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https://www.coursehero.com/tutors-problems/Statistics-and-Probability/470023-Figure-out-1-H0-and-H1-and-1-the-decision-rule-The-Anderson/
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math
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The Andersons Super Dollar had two grocery stores in Erie, Pennsylvania. The mean time customers wait in the checkout line at the Byrne Road store is 3.7 minute with a standard deviation of .8 minutes, for a sample of 40 customers. The mean waiting time for the I-90 store is 3.5 minutes with a standard deviation of .7 minutes for a sample of 45 customers. At the .05 significance level can we conclude there is a difference in the waiting time for the two stores?
Use Z Values to solve.
Recently Asked Questions
- Explain how cultural intelligence is important for success in the workplace
- Hey,I am having difficulties figuring out the steps to this question... I keep getting the wrong answer and it doesnt match the answer key. 1113.0- 14.6 X 10 2
- Please refer to the attachment to answer this question. This question was created from HW2. Additional comments: "This is a linear programming question, thank
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158001.44/warc/CC-MAIN-20180922005340-20180922025740-00212.warc.gz
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CC-MAIN-2018-39
| 914 | 6 |
http://comicbookdb.com/character.php?ID=114
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math
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Search for 'Hope Taya' on Amazon
First Appearance: None listed.
Hope Taya is a favorite character of 1 user
View a chronological listing of this character's appearances
Absolute Luthor/Joker (2013)
Action Comics (1938)
Adventures of Superman (1987)
#573 Batman (1940)
- 'Higher Ground'#575
- 'A Night at the Opera'#576
- 'A Tale of Two Cities'#578
- 'Getting Away From It All'#581
- 'Bachelor Party'#585
- 'Joker: Last Laugh: Rubber Crutch'#603
- 'Baby Talk'
#605 Batman: Bruce Wayne: Fugitive (2003)
- 'Bruce Wayne: Fugitive, Part Eighteen: Courage'
Batman: No Man's Land (1999)
Batman: Shadow of the Bat (1992)
#93 DC Comics Presents: Superman (2010)
- 'No Man's Land: Assembly Redux'
DC Comics Presents: Superman/Doomsday (2011)
Harley Quinn (2000)
Infinity Inc. (2007)
#2 Joker: Last Laugh (2001)
- 'Luthor's Monsters Part 2'
#3 Lex Luthor: Man of Steel (2005)
- 'Joker: Last Laugh, Part Three: Lunatic Fringe'
#2#4#5 Outsiders (2003)
- 'Lex Luthor: Man of Steel Conclusion'
#2 Secret Files President Luthor (2001)
- 'Role Call, Part Two: Lawyers, Guns and Monkeys'
#52 Superman (1987)
- 'Supergirl, Interrupted'#55
- 'Day of the Mule'
#162 Superman [GER] (2001)
- 'Superman in the American Dream'#163
- 'Where Monsters Lurk!'#175
- 'Joker: Last Laugh: Doomsday Rex'#182
- 'The Secret Part One: Dead Men'#183
- 'The Secret: Part Two'#194
- 'Secret Identity'
#13 Superman 80-Page Giant (1999)
- 'Triumph und Tragödie'
Superman Metropolis Secret Files (2000)
Superman Y2K (2000)
Superman: Lex 2000 (2001)
Superman: Our Worlds at War Secret Files (2001)
Superman: President Lex (2003)
Superman: The Man of Steel (1991)
#98 Superman/Shazam: First Thunder (2005)
- 'Thirty Minutes to Oblivion'#101
- 'All Fall Down'#107
- 'In the Zone'#108
- 'Metropolis is Burning'#110
Wonder Woman (1987)
- 'The Witch & the Warrior, Part 1'#175
- 'The Witch & the Warrior, Part 2: Girl Frenzy'
Famous Quotes: - Add a Famous Quote
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s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247487624.32/warc/CC-MAIN-20190218175932-20190218201932-00041.warc.gz
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CC-MAIN-2019-09
| 2,088 | 63 |
https://www.answers.com/Q/What_charge_does_nitrogen_have
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math
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What charge does nitrogen have?
Elemental nitrogen has no charge.
In ammonia (NH3) and ammonium ions (NH4+) it has a oxidation value of -3 (and actually only a partial negative charge as part from a polar covalent, non-ionic bond).
In Nitrate (NO3-) its oxidation value is +5, in nitrite +3 (but only a partial positve charge in both)
The formula for magnesium nitride is Mg3N2, so there are two nitrogen atoms present in a single molecule of magnesium nitride. In this case, the magnesium has a +2 charge, and the nitrogen has a -3 charge, which accounts for why more than one of each must come together and form a molecule (the total charge needs to be zero).
That depends on if the nitrogen ion is bonded with anything else. If it is a plain nitrogen ion it is called Nitride and has a charge of minus 3. If it is bonded with oxygen it is called Nitrate ion, NO4 (charge of minus 2) Nitrogen can also bond with hydrogen, in which case it can either take the form of the NH4 (+1) ion which is called Ammonium or the Amide ion which…
The nitride ion is N3-, three nitrogen atoms bound by three extra electrons to form one molecule of nitrogen. http://en.wikipedia.org/wiki/Nitride The nitrite ion is NO2-. One nitrogen atom with two oxygen atoms that share an electron to form a molecule of nitrogen dioxide. http://en.wikipedia.org/wiki/Nitrite The nitrate ion is NO32-. The nitrate ion carries a formal charge of negative two, where each oxygen carries a −2/3 charge while the nitrogen carries a +1 charge. http://en.wikipedia.org/wiki/Nitrate
There is no specific charