanocrystals" can be attached to specific human drugs/antibodies, to be used as fluorescent biological markers. In computer applications quantum dots can be made to switch like transistors, only better, since quantum states hold both a "0" and a "1" simultaneously, permitting parallel calculations. Materials specialists are even applying nanoparticle technology to mundane applications, such as suntan lotion. Nano-sized zinc oxide particles produced by Nanophase Technologies one of the few publicly traded nanotech companies create a transparent zinc-oxide sunscreen because their tiny size makes them invisible. The company is currently applying its nanotechnologies to ceramics based on nanocrystalline aluminum oxide and ZTA (zirconia-toughened alumina), as well as other transparent coatings that are abrasion-resistant, dissipate static and, when formed into films fabricated from antimony and indium, can conduct electricity.
<urn:uuid:1c480f5f-259b-4972-a368-7d9744c8fbad>
{ "date": "2014-09-22T00:27:25", "dump": "CC-MAIN-2014-41", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657136494.66/warc/CC-MAIN-20140914011216-00194-ip-10-234-18-248.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.931352972984314, "score": 3.6875, "token_count": 5100, "url": "http://www.eetimes.com/document.asp?doc_id=1145143" }
# 1998 AJHSME Problems/Problem 12 (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) ## Problem $2\left(1-\dfrac{1}{2}\right) + 3\left(1-\dfrac{1}{3}\right) + 4\left(1-\dfrac{1}{4}\right) + \cdots + 10\left(1-\dfrac{1}{10}\right)=$ $\text{(A)}\ 45 \qquad \text{(B)}\ 49 \qquad \text{(C)}\ 50 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55$ ## Solution Taking the first product, we have $\left(1-\frac{1}{2}\right)=\frac{1}{2}$ $\frac{1}{2}\times2=1$ Looking at the second, we get $\left(1-\frac{1}{3}\right)=\frac{2}{3}$ $\frac{2}{3}\times3=2$ We seem to be going up by $1$. Just to check, $1-\frac{1}{n}=\frac{n-1}{n}$ $\frac{n-1}{n}\times n=n-1$ Now that we have discovered the pattern, we have to find the last term. $1-\frac{1}{10}=\frac{9}{10}$ $\frac{9}{10}\times10=9$ The sum of all numbers from $1$ to $9$ is $\frac{9\cdot10}{2}=45=\boxed{A}$
crawl-data/CC-MAIN-2019-51/segments/1575540547165.98/warc/CC-MAIN-20191212205036-20191212233036-00532.warc.gz
null
GCSE Maths Ratio and Proportion Compound Measures # Compound Measures Here we will learn about compound measures including speed, density and pressure and look at problem solving using compound measures. There are also compound measures worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. ## What are compound measures? Compound measures are measures which are found from two other measures. The most common compound measures studied in GCSE maths are speed, density, and pressure. To calculate the value of a compound measure, we need to know the value and the units of the other two measures ### ● Speed Speed is a compound measure made from dividing a unit of distance by a unit of time. Speed is therefore a measure of how much an object has travelled over a certain time period. Common units for speed include metres per second (m/s) and kilometres per hour (km/h). Miles per hour (mph) is associated with the speed of a vehicle. At GCSE we tend to use metric units rather than imperial units. Step-by-step guide: Speed, distance, time Speed formula To calculate the speed of an object, we use the speed formula, \text{Speed}=\frac{\text{distance}}{\text{time}} . This can be written as a formula triangle. Step-by-step guide: Formula for speed ### ● Density Density is a compound measure made from dividing a unit of mass by a unit of volume. Density is a measure of how much matter there is in a certain volume. Common units for density include, grams per cubic centimetre (g/cm^{3}) and kilograms per cubic metre (kg/m^{3}). Step-by-step guide: Mass, density, volume Density formula To calculate the density of an object, we use the density formula, \text{Density}=\frac{\text{mass}}{\text{volume}} . This can be written as a formula triangle. Step-by-step guide: Formula for density ### ● Pressure Pressure is a compound measure made from dividing a unit of force by a unit of area. Pressure is therefore defined as the force per unit area. Different units of pressure include Pascals (Pa) where one Pascal is equivalent to 1 \ N/m^{2}. Step-by-step guide: Pressure, force, area Pressure formula To calculate the pressure an object makes with a surface, we use the pressure formula, \text{Pressure}=\frac{\text{force}}{\text{area}} . This can be written as a formula triangle. Step-by-step guide: Pressure formula There are other compound measures such as rates of pay (for example, £ per hour). We can also use compound measures when calculating the best buy (for example, grams per pence). ### ● Compound units Compound units are the units of measurement used with compound measures. For example, the compound units for speed include metres per second (m/s), kilometres per hours (km/h) and miles per hour (mph). The compound units for density include grams per cubic centimetre (g/cm^{3}) and kilogram per cubic metre (kg/m^{3}). ## How to calculate a compound measure In order to calculate a compound measure: 1. Write down the compound measure formula with the correct subject. 2. Substitute known values into the formula and carry out the calculation. 3. Write down the solution, including the units. ## Compound measures examples ### Example 1: speed A car travels 100 kilometres in 2 hours. Calculate the average speed of the car. 1. Write down the compound measure formula with the correct subject. To calculate the speed, we divide the distance by the time. S=\frac{D}{T} 2Substitute known values into the formula and carry out the calculation. Substituting the values D=100 and T=2, we have S=\frac{D}{T}=\frac{100}{2}=50. 3Write down the solution, including the units. The average speed of the car is 50 \ km/h. ### Example 2: speed A train travels at a speed of 120 \ km/h for 1\frac{1}{2} hours. Calculate the distance the train has travelled in this time. Write down the compound measure formula with the correct subject. Substitute known values into the formula and carry out the calculation. Write down the solution, including the units. ### Example 3: density A platinum bar has a volume of 40 \ cm^{3} and mass of 840 \ g. Calculate the density of the platinum bar. Write down the compound measure formula with the correct subject. Substitute known values into the formula and carry out the calculation. Write down the solution, including the units. ### Example 4: density A steel block has a mass of 1.17 \ kg. The density of steel is 7.8 \ g/cm^{3}. Calculate the volume of the steel block. Write down the compound measure formula with the correct subject. Substitute known values into the formula and carry out the calculation. Write down the solution, including the units. ### Example 5: pressure A force of 820 \ N is exerted on an area of 40 \ m^{2}. Calculate the pressure acting on the area. Write down the compound measure formula with the correct subject. Substitute known values into the formula and carry out the calculation. Write down the solution, including the units. ### Example 6: pressure A force of 860 \ N exerts a pressure of 47 \ N/m^{2}. Calculate the area the force is being applied to. Write your answer correct to 3 significant figures. Write down the compound measure formula with the correct subject. Substitute known values into the formula and carry out the calculation. Write down the solution, including the units. ### Common misconceptions Check that you give the answer in the right form. You may have an answer which needs to be rounded to a specific number of significant figures or decimal places. • Average speed Sometimes a journey may be in more than one part. You may be asked to find the average speed. To do this we would divide the total distance travelled by the total time taken. \text{Average speed}=\frac{\text{total distance}}{\text{total time}} ### Practice compound measures questions 1. A bus travels for 120 \ km in 3 hours. Calculate the average speed of the bus. 360 \ km/h 0.025 \ km/h 40 \ km/h 30 \ km/h \text{Speed}=\frac{\text{distance}}{\text{time}}=\frac{120}{3}=40 \ km/h 2. A person cycles at a speed of 10 \ km/h for 25 \ km. Calculate the time taken for the cyclist to complete the journey. 250 hours 3.5 hours 2.5 hours 35 hours \text{Time}=\frac{\text{distance}}{\text{speed}}=\frac{25}{10}=2.5 hours 3. Calculate the density of an object with a mass of 350 \ g and a volume of 25 \ cm^{3}. 14\ g/cm^3 325\ g/cm^3 375\ g/cm^3 8750\ g/cm^3 \text{Density}=\frac{\text{mass}}{\text{volume}}=\frac{350}{25}=14 \ g/cm^3 4. The density of a substance is 9 \ g/cm^{3} and its volume is 280 \ cm^{3}. Calculate the mass of the object in kg. 2.52 \ kg 31.1 \ kg 32.1 \ kg 289 \ kg \text{Mass}=\text{density}\times \text{volume}=9\times 280=2520\ g Converting grams to kilograms, we have 2520\ g= 2.52\ kg. 5. A force of 70 \ N acts on an area of 14 \ m^{2}. Calculate the pressure. 0.2 \ N/m^2 5 \ N/m^2 56 \ N/m^2 84 \ N/m^2 \text{Pressure}=\frac{\text{force}}{\text{area}}=\frac{70}{14}=5 \ N/m^2 6. A pressure of 53 \ N/m^{2} is exerted on an area of 4 \ m^{2}. Calculate the force the object applies to the area. 57 \ N 13.25 \ N 848 \ N 212 \ N \text{Force}=\text{pressure}\times \text{area}=53\times 4=212 \ N ### Compound measures GCSE questions \text{Density}=\frac{\text{mass}}{\text{volume}} \hspace{3cm} \text{Pressure}=\frac{\text{force}}{\text{area}} 1. Work out the pressure when the force is 72 \ N and the area is 8 \ m^{2}. (1 mark) B – 9 \ N/m^2 (1) 2. (a) Calculate the volume of the cuboid below. (b) The cuboid is made from copper. The density of copper is 8.6 \ g/cm^{3}. Calculate the mass of the cuboid. (4 marks) (a) 5\times 4\times 2 (1) 40 \ cm^3 (1) (b) 8.6\times 40 (1) 344 \ g (1) 3. (a) A bee flies from its hive to a flower. It flies at a constant speed of 9 metres per second for 12 seconds. Calculate the distance from the hive to the flower. (b) The bee flies back to the hive. It takes 15 seconds to return. Calculate the speed of the bees return flight. (4 marks) (a) 9 \times 12 (1) 108 \ m (1) (b) 108\div 15 (1) 7.2 \ m/s (1) 4. Population density is calculated by using this formula, \text{Population density}=\frac{\text{population}}{\text{area}} . The population of Belgium is 11 \ 482 \ 178 people and has an area of 30 \ 528 \ km^{2}. Calculate the population density of Belgium. (3 marks) 11 \ 482 \ 178 \div 30 \ 528=376.11956236897… (1) 374 \ (3sf) (1) people/km^2 (1) ## Learning checklist You have now learned how to: • Use compound units such as speed, unit pricing and density to solve problems ## Still stuck? Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths tuition programme.
crawl-data/CC-MAIN-2024-38/segments/1725700651498.46/warc/CC-MAIN-20240912210501-20240913000501-00441.warc.gz
null
# 4.7 Gravitational potential  (Page 2/3) Page 2 / 3 $\text{Δ}U=-\underset{{r}_{1}}{\overset{{r}_{2}}{\int }}{F}_{G}dr$ Clearly, change in gravitational potential is equal to the negative of work by gravitational force as a particle of unit mass is brought from one point to another in a gravitational field. Mathematically, : $⇒\text{Δ}V=\frac{\text{Δ}U}{m}=-\underset{{r}_{1}}{\overset{{r}_{2}}{\int }}Edr$ We can easily determine change in potential as a particle is moved from one point to another in a gravitational field. In order to find the change in potential difference in a gravitational field due to a point mass, we consider a point mass “M”, situated at the origin of reference. Considering motion in the reference direction of “r”, the change in potential between two points at a distance “r” and “r+dr” is : $⇒\text{Δ}V=-\underset{{r}_{1}}{\overset{{r}_{2}}{\int }}\frac{GMdr}{{r}^{2}}$ $⇒\text{Δ}V=-GM\left[-\frac{1}{r}\underset{{r}_{1}}{\overset{{r}_{2}}{\right]}}$ $⇒\text{Δ}V=GM\left[\frac{1}{{r}_{1}}-\frac{1}{{r}_{2}}\right]$ In the expression, the ratio “ $\frac{1}{{r}_{1}}$ ” is smaller than “ $\frac{1}{{r}_{2}}$ ”. Hence, change in gravitational potential is positive as we move from a point closer to the mass responsible for gravitational field to a point away from it. ## Example Problem 1: A particle of mass 2 kg is brought from one point to another. The increase in kinetic energy of the mass is 4 J, whereas work done by the external force is -10 J. Find potential difference between two points. Solution : So far we have considered work by external force as equal to change in potential energy. However, if we recall, then this interpretation of work is restricted to the condition that work is done slowly in such a manner that no kinetic energy is imparted to the particle. Here, this is not the case. In general, we know from the conservation of mechanical energy that work by external force is equal to change in mechanical energy: ${W}_{F}=\Delta {E}_{mech}=\Delta K+\Delta U$ Putting values, $⇒-10=4+\Delta U$ $⇒\Delta U=-10-4=-14\phantom{\rule{1em}{0ex}}J$ As the change in potential energy is negative, it means that final potential energy is less than initial potential energy. It means that final potential energy is more negative than the initial. Potential change is equal to potential energy change per unit mass. The change in potential energy per unit mass i.e. change in potential is : $⇒\Delta V=\frac{\Delta U}{m}=-\frac{14}{2}=-7\phantom{\rule{1em}{0ex}}J$ ## Absolute gravitational potential in a field due to point mass The expression for change in gravitational potential is used to find the expression for the potential at a point by putting suitable values. When, ${V}_{1}=0$ ${V}_{2}=V\left(\mathrm{say}\right)$ ${r}_{1}=\infty$ ${r}_{2}=r\left(\mathrm{say}\right)$ $⇒v=-\frac{GM}{r}$ This is the expression for determining potential at a point in the gravitational field of a particle of mass “M”. We see here that gravitational potential is a negative quantity. As we move away from the particle, 1/r becomes a smaller fraction. Therefore, gravitational potential increases being a smaller negative quantity. The magnitude of potential, however, becomes smaller. The maximum value of potential is zero for r = ∞. This relation has an important deduction. We know that particle of unit mass will move towards the particle responsible for the gravitational field, if no other force exists. This fact underlies the natural tendency of a particle to move from a higher gravitational potential (less negative) to lower gravitational potential (more negative). This deduction, though interpreted in the present context, is not specific to gravitational field, but is a general characteristic of all force fields. This aspect is more emphasized in the electromagnetic field. A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained 58asagravitasnal firce Amar water boil at 100 and why what is upper limit of speed what temperature is 0 k Riya 0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale Mustapha How MKS system is the subset of SI system? which colour has the shortest wavelength in the white light spectrum if x=a-b, a=5.8cm b=3.22 cm find percentage error in x x=5.8-3.22 x=2.58 what is the definition of resolution of forces what is energy? Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form Abdul motion Mustapha highlights of atomic physics Benjamin can anyone tell who founded equations of motion !? n=a+b/T² find the linear express أوك عباس Quiklyyy Moment of inertia of a bar in terms of perpendicular axis theorem How should i know when to add/subtract the velocities and when to use the Pythagoras theorem? Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
crawl-data/CC-MAIN-2019-09/segments/1550247480622.9/warc/CC-MAIN-20190216145907-20190216171907-00495.warc.gz
null
# Least squares and pseudo-inverses To appreciate the connections between solutions of the system $$Ax=b$$ and least squares, we begin with two illustrative examples. ###### Overdetermined systems: $$A$$ is $$m \times n$$ with $$m > n$$. In this case there are more equations than unknowns, $$A^{\top}A$$ is $$n\times n$$ and $$AA^{\top}$$ is $$m\times m$$. The connection with the pseudo-inverse is that $x = (A^{\top}A)^{-1}A^{\top}b = A^+b$ is the particular $$x$$ that minimizes $$\|Ax-b\|$$. Example: Solve the system $$(2\ 3\ 4\ 6)^\top(x_1) = (4\ 6\ 8\ 10)^\top.$$ Using $$A^{\top}A = (2\ 3\ 4\ 6)(2\ 3\ 4\ 6)^\top=65$$, $x = (A^{\top}A)^{-1}A^{\top}b = \frac{1}{65}\begin{pmatrix}2 &3 &4 &6\end{pmatrix}\begin{pmatrix}4\\6\\8\\10\end{pmatrix} = \frac{118}{65}.$ Considering the least squares problem, $$\|Ax – b\|^2 = (2x-4)^2+(3x-6)^2+(4x-8)^2+(6x-10)^2$$ which has a minimum at $$2(2x-4)2+2(3x-6)3+2(4x-8)4+2(6x-10)6 = 0$$ so that $x = \frac{8+18+32+60}{4+9+16+36} = \frac{118}{65}.$ ###### Underdetermined systems: $$A$$ is $$m \times n$$ with $$m < n$$. In this case there are more unknowns than equations, and the connection with the pseudo-inverse is that $x = A^{\top}(AA^{\top})^{-1}b = A^+b$ is the particular $$x$$ that minimizes $$\|x\|$$ amongst all of the possible solutions. Example: Solve the system $$(1\ -1\ 0)(x_1\ x_2\ x_3)^\top = (2).$$ In this case we find $$AA^{\top} = (1\ -1\ 0)(1\ -1\ 0)^\top = 2$$ and $x = A^{\top}(AA^{\top})^{-1}b = \begin{pmatrix}1\\-1\\0\end{pmatrix}\frac{1}{2}2 = \begin{pmatrix}1\\-1\\0\end{pmatrix}.$ To see the connection with the least squares problem, the system is row reduced (it is already row reduced) and we can choose $$x_1$$ as the pivot with $$x_2, x_3$$ as free parameters. Letting $$x_2 = s$$ and $$x_3 = t$$ we have $$x_1 = 2+s$$ so that the general solution is $x = \begin{pmatrix}2+s\\ s\\ t\end{pmatrix} = \begin{pmatrix}2\\0\\0\end{pmatrix} + s\begin{pmatrix}1\\1\\0\end{pmatrix} + t\begin{pmatrix}0\\0\\1\end{pmatrix}$ for any $$s,t\in\mathbb{R}$$. Considering $$\|x\|$$, we have $$\|x\|^2 = (2+s)^2 + s^2 + t^2$$ which has a minimum at $$2(2+s)+2s = 0$$ and $$2t = 0$$ or $$t = 0, s = -1$$ giving $$x = (1\ -1\ 0)^\top$$ as before. ###### Symmetric matrices: Decomposing the structure of the matrix $$A$$ can help understand the resulting solutions and in the case of a symmetric matrix, the eigenvectors form an orthogonal set which allows one to expand $$A = UDU^\top$$ where $$U$$ is the orthogonal matrix $$(U^{-1}=U^\top)$$ with the eigenvectors as columns and $$D$$ a diagonal matrix with the corresponding eigenvalues as the diagonal elements. Also, the eigenvalues could be anything, but if we specify that we want a non-negative definite matrix then the eigenvalues must be greater than or equal to zero. Example: Write $$A_1 = \begin{pmatrix}2 &1\\ 1 &2\end{pmatrix}$$ in the form $$A_1 = UDU^\top$$. A quick calculation gives $$\lambda_1 = 3$$ with corresponding eigenvector $$\mathbf{\xi}^{(1)} = \frac{1}{\sqrt{2}}(1\ 1)^\top$$ and a second pair $$\lambda_2 = 1, \mathbf{\xi}^{(2)} = \frac{1}{\sqrt{2}}(1\ -1)^\top.$$ This gives the decompositon $A_1 = \frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ 1 &-1\end{pmatrix}\begin{pmatrix}3 &0\\ 0 &1\end{pmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ 1 &-1\end{pmatrix}^\top.$ Using this decomposition the inverse of a matrix is easily computed by replacing the diagonal elements of $$D$$ with their reciprocals so that for example $A_1^{-1} = \frac{1}{3}\begin{pmatrix}2& -1\\ -1& 2\end{pmatrix} = \frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ 1 &-1\end{pmatrix}\begin{pmatrix}{\small\frac{1}{3}} &0\\ 0 &1\end{pmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ 1 &-1\end{pmatrix}^\top.$ What happens if one of the eigenvalues is zero? This will not effect the decomposition of $$A$$, in fact if we decompose $$A_2 = \begin{pmatrix}1&-1\\-1&1\end{pmatrix}$$ with eigenvalues $$\lambda_1 = 2, \lambda_2 = 0$$ and corresponding eigenvectors $$\xi^{(1)} = \frac{1}{\sqrt{2}}(1\ -1)^\top$$, $$\xi^{(2)} = \frac{1}{\sqrt{2}}(1\ 1)^\top$$ then $A_2 = \frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ -1 &1\end{pmatrix}\begin{pmatrix}2 &0\\ 0 &0\end{pmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ -1 &1\end{pmatrix}^\top.$ Notice that this matrix is not invertible since one of the eigenvalues is zero. But what if we took the reciprocal of all the nonzero diagonal elements to form $A_3 = \frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ -1 &1\end{pmatrix}\begin{pmatrix}{\small\frac{1}{2}} &0\\ 0 &0\end{pmatrix}\frac{1}{\sqrt{2}}\begin{pmatrix}1 &1\\ -1 &1\end{pmatrix}^\top = \frac{1}{4}\begin{pmatrix}1& -1\\ -1 &1\end{pmatrix}.$ Sadly, $$A_3$$ is not the inverse of $$A_2$$. This would be very surprising since $$A_2$$ is not invertible. So what then is $$A_3$$? Well, $$A_2$$ and $$A_3$$ are pseudo-inverses. This can be generalized later to non-square matrices by constructing the SVD of a matrix. As a refresher please watch the following video: Here is how the pseudo-inverse is connected to the solution of a least-squares problem. If the linear system $$Ax = b$$ has any solutions, then they will have the form$x = A^+ b + \left(I – A^+ A\right)\xi$ for some arbitrary vector $$\xi$$. Multiplying by $$A$$ on the left gives that condition that ($$A = A A^+ A$$ is a property of $$A^+$$)$Ax = A A^+ b + \left(A – A A^+ A\right)\xi = A A^+ b = b.$ So for a any solution to exist we need the admissibility condition $$AA^+ b = b$$. For linear systems $$A x = b$$ with non-unique solutions as in the underdetermined case, the pseudo-inverse may be used to construct the solution of minimum Euclidean norm $$\|x\|$$ among all solutions. If $$A x = b$$ is admissible ($$AA^+ b = b$$), the vector $$y = A^+b$$ is a solution, and satisfies $$\|y\| \le \|x\|$$ for all solutions. One final example should tie this all together. Example: Consider finding the solution to $$A_2x = b$$ that minimizes $$\|x\|$$. Row reducing $$A_2x = b, b = (b_1\ b_2)^\top$$ reveals the $$b_2=-b_1$$ to ensure a solution, and $\begin{pmatrix}x_1\\x_2\end{pmatrix} = \begin{pmatrix}b_1\\0\end{pmatrix} + s\begin{pmatrix}1\\1\end{pmatrix}$ for any $$s\in\mathbb{R}$$. Continuing, $$\|x\|^2 = (b_1+s)^2+s^2$$ which is minimized when $$2(b_1+s)+2s=0$$ or when $$s = -\frac{b_1}{2}$$ so that the solution is $\begin{pmatrix}x_1\\x_2\end{pmatrix} = \begin{pmatrix}b_1\\0\end{pmatrix} – \frac{b_1}{2}\begin{pmatrix}1\\1\end{pmatrix}=\frac{b_1}{2}\begin{pmatrix}1\\-1\end{pmatrix}.$ Using the pseudo-inverse of $$A_2$$, $$A_3 = A_2^+$$ gives the admissibility condition $$A_2A_2^+A_2b = b$$ which simplifies to $$b_2 = -b_1$$ and the solution $\begin{pmatrix}x_1\\x_2\end{pmatrix} = A_2^+b = \frac{1}{4}\begin{pmatrix}1&-1\\-1&1\end{pmatrix}=\frac{1}{4}\begin{pmatrix}b_1-b_2\\-b_1+b_2\end{pmatrix}=\frac{b_1}{2}\begin{pmatrix}1\\-1\end{pmatrix}.$ ### Summary At the beginning of this post, the Moore-Penrose pseudo-inverse generalized the idea of an inverse to non-square matrices and another notion of pseudo-inverse arose for symmetric matrices that have at least one zero eigenvalue. This second notion can be generalized (using the SVD) to non-square matrices and matrices that are not symmetric where the eigenvectors are not guaranteed to form an orthonormal set. In all cases, the pseudo-inverse is implicitly tied to the notion of finding solutions with minimal norm.
crawl-data/CC-MAIN-2024-10/segments/1707947474676.26/warc/CC-MAIN-20240227121318-20240227151318-00769.warc.gz
null
A Siberian, or Amur, tiger. These cats once teetered on the brink of extinction, and still face grave threats. Credit: David Lawson / WWF-UK. Chinese and Russian provincial officials have agreed to set up a protected area straddling their countries' common border to safeguard the highly endangered Amur tiger. It is estimated that only about 500 Amur tigers, also called Siberian tigers, survive in the wild. Officials representing China's Jilin province and Russia's Primorsky province, areas just north of the Korean peninsula, signed the agreement, which was facilitated by the World Wildlife Fund, a global conservation organization. "A new transboundary protected area would provide a wider and healthier habitat for Amur tigers and other endangered species, such as the Far East leopard, musk deer and goral," said Yu Changchun of the Jilin Forestry Department. A goral is a goat-like, mountain-dwelling animal. As part of the agreement, officials of the two provinces said they will increase information-sharing on Amur tiger and Far East leopard protection and will work to adopt identical monitoring systems for tigers and their prey. The two countries also plan to conduct joint ecological surveys and to launch an anti-poaching campaign along the border. Destruction and fragmentation of habitat, poaching and a lack of prey have reduced the number of wild Amur tigers. One of six remaining subspecies of tigers , the Amur tiger is primarily found in eastern Russia, with a small number in northeastern China. Among that population, 20 tigers have been periodically spotted within the borders of China's Jilin and Heilongjiang provinces. "This agreement is a great boost for Amur tiger habitats in Russia and China," said WWF-Russia official Sergey Aramilev. "Since both countries play a crucial role in terms of global tiger recovery, a future transboundary network would represent a big step in WWF's global tiger conservation effort." Aramilev is biodiversity coordinator for the Amur Branch of WWF-Russia. The announcement of the agreement coincides with China's Amur Tiger Cultural Festival, a two-day event designed to focus attention on the plight of the endangered animal. This is also the Year of the Tiger in the Chinese calendar, and conservation agencies have pushed to highlight tiger protection efforts around the world since January. While over 95 percent of Amur tigers are now found in Russia, the situation differed in the 1950s. An estimated 50 tigers were then found in the Russian Far East, while about 200 were in China. Anti-poaching efforts and other conservation policies allowed Russia's tiger population to rebound and remain stable, but the WWF says the big cats still face destruction at the hands of hunters who sell tiger parts for use in traditional Chinese medicine. "There's a lot of work to be done to implement this agreement, such as making sure it receives proper government funding, but this is a major step forward nonetheless," Aramilev said.
<urn:uuid:c7ea418d-e3ad-4845-aa39-cee46b5479c6>
{ "date": "2015-07-05T02:42:20", "dump": "CC-MAIN-2015-27", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375097199.58/warc/CC-MAIN-20150627031817-00149-ip-10-179-60-89.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9419882893562317, "score": 3.703125, "token_count": 616, "url": "http://www.livescience.com/29651-rare-siberian-tigers-to-get-haven-on-chinese-russian-border.html" }
What is the 'Cost Of Labor' The cost of labor is the sum of all wages paid to employees, as well as the cost of employee benefits and payroll taxes paid by an employer. The cost of labor is broken into direct and indirect (overhead) costs. Direct costs include wages for the employees that produce a product, including workers on an assembly line, while indirect costs are associated with support labor, such as employees who maintain factory equipment. BREAKING DOWN 'Cost Of Labor' When a manufacturer sets the sales price of a product, the firm takes into account the costs of labor, material and overhead. The sales price must include the total costs incurred by the firm; if any costs are left out of the sales price calculation, the amount of profit is lower than expected. If demand for a product declines, or if competition forces the business to cut prices, the company must reduce the cost of labor to remain profitable. A business can reduce the number of employees, cut back on production, require higher levels of productivity or reduce other factors in the cost of production. The Differences Between Direct and Indirect Costs Assume that XYZ Furniture is planning the sales price for dining room chairs. The direct labor costs are those expenses that can be directly traced to production. XYZ, for example, pays workers to run machinery that cuts wood into specific pieces for chair assembly, and those expenses are direct costs. On the other hand, XYZ has several employees who provide security for the factory and warehouse; those labor costs are indirect, because the cost cannot be traced to a specific level of production. Examples of Fixed and Variable Costs Labor costs are also classified as fixed costs or variable expenses. For example, the cost of labor to run the machinery is a variable cost, which varies with the firm's level of production. XYZ also has as a contract with an outside vendor to perform repair and maintenance on the equipment, and that is a fixed cost. Factoring in Undercosting and Overcosting Since indirect labor costs can be difficult to allocate to the correct product or service, XYZ Furniture may underallocate labor costs to one product and overallocate labor costs to another. This situation is referred to as undercosting and overcosting, and it can lead to incorrect product pricing. Assume, for example, that XYZ manufactures both dining room chairs and wooden bed frames, and that both products incur labor costs to run machinery, which total $20,000 per month. If XYZ allocates too much of the $20,000 labor costs to wooden bed frames, too little is allocated to dining room chairs. The labor costs for both products are incorrect, and the sale price cannot be calculated accurately.
<urn:uuid:bee82914-5dbd-4dcb-b8e6-d7accf4ab2db>
{ "date": "2016-09-26T05:29:39", "dump": "CC-MAIN-2016-40", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660706.30/warc/CC-MAIN-20160924173740-00147-ip-10-143-35-109.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9645330905914307, "score": 3.625, "token_count": 558, "url": "http://www.investopedia.com/terms/c/cost-of-labor.asp" }
Demonstration of the Affect of Evaporation on the Salinity of Ocean Water Category: Earth Science—Oceanography Project Idea by: Donald Van Velzen Salinity is the salt concentration in a salt and water solution. The average salinity of seawater is 35 parts per thousand. This is written as 35 ppt, and it means that 35 parts of salt are in every 1,000 parts of seawater. While most samples of seawater have a salinity of 35 ppt, the salinity does vary from place to place. The salinity of seawater is usually between 32 ppt and 38 ppt. Density is the ratio of mass to volume of a material. This property of matter allows you to compare materials of the same size and determine which is heavier. Specific gravity is the ratio of the density of a material to the density of water. Specific gravity has no units. It compares the heaviness of a material to the same volume of water. No matter what units the densities are expressed in, specific gravity is the same. For example, mercury is 13.6 times as heavy as an equal volume of water. Thus, the specific gravity of mercury is 13.6. If the temperature is such that the density of water is 1 g/mL, the density of mercury would be 13.6 × 1 g/mL, or 13.6 g/mL. Specific gravity can be used to determine the salinity of a liquid. Salt water has a greater density than fresh water, so it also has a higher specific gravity. The higher the salinity of an aqueous salt solution, the greater its specific gravity. A hydrometer is an instrument used to measure the specific gravity of a liquid. A hydrometer floats in a liquid. The higher it floats in the liquid, the greater the specific gravity of the liquid. A project question might be, "How does evaporation affect the salinity of ocean water?" Clues for Your Investigation Place a liquid made of a measured amount of salt and distilled water in an open container. Design a way to measure evaporation rate such as placing a strip of tape down the side of the container and marking the surface level of the water. At predetermined intervals, use a hydrometer to measure the specific gravity of the liquid. The hydrometer can be purchased or homemade. You can make your own hydrometer using a straw, BBs, and clay. In the figure, the scale printed on the straw shows the specific gravity higher and lower than the water, which is 1.0. The weight of the straw, the BBs, and the clay should make the hydrometer stand upright in fresh water, with 1.0 at water level. Independent Variable: Evaporation rate Dependent Variable: Salinity of water (determined by specific gravity) Controlled Variables: Type of salt, distilled water, containers, amount of liquid, method of measuring, hydrometer, environmental conditions Control: Specific gravity of distilled water Other Questions to Explore - Does the type of solute affect the solution's specific gravity? - What effect does temperature have on specific gravity? Warning is hereby given that not all Project Ideas are appropriate for all individuals or in all circumstances. Implementation of any Science Project Idea should be undertaken only in appropriate settings and with appropriate parental or other supervision. Reading and following the safety precautions of all materials used in a project is the sole responsibility of each individual. For further information, consult your state’s handbook of Science Safety.
<urn:uuid:1f3b3864-aa16-4800-8960-30c9f5917cac>
{ "date": "2014-04-16T23:58:00", "dump": "CC-MAIN-2014-15", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00027-ip-10-147-4-33.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9107410907745361, "score": 3.65625, "token_count": 735, "url": "http://www.education.com/science-fair/article/evaporation-affect-salinity-ocean-water/" }
# Math I am a little confused with this: How do I change 8 1/3% into a fraction? Can someone explain or show me so I can understand? Thanks 1. 0 2. 0 1. 8 1/3 % = 25/3 % = (25/3)/100 = 25/300 = 1/12 check: 1/12 = .083333 = 8.333...% =8 1/3 % posted by Reiny ## Similar Questions 1. ### Basic Math A student claims that 2/3 = 6/7 because if you add 4 to both the top and the bottom of a fraction, the fraction does not change. How do you respond? I am a bit confused. Don't you need to have a common denominator? 2. ### math How do you change a decimal to a fraction?? you change a fration to a decimal by diving the fraction right? HOW DO YOU CHANGE A FRACTION TO A PERCENTAGE? In order of your questions, the answers are: (1) yes, (2) yes (divide 3. ### math fractions and decimals How do you can you change a decimal to a fraction when the fraction looks like this 0.43 3/4 or .16 2/3 .How can I change this to a fraction?I tried dividing it by 100 but it doesn't give me the right answer. 4. ### math Will someone please show me how to do this problem. I have to write this ratios in simplest form. The ratio of 5 3/5 to 2 1/10. Change each of your mixed fractions to an improper fraction, then divide the first by the second. 5. ### Physics If I have a diagram of Kepler's laws of planetary motion and it shows change in t1 larger than change in t2 and A1 larger than A2 and asks the question: which of the following is correct? 1.A3 = A3 2.change in t3 > change t3 3.if If I have a diagram of Kepler's laws of planetary motion and it shows change in t1 larger than change in t2 and A1 larger than A2 and asks the question: which of the following is correct? 1.A3 = A3 2.change in t3 > change t3 3.if 7. ### math 1. change to improper fraction: 9 5/9 2. change to improper fraction: 6 23/39 3. change the improper fraction to a whole number:115/20 4. multiply 4 3/4 x 1 1/7 5,subtract- 20 11/15- 17 1/3 6 2(-6)(-8)(0)(-5): multiply 7. solve 8. ### math How can I change 33(1/3) percent into fraction? I've done this so far: Change 1/3 into decimal, therefore =0.33 =33.33 TO change into fraction I have to divide by 100 0.33/100? Answer is 1/3 But i don't know how..?
crawl-data/CC-MAIN-2018-43/segments/1539583512332.36/warc/CC-MAIN-20181019062113-20181019083613-00209.warc.gz
null
Rhombic dodecahedron made by a cube and six pyramids We already know that the Rhombic Dodecahedron is related with honeycombs: We want to close a hexagonal prism as bees do, using three rhombi. Then, which is the shape of these three rhombi that closes the prism with the minimum surface area?. And that you can build a Rhombic Dodecahedron addign six pyramids to a cube: Adding six pyramids to a cube you can build new polyhedra with twenty four triangular faces. For specific pyramids you get a Rhombic Dodecahedron that has twelve rhombic faces. Cundy and Rollet wrote: "The rhombic dodecahedron and the cube. If a cube is divided by the six diametral planes which pass through pairs of opposite edges, it breaks up into six square pyramids. If these pyramids are assembled outwards on the faces of another cube, the result is a rhombic dodecahedron." (Cundy and Rollet, pag. 122) The cube is dissected into six congruent square-based pyramids. Four edges of one pyramid are half the space diagonals of the cube. This construction has several interesting consequences. First, you can see in the interactive application that this six pyramids fill a cube. The volume of one of this pyramids is one-sixth of the volume of the cube. Then you do not need the formula for the volume of a pyramid to calculate the volume of this particular pyramid. By the way, the volume of a pyramid is one third of the base area times the perpendicular height. We can check that these pyramids verify the formula: their base area is 1 and the height is 1/2. This is a very simple and important example of pyramid because after this example we can deduce the volume of pyramids with rectangular bases (expanding the cube in three directions). The second consequence of this construction is that we can calculate the volume of a Rhombic Dodecahedron. Remember that if inside the Rhombic Dodecahedron there is a unit cube, then the length of the edge of this Rhombic Dodecahedron is: Then the volume of this rhombic dodecahedron is twice the volume of the inside cube: To calculate the volume if the edge length is 1: Then, The general formula for the volume of a rhombic dodecahedron of edge length a is: You can play with the interactive application and see beautiful symmetries like these: The third consequence is that the Rhombic Dodecahedron fills the space. The Rhombic Dodecahedron fills the space without gaps. We already know that we could build a beautiful box inspired in honeycombs. Humankind has always been fascinated by how bees build their honeycombs. Kepler related honeycombs with a polyhedron called Rhombic Dodecahedron. Now we can build a rhombic dodecahedron that is also a box. You can download the template and build a model with cardboard. The designer of this box was John Edminster and you can find references in Beach Packaging Design. The rhombic dodecahedron is related with the cube. You can build a cube to put inside the rhombic dodecahedron. Inside the cube you can put a cuboctahedron (in this case, a omega star, a beautiful origami construction. Six pieces of paper are needed). The rhombic dodecahedron is also related with the octahedron (you know that the cube and the octahedron are dual polyhedra). And you can build an octahedron and put it inside the dodecahedron. REFERENCES Johannes Kepler - The Six Cornered Snowflake: a New Year's gif - Paul Dry Books, Philadelphia, Pennsylvania, 2010. English translation of Kepler's book 'De Nive Sexangula'. With notes by Owen Gingerich and Guillermo Bleichmar and illustrations by the spanish mathematician Capi Corrales Rodrigáñez. D'Arcy Thompson - On Growth And Form - Cambridge University Press, 1942. Hugo Steinhaus - Mathematical Snapshots - Oxford University Press - Third Edition. Magnus Wenninger - 'Polyhedron Models', Cambridge University Press. Peter R. Cromwell - 'Polyhedra', Cambridge University Press, 1999. H.Martin Cundy and A.P. Rollet, 'Mathematical Models', Oxford University Press, Second Edition, 1961. W.W. Rouse Ball and H.S.M. Coxeter - 'Matematical Recreations & Essays', The MacMillan Company, 1947. Humankind has always been fascinated by how bees build their honeycombs. Kepler related honeycombs with a polyhedron called Rhombic Dodecahedron. We want to close a hexagonal prism as bees do, using three rhombi. Then, which is the shape of these three rhombi that closes the prism with the minimum surface area?. A chain of six pyramids can be turned inwards to form a cube or turned outwards, placed over another cube to form the rhombic dodecahedron. The obtuse angle of a rhombic face of a Rhombic Dodecahedron is known as Maraldi angle. We need only basic trigonometry to calculate it. There are two essential different ways to pack spheres in an optimal disposition. One is related with the Rhombic Dodecaedron and the other to a polyhedron called Trapezo-rombic dodecahedron.. Using a basic knowledge about the Rhombic Dodecahedron, it is easy to calculate the density of the optimal packing of spheres. Tetraxis is a wonderful puzzle designed by Jane and John Kostick. We study some properties of this puzzle and its relations with the rhombic dodecahedron. We can build this puzzle using cardboard and magnets or using a 3D printer. There is a standarization of the size of the paper that is called DIN A. Successive paper sizes in the series A1, A2, A3, A4, and so forth, are defined by halving the preceding paper size along the larger dimension. Material for a session about polyhedra (Zaragoza, 9th May 2014). Simple techniques to build polyhedra like the tetrahedron, octahedron, the cuboctahedron and the rhombic dodecahedron. We can build a box that is a rhombic dodecahedron. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the truncated octahedron. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the cuboctahedron. A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of a cube. A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of an octahedron. The volume of an octahedron is four times the volume of a tetrahedron. It is easy to calculate and then we can get the volume of a tetrahedron. The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces. Its volume can be calculated knowing the volume of an octahedron. These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling. You can chamfer a cube and then you get a polyhedron similar (but not equal) to a truncated octahedron. You can get also a rhombic dodecahedron. A Cube can be inscribed in a Dodecahedron. A Dodecahedron can be seen as a cube with six 'roofs'. You can fold a dodecahedron into a cube. If you fold the six roofs of a regular dodecahedron into a cube there is an empty space. This space can be filled with an irregular dodecahedron composed of identical irregular pentagons (a kind of pyritohedron).
crawl-data/CC-MAIN-2024-26/segments/1718198862070.5/warc/CC-MAIN-20240621093735-20240621123735-00790.warc.gz
null
For more details on Professor Wadhams' calculations, see the earlier post Albedo change in the Arctic. Arctic sea ice area fell by 11.33629 million square km from March 28, 2012, to September 1, 2012, as shown on the image below, edited from The Cryosphere Today. That's an 82.7 percent fall in 157 days. The image below shows Arctic sea ice extent (total area of at least 15% ice concentration) for the last 7 years, compared to the average 1972-2011, as calculated by the Polar View team at the University of Bremen, Germany. There still are quite a few days to go in the melting season, so the fall could be even more dramatic. Peter Wadhams adds: “The point about summer conditions is that as long as there is SOME ice present on the sea surface, however thin the layer, then the ocean temperature below it is held to 0 degrees Celsius because the absorbed solar radiation melts the ice rather than warming the water. Also the atmospheric temperature is held to close to 0 degrees Celsius because warmer air melts the surface snow layer on top of the ice and is thereby cooled. The sea ice, even when thinned, continues to act with 100% efficiency as an air conditioning system for ocean and atmosphere alike.” “BUT”, Prof Wadhams continues, “as soon as the sea ice layer goes, this process ceases and the sea can warm up rapidly (to typically 7 degrees Celsius by the end of summer - which is not much colder than the North Sea), as can the atmosphere (which speeds up Greenland ice sheet melt when that warmed air passes over Greenland). Latent heat is an enormously powerful buffer - the amount of heat that you have to pump in to melt 1 kg of ice will subsequently heat that same amount of melted water to 80 degrees Celsius. So once the ice goes away entirely there is a big jump in temperatures in the upper ocean and atmosphere (with dire consequences for permafrost), and it is very difficult to see how one can ever go back to an ice-covered summer ocean once this has happened.” In the August 27, 2012, BBC article Arctic sea ice reaches record low, Nasa says, by Roger Harrabin, Professor Peter Wadhams said: “Implications are serious: the increased open water lowers the average albedo [reflectivity] of the planet, accelerating global warming; and we are also finding the open water causing seabed permafrost to melt, releasing large amounts of methane, a powerful greenhouse gas, to the atmosphere.” Indeed, there is a danger that loss of the sea ice will weaken the currents that currently cool the bottom of the sea, where huge amounts of methane may be present in the form of free gas or hydrates in sediments. This danger is illustrated by the image below by Reg Morrison. The image below, from a study by Polyakov et al., shows temperature differences in the vertical water column at selected stretches of water in the Arctic over the years. |[click images to enlarge]|
<urn:uuid:9a43faa8-0960-42b2-b240-1be5b8e31e0b>
{ "date": "2018-09-25T11:34:17", "dump": "CC-MAIN-2018-39", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267161501.96/warc/CC-MAIN-20180925103454-20180925123854-00136.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9450199007987976, "score": 3.90625, "token_count": 641, "url": "http://arctic-news.blogspot.com/2012/09/arctic-sea-ice-loss-is-effectively-doubling-mankinds-contribution-to-global-warming.html" }
This page is intended for college, or high school students. For younger students, a simpler explanation of the information on this page is available on the As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving speed of the object approaches the speed of sound, we on the gas. The density of the gas varies locally as the gas is compressed by the object. For compressible flows with little or small flow turning, the flow process is reversible and the The change in flow properties are then given by the (isentropic means "constant entropy"). But when an object moves faster than the speed of sound, and there is an abrupt decrease in the flow area, are generated in the flow. Shock waves are very small regions in the gas where the change by a large amount. Across a shock wave, the static increases almost instantaneously. The changes in the flow properties are irreversible and the of the entire system increases. Because a shock wave does no work, and there is no heat addition, the and the total temperature are constant. But because the flow is non-isentropic, the total pressure downstream of the shock is always less than the total pressure upstream of the shock. There is a loss of total pressure associated with a shock wave as shown on the slide. Because total pressure changes across the shock, we can not use the usual (incompressible) form of across the shock. The and speed of the flow also decrease across a shock wave. If the shock wave is perpendicular to the flow direction, it is called a normal shock. There are equations which describe the change in the flow variables. The equations are derived from the Depending on the shape of the object and the speed of the flow, the shock wave may be inclined to the flow direction. When a shock wave is inclined to the flow direction it is called an oblique shock. On this slide we have listed the equations which describe the change in flow variables for flow across an oblique shock. The equations presented here were derived by considering the conservation of mass, momentum, and energy for a compressible gas while ignoring viscous effects. The equations have been further specialized for a two-dimensional flow without heat addition. The equations only apply for those combinations of free stream Mach number and deflection angle for which an oblique shock occurs. If the deflection is too high, or the Mach too low, a normal shock occurs. For the Mach number change across an oblique shock there are two possible solutions; one supersonic and one subsonic. In nature, the supersonic ("weak shock") solution occurs most often. However, under some conditions the "strong shock", subsonic solution is possible. Oblique shocks are generated by the nose and by the leading edge of the wing and tail of a supersonic aircraft. Oblique shocks are also generated at the trailing edges of the aircraft as the flow is brought back to free stream conditions. Oblique shocks also occur downstream of a if the expanded pressure is different from free stream conditions. In high speed oblique shocks are used to compress the air going into the engine. The air pressure is increased without using any rotating machinery. On the slide, a supersonic flow at Mach number M approaches a shock wave which is inclined at angle s. The flow is deflected through the shock by an amount specified as the deflection angle - a. The deflection angle is determined by resolving the incoming flow velocity into components parallel and perpendicular to the shock wave. The component parallel to the shock is assumed to remain constant across the shock, the component perpendicular is assumed to decrease by the normal shock relations. Combining the components downstream of the shock determines the delflection angle. The right hand side of all these equations depend only on the free stream Mach number and the shock angle. The shock angle depends in a complex way on the free stream Mach number and the wedge angle. So knowing the Mach number and the wedge angle, we can determine all the conditions associated with the oblique shock. The equations describing oblique shocks were published in NACA report Here's a Java program based on the oblique shock equations. You can use this simulator to study the flow past a wedge. Due to IT security concerns, many users are currently experiencing problems running NASA Glenn educational applets. There are security settings that you can adjust that may correct Input to the program can be made using the sliders, or input boxes at the upper right. To change the value of an input variable, simply move the slider. Or click on the input box, select and replace the old value, and hit Enter to send the new value to the program. Output from the program is displayed in output boxes at the lower right. The flow variables are presented as ratios to free stream values. The graphic at the left shows the wedge (in red) and the shock wave generated by the wedge as a line. The line is colored blue for an oblique shock and magenta when the shock is a normal shock. The black lines show the streamlines of the flow past the wedge. Notice that downstream (to the right) of the shock wave, the lines are closer together than upstream. This indicates an increase in the density of the flow. There is more complete program that is avaliable at this web site. The program solves for flow past a wedge and for flow past a normal shock conditions. Another simulation, called describes the intersection and reflection of multiple shock waves. You can also download your own copy of the program to run off-line by clicking on this button:
<urn:uuid:63b6f3e1-58ec-4356-a683-7de557008315>
{ "date": "2017-07-22T10:47:54", "dump": "CC-MAIN-2017-30", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423992.48/warc/CC-MAIN-20170722102800-20170722122800-00498.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8765518069267273, "score": 4.3125, "token_count": 1287, "url": "https://www.grc.nasa.gov/WWW/k-12/airplane/oblique.html" }
# 2014 AMC 10B Problems/Problem 19 (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) ## Problem Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle? $\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$ ## Solution Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram. $[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("A",A,N); dot("O",O,NW); dot("B",B,W); dot("C",C,E); dot("H",H,S); label("2",O--(-.7,-.385),N); label("1",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]$ We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.
crawl-data/CC-MAIN-2024-30/segments/1720763518154.91/warc/CC-MAIN-20240724014956-20240724044956-00738.warc.gz
null
# Set Theory • Jul 22nd 2012, 08:42 AM iPod Set Theory Hello, I have attached the question I'm not sure how to do a parts ii), iii), & iv) I don't know how to express the sets they give. • Jul 22nd 2012, 08:48 AM Plato Re: Set Theory Quote: Originally Posted by iPod Hello, I have attached the question I'm not sure how to do a parts ii), iii), & iv) I don't know how to express the sets they give. Here is a hint: $\displaystyle A\cup B=\{25,30,35,40,23,33\}$ • Jul 22nd 2012, 08:52 AM HallsofIvy Re: Set Theory A is the set of all multiples of 5, B contains the two numbers 23 and 33, and C is the set of all prime numbers. (ii) Their union is {x: x is a multiple of 5 or x is prime or x = 33}. I did not need to include "x= 23" because 23 is prime. (iii) The complement is the set of all composite (non-prime) numbers that are NOT multiples of 5 and not equal to 33: {x: x is composite but not 33 or a multiple of 5}. (iv) should be very easy- what numbers in A or B are prime numbers? • Jul 22nd 2012, 09:49 AM iPod Re: Set Theory Ah I see, all the numbers in the sets are limited between 20 up to and including 40. So, $\displaystyle A\cup B \cup C = {25, 30, 35, 40, 23, 33, 29, 31, 37, 39}$ yeah? I think I can take it from here... • Jul 22nd 2012, 10:10 AM Plato Re: Set Theory Quote: Originally Posted by iPod Ah I see, all the numbers in the sets are limited between 20 up to and including 40. So, $\displaystyle A\cup B \cup C = \{25, 30, 35, 40, 23, 33, 29, 31, 37, {\color{red}39}\}$ yeah? 39 is not prime. • Jul 22nd 2012, 12:35 PM Soroban Re: Set Theory Hello, iPod! I have to ask: did you write out the sets? Quote: Given: .$\displaystyle \begin{Bmatrix} U &=& \{x\,|\,x\in I,\:20 < x \le 40\} \\ A &=& \{x\,|\,x\text{ is a multiple of 5\}} \\ B &=& \{23,\,33\} \\ C &=& \{x\,|\,x\text{ is prime}\} \end{Bmatrix}$ We have: .$\displaystyle \begin{array}{ccc}U &=& \{21,22,23\,\hdots\,40\} \\ A &=& \{25,30,35,40\} \\ B &=& \{23,\,33\} \\ C &=& \{23,29,31,37\} \end{array}$ Quote: List the following sets: . . $\displaystyle (i)\;B \cap C$ $\displaystyle B \cap C \;=\;\{23,33\} \,\cap\,\{23,29,31,37\} \;=\;\{23\}$ Quote: $\displaystyle (ii)\;A \cup B \cup C$ All three sets combined into one set . . . $\displaystyle A \cup B \cup C \;=\;\{23,25,29,30,31,33,35,37,40\}$ Quote: $\displaystyle (iii)\;\overline{A \cup B \cup C}$ This is the complement of the set in part (ii). $\displaystyle \overline{A \cup B \cup C)} \;=\;\{21,22,24,26,27,28,32,34,36,38,39\}$ Quote: $\displaystyle (iv)\;(A \cup B) \cap C$ $\displaystyle (A \cup B) \cap C \;=\;\bigg(\{25,30,35,40\} \,\cup \,\{23,33\}\bigg) \,\cap \,\{23,29,31,37\}$ . . . . . . . . . .$\displaystyle =\;\{23,25,30,33,35,40\} \cap \{23,29,31,37\}$ . . . . . . . . . .$\displaystyle =\;\{23\}$ Quote: . . $\displaystyle (i)\;(A \cup B) \cap C$ Code:       * - - - - - - - - - - - - - - - - - - - *       |                                      |       |          o o o      o o o          |       |      o          o          o      |       |    o    A    o  o    B    o    |       |    o          o    o          o    |       |                                      |       |  o          o      o          o  |       |  o          o o o o o          o  |       |  o        o o:::::::o o        o  |       |          o:::::::::::::::o          |       |    o    o:::::o:::::o:::::o    o    |       |    o    :::::::o:::o:::::::    o    |       |      o o:::::::::o:::::::::o o      |       |        o:o:o:o      o:o:o:o        |       |        o                  o        |       |                                      |       |          o                o          |       |          o      C      o          |       |            o          o            |       |                o o o                |       |                                      |       * - - - - - - - - - - - - - - - - - - - * Quote: $\displaystyle (ii)\;A \cup (B \cap C)$ Code:       * - - - - - - - - - - - - - - - - - - - *       |                                      |       |          .o o o.      o o o          |       |      o:::::::::::o          o      |       |    o:::::A:::::o:::o    B    o    |       |    o:::::::::::o:::::o          o    |       |  .::::::::::::::::::.                |       |  o:::::::::::o:::::::o          o  |       |  o:::::::::::o:o:o:o:o          o  |       |  o:::::::::o:o:::::::o o        o  |       |  ::::::::o:::::::::::::::o          |       |    o:::::o:::::o:::::o:::::o    o    |       |    o:::::::::::o:::o:::::::.  o    |       |      o:o:::::::::o:::::::::o o      |       |        o o o o      o:o:o:o        |       |        o                '''o        |       |                                      |       |          o-                o          |       |          o      C      o          |       |            o          o            |       |                o o o                |       |                                      |       * - - - - - - - - - - - - - - - - - - - *
crawl-data/CC-MAIN-2018-26/segments/1529267859904.56/warc/CC-MAIN-20180617232711-20180618012711-00319.warc.gz
null
What is the Salish Sea? The Salish Sea is one of the world’s largest and biologically rich inland seas. The Salish Sea is the unified bi-national ecosystem that includes Washington State’s Puget Sound, the Strait of Juan de Fuca and the San Juan Islands as well as British Columbia’s Gulf Islands and the Strait of Georgia. The name recognizes and pays tribute to the first inhabitants of the region, the Coast Salish. The name Salish Sea has been approved by naming boards in both British Columbia and Washington State as well as by the United States and Canadian naming boards. (Read a history of the naming issue on the Western Washington University website about the Salish Sea.) Politically the Salish Sea is governed by the USA and Canada, but the international boundary separating the Puget Sound Basin (USA) from the Georgia Basin (Canada) corresponds to no natural barrier or transition. The border is invisible to marine fish and wildlife. Species listed as threatened or endangered under the US Endangered Species Act or the Canadian Species at Risk Act, including Southern Resident killer whales (Orcinus orca), marbled murrelets (Brachyramphus marmoratus), and some ecologically significant units or species of Pacific salmon (Onchorynchus spp.), traverse the boundary daily. Oceanographic processes such as freshwater inflows and wind driven surface currents exchange biota, sediments and nutrients throughout the larger ecosystem. Take a look at some of the biggest and longest-lived animals in the world that make their home in the Salish Sea. Salish Sea Facts: - Coastline length, including islands: 7,470 km (1:250,000 scale World vector Shoreline and TEOPO2 topographic/bathymetric GIS grid) - Total number of islands: 419 (1:250,000 scale World vector Shoreline and TEOPO2 topographic/bathymetric GIS grid) - Total land area of islands: 3,660 square kilometers (1:250,000 scale World vector Shoreline and TEOPO2 topographic/bathymetric GIS grid) - Sea surface area: 16,925 square kilometers (1:250,000 scale World vector Shoreline and TEOPO2 topographic/bathymetric GIS grid) - Maximum depth: 650 meters (Bute Inlet, BC; 1:250,000 scale World vector Shoreline and TEOPO2 topographic/bathymetric GIS grid) - Total population approximately 8 million. (source) - Number of different marine animals species estimated: 37 species of mammals, 172 species of birds, 247 species of fish, and over 3000 species of invertebrates (See Gaydos & Pearson 2011 and Brown and Gaydos, 2011.) - Number of species listed as threatened, endangered or are candidates for listing: 113 (See Brown and Gaydos, 2011.) Note: the numbers of species in the ecosystem changes as we learn more about the ecosystem, and the number of species of concern goes up as more species are listed by federal, state and provincial entities. Population Map of the Salish Sea
<urn:uuid:d8471841-0c1c-47c6-94cc-95712076c160>
{ "date": "2015-02-27T16:47:51", "dump": "CC-MAIN-2015-11", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461359.90/warc/CC-MAIN-20150226074101-00083-ip-10-28-5-156.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8857024312019348, "score": 3.96875, "token_count": 662, "url": "http://www.seadocsociety.org/salish-sea-facts/" }
# Verify that: -(-x) = x for. (i) x = 11/15 (ii) x = -13/17 Harshit Singh 3 years ago Dear Student x = 11/15 We have, x = 11/15 Then, the additive inverse of 11/15 is–11/15 (as 11/15 + (-11/15) = 0) The same equality 11/15 + (-11/15) = 0, shows that the additive inverse of -11/15 is 11/15. Or, - (-11/15) = 11/15 i.e., -(-x) = x -13/17 We have, x = -13/17
crawl-data/CC-MAIN-2024-38/segments/1725700651405.61/warc/CC-MAIN-20240911215612-20240912005612-00572.warc.gz
null
# How do you find all the zeros of f(x) = 5x^4 - x^2 + 2? ##### 2 Answers Jul 9, 2016 $x = \pm \left(\sqrt{\frac{2 \sqrt{10} + 1}{20}}\right) \pm \left(\sqrt{\frac{2 \sqrt{10} - 1}{20}}\right) i$ #### Explanation: Since $f \left(x\right)$ has no odd terms, we could treat it as a quadratic in ${x}^{2}$, but the resulting quadratic has negative discriminant: $\Delta = {\left(- 1\right)}^{2} - 4 \left(5\right) \left(2\right) = 1 - 40 = - 39$ As a result it has only Complex zeros, of which we would then want to find square roots. This is a possible approach, but there is an alternative one... Note that: $\left({a}^{2} - k a b + {b}^{2}\right) \left({a}^{2} + k a b + {b}^{2}\right) = {a}^{4} + \left(2 - {k}^{2}\right) {a}^{2} {b}^{2} + {b}^{4}$ Let: $a = \sqrt[4]{5} x$ $b = \sqrt[4]{2}$ Then: ${a}^{4} + \left(2 - {k}^{2}\right) {a}^{2} {b}^{2} + {b}^{4} = 5 {x}^{4} + \left(2 - {k}^{2}\right) \sqrt{10} {x}^{2} + 2$ If we let: $k = \sqrt{\frac{20 + \sqrt{10}}{10}}$ Then: $\left(2 - {k}^{2}\right) \sqrt{10} = \left(2 - \frac{20 + \sqrt{10}}{10}\right) \sqrt{10} = - 1$ And: $k a b = \sqrt{\frac{20 + \sqrt{10}}{10}} \sqrt[4]{10} x = \sqrt{\frac{20 + \sqrt{10}}{10} \cdot \sqrt{10}} = \sqrt{2 \sqrt{10} + 1}$ So: $f \left(x\right) = \left({a}^{2} - k a b + {b}^{2}\right) \left({a}^{2} + k a b + {b}^{2}\right)$ $= \left(\sqrt{5} {x}^{2} - \left(\sqrt{2 \sqrt{10} + 1}\right) x + \sqrt{2}\right) \left(\sqrt{5} {x}^{2} + \left(\sqrt{2 \sqrt{10} + 1}\right) x + \sqrt{2}\right)$ Then the zeros of these quadratic factors are given by the quadratic formula as: $x = \frac{\pm \sqrt{2 \sqrt{10} + 1} \pm \sqrt{\left(2 \sqrt{10} + 1\right) - 4 \sqrt{10}}}{2 \sqrt{5}}$ $= \pm \left(\sqrt{\frac{2 \sqrt{10} + 1}{20}}\right) \pm \left(\sqrt{\frac{2 \sqrt{10} - 1}{20}}\right) i$ Jul 9, 2016 $x = \pm \left(\sqrt{\frac{2 \sqrt{10} + 1}{20}}\right) \pm \left(\sqrt{\frac{2 \sqrt{10} - 1}{20}}\right) i$ #### Explanation: $f \left(x\right) = 5 {x}^{4} - {x}^{2} + 2$ I will use the result I derived for another question (see https://socratic.org/s/aw38evei), that the square roots of $a \pm b i$ are: $\pm \left(\sqrt{\frac{\sqrt{{a}^{2} + {b}^{2}} + a}{2}}\right) \pm \left(\sqrt{\frac{\sqrt{{a}^{2} + {b}^{2}} - a}{2}}\right) i$ First treat $f \left(x\right)$ as a quadratic in ${x}^{2}$ and use the quadratic formula to find: ${x}^{2} = \frac{1 \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(5\right) \left(2\right)}}{2 \cdot 5} = \frac{1 \pm \sqrt{- 39}}{10} = \frac{1}{10} \pm \frac{\sqrt{39}}{10} i$ Let $a = \frac{1}{10}$ and $b = \frac{\sqrt{39}}{10}$ Then: $\sqrt{{a}^{2} + {b}^{2}} = \sqrt{\frac{1}{100} + \frac{39}{100}} = \sqrt{\frac{40}{100}} = \frac{2 \sqrt{10}}{10}$ So the square roots of $a + b i$ are: $\pm \left(\sqrt{\frac{\sqrt{{a}^{2} + {b}^{2}} + a}{2}}\right) \pm \left(\sqrt{\frac{\sqrt{{a}^{2} + {b}^{2}} - a}{2}}\right) i$ $= \pm \left(\sqrt{\frac{\frac{2 \sqrt{10}}{10} + \frac{1}{10}}{2}}\right) \pm \left(\sqrt{\frac{\frac{2 \sqrt{10}}{10} - \frac{1}{10}}{2}}\right) i$ $= \pm \left(\sqrt{\frac{2 \sqrt{10} + 1}{20}}\right) \pm \left(\sqrt{\frac{2 \sqrt{10} - 1}{20}}\right) i$ These are the zeros of our quartic.
crawl-data/CC-MAIN-2020-05/segments/1579250594101.10/warc/CC-MAIN-20200119010920-20200119034920-00163.warc.gz
null
The bizarre Ghost Slug made headlines in 2008 when described as a new species from a Cardiff garden. When the first specimens were found, very little was known about this animal. The story since then connects our collections and specialist expertise with sharp-eyed members of the British public, recording networks, other taxonomists in Europe, and the media to show how a picture is emerging. Emphasizing its spooky nature, we gave the species the scientific name Selenochlamys ysbryda, based on the Welsh word ysbryd, meaning a ghost or spirit. The common name “Ghost Slug” soon became popular. Identifying it with the obscure genus Selenochlamys was a specialist task and required dissection of several specimens including our holotype. (Incidentally, Selenochlamys already combines the Greek words for a cloak, and Selene, goddess of the moon, but “Moon-Cloaked Ghost Slug” sounded a little too melodramatic.) The Ghost Slug is strange in many ways. It is extremely elusive, living up to a metre deep in soil, only rarely visiting the surface. It seldom occurs in large numbers. This makes it an unusually difficult slug to look for, especially in other people’s gardens or other places that cannot be dug up. It is also very distinctive. After having examined one, most agree that it is unmistakeable in future (haunting, perhaps?). The slug is ghostly white, and almost eyeless. It does not eat plants, but kills and eats earthworms, whose burrows it can enter with its extremely extensible body. This differs from that of most other slugs in having the breathing hole right at the tail, and in retracting like the finger of a glove, appearing to suck its own head inside-out. Unlike some British slugs, it can be identified with certainty from a good photograph. The photos here show some similar species often confused with it. This combination of being elusive and distinctive makes the species perfect for a public recording project. We needed to know more, not just out of curiosity, but because the species might pose a threat to earthworm populations. It appeared to have been introduced from overseas, i.e. to be an alien or non-native species, whose spread might cause concern. We thank the then Countryside Council for Wales (now part of Natural Resources Wales) for funding early survey work and information dissemination in 2009, and others who have spread the word. Contributions from the public Since 2008, responses from over 300 people all over the UK (and a few from overseas) have been received and replied to. A large proportion were misidentifications, but many were correct and over 25 populations of Ghost Slugs are now known. These verified records have been submitted to the National Biodiversity Network via the Conchological Society of Great Britain and Ireland. We thank all respondents for their efforts, without which almost none of the populations would have been identified. As the map shows, the Ghost Slug is widespread in south-east Wales, occurring in all the main Valleys and in the cities of Cardiff and Newport, and at two sites in Bristol. It remains, however, rare or absent in some nearby areas (such as Swansea) and by no means occurs throughout this region. Virtually all the records are from gardens, allotments, or nearby roads and riversides in populated areas. This is also true of an unexpected outlier, reported in May 2013 from Wallingford, Oxfordshire, which might indicate an eastward spread. The species is evidently firmly established in Britain and has survived the unusually cold, dry, or wet winters of the last five years. Contributions from specialists This species has had at least 10 years to be spread around Britain, but has not yet been seen elsewhere in Western Europe. The earliest records are from Brecon Cathedral in 2004 (in a 2009 paper by German-based taxonomists) and from Caerphilly in 2006 (on a pet invertebrates forum). We expected its origin to be in the Caucasus Mountains of Georgia and Russia or in northern Turkey, where other Selenochlamys occur. However, a 2012 paper by a Ukraine-based taxonomist described a museum specimen of S. ysbryda collected in Crimea in 1989. This makes some sense – Crimea has a number of endemic molluscs, and several alien species now in Britain were originally described from the region. The UK also has a history of conflict and trade with Crimea (there is even a Sebastopol near a slug population in Cwmbran!) making a direct, accidental introduction plausible. DNA was sequenced from six specimens of the Ghost Slug, from Cardiff, Newport, Bristol, and Talgarth as part of our recent studies on British Slugs. The sequences were all but identical, supporting the theory that the species is not native to the UK. If you are going to report a sighting, please ensure that your slug is a true Ghost Slug (Selenochlamys ysbryda). This can be done by looking at the mantle and the eyes. The mantle (indicated by the grey lines) looks like a layer of skin through which the breathing hole is often visible. This Ghost Slug has a tiny, disc-shaped mantle at the rear end of its body. It has no eye spots on its tentacles (indicated by the arrow). Other white or pale slug species have a large, cloak-like mantle over their “shoulders” near the front of their body. They have black eye spots at the tips of two of their tentacles. The two shown here are the Netted Field Slug (Deroceras reticulatum) and Worm Slug (Boettgerilla pal lens). These species are very common in gardens, so there is no need to report them to us. The Ghost Slug was named one of the "Top 10 New Species of the Year" for 2009 by the US International Institute for Species Exploration. It has featured in exhibitions in Cardiff and Bristol, and even in school exam questions. It has also appeared in several books including Animal (Dorling Kindersley, 2011) and, most recently, in our own 2014 guide to the slug species of Britain and Ireland. To monitor any spread or document behaviours we are still interested in future observations of Selenochlamys ysbryda, verified with a specimen or photograph. Please ensure that they are not the Netted Field Slug Deroceras reticulatum, shown above. To report a Ghost Slug, email Ben Rowson.
<urn:uuid:44e1213f-f23d-4906-b43f-52a0a3a550f3>
{ "date": "2016-05-05T03:33:06", "dump": "CC-MAIN-2016-18", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860125857.44/warc/CC-MAIN-20160428161525-00074-ip-10-239-7-51.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9650960564613342, "score": 3.78125, "token_count": 1361, "url": "http://www.museumwales.ac.uk/articles/2014-08-11/The-Long-Reach-of-the-Ghost-Slug/" }
# TS Polycet (Polytechnic) 2018 Previous Question Paper with Answers And Model Papers With Complete Analysis TS Polycet (Polytechnic) 2018 Previous Question Paper with Answers And Model Papers With Complete Analysis TS Polycet (Polytechnic) Previous Year Question Papers And Model Papers: While preparing for TS Polycet (Polytechnic), candidates must also refer to the previous year question papers of the same. Scoring well in TS Polycet (Polytechnic) and understanding weaknesses and strengths in the respective sections. TS Polycet (Polytechnic) Previous Year Question Papers can be found on this page in PDF format. Students taking the exam to get into some of the best Polytechnic colleges/institutes in the state of Andhra Pradesh may practice these papers to get a clear idea of the structure of the exam, marking scheme, important topics, etc. ## Section — I MATHEMATICS Q). ab (c) = a (bc) is called property. A) Associative B) Inverse C) Identity D) None View Answer A) Associative Q). √5 +√7 is ……………….. number. A) Natural B) Rational C) Integer D) an Irrational View Answer D) an Irrational Explanation: Sum of two irrational numbers is an irrational number. Q). (log9) log10 0.01 = A) (7/8)1 B) (7/16)0 C) (1/16)-2 D) (1/8)2 View Answer Explanation: A, B, C, D Q). Exponential form of log464 = 3 is A) 34 = 64 B) 43 = 64 C) 42 = 81 D) None View Answer C) 42 = 81 Explanation: log464 = 3 ⇒ 43 = 64 Q). = A) 1 B) 3 C) 5 D) 6 View Answer C) 5 Explanation: Let x = X = ⇒ x2 = 20+x x2 -x – 20 = 0 => x2 – 5x + 4x – 20 = 0 x(x-5) + 4(x-5) = 0=> (x-5) (x + 4) = 0 => x = 5 Q). From the following Venn-diagram B – A =……………………. A) {1,2, 3} B) {4, 5} C) {6, 7} D) None View Answer C) {6, 7} Explanation: From the Venn-diagram B -A = {4,5,6,7} -{1, 2,3,4,5} = {6, 7} Q). If A = {a, b, c, d}, then the number of subsets for A is ……………………. A) 5 B) 6 C) 16 D) 65 View Answer C) 16 Explanation: Given A = {a, b, c, d} => n(A) = 4 No. of subsets = 2n = 24 = 16 Q). If α,β,ɣ are the zeroes of the polynomial f(x) = ax3 + bx2 + cx + d, then A) 1/d B) 1/c C) c/d D) –c/d View Answer D) –c/d Explanation: Given f(x) = ax3 + bx2 + cx + d = = = =-c/d Q). A quadratic polynomial whose zeroes are 5 and -2 is ……………… A) x2 + 5x-2 B) x2 + 3x-10 C) x2-3x-10 D) x2-2x + 5 View Answer C) x2-3x-10 Explanation: α = 5 β = -2 x2 – (α + β) X + αβ = 0 ⇒ x2 – (5 – 2) x + 5 (-2) = 0 ⇒ x2-3x-10 = 0 Q). The lines represented by 5x + 7y – 14 = 0 and 10x + 3y – 8 = 0 are…….. lines. A) Coincident B) Vertical C) Parallel D) Intersecting View Answer D) Intersecting Explanation: a1 = 5, b1 = 7, C1 = —14, a2 = 10, b2 = 3 and c2 = -8 ∴Given lines are intersecting lines. Spread the love About Us | Contact Us | Privacy Polocy error: Content is protected !!
crawl-data/CC-MAIN-2024-38/segments/1725700651981.99/warc/CC-MAIN-20240919025412-20240919055412-00869.warc.gz
null
The term processor is related to the heart of the computer, also referred to as a ‘brain’ of the computer. A processor is a little chip that resides in computer systems and other electronic peripheral devices which perform basic tasks such as processor handle all the arithmetical and mathematical computations such as addition, subtraction, multiplying, and dividing. “A processor that manages the performance of the software and hardware of the computer system .” We also called as the CPU, or “central processing unit.” This is the combinations of ALU “Airthmatic and logical unit” and CU “control Unit” which functions in term of following - Ability to handle all the operations being carried out. - Manage Communication between the memory and the ‘ALU’ arithmetic logic unit. - Perform logical operations and also responsible for Equal-to operations, Less-than condition and greater than conditional operations. “There are many types of processors available in the market. Its speed is usually one of the first things considered when buying a new computer. The type of processor and its working speed have the largest impact on the overall system performance and working of a computer. Its performance is directly relating to its speed of operation and its architecture. The speed of a computer processor measured in megahertz or cycles per second.”
<urn:uuid:042991c4-030d-4920-b3cd-93b910dafe71>
{ "date": "2019-02-16T20:36:34", "dump": "CC-MAIN-2019-09", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481111.41/warc/CC-MAIN-20190216190407-20190216212407-00377.warc.gz", "int_score": 4, "language": "en", "language_score": 0.960615336894989, "score": 4.09375, "token_count": 282, "url": "https://www.technicalreaders.com/what-is-processor/" }
Facts about this animal There are two species of elephants in Africa: the larger and more widespread savannah elephant (Loxodonta africana african) and the forest elephant of West and Central Africa (Loxodonta africana cyclotis), which is smaller, has downward-pointed tusks, and smaller, rounder ears. A third species, the West African Elephant, has also been postulated. All elephants kept in zoos outside the forest elephants range are savannah elephants. There are visible tusks in both sexes, although in some areas a certain percentage of elephants is tuskless. The animals' trunks, unique among living mammals, are versatile, enabling elephants to manipulate tiny objects or tear down huge tree limbs. Wide, padded feet enable them to walk quietly. Large, flappable ears help these huge animals to cool off, although elephants often must retreat to the shade or water during the hottest part of the day.Females, subadults and youngsters live in cohesive herds. The matriarch, usually the oldest and largest female, sets the pace of the group's activities. Males leave herds at puberty and travel alone or in bachelor groups. Elephants travel widely in search of food. Movements vary depending upon food availability. African elephants communicate with varied, low-frequency sounds which may travel over long distances. Gestation lasts 22 months, and usually only one calf is born. Newborn African elephants weigh about 110 kgs and their shoulder height is about 95 cm. Female African savanna elephants can usually breed by age ten and give birth to one young every four years. The life span of African elephants is up to 60 years. The African elephant differs from his Asian cousin in that the outline of the back is concave, the highest points of the silhouette being the withers and the loins, the receding forehead and the enormous ears. Did you know? That the African elephant is the largest terrestrial mammal? Male African elephants may reach a shoulder height of 4 m and their weight may exceed 7 tons. |Name (Scientific)||Loxodonta africana| |Name (English)||African Elephant| |Name (French)||Eléphant d'Afrique| |Name (German)||Afrikanischer Elefant| |Name (Spanish)||Elefante africano| |Local names||Afrikaans: Afrika-olifant, olifant chiShona: nzou, zhou isiNdebele, isiXhosa, isiZulu, siSwati: Indlovuki Swahili: Tembo, ndovu otjiHerero: Ndhlovu, oNdjou seSotho, seTswana: Thloutshi |CITES Status||Appendix I and II with annotations| |CMS Status||Appendix II| Photo Copyright by |Habitat||Rainforest (Loxodonta africana cyclotis), montane, dry, gallery forests, savannas, bushveld, grasslands, marshes, semideserts and deserts| |Wild population||The 2002 African Elephant Database (AED): 59,024 (probable), 99,813 (possible), and 99,307 (speculative) total numbers of elephants (EDGE 2011)| |Zoo population||358 reported to ISIS (2009)| In the Zoo How this animal should be transported For air transport, Container Requirement 71 of the IATA Live Animals Regulations should be followed. Road transport (according to the South African Standard SANS 10331): Transport in special crates under tranquillization. Special loading facilities are required and expert assistance from experienced nature conservation staff or a capture team is essential. Find this animal on ZooLex Photo Copyright by Kathrin Marthaler, Switzerland Why do zoos keep this animal Elephants are among the most emotive megafauna species. They are one of the great attractions for zoo visitors, and thus an ideal flagship species for African wildlife and wild lands. Zoos have also the opportunity of addressing the problem of illegal trade in ivory and may succeed in influencing consumers. Zoos may also keep elephants for animal welfare reasons by accepting to care for elephants kept under less suitable conditions in other zoos, circuses or by artists.
<urn:uuid:6c7a5060-d251-4f25-9c60-d45251c93176>
{ "date": "2013-12-13T03:27:11", "dump": "CC-MAIN-2013-48", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164836485/warc/CC-MAIN-20131204134716-00002-ip-10-33-133-15.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8540982007980347, "score": 3.53125, "token_count": 934, "url": "http://www.waza.org/en/zoo/choose-a-species/mammals/elephants/loxodonta-africana" }
# Dihedral group explained In mathematics, a dihedral group is the group of symmetries of a regular polygon,[1] which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, or refers to the symmetries of the -gon, a group of order . In abstract algebra, refers to this same dihedral group.[2] This article uses the geometric convention, . ## Definition ### Elements A regular polygon with n sides has 2n different symmetries: n rotational symmetries and n reflection symmetries. Usually, we take n\ge3 here. The associated rotations and reflections make up the dihedral group Dn . If n is odd, each axis of symmetry connects the midpoint of one side to the opposite vertex. If n is even, there are n/2 axes of symmetry connecting the midpoints of opposite sides and n/2 axes of symmetry connecting opposite vertices. In either case, there are n axes of symmetry and 2n elements in the symmetry group. Reflecting in one axis of symmetry followed by reflecting in another axis of symmetry produces a rotation through twice the angle between the axes. The following picture shows the effect of the sixteen elements of D8 on a stop sign: The first row shows the effect of the eight rotations, and the second row shows the effect of the eight reflections, in each case acting on the stop sign with the orientation as shown at the top left. ### Group structure As with any geometric object, the composition of two symmetries of a regular polygon is again a symmetry of this object. With composition of symmetries to produce another as the binary operation, this gives the symmetries of a polygon the algebraic structure of a finite group. The following Cayley table shows the effect of composition in the group D3 (the symmetries of an equilateral triangle). r0 denotes the identity; r1 and r2 denote counterclockwise rotations by 120° and 240° respectively, and s0, s1 and s2 denote reflections across the three lines shown in the adjacent picture. r0 r1 r2 s0 s1 r0 r1 r2 s0 s1 s2 r0 r1 r2 s0 s1 s2 r1 r2 r0 s1 s2 s0 r2 r0 r1 s2 s0 s1 s0 s2 s1 r0 r2 r1 s1 s0 s2 r1 r0 r2 s2 s1 s0 r2 r1 r0 For example,, because the reflection s1 followed by the reflection s2 results in a rotation of 120°. The order of elements denoting the composition is right to left, reflecting the convention that the element acts on the expression to its right. The composition operation is not commutative. In general, the group Dn has elements r0, ..., rn-1 and s0, ..., sn-1, with composition given by the following formulae: rirj=ri+j,risj=si+j,sirj=si-j,sisj=ri-j. In all cases, addition and subtraction of subscripts are to be performed using modular arithmetic with modulus n. ### Matrix representation If we center the regular polygon at the origin, then elements of the dihedral group act as linear transformations of the plane. This lets us represent elements of Dn as matrices, with composition being matrix multiplication.This is an example of a (2-dimensional) group representation. For example, the elements of the group D4 can be represented by the following eight matrices: \begin{matrix} r0=\left(\begin{smallmatrix}1&0\\[0.2em]0&1\end{smallmatrix}\right),& r1=\left(\begin{smallmatrix}0&-1\\[0.2em]1&0\end{smallmatrix}\right),& r2=\left(\begin{smallmatrix}-1&0\\[0.2em]0&-1\end{smallmatrix}\right),& r3=\left(\begin{smallmatrix}0&1\\[0.2em]-1&0\end{smallmatrix}\right),\\[1em] s0=\left(\begin{smallmatrix}1&0\\[0.2em]0&-1\end{smallmatrix}\right),& s1=\left(\begin{smallmatrix}0&1\\[0.2em]1&0\end{smallmatrix}\right),& s2=\left(\begin{smallmatrix}-1&0\\[0.2em]0&1\end{smallmatrix}\right),& s3=\left(\begin{smallmatrix}0&-1\\[0.2em]-1&0\end{smallmatrix}\right). \end{matrix} In general, the matrices for elements of Dn have the following form: \begin{align} rk&=\begin{pmatrix} \cos 2\pik n &-\sin 2\pik n \\ \sin 2\pik n &\cos 2\pik n \end{pmatrix}  and\\ sk&=\begin{pmatrix} \cos 2\pik n &\sin 2\pik n \\ \sin 2\pik n &-\cos 2\pik n \end{pmatrix} . \end{align} rk is a rotation matrix, expressing a counterclockwise rotation through an angle of . sk is a reflection across a line that makes an angle of with the x-axis. ### Other definitions Further equivalent definitions of are: ## Small dihedral groups is isomorphic to, the cyclic group of order 2. is isomorphic to, the Klein four-group. and are exceptional in that: • and are the only abelian dihedral groups. Otherwise, is non-abelian. • is a subgroup of the symmetric group for . Since for or, for these values, is too large to be a subgroup. • The inner automorphism group of is trivial, whereas for other even values of, this is . The cycle graphs of dihedral groups consist of an n-element cycle and n 2-element cycles. The dark vertex in the cycle graphs below of various dihedral groups represents the identity element, and the other vertices are the other elements of the group. A cycle consists of successive powers of either of the elements connected to the identity element. ## The dihedral group as symmetry group in 2D and rotation group in 3D An example of abstract group, and a common way to visualize it, is the group of Euclidean plane isometries which keep the origin fixed. These groups form one of the two series of discrete point groups in two dimensions. consists of rotations of multiples of about the origin, and reflections across lines through the origin, making angles of multiples of with each other. This is the symmetry group of a regular polygon with sides (for ; this extends to the cases and where we have a plane with respectively a point offset from the "center" of the "1-gon" and a "2-gon" or line segment). is generated by a rotation of order and a reflection of order 2 such that srs=r-1 In geometric terms: in the mirror a rotation looks like an inverse rotation. In terms of complex numbers: multiplication by e2\pi and complex conjugation. In matrix form, by setting r1=\begin{bmatrix} \cos{2\pi\overn}&-\sin{2\pi\overn}\\[4pt] \sin{2\pi\overn}&\cos{2\pi\overn} \end{bmatrix}    s0=\begin{bmatrix} 1&0\\ 0&-1 \end{bmatrix} and defining rj= j r 1 and sj=rjs0 for j\in\{1,\ldots,n-1\} we can write the product rules for Dn as \begin{align} rjrk&=r(j+k)\\ rjsk&=s(j+k)\\ sjrk&=s(j-k)\\ sjsk&=r(j-k)\end{align} (Compare coordinate rotations and reflections.) The dihedral group D2 is generated by the rotation r of 180 degrees, and the reflection s across the x-axis. The elements of D2 can then be represented as, where e is the identity or null transformation and rs is the reflection across the y-axis. D2 is isomorphic to the Klein four-group. For n > 2 the operations of rotation and reflection in general do not commute and Dn is not abelian; for example, in D4, a rotation of 90 degrees followed by a reflection yields a different result from a reflection followed by a rotation of 90 degrees. Thus, beyond their obvious application to problems of symmetry in the plane, these groups are among the simplest examples of non-abelian groups, and as such arise frequently as easy counterexamples to theorems which are restricted to abelian groups. The elements of can be written as,,, ...,,,,, ..., . The first listed elements are rotations and the remaining elements are axis-reflections (all of which have order 2). The product of two rotations or two reflections is a rotation; the product of a rotation and a reflection is a reflection. So far, we have considered to be a subgroup of, i.e. the group of rotations (about the origin) and reflections (across axes through the origin) of the plane. However, notation is also used for a subgroup of SO(3) which is also of abstract group type : the proper symmetry group of a regular polygon embedded in three-dimensional space (if n ≥ 3). Such a figure may be considered as a degenerate regular solid with its face counted twice. Therefore, it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group (in analogy to tetrahedral, octahedral and icosahedral group, referring to the proper symmetry groups of a regular tetrahedron, octahedron, and icosahedron respectively). ## Properties The properties of the dihedral groups with depend on whether is even or odd. For example, the center of consists only of the identity if n is odd, but if n is even the center has two elements, namely the identity and the element rn/2 (with Dn as a subgroup of O(2), this is inversion; since it is scalar multiplication by -1, it is clear that it commutes with any linear transformation). In the case of 2D isometries, this corresponds to adding inversion, giving rotations and mirrors in between the existing ones. For n twice an odd number, the abstract group is isomorphic with the direct product of and .Generally, if m divides n, then has n/m subgroups of type, and one subgroup Z m. Therefore, the total number of subgroups of (n ≥ 1), is equal to d(n) + σ(n), where d(n) is the number of positive divisors of n and σ(n) is the sum of the positive divisors of n. See list of small groups for the cases n ≤ 8. The dihedral group of order 8 (D4) is the smallest example of a group that is not a T-group. Any of its two Klein four-group subgroups (which are normal in D4) has as normal subgroup order-2 subgroups generated by a reflection (flip) in D4, but these subgroups are not normal in D4. ### Conjugacy classes of reflections All the reflections are conjugate to each other in case n is odd, but they fall into two conjugacy classes if n is even. If we think of the isometries of a regular n-gon: for odd n there are rotations in the group between every pair of mirrors, while for even n only half of the mirrors can be reached from one by these rotations. Geometrically, in an odd polygon every axis of symmetry passes through a vertex and a side, while in an even polygon there are two sets of axes, each corresponding to a conjugacy class: those that pass through two vertices and those that pass through two sides. Algebraically, this is an instance of the conjugate Sylow theorem (for n odd): for n odd, each reflection, together with the identity, form a subgroup of order 2, which is a Sylow 2-subgroup (is the maximum power of 2 dividing), while for n even, these order 2 subgroups are not Sylow subgroups because 4 (a higher power of 2) divides the order of the group. For n even there is instead an outer automorphism interchanging the two types of reflections (properly, a class of outer automorphisms, which are all conjugate by an inner automorphism). ## Automorphism group The automorphism group of is isomorphic to the holomorph of Z /n Z , i.e., to and has order (n), where ϕ is Euler's totient function, the number of k in coprime to n. It can be understood in terms of the generators of a reflection and an elementary rotation (rotation by k(2π/n), for k coprime to n); which automorphisms are inner and outer depends on the parity of n. • For n odd, the dihedral group is centerless, so any element defines a non-trivial inner automorphism; for n even, the rotation by 180° (reflection through the origin) is the non-trivial element of the center. • Thus for n odd, the inner automorphism group has order 2n, and for n even (other than) the inner automorphism group has order n. • For n odd, all reflections are conjugate; for n even, they fall into two classes (those through two vertices and those through two faces), related by an outer automorphism, which can be represented by rotation by π/n (half the minimal rotation). • The rotations are a normal subgroup; conjugation by a reflection changes the sign (direction) of the rotation, but otherwise leaves them unchanged. Thus automorphisms that multiply angles by k (coprime to n) are outer unless . ### Examples of automorphism groups has 18 inner automorphisms. As 2D isometry group D9, the group has mirrors at 20° intervals. The 18 inner automorphisms provide rotation of the mirrors by multiples of 20°, and reflections. As isometry group these are all automorphisms. As abstract group there are in addition to these, 36 outer automorphisms; e.g., multiplying angles of rotation by 2. has 10 inner automorphisms. As 2D isometry group D10, the group has mirrors at 18° intervals. The 10 inner automorphisms provide rotation of the mirrors by multiples of 36°, and reflections. As isometry group there are 10 more automorphisms; they are conjugates by isometries outside the group, rotating the mirrors 18° with respect to the inner automorphisms. As abstract group there are in addition to these 10 inner and 10 outer automorphisms, 20 more outer automorphisms; e.g., multiplying rotations by 3. Compare the values 6 and 4 for Euler's totient function, the multiplicative group of integers modulo n for n = 9 and 10, respectively. This triples and doubles the number of automorphisms compared with the two automorphisms as isometries (keeping the order of the rotations the same or reversing the order). The only values of n for which φ(n) = 2 are 3, 4, and 6, and consequently, there are only three dihedral groups that are isomorphic to their own automorphism groups, namely (order 6), (order 8), and (order 12).[3] [4] [5] ### Inner automorphism group The inner automorphism group of is isomorphic to:[6] • if n is odd; • if is even (for,). ## Generalizations There are several important generalizations of the dihedral groups:
crawl-data/CC-MAIN-2023-23/segments/1685224647525.11/warc/CC-MAIN-20230601010402-20230601040402-00292.warc.gz
null
Census Finds Unknown Young Stars of Orion Amateur stargazers may spot the Orion Nebula as a fuzzy patch in the constellation Orion, but they cannot see an interstellar birthing ground that spans the region of sky from above Orion's head to below his feet. Now astronomers have completed the most wide-ranging census of baby stars in and around the Orion nebula, and found a stellar nursery that's both chaotic and crowded. The work represents the first complete study of young stars, their gaseous clouds of dust and supersonic jets of hydrogen molecules shooting out from the poles of each star. Jets arise as young stars are born from a rotating cloud of gas and dust, but usually die out once a star has fully ignited and stopped consuming the surrounding material. In this case, the jets became signals that pinpointed the location of baby stars hidden within the stellar birthing grounds. "With such a large number of young stars, we can study the 'demographics' of star birth," said Tom Megeath, an astronomer at the University of Toledo in Ohio. "This study will give us an idea of how long it takes baby stars to bulk up by pulling in gas from the surrounding cloud, what ultimately stops a star from growing bigger, and how a star's birth is influenced by other stars in the stellar nursery." The Orion nebula represents just a blister on the surface of the much larger cloud. Astronomers turned to the United Kingdom Infra-Red Telescope (UKIRT) and the Spitzer Space Telescope to peer through the cloud using infrared vision, and also used the Institut de Radio Astronomie Millimetrique radio telescope in France to see beyond infrared at short radio wavelengths. Such international collaboration allowed astronomers to match up powerful gas jets with their young star origins, and find the cradles within the clouds where stars were created. "Each jet is travelling at tens or even hundreds of miles per second; the jets extend across many trillions of miles of interstellar space," said Chris Davis, an astronomer for UKIRT in Hawaii. UKIRT's wide field camera alone found more than 110 individual jets from the one region of the Milky Way. The results were presented on April 20 at the European Week of Astronomy and Space Science at the University of Hertfordshire, UK. - Top 10 Star Mysteries - Video - When Stars Collide - Vote - The Strangest Things in Space MORE FROM SPACE.com
<urn:uuid:e15f671d-6de4-4dc9-91d1-f14117870231>
{ "date": "2013-05-18T17:49:43", "dump": "CC-MAIN-2013-20", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696382584/warc/CC-MAIN-20130516092622-00000-ip-10-60-113-184.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9287340641021729, "score": 3.671875, "token_count": 503, "url": "http://www.space.com/6592-census-finds-unknown-young-stars-orion.html" }
Dr. Hackney STA Solutions pg 119 # Dr. Hackney STA Solutions pg 119 - 7-22 Solutions Manual... This preview shows page 1. Sign up to view the full content. This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: 7-22 Solutions Manual for Statistical Inference 7.56 Because T is sufficient, (T ) = E[h(X1 , . . . , Xn )|T ] is a function only of T . That is, (T ) is an estimator. If E h(X1 , . . . , Xn ) = (), then E h(X1 , , Xn ) = E [E ( h(X 1 , . . . , X n )| T )] = (), so (T ) is an unbiased estimator of (). By Theorem 7.3.23, (T ) is the best unbiased estimator of (). 7.57 a. T is a Bernoulli random variable. Hence, n Ep T = Pp (T = 1) = Pp i=1 n+1 i=1 Xi > Xn+1 = h(p). b. Xi is a complete sufficient statistic for , so E T estimator of h(p). We have n+1 n n+1 n+1 i=1 Xi is the best unbiased E T i=1 Xi = y = P i=1 n Xi > Xn+1 i=1 n+1 Xi = y n+1 = P i=1 Xi > Xn+1 , i=1 Xi = y P i=1 Xi = y . The denominator equals n+1 y py (1 - p)n+1-y . If y = 0 the numerator is n n+1 P i=1 Xi > Xn+1 , i=1 Xi = 0 = 0. If y > 0 the numerator is n n+1 n n+1 P i=1 Xi > Xn+1 , i=1 Xi = y, X n+1 = 0 +P i=1 Xi > Xn+1 , i=1 Xi = y, X n+1 = 1 which equals n n n n P i=1 Xi > 0, i=1 Xi = y P (Xn+1 = 0) + P i=1 Xi > 1, i=1 Xi = y - 1 P (Xn+1 = 1). For all y > 0, n n n P i=1 Xi > 0, i=1 Xi = y =P i=1 Xi = y = n y p (1 - p)n-y . y If y = 1 or 2, then n n P i=1 Xi > 1, i=1 Xi = y - 1 = 0. And if y > 2, then n n n P i=1 Xi > 1, i=1 Xi = y - 1 =P i=1 Xi = y - 1 = n py-1 (1 - p)n-y+1 . y-1 ... View Full Document {[ snackBarMessage ]} Ask a homework question - tutors are online
crawl-data/CC-MAIN-2018-05/segments/1516084887746.35/warc/CC-MAIN-20180119045937-20180119065937-00212.warc.gz
null
In a hyperbolic system such as LORAN, a receiver on an aircraft or ship picks up radio signals broadcast by one or more pairs of radio stations spaced hundreds of miles apart. The system works by measuring the time delays between signals from the two stations. By tuning in different pairs, the navigator could plot lines of position in the form of hyperbolas (arcs) that intersect to give a precise location. By 1943, Allied pilots in Europe were using the medium-range GEE hyperbolic system for all-weather navigation. But its limited range did not extend far into the North Atlantic, where ships and aircraft on antisubmarine patrol desperately needed it. In the Pacific, Navy patrol bombers like the Consolidated PB4Y-2 Privateer, B-29 bombers attacking Japan, and other aircraft also needed a long-range, all-weather navigation system.
<urn:uuid:7e5fad7c-abff-4494-9d34-ec28729928d6>
{ "date": "2015-01-25T22:16:50", "dump": "CC-MAIN-2015-06", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115891802.74/warc/CC-MAIN-20150124161131-00083-ip-10-180-212-252.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9473526477813721, "score": 4.4375, "token_count": 181, "url": "http://timeandnavigation.si.edu/navigating-air/navigation-at-war/new-era-in-time-and-navigation/hyperbolic-systems" }
Gallstones (commonly misspelled gall stones or gall stone) are solid particles that form from bile in the gallbladder. - The gallbladder is a small saclike organ in the upper right part of the abdomen. It is located under the liver, just below the front rib cage on the right side. - The gallbladder is part of the biliary system, which includes the liver and the pancreas. - The biliary system, among other functions, produces bile and digestive enzymes. Bile is a fluid made by the liver to help in the digestion of fats. - It contains several different substances, including cholesterol and bilirubin, a waste product of normal breakdown of blood cells in the liver. - Bile is stored in the gallbladder until needed. - When we eat a high-fat, high-cholesterol meal, the gallbladder contracts and injects bile into the small intestine via a small tube called the common bile duct. The bile then assists in the digestive process. There are two types of gallstones: 1) cholesterol stones and 2) pigment stones. - Patients with cholesterol stones are more common in the United States; cholesterol stones make up a majority of all gallstones. They form when there is too much cholesterol in the bile. - Pigment stones form when there is excess bilirubin in the bile. Gallstones can be any size, from tiny as a grain of sand to large as a golf ball. - Although it is common to have many smaller stones, a single larger stone or any combination of sizes is possible. - If stones are very small, they may form a sludge or slurry. - Whether gallstones cause symptoms depends partly on their size and their number, although no combination of number and size can predict whether symptoms will occur or the severity of the symptoms. Gallstones within the gallbladder often cause no problems. If there are many or they are large, they may cause pain when the gallbladder responds to a fatty meal. They also may cause problems if they move out of the gallbladder. - If their movement leads to blockage of any of the ducts connecting the gallbladder, liver, or pancreas with the intestine, serious complications may result. - Blockage of a duct can cause bile or digestive enzymes to be trapped in the duct. - This can cause inflammation and ultimately severe pain, infection, and organ damage. - If these conditions go untreated, they can even cause death. Up to 20% of adults in the United States may have gallstones, yet only 1% to 3% develop symptoms. - Hispanics, Native Americans, and Caucasians of Northern European descent are most likely to be at risk for gallstones. African Americans are at lower risk. - Gallstones are most common among overweight, middle-aged women, but the elderly and men are more likely to experience more serious complications from gallstones. - Women who have been pregnant are more likely to develop gallstones. The same is true for women taking birth control pills or on hormone/estrogen therapy as this can mimic pregnancy in terms of hormone levels. Medically Reviewed by a Doctor on 5/6/2014 Must Read Articles Related to Gallstones Abdominal Pain in Adults Abdominal pain in adults can range from a mild stomach ache to severe pain. Examples of causes of abdominal pain in adults include appendicitis, gallbladder dis...learn more >> Cirrhosis is a chronic (ongoing, long-term) disease of the liver. It means damage to the normal liver tissue that keeps this important organ from working as it ...learn more >> Pancreatitis is inflammation of the pancreas. There are two kinds of pancreatitis, acute and chronic. The primary causes of pancreatitis are alcohol and gallsto...learn more >> Patient Comments & Reviews The eMedicineHealth doctors ask about Gallstones:
<urn:uuid:53b6c14d-299d-4f0e-adac-f18e9bccdc09>
{ "date": "2015-04-28T07:08:22", "dump": "CC-MAIN-2015-18", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246660743.58/warc/CC-MAIN-20150417045740-00133-ip-10-235-10-82.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9202869534492493, "score": 3.96875, "token_count": 840, "url": "http://www.emedicinehealth.com/gallstones/article_em.htm" }
Board Central Board of Secondary Education [CBSE] Class 10th / X Download Sample Question Paper 2023-24 Subject Maths Document Type PDF Official Website http://cbseacademic.nic.in/ ## CBSE Class X Maths Sample Question Paper Download Central Board of Secondary Education [CBSE] Class 10th Maths Sample Question Paper 2023-24 PDF Free Online ## CBSE Class X Maths Sample Questions 1. The LCM of smallest two-digit composite number and smallest composite number is: a) 12 b) 4 c) 20 d) 44 2. The pair of equations y = 0 and y = -7 has: a) One solution b) Two solutions c) Infinitely many solutions d) No solution 3. The distance of the point(3, 5) from x-axis is k units, then k equals: a) 3 b) – 3 c) 5 d) -5 4. Which of the following is NOT a similarity criterion? a) AA b) SAS c) AAA d) RHS 5. If the height of the tower is equal to the length of its shadow, then the angle of elevation of the sun is _____ a) 30° b) 45° c) 60° d) 90° 6. The radius of a circle is same as the side of a square. Their perimeters are in the ratio a) 1 : 1 b) 2 : 𝜋 c) 𝜋 : 2 d) √𝜋 : 2 7. The area of the circle is 154cm2. The radius of the circle is a) 7cm b) 14cm c) 3.5cm d) 17.5cm 8. A rectangular sheet of paper 40cm x 22cm, is rolled to form a hollow cylinder of height 40cm. The radius of the cylinder(in cm) is : a) 3.5 b) 7 c)80/7 d) 5 9. Assertion (A): The point (0, 4) lies on y-axis. Reason(R): The x coordinate of the point on y-axis is zero (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertions (A) is true but reason (R) is false. (d) Assertions (A) is false but reason (R) is true. 10. Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40. Reason(R): For any two positive integers a and b, HCF (a, b) x LCM (a, b) = a x b. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertions (A) is true but reason (R) is false. (d) Assertions (A) is false but reason (R) is true. General Instructions: 1. This Question Paper has 5 Sections A, B, C, D, and E. 2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each. 3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each. 4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each. 5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each. 6. Section E has 3 sourced based/Case Based/passage based/integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1 and 2 marks each respectively. 7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E. 8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated. Similar Searches: cbse class x sample paper 2022, cbse 2022 sample paper class 10, cbse 2022 sample paper, cbse class x sample paper 2021-22, cbse class x sample question paper 2022 23 answers, cbse class x sample question paper 2022 23 answers pdf, cbse class x sample question paper 2022 23 all subjects, cbse class x sample question paper 2022 23 ai, cbse class x sample question paper 2022 23 and literature. Have a question? Please feel free to reach out by leaving a comment below (Visited 34 times, 1 visits today)
crawl-data/CC-MAIN-2024-30/segments/1720763515079.90/warc/CC-MAIN-20240720083242-20240720113242-00629.warc.gz
null
From a runny nose to non-stop sneezing, you can't miss the symptoms of a common cold. However, there is a lot more information about the common cold that you should be aware of. Here we break down all the information about this all-too-common disease. The common cold is an illness caused by a virus. In fact, more than 200 types of viruses can lead to this misery. The most common pathogen is the rhinovirus which causes around 50 percent of colds. Other viruses responsible for colds include respiratory syncytial virus, coronavirus, parainfluenza, and influenza. The common cold is also one of the major diseases that causes a lot of people to stay at home. According to the CDC, common colds lead to the loss of nearly 22 million school days every year. In the U.S. it is estimated that Americans suffer from 1 billion colds every year. Cold viruses can enter your body through your nose, eyes, or mouth. The common cold, as many are aware, is a contagious disease. Thus, the viruses spread through droplets in the air when a patient talks, coughs, or sneezes. Colds can also spread through contact from sharing contaminated objects such as toys, utensils, or mobile phones. The symptoms of a common cold may take a few days to surface. Generally, symptoms appear one to three days after exposure to the virus. The signs and symptoms vary from person to person, and include: • Runny/ stuffy nose • Slight body aches • Mild Headache • Low-grade fever • Sore throat • Watery eyes • Loss of smell or taste • Swollen lymph nodes • Chest discomfort If you are experiencing more severe symptoms such as muscle aches and a high fever, you may have the flu. In the case of most adults, the common cold is treated with over-the-counter medicine or through home remedies. Antihistamines, decongestants, and pain relievers are commonly used to treat cold symptoms. Popular home remedies include gargling with salt water, staying hydrated, rest and consuming herbs like Echinacea. These remedies won't cure a cold but may lessen the intensity of the symptoms. In the case of children, The U.S. Food and Drug Administration (FDA) recommends speaking with a doctor before administering over-the-counter medicines. The common cold affects your upper respiratory tract. As antibiotics can't treat viruses, the common cold will subside once it runs its course. Nonetheless, you can treat the symptoms and lessen your misery. Typically, a common cold can last anywhere from 7 to 10 days. If you find your symptoms do not disappear after 10 days, it is important that you consult your doctor. Colds are minor illnesses, but they can be inconvenient for many. There is no vaccine to prevent the common cold. However, these preventive measures may help you from catching a cold: • Wash your hands frequently throughout the day. • Eat plenty of bacteria-rich food like yogurt. • Cover your cough. • Avoid interacting with sick people. If you need urgent care for the common cold visit BASS Advanced Urgent Care in Walnut Creek today. Call us or book an appointment via our website.
<urn:uuid:a3e4256f-7272-44f2-bac1-d1a518ba0a0e>
{ "date": "2021-01-17T09:00:41", "dump": "CC-MAIN-2021-04", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703511903.11/warc/CC-MAIN-20210117081748-20210117111748-00017.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9482465386390686, "score": 3.65625, "token_count": 697, "url": "https://www.bassadvancedurgentcare.com/conditions/common-cold" }
What Is Pancreatitis, and What Causes It? Pancreatitis has been in the news cycle lately as celebrities like Travis Barker and Maria Menounos have opened up about their health complications with pancreatitis and pancreatic cancer, respectively. Pancreatitis can be a serious and painful experience. The condition occurs when the pancreas (an organ that produces enzymes to help the body digest its food) becomes inflamed, causing stomach pain, nausea, and more. Unfortunately, because pancreatitis can resemble other conditions like ulcers, gallstones, irritable bowel syndrome, and even pancreatic cancer, research has found that doctors may misdiagnose the condition. But being aware of the causes and the symptoms can be useful in distinguishing the condition and knowing what signs to look for in your own body. What Is Pancreatitis? Your stomach takes in food, and your pancreas — a small organ located behind your stomach, next to your small intestine — helps digest it. It releases digestive enzymes to help process food and releases glucagon and insulin, which help your body break down food into energy. "Pancreatitis occurs when digestive enzymes become activated while still in the pancreas, irritating the cells of your pancreas and causing inflammation," according to the Mayo Clinic. Pancreatitis can be acute and temporary, which usually happens when your pancreas is recovering from a minor, short-term injury, per Cleveland Clinic. But it can also be chronic. Chronic pancreatitis is a long-term condition that gets progressively worse over time. What Typically Causes Pancreatitis? Gallstones account for up to 70 percent of cases of acute pancreatitis, according to an UpToDate article written by Santhi Swaroop Vege, MD. Up to 25 percent of acute cases are linked to chronic alcohol overuse. Medications, high triglyceride levels, cystic fibrosis, high calcium levels, infection, and injury are all other possible causes for the issue, reports the Mayo Clinic. While it's possible for procedures like colonoscopies to cause acute pancreatitis, it's thought to be very uncommon, according to a case report in The Cureus Journal of Medical Science. It's possible that during a colonoscopy, the pancreas could undergo some trauma, which would then result in inflammation. Pancreatitis can also be chronic; this occurs when the acute inflammation has been treated, but the pancreas has sustained damage, according to Johns Hopkins Medicine. What Are the Symptoms of Pancreatitis? According to the Mayo Clinic, the symptoms of acute pancreatitis may include: - Upper abdominal pain - Abdominal pain that radiates to your back - Tenderness when touching the abdomen - Rapid pulse Chronic pancreatitis sign and symptoms also include upper abdominal pain, in addition to abdominal pain that worsens after eating, unintended weight loss, and oily or smelly stools (aka steatorrhea). How Is Pancreatitis Treated? Pancreatitis is serious, and if you think you have it, you should visit your doctor ASAP. Acute attacks might require treatment with medications for the pain, IV fluids to prevent dehydration, a diet of clear liquids and bland food while your pancreas recovers, and sometimes even a feeding tube, reports the Mayo Clinic. Your doctors will also try to determine what caused the episode and treat that to prevent it from happening again — so if gallstones were behind the acute pancreatitis, you may need gallbladder-removal surgery. In the case of chronic pancreatitis, patients may need additional pain-management therapy, digestive-enzyme supplements, and dietary changes.
<urn:uuid:08a9c74f-5f69-4e02-9d6e-1fd6d4995c13>
{ "date": "2024-02-26T18:08:24", "dump": "CC-MAIN-2024-10", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474661.10/warc/CC-MAIN-20240226162136-20240226192136-00257.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9376052021980286, "score": 3.6875, "token_count": 761, "url": "http://cambjohnson.com/what-is-pancreatitis-types-symptoms-causes-treatment-48871833.html" }
Photograph showing a steam dredger manufactured by Lobnitz & Co at Renfrew, Scotland, at work in a harbour in Mexico. The growth in shipping trade in the second half of the 19th century, together with the increasing size of ships themselves, led to a considerable demand for dredgers to improve access to ports all over the world. Material is excavated from the seabed, then deposited on deck or in barges alongside the dredger, to be disposed of afterwards, often in deeper water elsewhere. Lobnitz & Co's shipyards on Clydeside were one of the foremost builders of dredgers. © Science Museum / Science & Society Picture Library
<urn:uuid:ba3ac2f4-911a-4c6c-8ac0-478ed3b6dfbc>
{ "date": "2017-05-25T12:53:52", "dump": "CC-MAIN-2017-22", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608067.23/warc/CC-MAIN-20170525121448-20170525141448-00053.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9313570261001587, "score": 3.71875, "token_count": 138, "url": "http://www.ssplprints.com/image/130215/the-dredger-the-chief-mexico-29-december-1919" }
Editor's Note: This story, originally published in the February 1992 issue of Scientific American, is being re-posted in light of Steven Chu's nomination as U.S. secretary of energy. Before you turn another page of this magazine, consider your actions carefully. Every time you wish to grasp a page, you must place one finger above the paper and another below so that the distance between each finger and the paper is about equal to the diameter of an atom. At that point, the electrons at the surface of your fingers repel the electrons on either side of the page. This slight redistribution of charges produces an electric field that is strong enough to allow you to squeeze the page between your fingers. Remarkably, by applying electric forces at the atomic scale, you can hold onto objects that are, on the whole, electrically neutral. In contrast, manipulating neutral objects that are atomic in size is a formidable technical challenge. Charged objects are much easier to control because electric and magnetic fields can exert much stronger forces over them. Indeed, for more than a century, scientists have applied electromagnetic forces to manipulate charged particles such as electrons and ions from a distance. But only in the past few years have researchers been able to move neutral particles at a distance with any facility. In particular, investigators have developed instruments that use lasers to trap and manipulate atoms and micron-size particles with astonishing control. These innovations have quickly led to a wide range of applications. My research group and others have cooled atoms to temperatures near absolute zero-conditions that allow us to examine quantum states of matter and unusual interactions between light and ultra-cold atoms. We have begun to develop atomic clocks and extremely sensitive accelerometers. Our techniques are being applied to handle such individual molecules as large polymers. In addition, we have devised an "optical tweezers" that uses laser beams to hold and move organelles inside of cells without puncturing the intervening membranes. Almost a decade before scientists learned how to control neutral particles at a distance with laser light, they achieved some of the same tasks using magnetic fields. They applied fields to focus atoms in beams and trap them. After learning how to trap atoms with laser light, they turned to the vast arsenal of laser techniques to gain precise control over neutral particles. The first trap for neutral particles was developed by Wolfgang Paul of the University of Bonn. In 1978 he and his colleagues succeeded in trapping neutrons in a magnetic field. Seven years later, using the same basic principles, William D. Phillips and his colleagues at the National Bureau of Standards were able to trap atoms. The magnetic trap can hold onto particles that have magnetic properties similar to those of a tiny bar magnet. To be more precise, the particle must carry a small magnetic dipole moment. If such a particle is placed in a magnetic field whose strength varies from region to region, it will move toward the weakest or strongest part of the field, depending on the particle's orientation [see illustration on next page]. Paul realized that it is possible to design a magnetic field with a local minimum in the field strength, and if the magnetic dipole is originally aligned to seek a position where the field is weakest, it will remain aligned in the "weak field-seeking" orientation [see "Cooling and Trapping Atoms," by W. D. Phillips and H. ]. Metcalf; SCIENTIFIC AMERICAN, March 1987]. Atoms can also be trapped by laser light. Light can exert forces on atoms and other neutral particles because it carries momentum. If an atom is bombarded with a beam of light of a particular frequency, it will continuously absorb and reemit photons, the quanta of light. As the atom absorbs photons, it will receive a barrage of momentum kicks in the direction that the light beam propagates. The kicks add up to produce a "scattering" force, which is proportional to the momentum of each photon and the number of photons that the atom scatters per second. Of course, for every photon the atom absorbs, it must emit one. But because the photons are released with no preferred direction, the changes in momentum caused by the emission average to zero. Absorption and emission have the net effect of pushing the atom in the direction that the light travels. The magnitude of this scattering force is quite low. If an atom absorbs a single photon, its change in velocity is tiny compared with the average velocity of atoms in a gas at room temperature. (The change is on the order of one centimeter per second, the crawling speed of an ant, whereas an atom at room temperature moves at the speed of a supersonic jet.) This scattering force was first detected in 1933 , when Otto R. Frisch used it to deflect a beam of sodium atoms. He prepared the atoms by vaporizing sodium in a container. To form the beam, he allowed the atoms to pass through a hole in the container and a series of slits. Once established, the beam was bombarded with light from a sodium lamp. Although, on average, each sodium atom absorbed only a single photon, Frisch was able to detect a slight deflection of the beam. The scattering force that Frisch generated was far too weak to capture atoms. Decades later workers realized that the photon-scattering rate could be increased to more than 10 million photons per second, corresponding to a force 100,000 times greater than the pull of gravity by the earth. The first dramatic demonstration of the scattering force on atoms was made by two separate groups led by Phillips and John L. Hall at the National Bureau of Standards. In 1985 they stopped a beam of atoms and reduced the temperature of the atoms from roughly 3 00 kelvins (room temperature) to 0. 1 kelvin. The power of the scattering force attainable with lasers gave researchers hope that they could not only stop atoms but trap them as well. But attempts to configure several laser beams so that they could collect and concentrate atoms in some region of space seemed doomed to failure. According to a principle known as the Optical Earnshaw Theorem, it is impossible to fashion a light trap out of any configuration of light beams if the scattering force is proportional to the light intensity. The problem is that the beams cannot be arranged to generate only inward directed forces. Any light that enters a trapping region must eventually escape and must therefore carry outward directed forces as well. Even if Luke Skywalker were a physicist, the (scattering) force would not always be with him. Fortunately, an atomic trap can be based on another kind of force that light can exert on atoms. To understand this force, it is instructive to consider how small particles can be attracted to a positively charged object, such as a glass rod rubbed with cat's fur. The rod produces an electric field that polarizes the particle. Consequently, the average position of positive charges in the particle will be slightly farther away from the rod than the average position of the negative charges. This asymmetric distribution of charge is said to have a dipole moment. The attractive dipole force exerted by the electric field on the negative charges of the particle is stronger than the repulsive force on the positive charges. As a result, the particle is pulled toward the regions where the electric field is strongest. Notice that this force is analogous to the magnetic dipole force first used to trap neutrons and atoms. If the charge on the rod were negative, the electric field would induce a dipole moment of reversed polarity, and the particle would still be attracted to regions of high electric field. Because of the dipole force, atoms can be trapped by an electric field that has a local maximum of some point in space. Could such fields be produced by some clever arrangement of electric charges? For any system of fixed charges, the answer is no. Yet an electric field with a local maximum can be achieved in a dynamic system. In particular, because light is made up of rapidly oscillating electric and magnetic fields, a focused laser beam can produce an alternating electric field with a local maximum. When the field interacts with an atom, it alters the distribution of electrons around the atom, thereby inducing an electric dipole moment. The atom will thus be attracted to the local maximum in the field, just as the charged particle was drawn toward the rod. The fact that the electric field changes rapidly does not present a problem. As the field changes polarity, the dipole moment of the atom also switches around. As long as the field changes at a rate slower than the natural oscillation frequencies of the atom, the dipole moment remains aligned with the field. The atom therefore continues to move toward the local maximum. As a result, this dipole force can be used to confine atoms. In 1968 Vladilen S. Letokhov first proposed that atoms could be trapped in a light beam using the dipole force, and 10 years later Arthur Ashkin of AT&T Bell Laboratories suggested a more practical trap based on focused laser beams. Although the dipole-force trap is elegant in conception, it had practical problems. To minimize the scattering force, the light must be tuned well below the frequency at which the atoms readily absorb photons. At those large de tunings , the trapping forces are so feeble that atoms as cold as 0.01 kelvin cannot be held in the trap. Even when colder atoms were placed in the trap, they would boil out of the trap in a matter of a few thousandths of a second as a result of the ever present photon scattering. In addition, the task of injecting atoms into the trap seemed daunting because the volume of the trap would only be 0.001 cubic millimeter. For these reasons, the challenges to optical trapping seemed formidable. Then, in 1985 , a scheme for a workable optical trap became apparent after atoms were laser cooled in all dimensions and to much lower temperatures than the stopped atomic beams. The laser-cooling idea was first proposed in 1975 by Theodor Hansch and Arthur Schawlow of Stanford University. In the same year, a similar scheme for cooling trapped ions with lasers was proposed by David J. Wineland and Hans G. Dehmelt of the University of Washington. The researchers predicted that an atom could be cooled if it is irradiated from two sides by laser light at a frequency slightly lower than the frequency needed for maximum absorption. If the atom moves in a direction oppo- sing one of the light beams, the light, from the atom's perspective, increases in frequency. The light that has been shifted up in frequency is then likely to be absorbed by the atom. The light that the atom absorbs exerts a scattering force that slows the atom down. How does the atom interact with the light traveling in the same direction? The atom is less likely to absorb the light because the light, again from the atom's perspective, has been shifted down in frequency. The net effect of both of the beams is that a scattering force is generated, opposing the motion of the atom. The beauty of this idea is that an atom mOving in the opposite direction will also experience a scattering force dragging it toward zero velocity. By surrounding the atom with three sets of counterpropagating beams along three mutually perpendicular axes, the atom can be cooled in all three dimensions. In 1985 Ashkin, Leo Hollberg, John E. Bjorkholm, Alex Cable and I at AT&T Bell Labs were able to cool sodium atoms to 240 millionths of a kelvin. Because the light field acts as a viscous force, we dubbed the combination of laser beams used to create the drag force "optical molasses." Although not a trap, the atoms were confined in the viscous medium for periods as long as 0.5 second, until eventually they would leak out of the cooling beams. Optical molasses enabled us to solve the three major problems that stood in the way of constructing a laser trap. First, by cooling the atoms to extremely low temperatures, we could reduce the random thermal motions of the atoms, making them easy to trap. Second, we could easily load the atoms into the trap. Simply by focusing the trapping beam in the center of the optical molasses, atoms would be snagged as they randomly wandered into the trapping beam. Third, by alternating between trapping and cooling light, we could reduce the heating effects of the trapping light. A year after we had perfected optical molasses, atoms could finally be trapped with light. Even with the loading technique used in our first trap, an optical trap with a larger capture volume was desirable. A trap that could use the scattering force would need much less light intensity, which meant the constraints imposed by the Optical Earnshaw Theorem had to be circumvented. The important clue of how to design such a trap came from David E. Pritchard of the Massachusetts Institute of Technology and Carl E. Wieman of the University of Colorado and their colleagues. They pointed out that if magnetic or electric fields that varied over space were applied to atoms, the scattering force caused by the laser light would not necessarily be proportional to the light intensity. This suggestion led Jean Dalibard of the Ecole Normale Superieure in Paris to propose a "magneto-optic" trap, which used a weak magnetic field and circularly polarized light. In 1987 Pritchard's group and my own at AT&T collaborated to construct such a trap. Three years later Wieman's team went on to show that this technique could be used to trap atoms in a glass cell, using inexpensive diode lasers. Their method eliminated the precooling procedures needed in our first trapping experiments. The fact that atoms could be trapped in a sealed cell also meant rare species of atoms, such as radioactive isotopes, could be optically manipulated. The magneto-optic trap has become the most widely used optical trap today. Meanwhile researchers were making rapid progress in laser cooling. Phillips and his colleagues discovered that under certain conditions, optical molasses could be used to cool atoms to temperatures far below the lower limit predicted by the existing theory. This discovery prompted Dalibard and Claude Cohen-Tannoudji of the College de France and the Ecole Normale and my group at Stanford to construct a new theory of laser cooling based on a complex but beautiful interplay between the atoms and their interaction with the light fields. Currently atoms can be cooled to a temperature with an average velocity equal to three and a half photon recoils. For cesium atoms, it means a temperature lower than three microkelvins. Going beyond optical molasses, Cohen- Tannoudji, Alain Aspect, Ennio Arimondo, Robin Kaiser and Nathalie Vansteenkiste, then all at the Ecole Normale, invented an ingenious scheme capable of cooling helium atoms below the recoil velocity of a single scattered photon. Helium atoms have been cooled to two microkelvins along one dimension, and work is under way to extend this technique to two and three dimensions. This cooling method captures an atom in a well-defined velocity state in much the same way atoms were trapped in space in our first optical trap. As the atom scatters photons, its velocity randomly changes. The French experiment establishes conditions that allow an atom to recoil and land in a particular quantum state, which is a combination of two states with two distinct velocities close to zero. Once in this state, the chance of scattering more photons is greatly reduced, meaning that additional photons cannot scatter and increase the velocity. If the atom does not happen to land in this quantum state, it continues to scatter photons and has more opportunities to seek out the desired low-velocity state. Thus, the atoms are cooled by letting them randomly walk into a "velocity trapped" quantum state. Besides the cooling and trapping of atoms, investigators have demonstrated various atomic lenses, mirrors and diffraction gratings for manipulating atoms. They have also fashioned devices that have no counterpart in light optics. Researchers at Stanford and the University of Bonn have made "atomic funnels" that transform a collection of hot atoms into a well-controlled stream of cold atoms. The Stanford group has also made an "atomic trampoline" in which atoms bounce off a sheet of light extending out from a glass surface. With a curved glass surface, an atom trap based on gravity and light can be made. Clearly, we have learned to push atoms around with amazing facility, but what do all these tricks enable us to do? With very cold atoms in vapor form, physicists are in a position to study how the atoms interact with one another at extremely low temperatures. According to quantum theory, an atom behaves like a wave whose length is equal to Planck's constant divided by the particle's momentum. As the atom is cooled, its momentum decreases, thereby increasing its wavelength. At sl\fficiently low temperatures, the average wavelength becomes comparable to the average distance between the atoms. At these low temperatures and high densities, quantum theory says that a significant fraction of all the atoms will condense into a single quantum ground state. This unusual form of matter, called a Bose-Einstein condensation, has been predicted but never observed in a vapor of atoms. Thomas]. Greytak and Daniel Kleppner of M.LT. and look T. M. Walraven of the University of Amsterdam are trying to achieve such a condensation with a collection of hydrogen atoms in a magnetic trap. Meanwhile other groups are attempting the same feat in a laser-cooled sample of alkali atoms such as cesium or lithium. Atom-manipulation techniques are also offering new opportunities in highresolution spectroscopy. By combining several such techniques, the Stanford group has created a device that will allow the spectral features of atoms to be measured with exquisite accuracy. We have devised an atomic fountain that launches ultra-cold atoms upward gently enough to have gravity turn them around. Atoms for the fountain are collected by a magneto-optic trap for 0. 5 second. After that amount of time, about 10 million atoms are launched upward at a velocity of roughly two meters per second. At the top of the trajectory, an atom is probed with two pulses of microwave radiation separated in time. If the frequency of the radiation is properly tuned, the two pulses cause the atom to change from one quantum state to another. (Norman Ramsey shared the Nobel Prize in Physics in 1989 for inventing and applying this technique.) In our first experiment we measured the energy difference between two states of an atom with a resolution of two parts in 100 billion. How does the fountain make such precise measurements possible? First, the atoms fall freely and are easy to shield from any perturbation that might alter their energy levels. Second, such measurements are limited in precision by the Heisenberg uncertainty prinCiple. This principle states that the resolution of an energy measurement will be limited to Planck's constant divided by the time of the "measurement." In our case, this time corresponds to the time between the two microwave pulses. With an atomic fountain the measurement time for unperturbed atoms can be as long as one second, a period impossible with atoms at room temperature. Because the atomic fountain allows extremely precise measurements of the energy levels of atoms, it may be possible to adapt the device to make an improved atomic clock. At present, the world time standard is defined by the energy difference between two particular energy levels in ground states of the cesium atom. Two years after the first atomic fountain, the group at the Ecole Normale used a fountain to measure the "clock transition" in the cesium atom with high precision. These two experiments suggested that a properly engineered instrument might be able to measure the absolute frequency of this transition to one part in 10^16, 1,000 times better than the accuracy of our best clocks. Lured by this potential, more than eight groups around the world are now trying to improve the cesium time standard with an atomic fountain. Another application being intensively studied is atom interferometry. The first atom interferometers were built in 1991 by investigators at the University of Konstanz, M.LT., the Physikalisch-Technische Bundesanstalt and Stanford. An atom interferometer splits an atom into two waves separated in space. The two parts of the atom are then recombined and allowed to interfere with each other. The simplest example of such a splitting occurs when the atom is made to go through two separated mechanical slits. If the atom is recombined after passing through the slits, wavelike interference fringes can be observed. The interference effects from atoms dramatically demonstrate the fact that their behavior needs both a wave and a particle description. More important, atom interferometers offer the possibility of measuring physical phenomena with high sensitivity. In the first demonstration of the potential sensitivity, Mark Kasevich and I have created an interferometer that uses slow atoms. The atoms were split apart and recombined in a fountain. With this instrument we have already shown that the acceleration of gravity can be measured with a resolution of at least three parts in 100 million, and we expect another 100-fold improvement shortly. Previously, the effects of gravity on an atom have been measured at a level of roughly one part in 100. In recent years the work on atom trapping has stimulated renewed interest in manipulating other neutral particles. The basic principles of atom trapping can be applied to micron-size particles, such as polystyrene spheres. The intense electric field at the center of a focused laser beam polarizes the particle, just as it would polarize an atom. The particle, like an atom, will also absorb light of certain frequencies. Glass, for example, strongly absorbs ultraviolet radiation. But as long as the light is tuned below absorption frequency, the particle will be drawn into the region of highest laser intensity. In 1986 Ashkin, Bjorkholm, ]. B. Dziedzic and I showed that particles that range in size between 0.02 and 10 microns can be trapped in a single focused laser beam. In 1970 Ashkin trapped micron-size latex spheres suspended in water in between two fo- cused, counterpropagating beams of light [see "The Pressure of Laser Light," by Arthur Ashkin; SCIENTIFIC AMERICAN, February 1972]. But only much later was it realized that if a single beam is focused tightly enough, the dipole force would suffice to overcome the scattering force that pushes the particle in the direction that the laser beam is traveling. The great advantage of using a single beam is that it can be used as an optical tweezers to manipulate small particles. The optical tweezers can easily be integrated with a conventional microscope by introducing the laser light into the body of the scope and focusing it with the viewing objective. A sample placed on an ordinary microscope slide can be viewed and manipulated at the same time by moving the focused laser beam. One application of the optical tweezers, discovered by Dziedzic and Ashkin, has captured the imagination of biologists. They found that the tweezers can handle live bacteria and other organisms without apparent damage. The ability to trap live organisms without harm is surprising, considering that the typical laser intensity at the focal point of the optical tweezers is about 10 million watts per square centimeter. It turns out that as long as the organism is very nearly transparent at the frequency of the trapping light, it can be cooled effectively by the surrounding water. To be sure, if the laser intensity is too high, the creature can be "optocuted." Many applications have been found for the optical tweezers. Ashkin showed that objects within a living cell can be manipulated without puncturing the cell wall. Steven M. Block and his colleagues at the Rowland Institute in Cambridge, Mass., and at Harvard University have studied the mechanical properties of bacterial flagella. Michael W. Berns and his co-workers at the University of California at Irvine have manipulated chromosomes inside a cell nucleus. Optical tweezers can be used to examine even smaller biological systems. My colleagues Robert Simmons, Jeff Finer, James A. Spudich and I are applying the optical tweezers to study muscle contraction at the molecular level. Related studies are being carried out by Block and also by Michael P. Sheetz of Duke University. One of the goals of this work is to measure the force generated by a single myosin molecule pulling against an actin filament. We are probing this "molecular motor" by attaching a polystyrene sphere to an actin filament and using the optical tweezers to grab onto the bead. When the myosin head strokes against the actin filament, the motion is sensed by a photodiode at the viewing end of the microscope. A feedback circuit then directs the optical tweezers to pull against the myosin in order to counteract any motion. In this way, we have measured the strength of the myosin pull under tension. On an even smaller scale, Spudich, Steve Kron, Elizabeth Sunderman, Steve Quake and I are manipulating a single DNA molecule by attaching polystyrene spheres to the ends of a strand of DNA and holding the spheres with two optical tweezers. We can observe the molecule as we pull on it by staining the DNA vvith dye molecules, illuminating the dye with green light from an argon laser and detecting the fluorescence with a sensitive video camera. In our first experiments we measured the elastic properties of DNA. The two ends were pulled apart until the molecule was stretched out straight to its full length, and then one of the ends was released. By studying how the molecule springs back, we can test basic theories of polymer physics far from the equilibrium state. The tweezers can also be used to prepare a single molecule for other ex- periments. By impaling the beads onto the microscope slide and increasing the laser power, we found that the bead can be "spot-welded" to the slide, leaving the DNA in a stretched state. That technique might be useful in preparing long strands of DNA for examination with state-of-the-art microscopes. Ultimately, we hope to use these manipulation abilities to examine the motion of enzymes along the DNA and to address questions related to gene expression and repair. It has only been six years since workers have stopped atoms, captured them in optical molasses and made the first atom traps. Optical traps, to paraphrase a popular advertising slogan, have enabled us to "reach out and touch" particles in powerful new ways. We have shown that if we can "see" an atom or microscopic particle, we may be able to hold onto it regardless of intervening membranes. It has been a personal joy to see how esoteric conjectures in atomic physics have blossomed: the techniques and applications of laser cooling and trapping have gone well beyond our dreams during those early days. We now have important new tools for physics, chemistry and biology.
<urn:uuid:2858f46b-62f5-4042-b8cb-532fd6f4b53b>
{ "date": "2014-07-31T14:48:57", "dump": "CC-MAIN-2014-23", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510273350.41/warc/CC-MAIN-20140728011753-00396-ip-10-146-231-18.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9418559670448303, "score": 3.671875, "token_count": 5522, "url": "http://www.scientificamerican.com/article/steven-chu-laser-trapping-of-neutral/" }
# 721 dry gallons in centiliters ## Conversion 721 dry gallons is equivalent to 317592.119879006 centiliters.[1] ## Conversion formula How to convert 721 dry gallons to centiliters? We know (by definition) that: $1\mathrm{drygallon}\approx 440.488377086\mathrm{centiliter}$ We can set up a proportion to solve for the number of centiliters. $1 ⁢ drygallon 721 ⁢ drygallon ≈ 440.488377086 ⁢ centiliter x ⁢ centiliter$ Now, we cross multiply to solve for our unknown $x$: $x\mathrm{centiliter}\approx \frac{721\mathrm{drygallon}}{1\mathrm{drygallon}}*440.488377086\mathrm{centiliter}\to x\mathrm{centiliter}\approx 317592.119879006\mathrm{centiliter}$ Conclusion: $721 ⁢ drygallon ≈ 317592.119879006 ⁢ centiliter$ ## Conversion in the opposite direction The inverse of the conversion factor is that 1 centiliter is equal to 3.14869273324846e-06 times 721 dry gallons. It can also be expressed as: 721 dry gallons is equal to $\frac{1}{\mathrm{3.14869273324846e-06}}$ centiliters. ## Approximation An approximate numerical result would be: seven hundred and twenty-one dry gallons is about three hundred and seventeen thousand, five hundred and ninety-two point one one centiliters, or alternatively, a centiliter is about zero times seven hundred and twenty-one dry gallons. ## Footnotes [1] The precision is 15 significant digits (fourteen digits to the right of the decimal point). Results may contain small errors due to the use of floating point arithmetic.
crawl-data/CC-MAIN-2022-27/segments/1656104669950.91/warc/CC-MAIN-20220706090857-20220706120857-00382.warc.gz
null
posted by lollzzz . In order to make sure that their bags of chips are of sufficient weight, the Chipper Chip Company try to fill their 200 gram bags of chips with more than 203 grams. You have been given the task of investigating what proportion of bags produced do have over 203 grams of chips in them. You sample 112 bags and find that the proportion of these with over 203 grams is 0.77. You decide to construct a 95% confidence interval for the population proportion of chip bags that have more than 203 grams of chips. a)Calculate the lower bound for this confidence interval. Give your answer as a decimal to 3 decimal places. Lower bound for confidence interval = b)Calculate the upper bound for this confidence interval. Give your answer as a decimal to 3 decimal places. Upper bound for confidence interval = A quality inspector proposes that the true proportion of chip bags with over 203 grams of chips is 0.742. c)With a level of confidence of 95%, can/ cannot you rule out this possibility.
<urn:uuid:807eb138-cfee-456c-a487-7f4ebb865a98>
{ "date": "2017-06-25T03:51:53", "dump": "CC-MAIN-2017-26", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320395.62/warc/CC-MAIN-20170625032210-20170625052210-00297.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9252240061759949, "score": 3.53125, "token_count": 220, "url": "http://www.jiskha.com/display.cgi?id=1288495660" }
# Limit of a sequence Short description: Value to which tends an infinite sequence The sequence given by the perimeters of regular n-sided polygons that circumscribe the unit circle has a limit equal to the perimeter of the circle, i.e. $\displaystyle{ 2\pi r }$. The corresponding sequence for inscribed polygons has the same limit. $\displaystyle{ n }$ $\displaystyle{ n\times \sin\left(\tfrac1{n}\right) }$ 1 0.841471 2 0.958851 ... 10 0.998334 ... 100 0.999983 As the positive integer $\displaystyle{ n }$ becomes larger and larger, the value $\displaystyle{ n\times \sin\left(\tfrac1{n}\right) }$ becomes arbitrarily close to $\displaystyle{ 1 }$. We say that "the limit of the sequence $\displaystyle{ n \times \sin\left(\tfrac1{n}\right) }$ equals $\displaystyle{ 1 }$." In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the $\displaystyle{ \lim }$ symbol (e.g., $\displaystyle{ \lim_{n \to \infty}a_n }$).[1] If such a limit exists, the sequence is called convergent.[2] A sequence that does not converge is said to be divergent.[3] The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.[1] Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers. ## History The Greek philosopher Zeno of Elea is famous for formulating paradoxes that involve limiting processes. Leucippus, Democritus, Antiphon, Eudoxus, and Archimedes developed the method of exhaustion, which uses an infinite sequence of approximations to determine an area or a volume. Archimedes succeeded in summing what is now called a geometric series. Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work Opus Geometricum (1647): "The terminus of a progression is the end of the series, which none progression can reach, even not if she is continued in infinity, but which she can approach nearer than a given segment."[4] Newton dealt with series in his works on Analysis with infinite series (written in 1669, circulated in manuscript, published in 1711), Method of fluxions and infinite series (written in 1671, published in English translation in 1736, Latin original published much later) and Tractatus de Quadratura Curvarum (written in 1693, published in 1704 as an Appendix to his Optiks). In the latter work, Newton considers the binomial expansion of $\displaystyle{ (x+o)^n }$, which he then linearizes by taking the limit as $\displaystyle{ o }$ tends to $\displaystyle{ 0 }$. In the 18th century, mathematicians such as Euler succeeded in summing some divergent series by stopping at the right moment; they did not much care whether a limit existed, as long as it could be calculated. At the end of the century, Lagrange in his Théorie des fonctions analytiques (1797) opined that the lack of rigour precluded further development in calculus. Gauss in his etude of hypergeometric series (1813) for the first time rigorously investigated the conditions under which a series converged to a limit. The modern definition of a limit (for any $\displaystyle{ \varepsilon }$ there exists an index $\displaystyle{ N }$ so that ...) was given by Bernard Bolzano (Der binomische Lehrsatz, Prague 1816, which was little noticed at the time), and by Karl Weierstrass in the 1870s. ## Real numbers The plot of a convergent sequence {an} is shown in blue. Here, one can see that the sequence is converging to the limit 0 as n increases. In the real numbers, a number $\displaystyle{ L }$ is the limit of the sequence $\displaystyle{ (x_n) }$, if the numbers in the sequence become closer and closer to $\displaystyle{ L }$, and not to any other number. ### Examples • If $\displaystyle{ x_n = c }$ for constant $\displaystyle{ c }$, then $\displaystyle{ x_n \to c }$.[proof 1][5] • If $\displaystyle{ x_n = \frac{1}{n} }$, then $\displaystyle{ x_n \to 0 }$.[proof 2][5] • If $\displaystyle{ x_n = \frac{1}{n} }$ when $\displaystyle{ n }$ is even, and $\displaystyle{ x_n = \frac{1}{n^2} }$ when $\displaystyle{ n }$ is odd, then $\displaystyle{ x_n \to 0 }$. (The fact that $\displaystyle{ x_{n+1} \gt x_n }$ whenever $\displaystyle{ n }$ is odd is irrelevant.) • Given any real number, one may easily construct a sequence that converges to that number by taking decimal approximations. For example, the sequence $\displaystyle{ 0.3, 0.33, 0.333, 0.3333, \dots }$ converges to $\displaystyle{ \frac{1}{3} }$. Note that the decimal representation $\displaystyle{ 0.3333\dots }$ is the limit of the previous sequence, defined by $\displaystyle{ 0.3333... : = \lim_{n\to\infty} \sum_{k=1}^n \frac{3}{10^k} }$ • Finding the limit of a sequence is not always obvious. Two examples are $\displaystyle{ \lim_{n\to\infty} \left(1 + \tfrac{1}{n}\right)^n }$ (the limit of which is the number e) and the arithmetic–geometric mean. The squeeze theorem is often useful in the establishment of such limits. ### Definition We call $\displaystyle{ x }$ the limit of the sequence $\displaystyle{ (x_n) }$, which is written $\displaystyle{ x_n \to x }$, or $\displaystyle{ \lim_{n\to\infty} x_n = x }$, if the following condition holds: For each real number $\displaystyle{ \varepsilon \gt 0 }$, there exists a natural number $\displaystyle{ N }$ such that, for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ |x_n - x| \lt \varepsilon }$.[6] In other words, for every measure of closeness $\displaystyle{ \varepsilon }$, the sequence's terms are eventually that close to the limit. The sequence $\displaystyle{ (x_n) }$ is said to converge to or tend to the limit $\displaystyle{ x }$. Symbolically, this is: $\displaystyle{ \forall \varepsilon \gt 0 \left(\exists N \in \N \left(\forall n \in \N \left(n \geq N \implies |x_n - x| \lt \varepsilon \right)\right)\right) }$. If a sequence $\displaystyle{ (x_n) }$ converges to some limit $\displaystyle{ x }$, then it is convergent and $\displaystyle{ x }$ is the only limit; otherwise $\displaystyle{ (x_n) }$ is divergent. A sequence that has zero as its limit is sometimes called a null sequence. ### Properties Some other important properties of limits of real sequences include the following: • When it exists, the limit of a sequence is unique.[5] • Limits of sequences behave well with respect to the usual arithmetic operations. If $\displaystyle{ \lim_{n\to\infty} a_n }$ and $\displaystyle{ \lim_{n\to\infty} b_n }$ exists, then $\displaystyle{ \lim_{n\to\infty} (a_n \pm b_n) = \lim_{n\to\infty} a_n \pm \lim_{n\to\infty} b_n }$[5] $\displaystyle{ \lim_{n\to\infty} c a_n = c \cdot \lim_{n\to\infty} a_n }$[5] $\displaystyle{ \lim_{n\to\infty} (a_n \cdot b_n) = \left(\lim_{n\to\infty} a_n \right)\cdot \left( \lim_{n\to\infty} b_n \right) }$[5] $\displaystyle{ \lim_{n\to\infty} \left(\frac{a_n}{b_n}\right) = \frac{\lim\limits_{n\to\infty} a_n}{\lim\limits_{n\to\infty} b_n} }$ provided $\displaystyle{ \lim_{n\to\infty} b_n \ne 0 }$[5] $\displaystyle{ \lim_{n\to\infty} a_n^p = \left( \lim_{n\to\infty} a_n \right)^p }$ • For any continuous function $\displaystyle{ f }$, if $\displaystyle{ \lim_{n\to\infty}x_n }$ exists, then $\displaystyle{ \lim_{n\to\infty} f \left(x_n \right) }$ exists too. In fact, any real-valued function $\displaystyle{ f }$ is continuous if and only if it preserves the limits of sequences (though this is not necessarily true when using more general notions of continuity). • If $\displaystyle{ a_n \leq b_n }$ for all $\displaystyle{ n }$ greater than some $\displaystyle{ N }$, then $\displaystyle{ \lim_{n\to\infty} a_n \leq \lim_{n\to\infty} b_n }$. • (Squeeze theorem) If $\displaystyle{ a_n \leq c_n \leq b_n }$ for all $\displaystyle{ n }$ greater than some $\displaystyle{ N }$, and $\displaystyle{ \lim_{n\to\infty} a_n = \lim_{n\to\infty} b_n = L }$, then $\displaystyle{ \lim_{n\to\infty} c_n = L }$. • (Monotone convergence theorem) If $\displaystyle{ a_n }$ is bounded and monotonic for all $\displaystyle{ n }$ greater than some $\displaystyle{ N }$, then it is convergent. • A sequence is convergent if and only if every subsequence is convergent. • If every subsequence of a sequence has its own subsequence which converges to the same point, then the original sequence converges to that point. These properties are extensively used to prove limits, without the need to directly use the cumbersome formal definition. For example, once it is proven that $\displaystyle{ 1/n \to 0 }$, it becomes easy to show—using the properties above—that $\displaystyle{ \frac{a}{b+\frac{c}{n}} \to \frac{a}{b} }$ (assuming that $\displaystyle{ b \ne 0 }$). ### Infinite limits A sequence $\displaystyle{ (x_n) }$ is said to tend to infinity, written $\displaystyle{ x_n \to \infty }$, or $\displaystyle{ \lim_{n\to\infty}x_n = \infty }$, if the following holds: For every real number $\displaystyle{ K }$, there is a natural number $\displaystyle{ N }$ such that for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ x_n \gt K }$; that is, the sequence terms are eventually larger than any fixed $\displaystyle{ K }$. Symbolically, this is: $\displaystyle{ \forall K \in \mathbb{R} \left(\exists N \in \N \left(\forall n \in \N \left(n \geq N \implies x_n \gt K \right)\right)\right) }$. Similarly, we say a sequence tends to minus infinity, written $\displaystyle{ x_n \to -\infty }$, or $\displaystyle{ \lim_{n\to\infty}x_n = -\infty }$, if the following holds: For every real number $\displaystyle{ K }$, there is a natural number $\displaystyle{ N }$ such that for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ x_n \lt K }$; that is, the sequence terms are eventually smaller than any fixed $\displaystyle{ K }$. Symbolically, this is: $\displaystyle{ \forall K \in \mathbb{R} \left(\exists N \in \N \left(\forall n \in \N \left(n \geq N \implies x_n \lt K \right)\right)\right) }$. If a sequence tends to infinity or minus infinity, then it is divergent. However, a divergent sequence need not tend to plus or minus infinity, and the sequence $\displaystyle{ x_n=(-1)^n }$ provides one such example. ## Metric spaces ### Definition A point $\displaystyle{ x }$ of the metric space $\displaystyle{ (X, d) }$ is the limit of the sequence $\displaystyle{ (x_n) }$ if: For each real number $\displaystyle{ \varepsilon \gt 0 }$, there is a natural number $\displaystyle{ N }$ such that, for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ d(x_n, x) \lt \varepsilon }$. Symbolically, this is: $\displaystyle{ \forall \varepsilon \gt 0 \left(\exists N \in \N \left(\forall n \in \N \left(n \geq N \implies d(x_n, x) \lt \varepsilon \right)\right)\right) }$. This coincides with the definition given for real numbers when $\displaystyle{ X = \R }$ and $\displaystyle{ d(x, y) = |x-y| }$. ### Properties • When it exists, the limit of a sequence is unique, as distinct points are separated by some positive distance, so for $\displaystyle{ \varepsilon }$ less than half this distance, sequence terms cannot be within a distance $\displaystyle{ \varepsilon }$ of both points. • For any continuous function f, if $\displaystyle{ \lim_{n \to \infty} x_n }$ exists, then $\displaystyle{ \lim_{n \to \infty} f(x_n) = f\left(\lim_{n \to \infty}x_n \right) }$. In fact, a function f is continuous if and only if it preserves the limits of sequences. ### Cauchy sequences Main page: Cauchy sequence The plot of a Cauchy sequence (xn), shown in blue, as $\displaystyle{ x_n }$ versus n. Visually, we see that the sequence appears to be converging to a limit point as the terms in the sequence become closer together as n increases. In the real numbers every Cauchy sequence converges to some limit. A Cauchy sequence is a sequence whose terms ultimately become arbitrarily close together, after sufficiently many initial terms have been discarded. The notion of a Cauchy sequence is important in the study of sequences in metric spaces, and, in particular, in real analysis. One particularly important result in real analysis is the Cauchy criterion for convergence of sequences: a sequence of real numbers is convergent if and only if it is a Cauchy sequence. This remains true in other complete metric spaces. ## Topological spaces ### Definition A point $\displaystyle{ x \in X }$ of the topological space $\displaystyle{ (X, \tau) }$ is a limit or limit point[7][8] of the sequence $\displaystyle{ \left(x_n\right)_{n \in \N} }$ if: For every neighbourhood $\displaystyle{ U }$ of $\displaystyle{ x }$, there exists some $\displaystyle{ N \in \N }$ such that for every $\displaystyle{ n \geq N }$, we have $\displaystyle{ x_n \in U }$.[9] This coincides with the definition given for metric spaces, if $\displaystyle{ (X, d) }$ is a metric space and $\displaystyle{ \tau }$ is the topology generated by $\displaystyle{ d }$. A limit of a sequence of points $\displaystyle{ \left(x_n\right)_{n \in \N} }$ in a topological space $\displaystyle{ T }$ is a special case of a limit of a function: the domain is $\displaystyle{ \N }$ in the space $\displaystyle{ \N \cup \lbrace + \infty \rbrace }$, with the induced topology of the affinely extended real number system, the range is $\displaystyle{ T }$, and the function argument $\displaystyle{ n }$ tends to $\displaystyle{ +\infty }$, which in this space is a limit point of $\displaystyle{ \N }$. ### Properties In a Hausdorff space, limits of sequences are unique whenever they exist. Note that this need not be the case in non-Hausdorff spaces; in particular, if two points $\displaystyle{ x }$ and $\displaystyle{ y }$ are topologically indistinguishable, then any sequence that converges to $\displaystyle{ x }$ must converge to $\displaystyle{ y }$ and vice versa. ## Hyperreal numbers The definition of the limit using the hyperreal numbers formalizes the intuition that for a "very large" value of the index, the corresponding term is "very close" to the limit. More precisely, a real sequence $\displaystyle{ (x_n) }$ tends to L if for every infinite hypernatural $\displaystyle{ H }$, the term $\displaystyle{ x_H }$ is infinitely close to $\displaystyle{ L }$ (i.e., the difference $\displaystyle{ x_H - L }$ is infinitesimal). Equivalently, L is the standard part of $\displaystyle{ x_H }$: $\displaystyle{ L = {\rm st}(x_H) }$. Thus, the limit can be defined by the formula $\displaystyle{ \lim_{n \to \infty} x_n= {\rm st}(x_H) }$. where the limit exists if and only if the righthand side is independent of the choice of an infinite $\displaystyle{ H }$. ## Sequence of more than one index Sometimes one may also consider a sequence with more than one index, for example, a double sequence $\displaystyle{ (x_{n, m}) }$. This sequence has a limit $\displaystyle{ L }$ if it becomes closer and closer to $\displaystyle{ L }$ when both n and m becomes very large. ### Example • If $\displaystyle{ x_{n, m} = c }$ for constant $\displaystyle{ c }$, then $\displaystyle{ x_{n,m} \to c }$. • If $\displaystyle{ x_{n, m} = \frac{1}{n + m} }$, then $\displaystyle{ x_{n, m} \to 0 }$. • If $\displaystyle{ x_{n, m} = \frac{n}{n + m} }$, then the limit does not exist. Depending on the relative "growing speed" of $\displaystyle{ n }$ and $\displaystyle{ m }$, this sequence can get closer to any value between $\displaystyle{ 0 }$ and $\displaystyle{ 1 }$. ### Definition We call $\displaystyle{ x }$ the double limit of the sequence $\displaystyle{ (x_{n, m}) }$, written $\displaystyle{ x_{n, m} \to x }$, or $\displaystyle{ \lim_{\begin{smallmatrix} n \to \infty \\ m \to \infty \end{smallmatrix}} x_{n, m} = x }$, if the following condition holds: For each real number $\displaystyle{ \varepsilon \gt 0 }$, there exists a natural number $\displaystyle{ N }$ such that, for every pair of natural numbers $\displaystyle{ n, m \geq N }$, we have $\displaystyle{ |x_{n, m} - x| \lt \varepsilon }$.[10] In other words, for every measure of closeness $\displaystyle{ \varepsilon }$, the sequence's terms are eventually that close to the limit. The sequence $\displaystyle{ (x_{n, m}) }$ is said to converge to or tend to the limit $\displaystyle{ x }$. Symbolically, this is: $\displaystyle{ \forall \varepsilon \gt 0 \left(\exists N \in \N \left(\forall n, m \in \N \left(n, m \geq N \implies |x_{n, m} - x| \lt \varepsilon \right)\right)\right) }$. Note that the double limit is different from taking limit in n first, and then in m. The latter is known as iterated limit. Given that both the double limit and the iterated limit exists, they have the same value. However, it is possible that one of them exist but the other does not. ### Infinite limits A sequence $\displaystyle{ (x_{n,m}) }$ is said to tend to infinity, written $\displaystyle{ x_{n,m} \to \infty }$, or $\displaystyle{ \lim_{\begin{smallmatrix} n \to \infty \\ m \to \infty \end{smallmatrix}}x_{n,m} = \infty }$, if the following holds: For every real number $\displaystyle{ K }$, there is a natural number $\displaystyle{ N }$ such that for every pair of natural numbers $\displaystyle{ n,m \geq N }$, we have $\displaystyle{ x_{n,m} \gt K }$; that is, the sequence terms are eventually larger than any fixed $\displaystyle{ K }$. Symbolically, this is: $\displaystyle{ \forall K \in \mathbb{R} \left(\exists N \in \N \left(\forall n, m \in \N \left(n, m \geq N \implies x_{n, m} \gt K \right)\right)\right) }$. Similarly, a sequence $\displaystyle{ (x_{n,m}) }$ tends to minus infinity, written $\displaystyle{ x_{n,m} \to -\infty }$, or $\displaystyle{ \lim_{\begin{smallmatrix} n \to \infty \\ m \to \infty \end{smallmatrix}}x_{n,m} = -\infty }$, if the following holds: For every real number $\displaystyle{ K }$, there is a natural number $\displaystyle{ N }$ such that for every pair of natural numbers $\displaystyle{ n,m \geq N }$, we have $\displaystyle{ x_{n,m} \lt K }$; that is, the sequence terms are eventually smaller than any fixed $\displaystyle{ K }$. Symbolically, this is: $\displaystyle{ \forall K \in \mathbb{R} \left(\exists N \in \N \left(\forall n, m \in \N \left(n, m \geq N \implies x_{n, m} \lt K \right)\right)\right) }$. If a sequence tends to infinity or minus infinity, then it is divergent. However, a divergent sequence need not tend to plus or minus infinity, and the sequence $\displaystyle{ x_{n,m}=(-1)^{n+m} }$ provides one such example. ### Pointwise limits and uniform limits For a double sequence $\displaystyle{ (x_{n,m}) }$, we may take limit in one of the indices, say, $\displaystyle{ n \to \infty }$, to obtain a single sequence $\displaystyle{ (y_m) }$. In fact, there are two possible meanings when taking this limit. The first one is called pointwise limit, denoted $\displaystyle{ x_{n, m} \to y_m\quad \text{pointwise} }$, or $\displaystyle{ \lim_{n \to \infty} x_{n, m} = y_m\quad \text{pointwise} }$, which means: For each real number $\displaystyle{ \varepsilon \gt 0 }$ and each fixed natural number $\displaystyle{ m }$, there exists a natural number $\displaystyle{ N(\varepsilon, m) \gt 0 }$ such that, for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ |x_{n, m} - y_m| \lt \varepsilon }$.[11] Symbolically, this is: $\displaystyle{ \forall \varepsilon \gt 0 \left( \forall m \in \mathbb{N} \left(\exists N \in \N \left(\forall n \in \N \left(n \geq N \implies |x_{n, m} - y_m| \lt \varepsilon \right)\right)\right)\right) }$. When such a limit exists, we say the sequence $\displaystyle{ (x_{n, m}) }$ converges pointwise to $\displaystyle{ (y_m) }$. The second one is called uniform limit, denoted $\displaystyle{ x_{n, m} \to y_m \quad \text{uniformly} }$, $\displaystyle{ \lim_{n \to \infty} x_{n, m} = y_m \quad \text{uniformly} }$, $\displaystyle{ x_{n, m} \rightrightarrows y_m }$, or $\displaystyle{ \underset{n\to\infty}{\mathrm{unif} \lim} \; x_{n, m} = y_m }$, which means: For each real number $\displaystyle{ \varepsilon \gt 0 }$, there exists a natural number $\displaystyle{ N(\varepsilon) \gt 0 }$ such that, for every natural number $\displaystyle{ m }$ and for every natural number $\displaystyle{ n \geq N }$, we have $\displaystyle{ |x_{n, m} - y_m| \lt \varepsilon }$.[11] Symbolically, this is: $\displaystyle{ \forall \varepsilon \gt 0 \left(\exists N \in \N \left( \forall m \in \mathbb{N} \left(\forall n \in \N \left(n \geq N \implies |x_{n, m} - y_m| \lt \varepsilon \right)\right)\right)\right) }$. In this definition, the choice of $\displaystyle{ N }$ is independent of $\displaystyle{ m }$. In other words, the choice of $\displaystyle{ N }$ is uniformly applicable to all natural numbers $\displaystyle{ m }$. Hence, one can easily see that uniform convergence is a stronger property than pointwise convergence: the existence of uniform limit implies the existence and equality of pointwise limit: If $\displaystyle{ x_{n, m} \to y_m }$ uniformly, then $\displaystyle{ x_{n, m} \to y_m }$ pointwise. When such a limit exists, we say the sequence $\displaystyle{ (x_{n, m}) }$ converges uniformly to $\displaystyle{ (y_m) }$. ### Iterated limit For a double sequence $\displaystyle{ (x_{n,m}) }$, we may take limit in one of the indices, say, $\displaystyle{ n \to \infty }$, to obtain a single sequence $\displaystyle{ (y_m) }$, and then take limit in the other index, namely $\displaystyle{ m \to \infty }$, to get a number $\displaystyle{ y }$. Symbolically, $\displaystyle{ \lim_{m \to \infty} \lim_{n \to \infty} x_{n, m} = \lim_{m \to \infty} y_m = y }$. This limit is known as iterated limit of the double sequence. Note that the order of taking limits may affect the result, i.e., $\displaystyle{ \lim_{m \to \infty} \lim_{n \to \infty} x_{n, m} \ne \lim_{m \to \infty} \lim_{n \to \infty} x_{n, m} }$ in general. A sufficient condition of equality is given by the Moore-Osgood theorem, which requires the limit $\displaystyle{ \lim_{n \to \infty}x_{n, m} = y_m }$ to be uniform in $\displaystyle{ m }$.[10] ## Notes 1. Courant (1961), p. 29. 2. Weisstein, Eric W.. "Convergent Sequence" (in en). 3. Courant (1961), p. 39. 4. Van Looy, H. (1984). A chronology and historical analysis of the mathematical manuscripts of Gregorius a Sancto Vincentio (1584–1667). Historia Mathematica, 11(1), 57-75. 5. Weisstein, Eric W.. "Limit" (in en). 6. Dugundji 1966, pp. 209-210. 7. Császár 1978, p. 61. 8. Zeidler, Eberhard (1995). Applied functional analysis : main principles and their applications (1 ed.). New York: Springer-Verlag. p. 29. ISBN 978-0-387-94422-7. 9. Zakon, Elias (2011). "Chapter 4. Function Limits and Continuity". Mathematical Anaylysis, Volume I. pp. 223. ISBN 9781617386473. 10. ### Proofs 1. Proof: Choose $\displaystyle{ N = 1 }$. For every $\displaystyle{ n \geq N }$, $\displaystyle{ |x_n - c| = 0 \lt \varepsilon }$ 2. Proof: choose $\displaystyle{ N = \left\lfloor\frac{1}{\varepsilon}\right\rfloor + 1 }$ (the floor function). For every $\displaystyle{ n \geq N }$, $\displaystyle{ |x_n - 0| \le x_N = \frac{1}{\lfloor 1/\varepsilon \rfloor + 1} \lt \varepsilon }$.
crawl-data/CC-MAIN-2023-40/segments/1695233510967.73/warc/CC-MAIN-20231002033129-20231002063129-00070.warc.gz
null
EFRC researchers construct an artificial version of a bacterium’s light-absorbing ‘antenna’ By Diana Lutz Image courtesy of Martin Hohmann-Marriott and Robert Blankenship Electron microscopic tomogram of dividing cells of the green sulfur bacterium Chlorobaculum tepidum, with chlorosomes rendered in simulated color. Sometimes when people talk about solar energy, they tacitly assume that we’re stuck with some version of the silicon solar cell and its technical and cost limitations. The invention of the solar cell, in 1941, was inspired by a newfound understanding of semiconductors, materials that can use light energy to ultimately create an electrical current. Silicon solar cells have little in common with the biological photosystems in tree leaves and pond scum that use light energy to ultimately create sugars and other organic molecules. At the time, nobody understood these complex assemblages of proteins and pigments well enough to exploit their secrets for the design of solar cells. But things have changed. At Washington University in St. Louis’s Photosynthetic Antenna Research Center (PARC), scientists are exploring biological photosystems to build both hybrids that combine natural and synthetic parts as well as fully synthetic versions of natural systems. PARC is one of 46 Energy Frontier Research Centers (EFRCs) established by the DOE Office of Science in 2009 at universities, national laboratories, and other institutions around the nation to accelerate advanced basic research related to energy. The PARC team has just succeeded in making a crucial photosystem component – a light-harvesting antenna – from scratch. The new antenna is modeled on the chlorosome, or biological antenna, found in green photosynthetic bacteria. Chlorosomes are giant assemblies of pigment molecules. Perhaps nature’s most spectacular light-harvesting antennae, they allow green bacteria to photosynthesize even in the dim light of the deep ocean. Dewey Holten, professor of chemistry at Washington University, and collaborator Christine Kirmaier, research professor of chemistry, are part of a team that is trying to make synthetic chlorosomes. Holten and Kirmaier use ultra-fast laser spectroscopy and other analytic techniques to follow the rapid-fire energy transfers in photosynthesis. The team’s results are described in the New Journal of Chemistry. Although this project focused on self-assembly, the PARC scientists have already taken the next step toward a practical solar device. “With Pratim Biswas, the Lucy and Stanley Lopata Professor and Chair of the Department of Energy, Environmental & Chemical Engineering at Washington University, we’ve since demonstrated that we can get the pigments to self-assemble on surfaces, which is the next step in using them to design solar devices,” said Holten. “We’re not trying to make a more efficient solar cell in the next six months,” Holten cautions. “Our goal instead is to develop fundamental understanding so that we can enable the next generation of more efficient solar powered devices.” As biological knowledge has exploded in the past 50 years, mimicking nature has become a smarter, more realistic strategy. While biomimicry hasn’t always worked as in the case of designing early flying machines, biomimetic or biohybrid designs already have solved significant engineering problems in other areas and promise to greatly improve the design of solar- powered devices as well. After all, nature has had billions of years to experiment with ways to harness the energy in sunlight for useful work. —Diana Lutz, Washington University in St. Louis, email@example.com Reprinted with permission by the U.S. Department of Energy Office of Science. To read the entire article, go to: http://science.energy.gov/stories-of-discovery-and-innovation/127025/.
<urn:uuid:fbc938b9-43c2-40aa-ab4d-d4eaf8c0a2a0>
{ "date": "2018-04-25T03:00:13", "dump": "CC-MAIN-2018-17", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947690.43/warc/CC-MAIN-20180425022414-20180425042414-00298.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9028254747390747, "score": 3.71875, "token_count": 824, "url": "https://www.aps.org/publications/capitolhillquarterly/201202/innovation.cfm" }
• #### Symmetry of Graphs: Odd and Even Functions - Problem 3 ##### Math›Precalculus›Introduction to Functions How to determine whether an odd function times an even function, or an odd function divided by an odd function, is even or odd. • #### Symmetry of Graphs: Odd and Even Functions - Problem 2 ##### Math›Precalculus›Introduction to Functions How to prove whether a function is even or odd. • #### Symmetry of Graphs: Odd and Even Functions - Problem 1 ##### Math›Precalculus›Introduction to Functions How to prove whether a function, f(x) = x - 0.04*x^3, is even or odd. • #### Symmetry of Graphs: Odd and Even Functions - Concept ##### Math›Precalculus›Introduction to Functions How to recognize the graph of an even or odd function. • #### Radicals and Absolute Values - Problem 3 ##### Math›Algebra 2›Roots and Radicals How to simplify an odd root by not using absolute values. • #### Trigonometric Identities - Problem 2 ##### Math›Trigonometry›Trigonometric Functions How to use the unit circle to show that cosine is an even function, and sine and tangent are odd functions. • #### Trigonometric Identities - Problem 2 ##### Math›Precalculus›Trigonometric Functions How to use the unit circle to show that cosine is an even function, and sine and tangent are odd functions. • #### Applied Linear Equations: Consecutive Numbers - Problem 1 ##### Math›Algebra 2›Linear Equations How to solve a problem involving consecutive odd integers. • #### Applied Linear Equations: Consecutive Numbers - Problem 1 ##### Math›Precalculus›Linear Equations and Inequalities How to solve a problem involving consecutive odd integers. • #### Integer Power Functions - Concept ##### Math›Precalculus›Polynomial and Rational Functions How we identify odd power functions and even power functions. • #### Rational Exponents with Negative Coefficients - Problem 2 ##### Math›Algebra 2›Roots and Radicals How to evaluate a rational exponent with an odd root (an odd power) of a negative number. • #### Completing the Square - Problem 6 ##### Math›Algebra›Quadratic Equations and Functions How to complete the square when "a" is one and "b" is odd. Tags: • #### Polynomial Function - Problem 9 ##### Math›Algebra 2›Polynomials Write a polynomial with given real zeros, considering even or odd multiplicity, assuming the "a" value is one. Tags: • #### Basic Transformations - Problem 3 ##### Math›Algebra 2›Polynomials Using transformations on cubic graphs to look at end behavior for higher odd degree polynomials. Tags: • #### Mathematical Induction - Problem 2 ##### Math›Precalculus›Sequences and Series How to use mathematical induction to prove the equation for the sum of the first n odd integers. • #### Mathematical Induction - Problem 2 ##### Math›Algebra 2›Sequences and Series How to use mathematical induction to prove the equation for the sum of the first n odd integers. • #### Using the Complement to Calculate Probability - Concept ##### Math›Algebra 2›Combinatorics How to use the complement to calculate the probability of an event. • #### Using the Complement to Calculate Probability - Problem 1 ##### Math›Algebra 2›Combinatorics How to use the complement to calculate the probability of a dice roll. • #### Radicals and Absolute Values - Concept ##### Math›Algebra 2›Roots and Radicals How to know when to include a absolute value when simplifying a square root. • #### Using the Complement to Calculate Probability - Concept ##### Math›Precalculus›Topics in Discrete Math How to use the complement to calculate the probability of an event. © 2015 Brightstorm, Inc. All Rights Reserved.
crawl-data/CC-MAIN-2015-48/segments/1448398460519.28/warc/CC-MAIN-20151124205420-00198-ip-10-71-132-137.ec2.internal.warc.gz
null
# 2004 Indonesia MO Problems/Problem 7 (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff) ## Problem Prove that in a triangle $ABC$ with $C$ as the right angle, where $a$ denote the side in front of angle $A$, $b$ denote the side in front of angle $B$, $c$ denote the side in front of angle $C$, the diameter of the incircle of $ABC$ equals to $a + b - c$. ## Solution $[asy] draw((0,0)--(30,0)--(0,40)--cycle); draw(circle((10,10),10)); draw((0,10)--(10,10)--(10,0)); draw((10,10)--(18,16)); dot((0,0)); label("C",(0,0),SW); dot((30,0)); label("B",(30,0),SE); dot((0,40)); label("A",(0,40),NW); dot((0,10)); label("X",(0,10),W); dot((10,0)); label("Y",(10,0),S); dot((18,16)); label("Z",(18,16),NE); dot((10,10)); label("O",(10,10),N); draw((0,8)--(2,8)--(2,10)); draw((0,2)--(2,2)--(2,0)); draw((8,0)--(8,2)--(10,2)); [/asy]$ Let $O$ be the center of the circle, $X$ be the intersection of the incircle and $AC$, $Y$ be the intersection of the incircle and $BC$, and $Z$ be the intersection of the incircle and $AB$. Note that $X$ and $Y$ are tangent points of the circle, so $OX \perp AC$ and $OY \perp BC.$ Since $XC \perp YC$, we know that $XOYC$ is a square, so $XO = OY = YC = XC.$ Let $x = XC = YC$, $y = AX$, and $z = BY.$ Since $X,Y,Z$ are tangent points to the incircle, we know that $y = AZ$ and $z = BZ.$ Thus, \begin{align*} x + z &= a \\ x + y &= b \\ y + z &= c \end{align*} Adding the three equations yields \begin{align*} 2x+2y+2z &= a+b+c \\ x+y+z &= \frac{a+b+c}{2} \end{align*} Thus, $x = \frac{a+b-c}{2},$ so the diameter of the incircle is $a+b-c$.
crawl-data/CC-MAIN-2021-17/segments/1618038921860.72/warc/CC-MAIN-20210419235235-20210420025235-00523.warc.gz
null
Many of today’s popular desktop, web, and mobile apps were developed with the C++ programming language. With software development roles expected to grow at 22 percent from 2012-2022, learning C++ is an important first step to a career in computer science. This course is designed to introduce you to the concepts, terminology, application, and coding of the C++ programming language. This course consists of 18 lessons that use text, full programming scenarios, instructional videos, and hundreds of live coding labs that give you real-time feedback on your work. You will learn fundamental programming concepts, including decision making and looping, with the support of practical, step-by-step examples. After working through these lessons, you will understand the basics of structured and object-oriented programming techniques. Most importantly, you will be able to build C++ programs to strengthen your developer portfolio.
<urn:uuid:ab3738b4-6e69-41f2-a9c4-be98fdec327f>
{ "date": "2019-04-26T06:42:36", "dump": "CC-MAIN-2019-18", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578760477.95/warc/CC-MAIN-20190426053538-20190426075538-00418.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9265657663345337, "score": 3.5625, "token_count": 179, "url": "https://careertraining.ed2go.com/abac/training-programs/c-plus-plus-programmer" }
What Nests Tell Us A nest is an intimate thing. It’s not a home, but a place only for birth and nurturing. The first publicly heralded discovery of dinosaur eggs took place in Mongolia in 1923. Since then, paleontologists have discovered and described dinosaurs nests all over the world. These relics from the distant past shed light on how life began in the Mesozoic. In the 1970s, dinosaur nesting colonies were discovered in Montana–giving scientists clues about the parenting skills of dinosaurs. Eggshells were found crushed in the nest, and the associated remains of youngsters showed that their bones hadn’t developed enough for walking. This means that the adults were bringing food back to the nest until the young were large enough to walk out on their own. Other species exhibited largely intact eggshells, meaning that the baby dinosaurs were up and out of the nest quickly and foraging alongside their parents. We also find that dinosaur colonies resemble bird nest sites, in that the spacing between the nests is equal to the length of an adult. So the dinosaurs were closely packed together, as avian colonies are today. Unlike birds, the big dinosaurs were too heavy to sit on their eggs. They’d crush the little things, rather than incubate them. Dinosaurs relied on rotting vegetation to provide the necessary heat. Smaller dinosaurs, like Citipati (pictured above) were able to incubate their eggs in a more typically avian fashion. Dinosaurs are often regarded as large animals, but their eggs don’t get very big. The eggshell needed to be thin enough for the baby’s respiration to occur, while also being thick enough to hold the egg together. This means that even the largest dinosaurs began life in small eggs, and by studying the bones of youngsters, we can see how fast they grew–and in many cases, their growth rates were astronomical, reaching adult size in just a few years.
<urn:uuid:c4e72641-e926-4d9a-9f6c-633b6fdd8e01>
{ "date": "2017-10-21T01:06:51", "dump": "CC-MAIN-2017-43", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824537.24/warc/CC-MAIN-20171021005202-20171021025202-00356.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9833980202674866, "score": 3.9375, "token_count": 401, "url": "https://thisdayindinosaurs.com/2017/05/29/may-29th/" }
The goal of this experiment is to determine the concentration of a known solution, by titrating it with another strong electrolyte that will react with the first substance, and enter a non-ionic state. By doing this, we change the number of ions in the solution, and thus change its conductivity. One can accomplish by reacting a Barium Hydroxide solution of an unknown concentration with a titrant of Sulfuric Acid of known molarity. Then, by measuring the conductivity of the solution as one continues to add titrant to, and beyond the equivalence point, we can locate the point at which the conductivity is lowest, due to the lack of ions, as those from both compounds will have reacted completely. Then, as we know the chemical composition of both compounds, we can then calculate their stoichiometric ratio, and then use that, coupled with the known molarity of the Sulfuric Acid solution, to calculate the molarity of the Barium Hydroxide solution.
<urn:uuid:f3edf8f2-38a7-4d2f-8a84-c2698ff6f1d8>
{ "date": "2020-02-28T15:43:10", "dump": "CC-MAIN-2020-10", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875147234.52/warc/CC-MAIN-20200228135132-20200228165132-00536.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9688383340835571, "score": 3.765625, "token_count": 207, "url": "https://salve.digication.com/alexanderantonopoulos/Abstract2" }
An important Italian seaport on the Gulf of Genoa; also a former republic of the same name. It is very probable that even before the destruction of the Second Temple Jews from Rome settled in Genoa and took part in its commerce. The first authentic record of Jews in Genoa, however, is contained in two letters of the emperor Theodoric (fifth century) given by Cassiodorus, and referring to a synagogue and to previous grants. The Jews in Genoa suffered, although not as much as their coreligionists in northern lands, at the hands of the Crusaders, who found the large seaport a convenient gathering-place. In 1134 a special tax was levied upon the Genoese Jews to provide oil for the altars of Christian churches. Shortly afterward they were either driven out or else emigrated voluntarily in consequence of organized persecutions. Benjamin of Tudela, who passed through Genoa about 1165, found only two Jews residing there. It is certain that, later, Jews were forbidden to remain longer than three days in Genoa. This prohibition still existed in 1492. At that time many exiles from Spain landed at the port and begged permission to stay long enough to repair their ships, which had suffered heavy damage, and to recuperate from the voyage. The unfortunate fugitives presented a pitiful appearance. "And while they were making their preparations to journey farther, winter came on, and many died on the wharves." Such was the account given by Bartolomeo Senarega, secretary to the republic, and his report confirms a description given by Joseph ha-Kohen in his "'Emeḳ ha-Baka" (ed. Letteris, p. 85). The Genoese doubtless felt pity for the persecuted exiles, but commercial jealousy and religious fanaticism, increased by the sermons of Bernardino da Feltre, caused the repeal of the permission for a temporary stay in the harbor, which had been obtained with such difficulty in 1492. In the hope of converting them the Jews were later granted shelter and support again, but only one single case of conversion resulted. Twenty-one of the families which landed in Genoa were allowed to settle in Ferrara. The number of Jews that came to Genoa increased with the spread of persecutions in Portugal, so that at the beginning of the sixteenth century a special office was established in Genoa, "Ufficio per gli Ebrei." The wearing of a badge was ordered, and the prohibition to reside in Genoa was renewed under penalty of a large fine, of imprisonment, and even of being sold into slavery. Only wholesale merchants and physicians holding papal permits were exempt from these acts of oppression, and an attempt was made to prevent even them from settling in the city. Nevertheless, petitions for permission to settle became more and more numerous, and in 1550 a number of Jews obtained the right of free residence and of free commerce for several years; even the wearing of the badge and the seclusion in a ghetto were abolished. Such privileges were renewed in 1578, 1582, and 1586, but only for a few years. In 1587 the wearing of the yellow badge was restored, but at the petition of the Jews again abolished.Banished in 1598. The combined hostility of the clergy and of the Inquisition brought about a new decree of banishment Jan. 8, 1598; but individual Jews still remained in the city. They were compelled to wear the Jewish badge, but by paying a certain sum could buy the privilege of discarding it. Commercial considerations in general demanded a milder treatment of the Jews, and in the free harbor law of 1648 and 1658 the Jews were again recognized, and special regulations were made for importing their goods. The Inquisition considered this treatment too lenient, and called forth a similar expression of opinion from the Holy Office at Rome. Although the republic at first refused to listen to these complaints, it was nevertheless compelled in 1659 to make new and oppressive regulations concerning the Jews, and their right of residence was limited to ten years.The Ghetto. The Jews from Spain and Portugal were glad to be received anywhere under any conditions, and hence new arrivals submitted to the new regulations. Land for a ghetto was granted in 1660, and there a synagogue was built. The ghetto had two iron gates, which remained closed from sunset until morning. The number of the Jews at that time amounted to about 700; among them were many prosperous merchants, who, owing to the importance of their business, received better treatment and were allowed to live outside the ghetto. All Jews, however, were obliged to attend Christian sermons during Lent, a compulsion which was felt to be the deepest humiliation; on these occasions, besides being reviled by the preacher, they met with insults and even acts of violence on the part of the mob.Emancipation. At the end of the ten years (1669) an attempt was made to drive the Jews out again, under all sorts of pretexts. The Senate opposed this, and in 1674 obtained an extension of the right of residence for ten years more, under a new charter and in a different part of the city. But the rules were too severe, and especially the attendance at the sermons was felt tobe so degrading that the Jews rebelled, and in 1679 were all driven from the city. As before, Jews were later allowed to settle there again singly and only for a limited time. Even that privilege was abolished by a decree of banishment in 1752. However, only the poor were affected by the decree; the rich remained and were even favorably regarded on account of their acknowledged importance for the commerce of the republic. Through their influence a new charter was drawn up in 1752 upon fairly liberal terms, and the opposition of Pope Benedict XIV. remained without effect. The Senate at that time was very friendly to the Jews; it recognized the advantages they might bring to the city, the more so as it saw with regret how the neighboring port of Leghorn, where Jews enjoyed the most extensive liberties, was flourishing and injuring the commerce of Genoa. The Jews, however, had recognized the indecisive nature of this favor and kept at a distance from Genoa. Not until toward the end of the eighteenth century did they establish large commercial houses there. Their legal status remained precarious and rested upon the personal tolerance of the mercantile class, not upon the firm basis of the law; and it was not until 1848, when the constitution of the kingdom of Sardinia was promulgated, that the Jews received the full rights of citizenship, and there still exists among the population a feeling of animosity against them, which is due to clerical leaning. Since 1848 the community has steadily increased; in 1901 it numbered about 1,000 souls. The Jews have taken a large share in the flourishing commerce of Genoa, while the commerce of Leghorn has almost ceased, and a large proportion of its Jewish community has emigrated to the former city. In consequence of this influx from Leghorn the ritual of the Sephardim has been introduced into the only synagogue of Genoa. The community possesses a school for religious instruction, a good library, and a very good charitable organization. There is little to be said concerning the scholars and rabbis who lived and labored in Genoa, for their number was small and their existence precarious. Judah Abravanel (Leo Hebræus) practised medicine there. The historian Joseph ha-Kohen lived there with his parents and family from 1501 until 1547, when he was exiled in spite of the intercession of his patients. Two rabbis are mentioned as residing in the city in 1680, Abitur Abba Mari and Abraham Ẓarfati. In the latter part of the nineteenth century Felice Finzi was the rabbi of the community; since his death the post has been vacant. In 1516 the "Psalterium Octaplum" was printed in Genoa at the press of Nicolaus Giustiniani; this is celebrated because it contains the history of Columbus' discovery of America in the scholia to Psalm XiX. - Massa'ot of Benjamin of Tudela; - Joseph ha-Kohen, 'Emeḳ ha-Baka, passim; - M. Stagliero, Degli Ebrei di Genoa, in Giornale Ligustico di Archeologia, Storia e Belle Arti, 1876; - Perreau, in Vessillo Israelitico, 1881, xxix. On the rabbis see Mortara, Indice, s.v.; - on the Psalter, see Luzzatto, Oheb Ger, Appendix; - Steinschneider, Cat. Bodl. col. 5.
<urn:uuid:78f35be3-db61-45af-990a-a58c96524179>
{ "date": "2016-12-09T17:25:31", "dump": "CC-MAIN-2016-50", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542714.38/warc/CC-MAIN-20161202170902-00144-ip-10-31-129-80.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9826789498329163, "score": 3.625, "token_count": 1829, "url": "http://www.jewishencyclopedia.com/articles/6584-genoa" }
# What is the Cartesian form of ( 3, (-5pi)/2 ) ? Feb 14, 2018 Using the formulas: $x = r \cdot \cos \left(\theta\right)$ $y = r \cdot \sin \left(\theta\right)$ our answer is $\left(0 , - 3\right)$ in Cartesian #### Explanation: To convert from Polar coordinates to Cartesian, we must apply the following formulas: $x = r \cdot \cos \left(\theta\right)$ $y = r \cdot \sin \left(\theta\right)$ where polar form is $\left(r , \theta\right)$ and Cartesian form is $\left(x , y\right)$ for x: $x = 3 \cdot \cos \left(- 5 \frac{\pi}{2}\right) = 3 \cdot 0 = 0$ $y = 3 \cdot \sin \left(- 5 \frac{\pi}{2}\right) = 3 \cdot - 1 = - 3$ thus converting from polar to Cartesian: Cartesian = $\left(0 , - 3\right)$
crawl-data/CC-MAIN-2022-27/segments/1656103945490.54/warc/CC-MAIN-20220701185955-20220701215955-00478.warc.gz
null
LA: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners and texts, building on others’ ideas and expressing their own clearly. LA: Write informative/explanatory texts to examine a topic and convey ideas and information clearly. LA: Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation. LA: Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience. LA: Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations. SCI: Ask questions about the natural and human-built worlds. SS: Identify and describe ways family, groups, and community influence the individual's daily life and personal choices. SS: Explore factors that contribute to one's personal identity such as interests, capabilities, and perceptions. SS: Work independently and cooperatively to accomplish goals. VA: Use art materials and tools in a safe and responsible manner. VA: Use visual structures of art to communicate ideas. VA: Select and use subject matter, symbols, and ideas to communicate meaning.
<urn:uuid:f425ce26-1833-422d-b813-445b2f60fccc>
{ "date": "2017-09-20T20:10:12", "dump": "CC-MAIN-2017-39", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687447.54/warc/CC-MAIN-20170920194628-20170920214628-00097.warc.gz", "int_score": 4, "language": "en", "language_score": 0.8989238739013672, "score": 3.578125, "token_count": 265, "url": "https://www.crayola.com/lesson-plans/aim-for-your-goal-lesson-plan/" }
- 5 a day 5 a day Eating a good variety of fruit and vegetables is an important element of healthy eating. The World Health Organisation (WHO) advises that we eat a minimum of 400g of fruit and veg every day, equating to five portions. This recommended daily amount is thought to help reduce risk of serious health conditions including stroke, heart disease, obesity and type 2 diabetes. The 5 a day message looks to encourage people to enjoy a variety of different fruits and vegetables as part of a healthy balanced diet. On this page we'll look at why fruit and veg are so important to our health, what counts towards your 5 a day and tips for you and your family. On this page Why are fruit and veg so important? In the UK most of us are lucky enough to be surrounded with a wide variety of foods, catering to all tastes and preferences. The problem for some of us however is that within this expanse of food lie some unhealthy options - and while they may taste great, they aren't likely to be doing our health any favours. In an attempt to reinforce the importance of unprocessed, healthy foods - the 5 a day campaign was officially backed by the UK Government in 2003. This campaign advised that eating 5 portions of fruit and veg (in total) would help protect against common health problems like obesity and heart disease. So why exactly are fruit and veg so important? The following list highlights some key nutritional benefits of fruit and veg: - They are a fantastic source of vitamins and minerals, including: vitamin C, potassium and folate. - They provide dietary fibre, helping to maintain a healthy digestive system and lower risk of bowel cancer. - As part of a healthy diet they can lower risk of stroke, heart disease and some cancers. - They are often low in fat, helping you to maintain a healthy weight. Because different fruit and veg have different nutritional benefits, you are advised to enjoy a variety of types to get the most from your 5 a day. What counts towards your 5 a day? A common question for those trying to fit 5 portions of fruit and veg in their diet is: what counts towards the 5 a day guide? The answer is almost all fruits and vegetables. As well as fresh varieties, the following also count towards your recommended daily amount: - Fruit and veg that has been cooked within dishes like soups, stews and pasta. - Beans and pulses - however it is worth noting that they only count as one portion, regardless of how much you eat. This is because while they are great sources of fibre, they do contain fewer nutrients than other varieties of fruits and vegetables. - Frozen fruit and veg. - Canned and tinned fruit/veg (aim to eat those canned in natural juices or water). - Dried fruit. Does fruit/vegetable juice count? This question has been hotly debated recently however, as it stands, 150ml of unsweetened 100% juice counts as a maximum of one portion of your 5 a day. The reason juice has been debated as part of your 5 a day is the high levels of sugars that are released when fruit is juiced. Because of this, when it comes to fruit juices and smoothies it is recommended that you enjoy those with no added sugar and not to rely on these as your main source of fruit and veg. The sugars and acids within fruit juice can also be harmful for your dental health, so it may be worth diluting juices in water to help neutralise them. Do potatoes count? As much as we would love to tell you that a portion of chips will go towards your 5 a day - potatoes don't count. Potatoes are a good source of fibre, potassium and B vitamins; however, as they are usually eaten in place of starch (like bread and pasta) they do not count. Similar vegetables that don't count are yams, plantain and cassava. Sweet potatoes, swedes, turnips and parsnips do count towards your 5 a day - so feel free to stock up on these and remember that even though potatoes don't count towards your 5 a day, they are still important as part of a balanced diet. Tips for getting your 5 a day When people hear that they should be eating 5 portions of fruit and veg a day, the initial response may be 'how can I do that?' Luckily there is a wide variety of different fruits and vegetables on offer and plenty of ways they can be incorporated into your diet. Take a look at the following ideas to help bump up your fruit and veg intake: - add a portion of mushrooms or tomatoes with scrambled egg on toast - add some chopped fruit or berries to cereal, porridge or yoghurt - have a glass of unsweetened fruit juice with your breakfast - enjoy a smoothie made up of different fruits and veg - add spinach and pepper to a breakfast omelette. - add some vegetable crudité to your lunch-time meal - add some salad to your sandwich - finish off your lunch with a fruit pot - add some mushrooms and peppers to a stir-fry - enjoy a salad made up of different vegetables. - add some vegetables to your main meal - replace potatoes with sweet potatoes - have a side-salad - enjoy some fruit for dessert - add a handful of beans/pulses to soups or sauces. - dried fruit makes for a great on-the-go snack - enjoy fresh fruit as a snack - have some carrot/cucumber sticks dipped in hummus - add cucumber to cream cheese on crackers - try vegetable crisps. 5 a day for children Getting your children used to eating fruit and vegetables early can help them grow up to enjoy a healthy and balanced diet. Rather than forcing children to eat vegetables or trying to hide them in dishes, try to make the experience a fun one. Let your children pick which fruit and veg they want to try and let them help you prepare them. By letting them try a variety they will quickly learn that not all fruit and veg taste the same, allowing them to discover new flavours. If you find they aren't interested, start them off with tinned vegetables (like sweetcorn and peas) and tinned fruit (like pineapple and peach) before moving on to more adventurous varieties. Try to incorporate fruit and veg into every meal and make the presentation fun.
<urn:uuid:79c45490-e94c-4781-891c-e034989c0ab9>
{ "date": "2018-11-18T06:28:53", "dump": "CC-MAIN-2018-47", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743968.63/warc/CC-MAIN-20181118052443-20181118073814-00026.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9589094519615173, "score": 3.546875, "token_count": 1354, "url": "https://www.nutritionist-resource.org.uk/content/5-a-day.html" }
# What Are the Factors of 54? The factors of the number 54 are 1, 2, 3, 6, 9, 18, 27 and 54. 54 is a composite number because it has other factors besides 1 and itself. The term factors in mathematics are numbers multiplied together to give another number. Q&A Related to "What Are the Factors of 54" 2x3x3x3. 3^3x2. 2 and 3 are the prime number. Because 2 times 3 times 3 times 3 equals 54. 2 x 3 x 3 x 3 = 54. http://wiki.answers.com/Q/What_are_the_prime_facto... The common factors of 126 and 54 are: 1, 2, 3, 6, 9, and 18 http://wiki.answers.com/Q/What_are_the_common_fact... 54 = 2 × 3. 3. 210 = 2 × 3 × 5 × 7. http://wiki.answers.com/Q/What_is_the_prime_factor... The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. http://wiki.answers.com/Q/What_are_the_factors_of_...
crawl-data/CC-MAIN-2014-41/segments/1410657131545.81/warc/CC-MAIN-20140914011211-00031-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
null
Apples All Around • Use informational text to identify the natural process that produces apples, from seed to fruitCommon Core Standard • Use informational text to identify the different parts of an apple (RI.1.6) Distinguish between information provided by pictures or other illustrations and information provided by the words in a text. SET UP AND PREPARE Apples are a hallmark of fall and a staple in every elementary classroom. However, few students realize how interesting and intricate apples can be. First, an apple has various parts: • The skin covers the outside of the apple and protects it.As you study apples, these apple facts will interest your students: • The flesh inside is full of water, which is why it’s so juicy. • The core is the center of the apple. It holds the seeds. • Apples have five carpels, or seed pockets. The healthier a plant is, the more seeds it has. • Apple seeds can grow into new apple trees if you plant them. • The stem connects the apple to the tree and carries water and nutrients from the tree to the apple while it is growing. • Apples come in many different colors (red, green, and yellow) and varieties (Red Delicious, Granny Smith, etc.).(For more apple facts, go to: http://urbanext.illinois.edu/apples/facts.cfm) • Apples are grown in all 50 states. • The Pilgrims planted the first apple trees in the United States. • Apple trees start producing fruit after they have been planted for four or five years. • Apples are part of the rose family. • Apple blossoms are pink when they open, but become white over time. • The energy from 50 leaves is used to produce one apple. Skin, stem, flesh, core, carpels, seeds Introduction (5 minutes) Tell students that they are going to be botanists, or scientists who study plants. Today they are going to study the apple. Ask students what they already know about apples and what experiences they have had with apples. On the whiteboard, record student knowledge in the "K" column of the Apple KWL chart. First- and second-grade students can follow along and take notes on their own KWL chart as you write. Then, ask students what questions they have about apples. Record their questions in the "W" column. Apple Research (10 minutes) Tell students that the first thing you must do as botanists is learn more about the apple plant. On the whiteboard, complete the Apple Diagram printable. • Kindergarten students: Color each part of the apple as you talk about it. • 1st grade students: Add a word to label each part as they color. • 2nd grade students: Label each part of the apple and its purpose. Students use paper, scissors, and glue alongside the notes from their apple diagram printable to create a paper model of the inside of an apple. Remind students that apples come in many different types and colors. Wrap-up (5 minutes) Complete the L section of the Apple KWL chart. What have students learned about apples? Whiteboard Extension Activities • Using the interactive whiteboard, post a collection of apple-related words and have students label the parts of an apple.Literature Extension Activities • Post images of various amounts of apples. Have students identify which amount looks heavier or lighter. Introduce students to the symbols that demonstrate "greater than," "equal to," and "less than." Then apply those symbols to compare the amounts of apples. • Using images of apples, move the apples into addition and subtraction problems as you introduce and review these math concepts. • Provide students with sets of nonfiction apple books to explore in small groups. As students explore their books, tell them to look for answers to the questions that they recorded in the Apple KWL chart.Extension Activities • Read a book about apples as a class (for example, The Seasons of Arnold's Apple Tree by Gail Gibbons, or The Apple Pie Tree by Zoe Hall). As you read, discuss what students are noticing--the parts of an apple, for example, or the process that a seed goes through as it grows into a tree. • Read American myths or legends that involve apples (Johnny Appleseed by Gwenyth Swain, or a story about George Washington and the apple tree). Then, as a class, write your own story involving an apple. • As you read during the first month of school, keep track of the ways in which apples are used in literature. For example, apples appear as symbols in stories such as Snow White, and William Tell. • Introduce students to the idea of idioms, or figures of speech. Have students choose one apple idiom to illustrate and post around your classroom. Some apple-related idioms: o An apple a day keeps the doctor away o One bad apple spoils the bunch o As American as apple pie o In apple-pie order o The apple of my eye o Comparing apples to oranges o How about them apples? o A bad apple o Don't upset the apple cart • Make applesauce, and explore the physical and chemical changes that apples go through. What physical changes do students notice? (Possible answer: the color changes when cut up or mashed.) What chemical changes do students notice? (Possible answer: the consistency changes when they are heated.)Technology Extension • Discuss how energy is used in the process of producing apples. Trees take in energy through the leaves, transform that energy into the apples, and we use the apples for energy when we eat them. Students create a model of how energy is created, stored, and used. Then they can apply this knowledge to figuring out how another fruit or vegetable uses energy. • Bring in five different apple varieties for students to taste and classify. First, brainstorm taste words (sour, sweet, crunchy, crisp, soft, smooth, refreshing, watery). Then as students try each apple, they rate each one on its taste and texture. At the end, discuss your findings. Why might some people have different classifications? What can you do with the information that you collected? (For example, write a letter to the cafeteria staff persuading them to buy more than one type of apple.) • Apples are kept in pecks (10.5 pounds = 1 peck) and bushels (42 pounds = 1 bushel). Have students estimate, then measure, the weight of individual and bunches of apples. Visit http://the1stday.com/ and download the Elmer's 1st Day app to capture and share the first day of school and beyond. You can create slideshows, personalize photos, share "first day" albums, and more. In this home-connection activity, students will incorporate apples into their everyday lives. Over the course of a week, students work with their parents to document all the things they do with apples (i.e., eat apple butter, pick apples at an apple farm, make applesauce). Each day, students record what they did through pictures and words in a scrapbook or on a display board. Students share their experiences with their classmates at the end of the week. As a class, tally how many different apple-related activities students completed. How many students did each activity? (Visited an apple orchard? Made applesauce?) Which activity was the most popular? Which activity would students do every day if they could?
<urn:uuid:bf106175-7d2c-4113-b29c-939817333702>
{ "date": "2016-09-27T08:55:59", "dump": "CC-MAIN-2016-40", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660996.20/warc/CC-MAIN-20160924173740-00185-ip-10-143-35-109.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9374686479568481, "score": 3.875, "token_count": 1602, "url": "http://www.scholastic.com/browse/lessonplan.jsp?id=1544" }
Leonardo da Vinci(1452-1519) "Leonardo da Vinci was like a man who awoke too early in the darkness, while the others were all still asleep" THE heavens often rain down the richest gifts on human beings, naturally, but sometimes with lavish abundance bestow upon a single individual beauty, grace and ability, so that, whatever he does, every action is so divine that he distances all other men, and clearly displays how his genius is the gift of God and not an acquirement of human art. Men saw this in Leonardo da Vinci, whose personal beauty could not be exaggerated, whose every movement was grace itself and whose abilities were so extraordinary that he could readily solve every difficulty. He possessed great personal strength, combined with dexterity, and a spirit and courage invariably royal and magnanimous, and the fame of his name so spread abroad that, not only was he valued in his own day, but his renown has greatly increased since his death.Early Life in Florence Leonardo was born on April 15, 1452, in the small Tuscan town of Vinci, near Florence. He was the son of a wealthy Florentine notary and a peasant woman. In the mid-1460s the family settled in Florence, where Leonardo was given the best education that Florence, the intellectual and artistic center of Italy, could offer. He rapidly advanced socially and intellectually. About 1466 he was apprenticed as a garzone (studio boy) toAndrea del Verrocchio, the leading Florentine painter and sculptor of his day. InVerrocchio's workshop Leonardo was introduced to many activities, from the painting of altarpieces and panel pictures to the creation of large sculptural projects in marble and bronze. In 1472 he was entered in the painter's guild of Florence, and in 1476 he is still mentioned asVerrocchio's assistant. InVerrocchio'sBaptism of Christ (circa 1470, Uffizi, Florence), the kneeling angel at the left of the painting is by Leonardo. In 1478 Leonardo became an independent master. His first commission, to paint an altarpiece for the chapel of the Palazzo Vecchio, the Florentine town hall, was never executed. His first large painting, TheAdoration of the Magi (begun 1481, Uffizi), left unfinished, was ordered in 1481 for the Monastery of San Donato a Scopeto, Florence. Other works ascribed to his youth are the so-called Benois Madonna (c. 1478, Hermitage, Saint Petersburg), the portrait Ginerva de' Benci (c. 1474, National Gallery, Washington, D.C.), and the unfinishedSaint Jerome (c. 1481, Pinacoteca, Vatican).Years in Milan About 1482 Leonardo entered the service of the duke of Milan, Ludovico Sforza, having written the duke an astonishing letter in which he stated that he could build portable bridges; that he knew the techniques of constructing bombardments and of making cannons; that he could build ships as well as armored vehicles, catapults, and other war machines; and that he could execute sculpture in marble, bronze, and clay. He served as principal engineer in the duke's numerous military enterprises and was active also as an architect. In addition, he assisted the Italian mathematician Luca Pacioli in the celebrated work Divina Proportione (1509). Evidence indicates that Leonardo had apprentices and pupils in Milan, for whom he probably wrote the various texts later compiled as Treatise on Painting (1651; trans. 1956). The most important of his own paintings during the early Milan period wasThe Virgin of the Rocks, two versions of which exist (1483-85,Louvre, Paris; 1490s to 1506-08,National Gallery, London); he worked on the compositions for a long time, as was his custom, seemingly unwilling to finish what he had begun. From 1495 to 1497 Leonardo labored on his masterpiece, TheLast Supper, a mural in the refectory of the Monastery of Santa Maria delle Grazie, Milan. Unfortunately, his experimental use of oil on dry plaster (on what was the thin outer wall of a space designed for serving food) was technically unsound, and by 1500 its deterioration had begun. Since 1726 attempts have been made, unsuccessfully, to restore it; a concerted restoration and conservation program, making use of the latest technology, was begun in 1977 and is reversing some of the damage. Although much of the original surface is gone, the majesty of the composition and the penetrating characterization of the figures give a fleeting vision of its vanished splendor. During his long stay in Milan, Leonardo also produced other paintings and drawings (most of which have been lost), theater designs, architectural drawings, and models for the dome of Milan Cathedral. His largest commission was for a colossal bronze monument to Francesco Sforza, father of Ludovico, in the courtyard of Castello Sforzesco. In December 1499, however, the Sforza family was driven from Milan by French forces; Leonardo left the statue unfinished (it was destroyed by French archers, who used it as a target) and he returned to Florence in 1500.Return to Florence In 1502 Leonardo entered the service of Cesare Borgia, duke of Romagna and son and chief general of Pope Alexander VI; in his capacity as the duke's chief architect and engineer, Leonardo supervised work on the fortresses of the papal territories in central Italy. In 1503 he was a member of a commission of artists who were to decide on the proper location for the David (1501-04, Accademia, Florence), the famous colossal marble statue by the Italian sculptor Michelangelo, and he also served as an engineer in the war against Pisa. Toward the end of the year Leonardo began to design a decoration for the great hall of the Palazzo Vecchio. The subject was the Battle of Anghiari, a Florentine victory in its war with Pisa. He made many drawings for it and completed a full-size cartoon, or sketch, in 1505, but he never finished the wall painting. The cartoon itself was destroyed in the 17th century, and the composition survives only in copies, of which the most famous is the one by the Flemish painter Peter PaulRubens (c. 1615, Louvre). During this second Florentine period, Leonardo painted several portraits, but the only one that survives is the famousMona Lisa One of the most celebrated portraits ever painted, it is also known as La Gioconda, after the presumed name of the woman's husband. Leonardo seems to have had a special affection for the picture, for he took it with him on all of his subsequent travels.Later Travels and Death In 1506 Leonardo went again to Milan, at the summons of its French governor, Charles d'Amboise. The following year he was named court painter to King Louis XII of France, who was then residing in Milan. For the next six years Leonardo divided his time between Milan and Florence, where he often visited his half brothers and half sisters and looked after his inheritance. In Milan he continued his engineering projects and worked on an equestrian figure for a monument to Gian Giacomo Trivulzio, commander of the French forces in the city; although the project was not completed,drawings and studies have been preserved. From 1514 to 1516 Leonardo lived in Rome under the patronage of Pope Leo X: he was housed in the Palazzo Belvedere in the Vatican and seems to have been occupied principally with scientific experimentation. In 1516 he traveled to France to enter the service of King Francis I. He spent his last years at the Château de Cloux (later called Clos-Lucé), near the King's summer palace at Amboise on the Loire, where he died on May 2, 1519.Paintings Although Leonardo produced a relatively small number of paintings, many of which remained unfinished, he was nevertheless an extraordinarily innovative and influential artist. During his early years, his style closely paralleled that ofVerrocchio, but he gradually moved away from his teacher's stiff, tight, and somewhat rigid treatment of figures to develop a more evocative and atmospheric handling of composition. The early TheAdoration of the Magi introduced a new approach to composition, in which the main figures are grouped in the foreground, while the background consists of distant views of imaginary ruins and battle scenes. Leonardo's stylistic innovations are even more apparent inThe Last Supper, in which he re-created a traditional theme in an entirely new way. Instead of showing the 12 apostles as individual figures, he grouped them in dynamic compositional units of three, framing the figure of Christ, who is isolated in the center of the picture. Seated before a pale distant landscape seen through a rectangular opening in the wall, Christ—who is about to announce that one of those present will betray him—represents a calm nucleus while the others respond with animated gestures. In the monumentality of the scene and the weightiness of the figures, Leonardo reintroduced a style pioneered more than a generation earlier byMasaccio, the father of Florentine painting. Leonardo's most famous work, is as well known for its mastery of technical innovations as for the mysteriousness of its legendary smiling subject. This work is a consummate example of two techniques—sfumato and chiaroscuro—of which Leonardo was one of the first great masters. Sfumato is characterized by subtle, almost infinitesimal transitions between color areas, creating a delicately atmospheric haze or smoky effect; it is especially evident in the delicate gauzy robes worn by the sitter and in her enigmatic smile. Chiaroscuro is the technique of modeling and defining forms through contrasts of light and shadow; the sensitive hands of the sitter are portrayed with a luminous modulation of light and shade, while color contrast is used only sparingly. An especially notable characteristic of Leonardo's paintings is his landscape backgrounds, into which he was among the first to introduce atmospheric perspective. The chief masters of the High Renaissance in Florence, includingRaphael,Andrea del Sarto, all learned from Leonardo; he completely transformed the school of Milan; and at Parma, Correggio's artistic development was given direction by Leonardo's work. Leonardo's many extantdrawings, which reveal his brilliant draftsmanship and his mastery of the anatomy of humans, animals, and plant life, may be found in the principal European collections; the largest group is at Windsor Castle in England. Probably his most famous drawing is the magnificentSelf-Portrait (c. 1510-13, Biblioteca Reale, Turin). Sculptural and Architectural Drawings Because none of Leonardo's sculptural projects was brought to completion, his approach to three-dimensional art can only be judged from his drawings. The same strictures apply to his architecture; none of his building projects was actually carried out as he devised them. In his architectural drawings, however, he demonstrates mastery in the use of massive forms, a clarity of expression, and especially a deep understanding of ancient Roman sources. Scientific and Theoretical Projects As a scientist Leonardo towered above all his contemporaries. His scientific theories, like his artistic innovations, were based on careful observation and precise documentation. He understood, better than anyone of his century or the next, the importance of precise scientific observation. Unfortunately, just as he frequently failed to bring to conclusion artistic projects, he never completed his planned treatises on a variety of scientific subjects. His theories are contained in numerous notebooks, most of which were written in mirror script. Because they were not easily decipherable, Leonardo's findings were not disseminated in his own lifetime; had they been published, they would have revolutionized the science of the 16th century. Leonardo actually anticipated many discoveries of modern times. In anatomy he studied the circulation of the blood and the action of the eye. He made discoveries in meteorology and geology, learned the effect of the moon on the tides, foreshadowed modern conceptions of continent formation, and surmised the nature of fossil shells. He was among the originators of the science of hydraulics and probably devised the hydrometer; his scheme for the canalization of rivers still has practical value. He invented a large number of ingenious machines, many potentially useful, among them an underwater diving suit. His flying devices, although not practicable, embodied sound principles of aerodynamics. A creator in all branches of art, a discoverer in most branches of science, and an inventor in branches of technology, Leonardo deserves, perhaps more than anyone, the title of Homo Universalis, Universal Man. t face="tahoma" size="2"> http://www.artist-biography.info/artist/leonardo_da_vinci/
<urn:uuid:605295f9-4421-44e6-b483-b80f6fd869cc>
{ "date": "2017-04-27T05:51:26", "dump": "CC-MAIN-2017-17", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121869.65/warc/CC-MAIN-20170423031201-00353-ip-10-145-167-34.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9741302132606506, "score": 3.5, "token_count": 2724, "url": "http://english.tebyan.net/newindex.aspx?pid=25176" }
Factors of 988: Prime Factorization, Methods, and Examples 988 is said to be an even number as well as a composite number because it includes more than 2 factors. The number 988 has 12 positive factors which can be used as divisors with 988 as a dividend their division result in 12 whole numbers without any decimal places. Factors of 988 Here are the factors of number 988. Factors of 988: 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494 and 988 Negative Factors of 988 The negative factors of 988 are similar to its positive aspects, just with a negative sign. Negative Factors of 988: -1, -2, -4, -13, -19, -26, -38, -52, -76, -247, -494 and -988 Prime Factorization of 988 The prime factorization of 988 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 2 x 13 x 19 In this article, we will learn about the factors of 988 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree. What Are the Factors of 988? The factors of 988 are 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494 and 988. These numbers are the factors as they do not leave any remainder when divided by 988. The factors of 988 are classified as prime numbers and composite numbers. The prime factors of the number 988 can be determined using the prime factorization technique. How To Find the Factors of 988? You can find the factors of 988 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero. To find the factors of 988, create a list containing the numbers that are exactly divisible by 988 with zero remainders. One important thing to note is that 1 and 988 are the 988’s factors as every natural number has 1 and the number itself as its factor. 1 is also called the universal factor of every number. The factors of 988 are determined as follows: $\dfrac{988}{1} = 988$ $\dfrac{988}{2} = 494$ $\dfrac{988}{4} = 247$ $\dfrac{988}{13} = 76$ $\dfrac{988}{19} = 52$ $\dfrac{988}{26} = 38$ $\dfrac{988}{38} = 26$ $\dfrac{988}{52} = 19$ $\dfrac{988}{76} = 13$ $\dfrac{988}{247} = 4$ $\dfrac{988}{494} = 2$ $\dfrac{988}{988} = 1$ Therefore, 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494 and 988 are the factors of 988. Total Number of Factors of 988 For 988, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 988. To find the total number of factors of the given number, follow the procedure mentioned below: 1. Find the factorization/prime factorization of the given number. 2. Demonstrate the prime factorization of the number in the form of exponent form. 3. Add 1 to each of the exponents of the prime factor. 4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number. By following this procedure, the total number of factors of 988 is given as: Factorization of 988 is 2 x 2 x 13 x 19. The exponent of 2, 13, and 19 is 2,1,1. Adding 1 to each and multiplying them together results in 12. Therefore, the total number of factors of 988 is 24. Twelve are positive, and twelve factors are negative. Important Notes Here are some essential points that must be considered while finding the factors of any given number: • The factor of any given number must be a whole number. • The factors of the number cannot be in the form of decimals or fractions. • Factors can be positive as well as negative. • Negative factors are the additive inverse of the positive factors of a given number. • The factor of a number cannot be greater than that number. • Every even number has 2 as its prime factor, the smallest prime factor. Factors of 988 by Prime Factorization The number 988 is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors. Before finding the factors of 988 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves. To start the prime factorization of 988, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor. Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 988 can be expressed as: 988 = 2 x 2 x 13 x 19 Factors of 988 in Pairs The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given. For 988, the factor pairs can be found as: 1 x 988 = 988 2 x 494 = 988 4 x 247 = 988 13 x 76 = 988 19 x 52 = 988 26 x 38 = 988 The possible factor pairs of 988 are given as (1, 988), (2, 494), (4, 247), (13, 76), (19, 52) and (26, 38). All these numbers in pairs, when multiplied, give 988 as the product. The negative factor pairs of 988 are given as: -1 x -988 = 988 -2 x -494 = 988 -4 x -247 = 988 -13 x -76 = 988 -19 x -52 = 988 -26 x -38 = 988 It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -4, -13, -19, -26, -38, -52, -76, -247, -494 and -988 are called negative factors of 988. The list of all the factors of 988, including positive as well as negative numbers, is given below. Factor list of 988: 1,-1, 2, -2, 4, -4, 13, -13, 19, -19, 26, -26, 38, -38, 52, -52, 76, -76, 247, -247, 494, -494, 988, and -988 Factors of 988 Solved Examples To better understand the concept of factors, let’s solve some examples. Example 1 How many factors of 988 are there? Solution The total number of Factors of 988 is 12. Factors of 988 are 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494 and 988. Example 2 Find the factors of 988 using prime factorization. Solution The prime factorization of 988 is given as: 988 $\div$ 2 = 494 494 $\div$ 2 = 247 247 $\div$ 13 = 19 19 $\div$ 19 = 1 So the prime factorization of 988 can be written as: 2 x 2 x 13 x 19 = 988
crawl-data/CC-MAIN-2024-33/segments/1722641052535.77/warc/CC-MAIN-20240812221559-20240813011559-00521.warc.gz
null
# CHAPTER 1 REFLECTION AND REFRACTION Document Sample ``` 1 CHAPTER 1 REFLECTION AND REFRACTION 1.1 Introduction This “book” is not intended to be a vast, definitive treatment of everything that is known about geometric optics. It covers, rather, the geometric optics of first-year students, whom it will either help or confuse yet further, though I hope the former. The part of geometric optics that often causes the most difficulty, particularly in getting the right answer for homework or examination problems, is the vexing matter of sign conventions in lens and mirror calculations. It seems that no matter how hard we try, we always get the sign wrong! This aspect will be dealt with in Chapter 2. The present chapter deals with simpler matters, namely reflection and refraction at a plane surface, except for a brief foray into the geometry of the rainbow. The rainbow, of course, involves refraction by a spherical drop. For the calculation of the radius of the bow, only Snell’s law is needed, but some knowledge of physical optics will be needed for a fuller understanding of some of the material in section 1.7, which is a little more demanding than the rest of the chapter. 1.2 Reflection at a Plane Surface i r FIGURE I.1 The law of reflection of light is merely that the angle of reflection r is equal to the angle of incidence r. There is really very little that can be said about this, but I’ll try and say what little need be said. i. It is customary to measure the angles of incidence and reflection from the normal to the reflecting surface rather than from the surface itself. 2 ii. Some curmudgeonly professors may ask for the lawS of reflection, and will give you only half marks if you neglect to add that the incident ray, the reflected ray and the normal are coplanar. iii. A plane mirror forms a virtual image of a real object: O• °I FIGURE I.2 or a real image of a virtual object: I • °O FIGURE I.3 3 iv. It is usually said that the image is as far behind the mirror as the object is in front of it. In the case of a virtual object (i.e. light converging on the mirror, presumably from some large lens somewhere to the left) you’d have to say that the image is as far in front of the mirror as the object is behind it! v. If the mirror were to move at speed v away from a real object, the virtual image would move at speed 2v. I’ll leave you to think about what happens in the case of a virtual object. vi. If the mirror were to rotate through an angle θ (or were to rotate at an angular speed ω), the reflected ray would rotate through an angle 2θ (or at an angular speed 2ω). vii. Only smooth, shiny surfaces reflect light as described above. Most surfaces, such as paper, have minute irregularities on them, which results in light being scattered in many directions. Various equations have been proposed to describe this sort of scattering. If the reflecting surface looks equally bright when viewed from all directions, the surface is said to be a perfectly diffusing Lambert’s law surface. Reflection according to the r = i law of reflection, with the incident ray, the reflected ray and the normal being coplanar, is called specular reflection (Latin: speculum, a mirror). Most surfaces are intermediate between specular reflectors and perfectly diffusing surfaces. This chapter deals exclusively with specular reflection. viii. The image in a mirror is reversed from left to right, and from back to front, but is not reversed up and down. Discuss. ix. If you haven’t read Through the Looking-glass and What Alice Found There, you are missing something. 1.3 Refraction at a Plane Surface I was taught Snell’s Law of Refraction thus: When a ray of light enters a denser medium it is refracted towards the normal in such a manner than the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, this constant being called the refractive index n. i n r FIGURE I.4 4 This is all right as far as it goes, but we may be able to do better. i. Remember the curmudgeonly professor who will give you only half marks unless you also say that the incident ray, the refracted ray and the normal are coplanar. ii. The equation sin i = n, 1.3.1 sin r where n is the refractive index of the medium, is all right as long as the light enters the medium from a vacuum. The refractive index of air is very little different from unity. Details on the refractive index of air may be found in my notes on Stellar Atmospheres (chapter 7, section 7.1) and Celestial Mechanics (subsection11.3.3). If light is moving from one medium to another, the law of refraction takes the form n1 sin θ1 = n2 sin θ2 . 1.3.2 θ1 n1 n2 FIGURE I.5 θ2 iii. The statement of Snell’s law as given above implies, if taken literally, that there is a one-to-one relation between refractive index and density. There must be a formula relating refractive index and density. If I tell you the density, you should be able to tell me the refractive index. And if I tell you the refractive index, you should be able to tell me the density. If you arrange substances in order of increasing density, this will also be their order of increasing refractive index. This is not quite true, and, if you spend a little while looking up densities and refractive indices of substances in, for example, the CRC Handbook of Physics and Chemistry, you will find many examples of less dense substances having a higher refractive index than more dense substances. It is true in a general sense usually that denser substances have higher indices, but there is no one-to-one correspondence. In fact light is bent towards the normal in a “denser” medium as a result of its slower speed in that medium, and indeed the speed v of light in a medium of refractive index n is given by n = c /v , 1.3.3 5 where c is the speed of light in vacuo. Now the speed of light in a medium is a function of the electrical permittivity ε and the magnetic permeability µ: v = 1 / εµ . 1.3.4 The permeability of most nonferromagnetic media is very little different from that of a vacuum, so the refractive index of a medium is given approximately by ε n ≈ . 1.3.5 ε0 Thus there is a much closer correlation between refractive index and relative permittivity (dielectric constant) than between refractive index and density. Note, however, that this is only an approximate relation. In the detailed theory there is a small dependence of the speed of light and hence refractive index on the frequency (hence wavelength) of the light. Thus the refractive index is greater for violet light than for red light (violet light is refracted more violently). The splitting up of white light into its constituent colours by refraction is called dispersion. 1.4 Real and Apparent Depth When we look down into a pool of water from above, the pool looks less deep than it really is. Figure I.6 shows the formation of a virtual image of a point on the bottom of the pool by refraction at the surface. n h' h FIGURE I.6 θ' θ • 6 The diameter of the pupil of the human eye is in the range 4 to 7 mm, so, when we are looking down into a pool (or indeed looking at anything that is not very close to our eyes), he angles involved are small. Thus in figure I.6 you are asked to imagine that all the angles are small; actually to draw them small would make for a very cramped drawing. Since angles are small, I can approximate Snell’s law by tan θ' n ≈ 1.4.1 tan θ and hence real depth h tan θ' = = = n. 1.4.2 apparent depth h' tan θ For water, n is about 4 3 , so that the apparent depth is about ¾ of the real depth. Exercise. An astronomer places a photographic film, or a CCD, at the primary focus of a telescope. He then decides to insert a glass filter, of refractive index n and thickness t, in front of the film (or CCD). In which direction should he move the film or CCD, and by how much, so that the image remains in focus? Now if Snell’s law really were given by equation 1.4.1, all refracted rays from the object would, when produced backwards, appear to diverge from a single point, namely the sin θ' , virtual image. But Snell’s law is really n = so what happens if we do not make sin θ the small angle approximation? h tan θ' sin θ We have = and, if we apply the trigonometric identity tan θ = h' tan θ 1 − sin 2 θ and apply Snell’s law, we find that h n cos θ . = 1.4.3 h' 1 − n sin θ 2 2 Exercise. Show that, to first order in θ this becomes h/h' = n. Equation 1.4.3 shows h' is a function of θ − that the refracted rays, when projected backwards, do not all appear to come from a single point. In other words, a point object does not result in a point image. Figure I.7 shows (for n = 1.5 – i.e. glass rather than water) the backward projections of the refracted rays for θ' = 15, 30, 45, 60 and 75 degrees, together with their envelope or “caustic curve”. The “object” is at the bottom left corner of the frame, and the surface is the upper side of the frame. 7 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 I,7 FIGURE I.6 -0.8 -0.9 -1 0 0.2 0.4 0.6 0.8 1 Exercise (for the mathematically comfortable). Show that the parametric equations for the caustic curve are x − y tan θ' − h tan θ = 0 1.4.4 and ny sec3 θ' + h sec 2 θ = 0 . 1.4.5 Here, y = 0 is taken to be the refractive surface, and θ and θ' are related by Snell’s law. Thus refraction at a plane interface produces an aberration in the sense that light from a point object does not diverge from a point image. This type of aberration is somewhat similar to the type of aberration produced by reflection from a spherical mirror, and to that extent the aberration could be referred to as “spherical aberration”. If a point at the bottom of a pond is viewed at an angle to the surface, rather than perpendicular to it, a further aberration called “astigmatism” is produced. If I write a chapter on aberrations, this will be included there. 8 1.5 Reflection and Refraction We have described reflection and refraction, but of course when a ray of light encounters an interface between two transparent media, a portion of it is reflected and a portion is refracted, and it is natural to ask, even during an early introduction to the subject, just what fraction is reflected and what fraction is refracted. The answer to this is quite complicated, for it takes depends not only on the angle of incidence and on the two refractive indices, but also on the initial state of polarization of the incident light; it takes us quite far into electromagnetic theory and is beyond the scope of this chapter, which is intended to deal largely with just the geometry of reflection and refraction. However, since it is a natural question to ask, I can give explicit formulas for the fractions that are reflected and refracted in the case where the incident light in unpolarized. FI FR n1 θ1 n2 θ2 FT FIGURE I.8 Figure I.8 shows an incident ray of energy flux density (W m−2 normal to the direction of propagation) FI arriving at an interface between media of indices n1 and n2. It is subsequently divided into a reflected ray of flux density FR and a transmitted ray of flux density FT. The fractions transmitted and reflected (t and r) are FT  1 1  t =  (n cos θ + n cos θ ) 2 + (n cos θ + n cos θ ) 2  1.5.1 = 2n1n2 cos θ1 cos θ2   FI  1 1 2 2 1 2 2 1  9 and 1  n1 cos θ1 − n2 cos θ2   2 2 FR  n cos θ 2 − n2 cos θ1  r = =   +  1  . 1.5.2 FI 2  n1 cos θ1 + n2 cos θ2    n cos θ + n cos θ   1 1   2 2  Here the angles and indices are related through Snell’s law, equation 1.3.2. If you have the energy, show that the sum of these is 1. Both the transmitted and the reflected rays are partially plane polarized. If the angle of incidence and the refractive index are such that the transmitted and reflected rays are perpendicular to each other, the reflected ray is completely plane polarized – but such details need not trouble us in this chapter. 1 0.9 r 0.8 0.7 0.6 0.5 0.4 I.9 FIGURE I.8 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 θ1, degrees Figure I.9 shows the reflection coefficient as a function of angle of incidence for unpolarized incident light with n1 = 1.0 and n2 = 1.5 (e.g. glass). Since n2 > n1, we have external reflection. We see that for angles of incidence less than about 45 degrees, very little of the light is reflected, but after this the reflection coefficient increases rapidly with angle of incidence, approaching unity as θ1 → 90o (grazing incidence). If n1 = 1.5 and n2 = 1.0, we have internal reflection, and the reflection coefficient for this case is shown in figure I.10. For internal angles of incidence less than about 35o, little 10 light is reflected, the rest being transmitted. After this, the reflection coefficient increases rapidly, until the internal angle of incidence θ1 approaches a critical angle C, given by n2 , sin C = 1.5.3 n1 This corresponds to an angle of emergence of 90o. For angles of incidence greater than this, the light is totally internally reflected. For glass of refractive index 1.5, the critical angle is 41o.2, so that light is totally internally reflected inside a 45o prism such as is used in binoculars. 1 0.9 r 0.8 0.7 0.6 0.5 0.4 I.10 FIGURE I.9 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 θ1, degrees 11 1.6 Refraction by a Prism α n θ2 φ2 θ1 φ1 FIGURE I.11 Figure I.11 shows an isosceles prism of angle α, and a ray of light passing through it. I have drawn just one ray of a single colour. For white light, the colours will be dispersed, the violet light being deviated by the prism more than the red light. We’ll choose a wavelength such that the refractive index of the prism is n. The deviation D of the light from its original direction is θ1 − φ1 + θ2 − φ2 . I want to imagine, now, if we keep the incident ray fixed and rotate the prism, how does the deviation vary with angle of incidence θ1? By geometry, φ2 = α − φ1, so that the deviation is D = θ1 + θ 2 − α. 1.6.1 Apply Snell’s law at each of the two refracting surfaces: sin θ1 sin θ 2 =n and =n, 1.6.2a,b sin φ1 sin(α − φ1 ) and eliminate φ1: sin θ 2 = sin α n 2 − sin 2 θ1 − cos α sin θ1 . 1.6.3. Equations 1.6.1 and 1.6.3 enable us to calculate the deviation as a function of the angle of incidence θ1. The deviation is least when the light traverses the prism symmetrically, 12 with θ1 = θ2, the light inside the prism then being parallel to the base. Putting θ1 = θ2 in equation shows that minimum deviation occurs for an angle of incidence given by n sin α sin θ1 = = n sin 1 α . 2 1.6.4 2(1 + cos α) The angle of minimum deviation Dmin is 2θ1 − α, where θ1 is given by equation 1.6.4, and this leads to the following relation between the refractive index and the angle of minimum deviation: sin 1 ( Dmin + α) n = 2 . 1.6.5 sin 1 α 2 Of particular interest are prisms with α = 60o and α = 90o. I have drawn, in figure I.12 the deviation versus angle of incidence for 60- and 90-degree prisms, using (for reasons I shall explain) n = 1.31, which is approximately the refractive index of ice. For the 60o ice prism, the angle of minimum deviation is 21o.8, and for the 90o ice prism it is 45o.7. 55 50 90o 45 I.12 FIGURE I.11 Deviation, degrees 40 35 30 25 60o 20 10 20 30 40 50 60 70 80 90 Angle of incidence, degrees 13 The geometry of refraction by a regular hexagonal prism is similar to refraction by an equilateral (60o) triangular prism (figure I.13): FIGURE I.13 When hexagonal ice crystals are present in the atmosphere, sunlight is scattered in all directions, according to the angles of incidence on the various ice crystals (which may or may not be oriented randomly). However, the rate of change of the deviation with angle of incidence is least near minimum deviation; consequently much more light is deviated by 21o.8 than through other angles. Consequently we see a halo of radius about 22o around the Sun. Seen sideways on, a hexagonal crystal is rectangular, and consequently refraction is as if through a 90o prism (figure I.14): FIGURE I.14 Again, the rate of change of deviation with angle of incidence is least near minimum deviation, and consequently we may see another halo, or radius about 46o. For both 14 haloes, the violet is deviated more than the red, and therefore both haloes are tinged violet on the outside and red on the inside. 1.7 The Rainbow I do not know the exact shape of a raindrop, but I doubt very much if it is drop-shaped! Most raindrops will be more or less spherical, especially small drops, because of surface tension. If large, falling drops are distorted from an exact spherical shape, I imagine that they are more likely to be flattened to a sort of horizontal pancake shape rather than drop- shaped. Regardless, in the analysis in this section, I shall assume drops are spherical, as I am sure small drops will be. We wish to follow a light ray as it enters a spherical drop, is internally reflected, and finally emerges. See figure I.15. θ θ' y θ' θ' θ' θ FIGURE I.15 15 We see a ray of light headed for the drop, which I take to have unit radius, at impact parameter y. The deviation of the direction of the emergent ray from the direction of the incident ray is D = θ − θ' + π − 2θ' + θ − θ' = π + 2θ − 4θ' . 1.7.1 However, we shall be more interested in the angle r = π − D. A ray of light that has been deviated by D will approach the observer from a direction that makes an angle r from the centre of the rainbow, which is at the anti-solar point (figure I.16): From Sun FIGURE I.16 raindrop D Observer • r To centre of rainbow We would like to find the deviation D as a function of impact parameter. The angles of incidence and refraction are related to the impact parameter as follows: sin θ = y , 1.7.2 cos θ = 1 − y2 , 1.7.3 sin θ' = y / n , 1.7.4 and cos θ = 1 − y2/ n2 . 1.7.5 These, together with equation 1.7.1, give us the deviation as a function of impact parameter. The deviation goes through a minimum – and r goes through a maximum. The deviation for a light ray of impact parameter y is 16 D = π + 2 sin −1 y − 4 sin −1 ( y / n). 1.7.6 This is shown in figure I.17 for n = 1.3439 (blue - λ = 400 nm) and n = 1.3316 (red - λ = 650 nm). 180 175 170 165 I.17 FIGURE I.16 Deviation, degrees 160 155 150 145 140 135 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Impact parameter The angular distance r from the centre of the bow is r = π − D, so that r = 4 sin −1 ( y / n) − 2 sin −1 y. 1.7.7 Differentiation gives the maximum value, R, of r - i.e. the radius of the bow – or the minimum deviation Dmin. We obtain for the radius of the bow 4 − n2 4 − n2 . R = 4 sin −1 − 2 sin −1 1.7.8 3n 2 3 For n = 1.3439 (blue) this is 40o 31' and for n = 1.3316 (red) this is 42o 17'. Thus the blue is on the inside of the bow, and red on the outside. For grazing incidence (impact parameter = 1), the deviation is 2π − 4 sin −1 (1 / n), or 167 o 40' for blue or 165o 18' for red. This corresponds to a distance from the center of the bow r = 4 sin −1 (1 / n) − π , which is 12o 20' for blue and 14o 42' for red. It will be 17 seen from figure I.17 that for deviations between Dmin and about 166o there are two impact parameters that result in the same deviation. The paths of two rays with the same deviation are shown in figure I.18. One ray is drawn as a full line, the other as a dashed line. They start with different impact parameters, and take different paths through the drop, but finish in the same direction. The drawing is done for a deviation of 145o, or 35o from the bow centre. The two impact parameters are 0.969 and 0.636. When these two rays are recombined by being brought to a focus on the retina of the eye, they have satisfied all the conditions for interference, and the result will be brightness or darkness according as to whether the path difference is an even or an odd number of half wavelengths. FIGURE I.18 18 If you look just inside the inner (blue) margin of the bow, you can often clearly see the interference fringes produced by two rays with the same deviation. I haven’t tried, but if you were to look through a filter that transmits just one colour, these fringes (if they are bright enough to see) should be well defined. The optical path difference for a given deviation, or given r, depends on the radius of the drop (and on its refractive index). For a drop of radius a it is easy to see that the optical path difference is 2a(cos θ2 − cos θ1 ) − 4n(cos θ'2 − cos θ'1 ) , where θ1 is the larger of the two angles of incidence. Presumably if you were to measure the fringe spacing, you could determine the size of the drops. Or, if you were to conduct a Fourier analysis of the visibility of the fringes, you could determine, at least in principle, the size distribution of the drops. θ' θ FIGURE I.19 Some distance outside the primary rainbow, there is a secondary rainbow, with colours reversed – i.e. red on the inside, blue on the outside. This is formed by two internal reflections inside the drop (figure I.19). The deviation of the final emergent ray from the 19 direction of the incident ray is (θ − θ') + (π − 2θ') + (π − 2θ') + (θ − θ'), or 2π + 2θ − 6θ' counterclockwise, which amounts to D = 6θ' − 2θ clockwise. That is, D = 6 sin −1 ( y / n ) − 2 sin −1 y . 1.7.9 clockwise, and, as before, this corresponds to an angular distance from the centre of the bow r = π − D. I show in figure I.20 the deviation as a function of impact parameter y. Notice that D goes through a maximum (and hence r has a minimum value). There is no light scattered outside the primary bow, and no light scattered inside the secondary bow. When the full glory of a primary bow and a secondary bow is observed, it will be seen that the space between the two bows is relatively dark, whereas it is brighter inside the primary bow and outside the secondary bow. 140 120 100 Deviation, degrees 80 60 I.20 FIGURE I.18 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Impact parameter Differentiation shows that the least value of r, (greatest deviation) corresponding to the radius of the secondary bow is 3 − n2 3 − n2 R = 6 sin −1 − 2 sin −1 . 1.7.10 2n 2 2 For n = 1.3439 (blue) this is 53o 42' and for n = 1.3316 (red) this is 50o 31'. Thus the red is on the inside of the bow, and blue on the outside. 20 Problem. In principle a tertiary bow is possible, involving three internal reflections. I don’t know if anyone has observed a tertiary bow, but I am told that the primary bow is blue on the inside, the secondary bow is red on the inside, and “therefore” the tertiary bow would be blue on the inside. On the contrary, I assert that the tertiary bow would be red on the inside. Why is this? Let us return to the primary bow. The deviation is (equation 1.7.1) D = π + 2θ − 4θ'. Let’s take n = 4/3, which it will be for somewhere in the middle of the spectrum. According to equation 1.7.8, the radius of the bow (R = π − Dmin) is then about 42o. That is, 2θ' − θ = 21o. If we combine this with Snell’s law, 3 sin θ = 4 sin θ' , we find that, at minimum deviation (i.e. where the primary bow is), θ = 60o.5 and θ' = 40o.8. Now, at the point of internal reflection, not all of the light is reflected (because θ' is less than the critical angle of 36o.9), and it will be seen that the angle between the reflected ands refracted rays is (180 − 60.6 − 40.8) degrees = 78o.6. Those readers who are familiar with Brewster’s law will understand that when the reflected and transmitted rays are at right angles to each other, the reflected ray is completely plane polarized. The angle, as we have seen, is not 90o, but is 78o.6, but this is sufficiently close to the Brewster condition that the reflected light, while not completely plane polarized, is strongly polarized. Thus, as can be verified with a polarizing filter, the rainbow is strongly plane polarized. I now want to address the question as to how the brightness of the bow varies from centre to circumference. It is brightest where the slope of the deviation versus impact parameter curve is least – i.e. at minimum deviation (for the primary bow) or maximum deviation (for the secondary bow). Indeed the radiance (surface brightness) at a given distance from the centre of the bow is (among other things) inversely proportional to the slope of that curve. The situation is complicated a little in that, for deviations between Dmin and 2π − 4 sin −1 (1 / n), (this latter being the deviation for grazing incidence), there are two impact parameters giving rise to the same deviation, but for deviations greater than that (i.e. closer to the centre of the bow) only one impact parameter corresponds to a given deviation. Let us ask ourselves, for example, how bright is the bow at 35o from the centre (deviation 145o)? The deviation is related to impact parameter by equation 1.7.6. For n = 4/3, we find that the impact parameters for deviations of 144, 145 and 146 degrees are as follows: Do y 144 0.6583 and 0.9623 145 0.6366 and 0.9693 146 0.6157 and 0.9736 Figure I.21 shows a raindrop seen from the direction of the approaching photons. 21 FIGURE I.21 Any photons with impact parameters within the two dark annuli will be deviated between 144o and 146o, and will ultimately approach the observer at angular distances between 36o and 34o from the centre. The radiance at a distance of 35o from the centre will be proportional, among other things, to the sum of the areas of these two annuli. I have said “among other things”. Let us now think about other things. I have drawn figure I.15 as if all of the light is transmitted as it enters the drop, and then all of it is internally reflected within the drop, and finally all of it emerges when it leaves the drop. This is not so, of course. At entrance, at internal reflection and at emergence, some of the light is reflected and some is transmitted. The fractions that are reflected or transmitted depend on the angle of incidence, but, for minimum deviation, about 94% is transmitted on entry to and again at exit from the drop, but only about 6% is internally reflected. Also, after entry, internal reflection and exit, the percentage of polarization of the ray increases. The formulas for the reflection and transmission coefficients (Fresnel’s equations) are somewhat complicated (equations 1.5.1 and 1.5.2 are for unpolarized incident light), but I have followed them through as a function of impact parameter, and have also taken account of the sizes of the one or two annuli involved for each impact parameter, and I have consequently calculated the variation of surface brightness for one colour (n = 4/3) from the centre to the circumference of the bow. I omit the details of the 22 calculations, since this chapter was originally planned as an elementary account of reflection and transmission, and we seem to have gone a little beyond that, but I show the results of the calculation in figure I.22. I have not, however, taken account of the interference phenomena, which can often be clearly seen just within the primary bow. Brightness of primary bow 8 7 I.22 FIGURE I.19 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 1.8 Problem θ ω * v FIGURE I.23 23 See figure I.23. A ray of light is directed at a glass cube of side a, refractive index n, eventually to form a spot on a screen beyond the cube. The cube is rotating at an angular speed ω. Show that, when the angle of incidence is θ, the speed of the spot on the screen is  n 2 cos 2θ + sin 4 θ  v = aω cos θ −    (n 2 − sin 2 θ)3 / 2   and that the greatest displacement of the spot on the screen from the undisplaced ray is a  1 − 1  . D = 2  n − sin θ  2 2  I refrain from asking what is the maximum speed and for what value of θ does it occur. However, I ran the equation for the speed on the computer, with n = 1.5, and, if the formula is right, the speed is 1 aω when θ = 0, and it increases monotonically up to 3 θ = 45o, which is as far as we can go for a cube. However, if we have a rectangular glass block, we can increase θ to 90o, at which time the speed is 0.8944 aω. The speed goes through a maximum of about 0.9843aω when θ = 79o.3. I’d be interested if anyone can confirm this, and do it analytically. 1.9 Differential Form of Snell’s Law Snell’s law in the form n sin θ = constant is useful in calculating how a light ray is bent in travelling from one medium to another where there is a discrete change of refractive index. If there is a medium in which the refractive index is changing continuously, a differential form of Snell’s law may be useful. This is obtained simply by differentiation of n sin θ = constant, to obtain the differential form of Snell’s law: dn cot θ dθ = − . 1.9.1 n Let us see how this might be used. Let us suppose, for example, that we have some medium in which the refractive index diminishes with height y according to a n = . 1.9.2 a− y 24 Here a is an arbitrary distance, and I am going to restrict our interest only to heights less than a – so that n doesn’t become infinite! I have chosen equation 1.9.2 only because it happens to lead to a rather simple result. Let us suppose that we direct a light ray upwards from the origin in a direction making an angle α with the horizontal, and we wish to trace the ray through the medium as the refractive index continuously changes. See figure I.24. y ψ θ α x FIGURE I.24 When the height is y, the angle of incidence is θ, and the slope dy / dx = tan ψ , where ψ = π /2 − θ . With this and equation 1.9.2, Snell’s law takes the form dy . tan ψ dψ = 1.9.3 a− y On integration, this becomes (a − y ) sec ψ = constant = a sec α . 1.9.4 Let a − y = η and a sec α = c . Equation 1.9.4 then becomes 25 sec ψ = c / η . 1.9.5 But tan ψ = sec 2 ψ − 1 = dy /dx = − dη / dx , so we obtain dη c 2 − η2 = − . 1.9.6 dx η On integration, this becomes x = c 2 − η2 + C . 1.9.7 We recall that a − y = η and a sec α = c , from which equation 1.9.7 becomes x = a 2 tan 2 α + 2ay − y 2 + C . 1.9.8 Since the ray starts at the origin, it follows that C = − a tan α . The path of the ray, therefore, is found, after some algebra, to be ( x + a tan α) 2 + ( y − a) 2 = a 2 sec 2 α , 1.9.9 which is a circle, centre (− a tan α , a ) , radius a sec α . ``` DOCUMENT INFO Shared By: Categories: Stats: views: 21 posted: 5/29/2010 language: English pages: 25 How are you planning on using Docstoc?
crawl-data/CC-MAIN-2013-48/segments/1387345760007/warc/CC-MAIN-20131218054920-00062-ip-10-33-133-15.ec2.internal.warc.gz
null
Here is exciting news, especially for the astrobiologists! Recent evidence is being considered the best proof till date for availability of water on Europa – the life-supporting moon of the greatest planet Jupiter. The alluring signs of the presence of water plume on Jupiter were located by the Hubble Space Telescope of National Aeronautics and Space Administration (NASA). However, the Hubble Telescope has its limits and sensitivity. The current proof got even stronger with a newly analyzed data provided by Galileo spacecraft. This data was based on the findings of Galileo. Galileo is an unmanned spacecraft of NASA which orbited around Jupiter to study about its planet and associated moons. The Galileo spacecraft revolved around Jupiter from the year 1995 to 2003. It also identified possibly a water plume while flying nearby the Europa moon in the year 1997. The lead author of the recent study, Xianzhe Jia said that the recently analyzed data of Galileo is a definite proof indicating that there exists a water plume on Jupiter. Mr. Xianzhe Jia is an associate professor at the Climate and Space Sciences and Engineering Department (University of Michigan). If the recent evidence turns out to be real, a great way will be paved to study in depth about the Europa moon. In such a case of the existence of water plume on Europa, the spacecraft will be able to take samples from the Europa ocean without actually touching the Europa moon surface. NASA is continually making efforts for this objective. It is worth mentioning that Europa is a bit smaller in size when compared with Earth. As per scientists, the Europa moon has an enormous quantity of liquid water. This quantity is expected to be double the amount of water available on Earth. The scientists involved with the study of Jupiter say that the moon has got liquid water under its ice coating. It is also noted that the water ocean is possibly in contact with the rocky center of Europa which indicates that there might be some interesting chemical reactions going over there. The same condition has also compelled many scientists to think that Europa might be one of the possible options for the existence of alien life. In the year 2012, the Hubble telescope had recognized signs of plume near the South pole of the Europa moon. The telescope did more similar observations in 2014 and 2016 which indicated the presence of plumes near the equator of Europa moon.
<urn:uuid:9c07949b-c663-42f9-b5e7-db84d6d378b5>
{ "date": "2018-10-17T13:55:35", "dump": "CC-MAIN-2018-43", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511175.9/warc/CC-MAIN-20181017132258-20181017153758-00057.warc.gz", "int_score": 4, "language": "en", "language_score": 0.949321448802948, "score": 3.65625, "token_count": 473, "url": "https://newsspaceflight.com/water-plume-on-jupiters-moon-europa/" }
# math posted by . convert y=x^2+9x+14 to factored form • math - (x+7)(x+2) ## Respond to this Question First Name School Subject Your Answer ## Similar Questions 1. ### Algebra 2 Well I'm curently taking this class as a sophmore and have taken geometry freshmen year of high school and also I am taking physics at the same time and in math class when I'm asked to factor i go absolutley nuts because guessing numbers … 2. ### Algebra F) Why is (3x + 5) (x - 2) + (2x - 3) (x - 2) not in factored form? 3. ### Mat 117 •I am having trouble figuring out this question. Why is (3x + 5) (x - 2) + (2x - 3) (x - 2) not in factored form? 4. ### math Q: Convert 4x^2 + 4y^2 -8x -16y -29 = 0 into standard form. I first started by pairing the like terms together, getting: 4x^2 -8x + 4y^2 -16y = 29 The next step, I'm a little confused. I know I need to complete the square, but I'm … 5. ### Math Can someone please tell me Why is (4x + 5) (2x - 1) + (x - 9) (2x - 1) not in factored form? 6. ### Math Can someone please tell me Why is (4x + 5) (2x - 1) + (x - 9) (2x - 1) not in factored form? 7. ### Integrated Math 1 Consider y=x^2+8x+16. What is the correct way to factor this equation? 8. ### Algebra 1. a) write y=4x+8 in factored form 2. a) write y=-2x-6 in factored form 3. a) write y=1/3x+3 in factored form These are the answers I got: 1. y=4(x+2) 2. y= -2(x+3) 3. y=1/3(x+9) If I got any of these wrong, tell me what I'd did wrong. 9. ### alegebra 1. What is the factored form of 4x 2 + 12x + 5? 10. ### Math This is the second part of a two part question for an online class. It gave me the degree and the zeros and I had to give the factored form. I got that part right, but I need to know how to get the expanded form from the factored form. … More Similar Questions
crawl-data/CC-MAIN-2018-05/segments/1516084890771.63/warc/CC-MAIN-20180121135825-20180121155825-00419.warc.gz
null
# Zeros Of Polynomials A polynomial of degree n has at most n distinct zeros. Let p(x) be a polynomial function with real coefficients. If a + ib is an imaginary zero of p(x), the conjugate a-bi is also a zero of p(x). For a polynomial f(x) and a constant c, 1. If f(c) = 0, then x - c is a factor of f(x). 2. If x - c is a factor of f(x), then f(c) = 0. The Factor Theorem says that if we find a value of c such that f(c) = 0, then x - c is a factor of f(x). And, if x - c is a factor of f(x), then f(c) = 0. f a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient. Example: Use the Rational Root Test to list all the possible rational zeros for . Solution: Step 1: Find factors of the leading coefficient 1, -1, 2, -2, 4, -4 Step 2: Find factors of the constant 1, -1, 2, -2, 5, -5, 10, -10 Step 3: Find all the POSSIBLE rational zeros or roots. Writing the possible factors as we get: Here is a final list of all the possible rational zeros, each one written once and reduced:
crawl-data/CC-MAIN-2019-13/segments/1552912202640.37/warc/CC-MAIN-20190322074800-20190322100800-00301.warc.gz
null
This lesson plan will explore the wide-ranging debate over American slavery by presenting the lives of its leading opponents and defenders and the views they held about America's "peculiar institution." Sometimes, people will fight to keep someone else from being treated poorly. Disagreement over slavery was central to the conflict between the North and the South. The nation was deeply divided. When children hear, write and recite poetry, they understand more deeply the qualities of verse — the importance of sound, compactness, internal integrity, imagination, and line. Working collaboratively on poetry provides a safe structure for student creativity. Poetry provides us with a rich vehicle for helping children explore how language sounds and works. Students will use their senses to experience poetry.
<urn:uuid:2d62887c-ed5a-4a83-9e3e-a96e43f74f77>
{ "date": "2014-12-22T16:22:32", "dump": "CC-MAIN-2014-52", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802775404.88/warc/CC-MAIN-20141217075255-00043-ip-10-231-17-201.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9645167589187622, "score": 4.28125, "token_count": 151, "url": "http://edsitement.neh.gov/calendar/2012-11-13" }
Being a machinist is precise work that calls for a precise mind. There is an abundance of measuring, cutting, calculating, and use of machines. It’s not a job that is for everyone, but it may be just the right fit for you. Machinist Job Responsibilities Machinist utilize machine tools like milling machines, grinders, and lathes to create metal parts. Precision machinists usually make small orders or unique items even though they may make substantial amounts of an individual part. They put their knowledge of the working components of metal and their ability with machine tools to good use to fulfill the operations necessary to make machined products to satisfy certain specifications. The parts machinists produce vary from automobile pistons to bolts. Production machinists may make make large numbers of one part, more specifically parts needing the use of intricate operations and substantial precision. Several current machine tools are “computer numerically controlled (CNC).” CNC machines carry out the instructions of a computer program to maintain proper cutting tool speed, exchange worn tools, and carry out all necessary cuts to make a part. Machinist usually work with computer-controlled programmers to find out how the programmed equipment will slice a part. It’s the machinist’s job to determine the slicing path, feed rate, and the speed of the slice. The programmer changes the path, feed information, and speed into a list of instructions for the CNC machine tool. Machinists have to be able to use computer-controlled machinery as well as manual machinery in their job. Maintenance machinists make new or fix existing parts for machinery. After a maintenance laborer or industrial machinery mechanic finds the broken part of a machine, they then inform and give the broken piece to the machinist. Machinists look to blueprints in order to fix broken parts and carry out the same machining operations that were required to produce the original piece. Maintenance machinists operate in several manufacturing industries where production machinists are focused on limited industries. The technology of machining is quickly advancing and for that reason machinists have to be able to successfully navigate a wide range of machines. Some of the machines out today use water jets, electrified wires, or lasers to cut the part. While a few of the computer controls are the same as other machine tools, machinists have to comprehend the special slicing properties of these different machines. Engineers are constantly producing new kinds of machine tools as well as new materials to machine; for that reason machinists have to always be up-to-date on new machining techniques and properties. Machinist Training and Education Requirements There are many paths that lead to becoming a skilled machinist. Several have previously worked as operators, machine setters, or tenders. High school students should have advanced math courses under their belts, especially geometry and trigonometry. Classes in blueprint reading, drafting, and metalworking are useful as well. Advanced positions call for the use of advanced applied physics and calculus. Because of the growing utilization of computer-controlled machinery, fundamental computer skills are required before embarking on a training program. Some machinists complete their learning in the field after high school, but a great deal gather their skills in a combination of on-the-job and classroom training. Formal apprenticeship programs are usually sponsored by a manufacturer or a union and are a great for aspiring machinists, but keep in mind that they can be challenging to get into. More often than not apprentices are required to have a high school diploma, GED, or the equivalent; and also have trigonometry and algebra classes. Machinist Salary and Wages The median hourly wages of machinists were $17.41 in May of 2008. The middle fifty percent made between $13.66 and $21.85. The lowest ten percent made less than $10.79, and the top ten percent made more than $26.60. Apprentices make substantially less than well-versed machinists, but wages increase rapidly as their skills develop. Most employers are even willing to pay for apprentices’ training courses.* *According to the BLS, http://www.bls.gov/oco/ In order to advance their level of skills and degree of competency, several State apprenticeship boards, training facilities, and colleges offer certification programs. Successful completion of certification programs awards a machinist with more and better career chances and assists employers in deciding the level of abilities of new hires. Journeyworker certification may be awarded from State apprenticeship boards after finishing an apprenticeship. This kind of certification is regarded by several employers and paves the way to better career chances. Machinist Professional Associations The International Association of Machinists and Aerospace Workers (IAMAW) was founded in 1888 by 19 machinists that called themselves The Order of United Machinist and Mechanical Engineers. The association remained clandestine for a number of years because of employer hostility directed at organized labor. In 1889 the first Machinist Union convention convened with 34 locals represented, hosted in the chambers of the Georgia State Senate. Tom Talbot was declared “Grand Master Machinist” and the IAM monthly journal began. At the gathering the union’s name was switched to ‘National Association of Machinists.’ Since The spread of NAM across North America forced the union once again to change their name, this time to ‘The International Association of Machinists.’ Get Your Degree! Find schools and get information on the program that’s right for you. Powered by Campus Explorer
<urn:uuid:cff5795f-acab-4bf6-a163-244da83443dc>
{ "date": "2017-09-24T13:50:29", "dump": "CC-MAIN-2017-39", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818690029.51/warc/CC-MAIN-20170924134120-20170924154120-00097.warc.gz", "int_score": 4, "language": "en", "language_score": 0.943961501121521, "score": 3.671875, "token_count": 1170, "url": "http://jobdescriptions.net/manufacturing/machinist/" }
# Inverse Square Law Formula • Last Updated : 12 May, 2022 The inverse square law describes the intensity of light in relation to its distance from the source. It states that the intensity of the radiation is inversely proportional to the square of the distance. In other words, the intensity of light to an observer from a source is inversely proportional to the square of the distance between the observer and the source. It is used to calculate the distance or intensity of a particular radiation. As the distance between the source and the observer rises, the intensity of the light from the source decreases. Formula The ratio of the intensity of the light source for two different time intervals is equal to the reciprocal of the squares of their respective distances of the object from the source. The intensity and distance are denoted by the symbol I and d respectively. The standard unit of intensity is candelas or lumens while for distance, it is meters. The dimensional formula of intensity and distance is [M1L0T-3] and [M0L1T0]. I ∝ 1/d2 where, I is the intensity of light, d is the distance between light source and observer. Consider light sources of intensity I1 and I2 at distances d1 and d2 respectively. For this scenario, the inverse square formula is given by, I1/I2 = d22/d12 ### Sample Problems Problem 1. A light source has an intensity of 20 candelas at a distance of 3 m from the object. Calculate its intensity if it is at a distance of 6 m from the object. Solution: We have, I1 = 20 d1 = 3 d2 = 6 Using the formula we get, I1/I2 = d22/d12 => 20/I2 = 62/32 => I2 = 20 (9/36) => I2 = 5 candelas Problem 2. A light source has the intensity of 50 candelas at a distance of 30 m from the object. Calculate its intensity if it is at a distance of 10 m from the object. Solution: We have, I1 = 50 d1 = 30 d2 = 10 Using the formula we get, => 50/I2 = 102/302 => I2 = 50 (900/100) => I2 = 50 (9) => I2 = 450 candelas Problem 3. A light source has the intensity of 100 candelas at a distance of 20 m from the object. Calculate its distance if its intensity is 80 candelas. Solution: We have, I1 = 100 I2 = 80 d1 = 20 Using the formula we get, => 100/80 = d22/202 => d22 = (400) (5/4) => d22 = 500 => d2 = 22.4 m Problem 4. A light source has the intensity of 20 candelas at a distance of 1 m from the object. Calculate its distance if its intensity is 40 candelas. Solution: We have, I1 = 20 I2 = 40 d1 = 1 Using the formula we get, => 20/40 = d22/12 => d22 = 1/2 => d2 = 0.7071 m Problem 5. Calculate the value of d1 for d2 = 100 m, I1 = 200 candelas and I2 = 300 candelas. Solution: We have, d2 = 100 I1 = 200 I2 = 300 Using the formula we get, => 200/300 = 100/d12 => d12 = 100 (2/3) => d1 = 122.48 m Problem 6. Calculate the value of I1 for I2 = 150 candelas, d1 = 5 m and d2 = 15 m. Solution: We have, I2 = 150 d1 = 5 d2 = 15 Using the formula we get, => I1/100 = 152/52 => I1 = 32 (100) => I1 = 900 candelas Problem 7. Calculate the value of I2 for I1 = 650 candelas, d1 = 36 m and d2 = 24 m. Solution: We have, I1 = 650 d1 = 36 d2 = 24 Using the formula we get, => 650/I2 = 242/362 => I2 = 650 (1296/576) => I2 = 1462.5 candelas My Personal Notes arrow_drop_up Related Articles
crawl-data/CC-MAIN-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00747.warc.gz
null
# Electric Dipole ## Homework Statement An electric dipole consists of two charges of equal magnitude ##q## and opposite sign, which are kept at a distance ##d## apart. The dipole moment is ##p= qd## . Let us next place two such dipoles, placed at distance ##r## apart, as shown in the accompanying figure. a) Assuming that the potential energy for the charges while at infinity is zero, find the exact potential energy of the configuration in terms of ##d, r, q ## and fundamental constants. b)When ##d<<r## , approximate your previous result in terms of ##p, r ## and fundamental constants. ## Homework Equations ##V = \frac {1}{4\pi \epsilon_0} \frac{q}{r}## ##W = Vq## ## The Attempt at a Solution For the positve charge of A dipole, I calculated the potential energy ##= +q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d}) ##, because, ##W = Vq## The potental energy for the other three charges are the same. So, the potential energy of the configuration is ## = 4q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d})## ##= \frac{q^2}{\pi \epsilon _0} (- \frac{1}{r} + \frac {1}{\sqrt{r^2 +d^2}} - \frac{1}{d})##; Then , I can't find any way how to approximate the result when ##d << r##; In this case, I substituted ##r^2## for ##r^2 + d^2## ; So, two of the terms in bracket are cancelled. Then I plugged in ## q = \frac{p}{d}## ; But, still ##d## is there. Orodruin Staff Emeritus Homework Helper Gold Member 2021 Award For the positve charge of A dipole, I calculated the potential energy ##= +q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d}) ##, because, ##W = Vq## The potental energy for the other three charges are the same. This is not correct. The potential energy (q1q2/4πεr) is for a pair of charges separated by a given distance. The way you are implementing it, you are double counting each pair and end up with double the potential energy. So, the potential energy of the configuration is ## = 4q \cdot \frac{1}{4\pi \epsilon _0} (\frac{-q}{r} + \frac {+q}{\sqrt{r^2 +d^2}} + \frac{-q}{d})## ##= \frac{q^2}{\pi \epsilon _0} (- \frac{1}{r} + \frac {1}{\sqrt{r^2 +d^2}} - \frac{1}{d})##; Then , I can't find any way how to approximate the result when ##d << r##; In this case, I substituted ##r^2## for ##r^2 + d^2## ; So, two of the terms in bracket are cancelled. Then I plugged in ## q = \frac{p}{d}## ; But, still ##d## is there. The term proportional to 1/d in your parenthesis is the energy from the construction of the dipoles themselves. This is generally going to be much higher than the potential between the dipoles. Just substituting ##r^2## for ##r^2 + d^2## is going to make the potential between the dipoles disappear (as you noticed, the terms cancelled) and you will end up with an uninteresting result. Instead, you should make an expansion of the square root for small ##d##. This is not correct. The potential energy (q1q2/4πεr) is for a pair of charges separated by a given distance. The way you are implementing it, you are double counting each pair and end up with double the potential energy. I agree with you. So, the potential energy will be half of my calculation. The term proportional to 1/d in your parenthesis is the energy from the construction of the dipoles themselves. This is generally going to be much higher than the potential between the dipoles. Just substituting r2r^2 for r2+d2r^2 + d^2 is going to make the potential between the dipoles disappear (as you noticed, the terms cancelled) and you will end up with an uninteresting result. Instead, you should make an expansion of the square root for small dd. So, I need to leave the term ##\frac {1}{d}## ? Then it becomes, ##\frac{1}{2} \cdot \frac{q^2}{\pi \epsilon _0}(- \frac{1}{r} + \frac{1}{\sqrt{d^2 + r^2}})## ##= \frac{q^2}{2 \pi \epsilon _0}(- \frac{1}{r} + \frac{1}{r} \cdot [1 + (\frac{d}{r})^2]^{- \frac{1}{2}})## ##= \frac{q^2}{2 \pi \epsilon _0} \frac{1}{r} (-1+ [1 - \frac{1}{2}(\frac{d}{r})^2] )## ##= \frac{q^2}{2 \pi \epsilon _0} \frac{1}{r} (- \frac{1}{2}(\frac{d}{r})^2))## ##= - \frac{p^2}{4 \pi \epsilon _0 r^3} ## Last edited: Orodruin Staff Emeritus $$\frac{q^2}{2 \pi \epsilon _0 r}\left(- 1 + \frac{1}{ \sqrt{1 + (\frac{d}{r})^2}}\right)$$
crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00126.warc.gz
null
February 12, 2016 Obstructive Sleep Apnea Obstructive sleep apnea (OSA) is a disorder in which a person stops breathing during the night, perhaps hundreds of times. These gaps in breathing are called apneas. The word apnea means absence of breath. An obstructive apnea episode is defined as the absence of airflow for at least 10 seconds. Sleep apnea is usually accompanied by snoring, disturbed sleep, and daytime sleepiness. People might not even know they have the condition. Obstructive Sleep Apnea Obstructive sleep apnea (OSA) occurs when tissues in the upper throat collapse at different times during sleep, thereby blocking the passage of air. In general, OSA occurs as follows: - On its way to the lungs, air passes through the nose, mouth, and throat (the upper airway). - Under normal conditions, the back of the throat is soft and tends to collapse inward as a person breathes. - Dilator (widening) muscles work against this collapse to keep the airway open. Interference or abnormalities in this process cause air turbulence. - If the tissues at the back of the throat collapse and become momentarily blocked, apnea occurs. Breath is temporarily stopped. In most cases the person is unaware of it, although sometimes they awaken and gasp for breath. - In some cases, the interference is incomplete (called obstructive hypopnea) and causes continuous but slow and shallow breathing. In response, the throat vibrates and makes the sound of snoring. Snoring can occur whether a person breathes through the mouth or the nose. (Snoring often occurs without sleep apnea.) - Apnea decreases the amount of oxygen in the blood, and eventually this lack of oxygen triggers the lungs to suck in air. - At this point, the patient may make a gasping or snorting sound but does not usually fully wake up. Obstructive sleep apnea is defined as five or more episodes of apnea or hypopnea per hour of sleep (called apnea-hypopnea index or AHI) in individuals who have excessive daytime sleepiness. Patients with 15 or more episodes of apnea or hypopnea per hour of sleep are considered to have moderate- sleep apnea. Other Causes of Apnea - Central sleep apnea is much less common. It is caused by some problem in the central nervous system, most likely a failure of the brain to signal the airway muscles to breathe. In such cases, oxygen levels drop abruptly and usually the sleeper wakes with a start. Often people with central sleep apnea recall waking up. They generally experience less sleepiness during the day than people with obstructive sleep apnea. Heart disease, and in particular heart failure, is the most common cause of central sleep apnea. - Mixed apnea is the term used when central and obstructive sleep apneas occur together. - Upper airway resistance syndrome (UARS) is a condition in which patients snore, wake frequently during the night, and have excessive daytime sleepiness. However, UARS patients do not have the breathing abnormalities that characterize sleep apnea and they do not show a reduction in blood oxygen levels. Unlike apnea, UARS is more likely to occur in women than in men. Treatments are similar to those of sleep apnea. It is not known if UARS has any serious health complications. MOST POPULAR - HEALTH - Disparity in Life Spans of the Rich and the Poor Is Growing - Well: How the ‘Dirt Cure’ Can Make for Healthier Families - Well: Why We Get Running Injuries (and How to Prevent Them) - The New Old Age: In Palliative Care, Comfort Is the Top Priority - Well: Ask Well: Are Pomegranates Good For You? - Well: Simple Remedies for Constipation - Education May Cut Dementia Risk, Study Finds - Well: To Reduce the Risk of Alzheimer’s, Eat Fish - Keeping Dr. Paul Kalanithi’s Voice Alive - Prepare for ‘Guerrilla Warfare’ With Zika-Carrying Mosquitoes, Experts Warn
<urn:uuid:0cfb88b6-7f6c-4430-b23a-c9a328d7e35a>
{ "date": "2016-02-13T06:50:36", "dump": "CC-MAIN-2016-07", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166222.10/warc/CC-MAIN-20160205193926-00137-ip-10-236-182-209.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9282829761505127, "score": 4.15625, "token_count": 881, "url": "http://www.nytimes.com/health/guides/disease/sleep-apnea/in-depth-report.html" }
Today’s Wonder of the Day was inspired by JONATHAN from , AL. JONATHAN Wonders, “How does a computer screen work? ” Thanks for WONDERing with us, JONATHAN! From mall kiosks to smartphones to tablet computers, touch screens are everywhere you look these days. As technology advances, keyboards and mice are quickly becoming a thing of the past. Why be burdened with cords when you can have what you want with just a touch? Touch screens are electronic visual displays that allow a user to interact directly with what is displayed on the screen, rather than using a pointing device, such as a mouse. Touch screens are designed to respond to the touch of a finger, although an object — like a stylus — can also be used. Touch screens are used in all sorts of modern electronic devices, including personal digital assistants (PDAs), satellite navigation systems and video games. Their popularity has surged recently, but the idea for the touch screen goes back several decades. Given the many different types of devices that use touch screens, it’s no surprise that there are several different types of touch screens. Each type of touch screen works a little differently from the others. Resistive touch screen systems use two thin layers separated by spacers. An electrical current runs through the two layers. When the screen is touched, the two layers make contact in the exact spot where the screen is touched. This contact creates a change in the electrical field, which a device’s computer operating system can understand. Capacitive touch screen systems feature a special layer that stores an electrical charge. When the screen is touched, some of the electrical charge is transferred to the user. This decreases the charge on the capacitive layer. The device’s computer operating system can determine from this change in electrical charge where the screen was touched. For a capacitive system to work, some of the electrical charge must be able to be transmitted to the user. This is why capacitive touch screens may not work properly if you wear gloves that block the transmission of the electrical charge. Capacitive systems are newer and tend to be more popular than resistive systems, because they transmit more light and provide a clearer picture. Of course, capacitive systems also tend to be more expensive than resistive systems, too. Surface acoustic wave touch screen systems use transducers and reflectors to measure changes in the reflection of ultrasonic waves caused when the screen is touched. These systems are the most advanced and offer the clearest picture possible. Unfortunately, they’re also extremely expensive. When touch screens first became popular, they could only sense one point of contact at a time. Technology has advanced greatly in recent years, though. Today, many touch screen devices feature multi-touch technology. This technology allows a touch screen device to interpret multiple points of contact simultaneously.
<urn:uuid:e7a82946-61b0-4571-9dca-4430d41bb9b1>
{ "date": "2015-11-27T08:09:24", "dump": "CC-MAIN-2015-48", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398448389.58/warc/CC-MAIN-20151124205408-00278-ip-10-71-132-137.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.93677818775177, "score": 4.0625, "token_count": 595, "url": "http://wonderopolis.org/wonder/how-do-touch-screens-work/" }
Forensic science is application of science to answer questions emerging from legal cases. Museum scientists are using their world-leading expertise in the natural world to provide a number of forensic services where knowledge of natural history can contribute forensic evidence. Forensic anthropology uses traditional anthropological techniques for identifying the deceased when their remains are in an advanced state of decomposition, burned, dismembered or fragmentary. Discover how the Museum's forensic anthropologists use their skills for identifying human remains in criminal investigations. Forensic entomology is the study of insects and other arthropods (ie spiders, mites) recovered from a crime scene. The Museum's entomologists have a wealth of experience and provide a range of forensic services. Find out more about how they can help with criminal investigations. Museum can also offer analysis on other types of evidence. Find out more about the other forensic services that are available within the Museum.
<urn:uuid:28e0b654-ffe3-4b84-a44a-140ffb654097>
{ "date": "2014-11-25T01:03:17", "dump": "CC-MAIN-2014-49", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416405325961.18/warc/CC-MAIN-20141119135525-00024-ip-10-235-23-156.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9231815934181213, "score": 3.5625, "token_count": 188, "url": "http://www.nhm.ac.uk/research-curation/science-facilities/consulting/forensic-science/index.html" }
The Canadarm, which made its debut in 1981 and was retired last year is, without a doubt, one of the most famous robots ever in space. But while Canada’s space program has become synonymous with this giant grappler, researchers here have contributed to space science in all sorts of ways. 1. Greenhouses in space: At the University of Guelph, Mike Dixon and his team are working on “biological life support”—systems that will help sustain long-term human exploration to distant planets. “Canada currently leads the world in research and technology development in this field,” says Dixon, director of Guelph’s Controlled Environment Systems Research Facility, where they’re finding ways to grow plants inside greenhouses with techniques that could one day allow us to grow crops on the moon or Mars. 2. Space vision system: Conditions in space can switch from extreme dark to brightness, making it hard for astronauts to gauge distance and speed with eyesight alone. The Canadian Space Vision System, which was first thought up about three decades ago, uses TV cameras as sensors to help astronauts see better, giving information about a specific target so they have an easier time locating it, and helping the Canadarm and Canadarm2 do their work. 3. Microgravity isolation mount: When astronauts attempt to do science experiments in space, they can find their results bungled by tiny disturbances in microgravity caused by on-board equipment like fans and thrusters, or even the movement of the astronauts themselves. To make it easier, Canadians developed the microgravity isolation mount, which uses magnetic levitation to protect fragile experiments from the spacecraft’s vibrations. It was first launched into space in 1996. 4. STEM antenna: Invented by Canadian inventor George J. Klein, the STEM antenna (short for “storable tubular extendible member”) looks like a roll of tightly coiled steel, like a large measuring tape. Once it’s in space, the roll can be unwound with a small motor into a strong tube to become an antenna. When Canada’s first satellite, Alouette I, was launched in 1962, it carried four STEM antennae; the design was also used on Mercury and Gemini spacecraft that brought the first Americans into space. 5. Landing gear on the Apollo lunar module: Using a landing system designed by Canada’s Héroux-Devtek, the Apollo lunar module was the first vehicle to take humans to another surface beyond Earth. Facing a tight timeline in the space race between the U.S. and Russia, Héroux-Devtek produced the landing gear systems used in all six moon landings; their hardware can still be found on the moon today. Sources: Canadian Space Agency, Mike Dixon Have you ever wondered which cities have the most bars, smokers, absentee workers and people searching for love? What about how Canada compares to the world in terms of the size of its military, the size of our houses and the number of cars we own? The nswers to all those questions, and many more, can be found in the first ever Maclean’s Book of Lists. Buy your copy of the Maclean’s Book of Lists at the newsstand or order online now.
<urn:uuid:99cc5b45-8610-44f4-9f37-97791fc6132f>
{ "date": "2014-12-19T15:46:56", "dump": "CC-MAIN-2014-52", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768724.86/warc/CC-MAIN-20141217075248-00115-ip-10-231-17-201.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.942620038986206, "score": 4.125, "token_count": 681, "url": "http://www.macleans.ca/society/life/5-canadian-space-inventions-that-arent-the-canadarm/" }
Over 750,000 people pass through New York City’s Grand Central Terminal each day. Located in the heart of the city, it’s one of the largest train stations in the world. Its historic significance dates back to 1913, when it opened its doors to the public. At the time, few were aware of the secret computer that sat deep in a sub basement below the hustle and bustle of the city’s busy travelers. Its existence was kept secret all the way into the 1980’s. Westinghouse had designed a system that would allow authorities to locate a stuck train in a tunnel. There were cords stretched the length of the tunnels. If a train stalled, the operator could reach out and yank on the cord. This would set off an alarm that would alert everyone of the stuck train. The problem being that even though they knew a train was down, they did not know exactly where. And that’s where the computer come in. Westinghouse designed it to calculate where the train was, and write its location on some ticker tape. So this is the part of the post where we tell you how the computer established where exactly the train breakdown occurred. Although the storyteller in the video is admirably enthusiastic about telling the story, our depth of detail on the engineering that went into this seems nowhere to be found. Let us know in the comments below if you have a source of more information. Or just post your own conjecture on how you would have done it with the early 20th century tech. The invention of the two way radio made the whole thing obsolete not long after is was built. Never-the-less, it remains intact to this day. Thanks to [Greg] for the tip! [James] is a frequent user of the London Underground, a subway system that is not immune to breakdowns and delays. He wanted a way to easily tell if any of the trains were being disrupted, and thanks to some LEDs, he now has that information available at a glance without having to check a webpage first. Inspired by the Blinky Tape project at FT Engineering, [James] thought he could use the same strip of addressable LEDs to display information about the tube. A Raspberry Pi B+ gathers data from the London Underground’s TfL API and does a few calculations on the data. If there is a delay, the LEDs in the corresponding section of the strip will pulse, alerting the user to a problem with just a passing glance. The project is one of many that displays data about the conditions you’ll find when you step outside the house, without having to look at a computer or smartphone. We recently featured an artistic lamp which displays weather forecasts for 12 hours into the future, and there was an umbrella stand which did the same thing. A lot is possible with LEDs and a good API! Continue reading “LEDs Strips Tell You the Trains Aren’t Running” Public transit can be a wonderful thing. It can also be annoying if the trains are running behind schedule. These days, many public transit systems are connected to the Internet. This means you can check if your train will be on time at any moment using a computer or smart phone. [Christoph] wanted to take this concept one step further for the Devlol hackerspace is Linz, Austria, so he built himself an electronic tracking system (Google translate). [Christoph] started with a printed paper map of the train system. This was placed inside what began as an ordinary picture frame. Then, [Christoph] strung together a series of BulletPixel2 LEDs in parallel. The BulletPixel2 LEDs are 8mm tri-color LEDs that also contain a small controller chip. This allows them to be controlled serially using just one wire. It’s similar to having an RGB LED strip, minus the actual strip. [Christoph] used 50 LEDs when all was said and done. The LEDs were mounted into the photo frame along the three main train lines; red, green, and blue. The color of the LED obviously corresponds to the color of the train line. The train location data is pulled from the Internet using a Raspberry Pi. The information must be pulled constantly in order to keep the map accurate and up to date. The Raspberry Pi then communicates with an Arduino Uno, which is used to actually control the string of LEDs. The electronics can all be hidden behind the photo frame, out of sight. The final product is a slick “radar” for the local train system. Sometimes it’s fun to take a step back from the normal electronics themes and feature a marvelous engineering project. This week’s Retrotechtacular looks at a pair of videos reporting on the progress of the Bay Area Rapid Transit system. Anyone who’s visited San Francisco will be familiar with the BART system of trains that serve the region. Let’s take a look at what went into building the system almost half a century ago. Continue reading “Retrotechtacular: Building BART” Before beginning his day, [Richard] needs to decide whether he should ride his bike to work or take the London tube. All the information to make that decision is available on the Internet – the current weather report, and the status of the subway lines and stations he’d be taking. The problem, though, is all these pieces of information are spread out in multiple places. [Richard]’s solution to this was to make a bicycle barometer that pulls data from these places and makes the decision to ride a bike or the tube for him. [Richard]’s barometer is built around a nanode and an old clock he found at a flea market. The nanode queries the UK’s weather bureau and the London underground’s line and station status. All the variables under consideration are weighted; if it’s snowing, the output is much more likely to decide on the tube than if there was a slight drizzle. It’s a really cool build that certainly makes a great use of the publicly accessible APIs made available by the London underground. You can check out a video of the barometer after the break. Continue reading “Barometer tells you to take your bike or the train” We love it when PCB artwork is actually artwork. Here’s one example of a radio whose layout mimics the map of London’s subway system. The build is for an exhibit at the London Design Museum. They have an artist in residence program which allowed Yuri Suzuki time and resources to undertake the project. He speaks briefly about the concepts behind it in the video after the break. The top layer of copper, and silk screen was positioned to mirror the subway lines and stops on a traditional transportation map. Major components represent various transfer hubs. In this way he hopes the functioning of the circuit can be followed by a layman in the same way one would plan a trip across town. This may be a bit more abstract than you’re willing to go with your own projects. But there are certainly other options to spicing you track layout. Continue reading “Radio built from the London Underground map” More and more today, it is becoming harder to avoid having some sort of RFID tag in your wallet. [bunnie], of bunnie:studios decided to ease the clutter (and wireless interference) in his wallet by transplanting the RFID chip from one of his subway cards into his mobile phone. Rather than the tedious and possibly impossible task of yanking out the whole antenna, he instead pulled the antenna of a much more accessible wristband with an RFID chip of similar frequency instead. Nothing too technical in this hack, just a great idea and some steady handiwork. We recommend you try this out on a card you haven’t filled yet, just in case.
<urn:uuid:15068536-59ed-45a4-9de8-1fa3c062ad53>
{ "date": "2016-07-01T04:32:16", "dump": "CC-MAIN-2016-26", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783400031.51/warc/CC-MAIN-20160624155000-00088-ip-10-164-35-72.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9517611265182495, "score": 3.71875, "token_count": 1642, "url": "http://hackaday.com/tag/subway/" }
# A problem about logarithmic inequality ## Homework Statement If a,b,c are positive real numbers such that ##{loga}/(b-c) = {logb}/(c-a)={logc}/(a-b)## then prove that (a) ##a^{b+c} + b^{c+a} + c^{a+b} >= 3## (b) ##a^a + b^b + c^c >=3## A.M ##>=## G.M ## The Attempt at a Solution Using the above inequation, I am able to get (b) but I have no idea to do (a) keeping in mind the exponents as a sum whereas in the question the denominators are as a difference. Homework Helper Gold Member 2020 Award It doesn't look like a one or two step problem, but I did get the result from the set of logarithmic equations (by combining a couple of them) that abc=1. It does appear when a=b=c=1 that the equality holds. For any other case, you then need to show that the "greater than" sign applies. Ray Vickson Homework Helper Dearly Missed It doesn't look like a one or two step problem, but I did get the result from the set of logarithmic equations (by combining a couple of them) that abc=1. It does appear when a=b=c=1 that the equality holds. For any other case, you then need to show that the "greater than" sign applies. It is not allowed to have ##a = b = 1## (or even ##a = b = c \neq 1##) because that would involve division by zero in the constraint $$\log(a)/(b-c) = \log(b)/(c-a) = \log(c)/(a-b)$$ Even trying to take limits as ##a \to 1##, ##b \to 1## and ##c \to 1## will not really work, because depending on exactly how those limits are taken, the quantities involved in the constraint can still fail to exist, or can exist but have more-or-less arbitrary values. Homework Helper Gold Member 2020 Award It is not allowed to have ##a = b = 1## (or even ##a = b = c \neq 1##) because that would involve division by zero in the constraint $$\log(a)/(b-c) = \log(b)/(c-a) = \log(c)/(a-b)$$ Even trying to take limits as ##a \to 1##, ##b \to 1## and ##c \to 1## will not really work, because depending on exactly how those limits are taken, the quantities involved in the constraint can still fail to exist, or can exist but have more-or-less arbitrary values. The use of the "logs" to state the problem appears to be largely algebraic. After processing these equations, the result emerges that abc=1 and the logs wind up being removed. The problem could actually begin with, given a,b, c positive real, such that abc=1, prove the two inequalities. I think you will find that the equality holds only for the case a=b=c=1. I did not do the proof in its entirety, partly because on a homework problem we are not supposed to present the whole solution, but I think the only case where the equal sign would apply is for a=b=c=1. (I agree, this puts a zero in the denominators of the original statement of the problem.) fresh_42 Mentor We may assume that either ##0 < a < b < c## or ##0 < a < c < b##. As @Ray Vickson pointed out they cannot be equal. Neither can one of them equal one for then all of them would be equal one, especially they would be equal. The rest is simply about cases. Assume now ##0<a<b<c##. If ##c < 1## then ##\frac{\log a}{b-c} > 0## and ##\frac{\log b}{c-a} < 0##, a contradiction. In the same way ##b < 1## leads to ##\log a < \log b < 0 ## and ##\frac{\log a}{b-c} > 0## and ##\frac{\log b}{c-a} < 0##, a contradiction. If ## a < 1 ## then ##\frac{\log a}{b-c} > 0## and ##\frac{\log c}{a-b} < 0##, a contradiction. This means ##a, b, c > 1## and both assertions are true. (The second case ##0 < a < c < b## should be analogue.) The principle behind it is the following: The assumption is symmetric in ##(a,b,c),## i.e. with positive signum. On the other side there has to be a change in signs if not all of them are positive factors which means greater than one for the nominators. Delta2 Ray Vickson Homework Helper Dearly Missed The use of the "logs" to state the problem appears to be largely algebraic. After processing these equations, the result emerges that abc=1 and the logs wind up being removed. The problem could actually begin with, given a,b, c positive real, such that abc=1, prove the two inequalities. I think you will find that the equality holds only for the case a=b=c=1. I did not do the proof in its entirety, partly because on a homework problem we are not supposed to present the whole solution, but I think the only case where the equal sign would apply is for a=b=c=1. (I agree, this puts a zero in the denominators of the original statement of the problem.) I suspect that as long as ##a,b,c## are valid (no division by 0) the inequalities to be shown will be strict. Homework Helper Gold Member 2020 Award I will show the algebra that gives the result ## abc=1 ##. Removing the log factors on both sides, ## a^{c-a}=b^{b-c} ## and ## a^{a-b}=c^{b-c} ##. (also ## b^{a-b}=c^{c-a} ##). Taking the first two equations and multiplying left sides and right sides, ## a^{c-b}=(bc)^{b-c} ## so that ## a^{c-b}=1/(bc)^{c-b} ##. Thereby ## (abc)^{c-b}=1 ##. I think it can be concluded that ## abc=1 ##. (You can write similar equations by combining the other pairs of equations also with the result that ## abc=1 ##).The way the problem is written with the factors in the denominators places additional restrictions, but otherwise, it would be possible to have ## a=b=c=1 ##. To proceed from here, I would let ## c=1/(ab) ## and write the inequalities as functions of ## a ## and ## b##. There are basically two cases that need to be tested, ## ab>1 ## and ## ab<1 ##. The way the problem is written yes, if one of the three letters is equal to 1, then all 3 must equal one (log 1=0, etc), but that makes the denominators all zero. Instead of using logs, they could simply have presented the condition ## abc=1 ##. (with a,b, c positive real). In that case, the problem would be less restrictive, but the same inequalities would apply. Last edited: Homework Helper Gold Member 2020 Award We may assume that either ##0 < a < b < c## or ##0 < a < c < b##. As @Ray Vickson pointed out they cannot be equal. Neither can one of them equal one for then all of them would be equal one, especially they would be equal. The rest is simply about cases. Assume now ##0<a<b<c##. If ##c < 1## then ##\frac{\log a}{b-c} > 0## and ##\frac{\log b}{c-a} < 0##, a contradiction. In the same way ##b < 1## leads to ##\log a < \log b < 0 ## and ##\frac{\log a}{b-c} > 0## and ##\frac{\log b}{c-a} < 0##, a contradiction. If ## a < 1 ## then ##\frac{\log a}{b-c} > 0## and ##\frac{\log c}{a-b} < 0##, a contradiction. This means ##a, b, c > 1## and both assertions are true. (The second case ##0 < a < c < b## should be analogue.) The principle behind it is the following: The assumption is symmetric in ##(a,b,c),## i.e. with positive signum. On the other side there has to be a change in signs if not all of them are positive factors which means greater than one for the nominators. If ## a<b<c ## then ## c>1 ##. But ## b ## could be greater than one or less than one, and ## a<1 ##. Please double-check your logic. fresh_42 Mentor If ## a<b<c ## then ## c>1 ##. But ## b ## could be greater than one or less than one, and ## a<1 ##. Please double-check your logic. The logic is ok, but you are right: there is no solution at all. Three positive real numbers can be ordered. They cannot be pairwise equal for this meant a division by zero. Therefore there has to be at least one change of sign in the denominators: ##b-c, c-a, a-b##. To be equal this means there is a change in the sign of the nominators. However, the nominators are somehow linearly ordered, e.g. ##0 < a < b < c,## and the denominators are cyclic. Since the logarithm is strictly monotone, the two orderings cannot be true at the same time. In your example with ##0 < a < b < c## we get ##\frac{\log a}{b-c} = \frac{\log b}{c-a}=\frac{\log c}{a-b}=\frac{\log a}{-}=\frac{\log b}{+}=\frac{\log c}{-}##. On the other hand ##\log a < \log b < \log c## and the nominator in the middle cannot have a different sign than the two left and right. The assumption is always wrong. Homework Helper Gold Member 2020 Award The logic is ok, but you are right: there is no solution at all. Three positive real numbers can be ordered. They cannot be pairwise equal for this meant a division by zero. Therefore there has to be at least one change of sign in the denominators: ##b-c, c-a, a-b##. To be equal this means there is a change in the sign of the nominators. However, the nominators are somehow linearly ordered, e.g. ##0 < a < b < c,## and the denominators are cyclic. Since the logarithm is strictly monotone, the two orderings cannot be true at the same time. In your example with ##0 < a < b < c## we get ##\frac{\log a}{b-c} = \frac{\log b}{c-a}=\frac{\log c}{a-b}=\frac{\log a}{-}=\frac{\log b}{+}=\frac{\log c}{-}##. On the other hand ##\log a < \log b < \log c## and the nominator in the middle cannot have a different sign than the two left and right. The assumption is always wrong. A very good observation. Yes, the problem statement is clearly inconsistent. (unless we are missing the obvious). I agree with your assessment. mfb Mentor Well that rules out a<b<c, but what about a<c<b? $$\frac{\log a}{b-c} = \frac{\log b}{c-a}=\frac{\log c}{a-b}=\frac{\log a}{+}=\frac{\log b}{+}=\frac{\log c}{-}$$ Clearly log(c) has a different sign than the others, so 0<a<b<1<c. The equalities are cyclic, but swapping the parity makes a difference. Edit: no, doesn't work either. c-a is the largest denominator, so log(b) has to be the largest numerator in magnitude, but log(a) is larger. Both cases are excluded, but the second one is a bit more subtle. Ray Vickson Homework Helper Dearly Missed Well that rules out a<b<c, but what about a<c<b? $$\frac{\log a}{b-c} = \frac{\log b}{c-a}=\frac{\log c}{a-b}=\frac{\log a}{+}=\frac{\log b}{+}=\frac{\log c}{-}$$ Clearly log(c) has a different sign than the others, so 0<a<b<1<c. The equalities are cyclic, but swapping the parity makes a difference. Edit: no, doesn't work either. c-a is the largest denominator, so log(b) has to be the largest numerator in magnitude, but log(a) is larger. Both cases are excluded, but the second one is a bit more subtle. There is no need to check other cases. The three numbers must all be different. Let's call the smallest of the three ##a##, the largest of the three ##c## and the one in the middle ##b##. In the original problem there were no characteristics distinguishing ##a, b## or ##c##, so there were no a priori ways to distinguish between them. Basically, it is just saying "without loss of generality, assume ##a < b < c##", and we do that type of thing all the time. Homework Helper Gold Member 2020 Award @fresh_42 made a very good observation. I've looked hard to try to find an exception to this that would make it work, but it seems the problem in the way it is formulated is inconsistent. Writing the expressions without the logs: ## a^{1/(b-c)}=b^{1/(c-a)}=c^{1/(a-b)} ## apparently it is impossible for all three terms to be greater than 1 or all three terms to be less than one. If two of them are greater than one, the third must be less than one, etc... Last edited: mfb Mentor Okay, checking that in more detail, swapping a and b doesn't change the equalities, but that is not as obvious as an a->b->c->a rotation.
crawl-data/CC-MAIN-2021-17/segments/1618038469494.59/warc/CC-MAIN-20210418073623-20210418103623-00343.warc.gz
null
How do kids acquire new vocabulary? This process is poorly understood. An influential theory has been that the phonological loop in working memory provides essential support. The phonological loop is like a little tape loop lasting perhaps two seconds; it allows you to keep active a sound you hear. The idea is that a new unfamiliar word can be placed on the loop for practice and to keep it around while the surrounding context helps you figure out the meaning. If so, you'd predict that the larger the capacity of the phonological loop and the greater the fidelity with which it "records" the better children will be able to learn new vocabulary. The efficacy of the phonological loop is measured by having kids repeat nonsense words. Initially they are short--tozzy--but they increase in length to pose greater challenge to the phonological loop--liddynappish. Several studies have shown correlations between phonological loop capacity and vocabulary size in children (for a review, see Melby-Lervag & Lervag, 2012). The problem: it could be that having a big vocabulary makes the phonological loop test easier, because it makes it more likely that some of the nonsense words remind you of a word you already know. (And so you have the semantics of that word helping you remember the to-be-remembered word.) Indeed, even proponents of the hypothesis argue that's what happens when kids get older. What you really need is a study that measures phonological loop capacity at time 1, and finds that it predicts vocabulary size at time 2. There is one such study (Gathercole et al, 1992) but it used a statistical analysis (cross-lagged correlation) that is now considered less than ideal. A new study (Melby-Lervag et al, 2012) used probably the best methodology of any used to date. It was a longitudinal study that tested nonword repetition ability and vocabulary once each year between the ages of 3 and 7. They used a different statistical technique--simplex models--to assess causal relationships. They found that both nonword repetition and vocabulary show growth, both show stability across children, and both are moderately correlated, but there was no evidence that one influenced the growth of the other over time. The group then reanalyzed the Gathercole et al (1992) data and found the same pattern. This is one depressing paper. Something we thought we knew--the phonological loop contributes to vocabulary learning--may well be wrong. If anyone is working on a remediation program for young children that centers on improving the working of the phonological loop, it's probably time to rethink that idea. Gathercole, S. E., Willis, C., Emslie, H., & Baddeley, A. (1992). Phonological memory and vocabulary development during the early school years: A longitudinal study. Developmental Psychology, 28, 887–898. Melby-Lervåg, M., & Lervåg, A. (2012). Oral language skills mod-erate nonword repetition skills in children with dyslexia: A meta-analysis of the role of nonword repetition skills in dyslexia. Scientific Studies of Reading, 16, 1–34. Melby-Lervåg, M., & Lervåg, A., Lyster, S-A H., Klem, M., Hagtvet, B., & Hulme, C. (in press). Nonword-repetition ability does not appear to be a causal influence on children's vocabulary development. Psychological Science.
<urn:uuid:98080140-26d6-4143-8a2e-8b47d8a72bed>
{ "date": "2014-11-27T04:10:49", "dump": "CC-MAIN-2014-49", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007797.72/warc/CC-MAIN-20141125155647-00207-ip-10-235-23-156.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9149369597434998, "score": 3.921875, "token_count": 750, "url": "http://www.danielwillingham.com/daniel-willingham-science-and-education-blog/new-data-cast-doubt-on-dominant-theory-of-vocab-learning" }
Maths – The strategies we use in school 1 / 34 # Maths – The strategies we use in school - PowerPoint PPT Presentation Maths – The strategies we use in school. Calculation. The 4 strands of Maths. Number Shape, Space and Measures Data Handling Using and Applying Maths Using and Applying Maths occurs in all 3 other strands, as well as in other lessons, such as Science. . Number. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described. ## Maths – The strategies we use in school Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - Presentation Transcript 1. Maths – The strategies we use in school Calculation 2. The 4 strands of Maths • Number • Shape, Space and Measures • Data Handling • Using and Applying Maths Using and Applying Maths occurs in all 3 other strands, as well as in other lessons, such as Science. 3. Number We are going to focus solely number. • The four operations (+, -, x and ÷) We are going to talk you through methods we teach children to use to add, subtract, multiply and divide and how build on each stage. 4. The Four Operations • The four operations in calculations are grouped into Adding and Multiplying – where the answer gets bigger Subtracting and dividing – where the answer gets smaller 5. Early YearsCounting • Count reliably to 20 • Count backwards from 10 6. Number Recognition • Recognise numbers to 20 • Order numbers to 20 7. Calculation • One more and one less • than a given number • Add and subtract two single digit numbers practically 8. Number Lines We use number lines in all four operations. We start with numbered lines like this one – 0 1 2 3 4 5 6 7 8 9 10 9. Adding We then move on to using number lines and counting up in ones. 14 + 5 = 19 +1 +1 +1 +1 +1 14 19 10. Partitioning Next we learn to partition – splitting the number into tens and units – to add. What is 72 + 14? T U 70 2 10 4 70+10= 80 2+4= 6 80+6=86 11. Adding by Partitioning Now we can add by partitioning – 86 + 57 = +50 +4 +3 86 136 140 143 12. Adding by Partitioning Or by rounding then adjusting, taking it to the nearest 10 and then subtracting 754 + 96 (rounding and adjusting) +100 -4 754 850 854 13. Column Addition Finally, we move on to adding in columns, using place value. HTU ThHTU 597 7648 + 475 and + 1486 12 160 9134 9001 1 1 1072 14. Multiplying Now we use the number line for repeated addition. 4 x 5 is the same as 5 + 5 + 5 + 5 = 20 I have four 5p coins, how much is that? +5 +5 +5 +5 0 5p 10p 15p 20p 15. The Grid Method We can partition to multiply using a grid, like this, this looks more complicated than it actually is – 72 x 38 = 70 2 30 2100 60 8 560 16 16. Column Method for multiplication 4346 x 8 48 320 2400 32000 34768 17. Subtracting We begin by ‘taking away’, ‘counting back’ and seeing ‘how many left.’ We have 6 teddies in the shop. We sold 2. How many teddies are left? 18. Subtracting (number lines) We can use a number line to count back. 22 – 7 = -5 -2 15 20 22 19. Subtracting (number lines) In Key Stage 2, we count UP the number line to find the difference. What is the difference between 34 and 72? +30 +8 34 64 72 20. Subtracting with ‘exchanging’ Th H T U 5 13 1 6 4 6 7 - 2 6 8 4 3 7 8 3 21. Dividing Division starts with practical sharing of objects again - If I share my 9 sweets between 3 people, how many do they each get? 22. Division with number lines Number lines are also used to count up in division. A baker bakes 24 buns. She puts 6 in every box. How many boxes can she fill? x1 x2 x3 x4 0 6 12 18 24 23. Division with remainders Finally, we can jump in groups and record remainders on the number line. What is 42 divided by 4? 10 groups (Remainders) x10 +1 +1 0 40 41 42 24. SATs KS1 • Typical questions: 25. Key Stage 2 SATs • Key Stage 2 SATS are held in May. • These are statutory, externally marked tests. • The children sit three papers: • Paper A - non-calculator paper • Paper B - calculator paper • Mental arithmetic paper • The paper assesses children working between level 3 and level 5. Children will receive a test mark and a teacher assessment. • A minority of children will be entered for the level 6 test. 26. Key Stage 2 SATs Sample Questions: 27. Key Stage 2 SATs Sample Questions: 28. Extra support for Numeracy Extra support for Numeracy • EYS and KS1 – Numicon 29. Key Stage 2 • Booster programme • Linked to numeracy lessons • Targeted at children who, with support, will reach level 4 • Sessions run three times a week for 30 minutes 30. Year 4 Mental/Oral Starter Activities 31. Cracking Times Tables • Is a scheme designed to support high standards in mathematics • Is a consistent approach to learning and testing tables across the school • Is based on a series of levels that the children work through at their own pace • Is motivating to children. They receive certificates for each level achieved
crawl-data/CC-MAIN-2019-30/segments/1563195524972.66/warc/CC-MAIN-20190716221441-20190717003441-00285.warc.gz
null
Training people to avoid falls by repeatedly exposing them to unstable situations in the laboratory helped them to later maintain their balance on a slippery floor, according to new research. The study furthered the understanding of how the brain develops fall prevention strategies that can be generalized to a variety of conditions. The research could eventually help people, including the elderly, for whom falling is an important health issue. The study was carried out by Tanvi Bhatt and Yi-Chung (Clive) Pai, of the University of Illinois at Chicago. Will training transfer? The researchers used a moveable platform which could be operated to disrupt a person's balance. Previous studies had shown that people could quickly learn to maintain balance and avoid a fall with a short training period on the platform. In this study, the researchers wanted to see whether training on the platform could transfer to prevent a fall on a slippery floor. Dr. Pai, who teaches in the department of physical therapy and whose work has been supported by National Institutes of Health, National Institute on Aging, said he aims to train people to maintain balance in the face of a situation that could cause a slip-related fall. In the study, eight participants trained on the moveable platform for a total of 37 times. The low-friction platform was set up so that it released unannounced, 24 of those times. This release created a low-friction condition to cause a frontward or backward slip. The platform does not allow the foot to slip from side to side, as would be the case in a real-life fall. The participants wore a harness to record the amount of assistance needed to catch them when they fell. Motion capture instruments and videos of the sessions also helped to document slip outcomes ("skate-over", "walkover" or "loss of balance") and falls. The participants were compared to a group of seven controls who did not receive any training on the platform. Both groups were later asked to walk on a vinyl surface that had one slippery spot that they could not see. Instruments and videos were used to record the extent of their slip. The vinyl surface represented a particular challenge following the laboratory training, in part because it could cause the foot to slide in any direction. Training inoculates against falls The researchers found: "Controlling this foot, which is sliding forward, plays an important role in maintaining stability and prevents a backward fall," Pai said. The researchers also found that the trained group unconsciously changed their gait. They used a flatter landing foot and bent the landing knee more. These changes reduced the landing force and the velocity of the slip. Interestingly, the trained group did this while walking at their customary speed. May help elderly The brain is able to generalize fall training from one situation to another by modifying gait to make loss of balance less likely, the authors concluded. These changes give the body greater stability when a slip begins to occur. In addition, the study found that with one session of such training, the brain pre-programs a response to slipping that can be drawn upon quickly to stop a slip or a fall, or even to skate-over the slippery surface without losing balance. Fall training may be particularly helpful for active elderly persons who put themselves in more challenging situations. Fall prevention training may cut down on hip fractures, surgery, rehabilitation and pain and suffering. So far, the research team has used younger subjects because the experiments carry some risk of injury. But in one study also funded by National Institutes of Health, the researchers found that older adults were able to learn as quickly as young adults. Further research is now being conducted to find out if older adults can retain the training as well as the young. Pai and Bhatt's research so far indicates that the effects of one such training session, as with an inoculation, should last for at least for four months, and perhaps much longer, to protect against one of most dangerous falls, the backward falls. Cite This Page:
<urn:uuid:70199376-e800-4e44-8be6-eb87fcb873fc>
{ "date": "2017-03-28T21:54:52", "dump": "CC-MAIN-2017-13", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189903.83/warc/CC-MAIN-20170322212949-00512-ip-10-233-31-227.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9677636027336121, "score": 3.625, "token_count": 815, "url": "https://www.sciencedaily.com/releases/2009/02/090204101304.htm" }
hermit_crab__in_eelgrass - Credit paul naylor Seagrasses are the only flowering plants that are able to live in seawater and able to pollinate while submerged. Seagrass often grow in large groups giving the appearance of terrestrial grassland – a kind of underwater meadow. There are four species of seagrass in the UK, two species of tasselweeds and two zostera species commonly known as eelgrass. What is it? The plants’ roots are anchored in mud, sand or fine gravel acting to stabilize the seabed and prevent erosion, which has the further effect of helping to stabilise and defend the wider coastline. The leaves are narrow and long, forming a three-dimensional habitat allowing a wide range of species to inhabit the area. The density of the grasses causes the water currents to slow down and allows nutrients to settle, in turn attracting wildlife. Where is it found? Seagrass is dependent on high levels of light for photosynthesis to grow and can therefore only be found in shallow water to a depth of around 4 metres. They are found around the coast of the UK in sheltered areas such as harbours, estuaries, lagoons and bays. Why is it important? Seagrass provides important habitat for species ranging from tiny invertebrates, worms and shellfish to young and adult fishes including the commercially important bass. In well-developed areas the leaves can become colonised by algae, stalked jellyfish and anemones, while the soft sediment surrounding the roots is home to molluscs (bivalves), tiny amphipods, polychaete worms and echinoderms. The sheltered habitat can provide ideal nurseries for flatfish and even cephalopods hiding from predators and thereby increasing their survival rate. Our two native species of seahorse can also be found living amongst seagrass in the southern UK. Seagrass is also an important food source for wildfowl such as widgeon and brent geese which feed on exposed seagrass at low tides. It is thought that only 5% of the seagrass is consumed in the form of the plant itself and that the majority of feeding is from decaying matter rich in invertebrates. It has also been calculated that seagrass absorbs 15% of the ocean’s total carbon absorption. Is it threatened? A wasting disease was the cause of a drastic reduction of seagrass in the UK in the 1930’s. The following recovery has been hampered by increased human disturbance such as pollution and physical disturbance from dredging, use of mobile fishing gear and coastal development. Increasingly high levels of nutrients, such as nitrogen and phosphorus, loading from sewage discharge is extremely toxic to seagrass directly but it also acts to stimulate epiphytic algae growth which can outcompete the seagrass by reducing the available sunlight. The ability of seagrass to reduce the speed of currents can result in pollutant materials accumulating in the seagrass bed. Several heavy metals have been found to be able to reduce the plants ability to fix nitrogen and thus reducing the viability of the plant. Alien species, including Spartina anglica and Sargassum Muticom, also affect their viability through competition. Globally 30,000km2 of seagrass has been lost in the last couple of decades which is equal to 18% of the global area. What are The Wildlife Trusts doing to help? Following the assent of the Marine & Coastal Access Act, four regional projects were established to identify potential Marine Conservation Zones within England. The projects are stakeholder led and Wildlife Trust staff sit on all projects, at local, regional and a national level. These projects will ultimately put forward sites to protect special areas of the sea. Additional work on Marine Protected Areas is also underway in Wales and Scotland, whilst in Northern Ireland we are still campaigning for Marine legislation with a commitment to establishing these areas. What can I do to help? Visit wildlifetrusts.org/livingseas to find out how you can help our marine conservation work in the UK. Depending on where you live, local Wildlife Trust volunteers help out with everything from recording marine wildlife sightings to beach cleans and educational work. Visit our Living Seas pages online or contact your local Trust to find out more.
<urn:uuid:c6eebd5b-903b-49c9-a112-d0d8fa257ff4>
{ "date": "2015-01-31T08:35:51", "dump": "CC-MAIN-2015-06", "file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422118108509.48/warc/CC-MAIN-20150124164828-00057-ip-10-180-212-252.ec2.internal.warc.gz", "int_score": 4, "language": "en", "language_score": 0.9488095641136169, "score": 3.875, "token_count": 934, "url": "http://www.wildlifetrusts.org/wildlife/habitats/seagrass" }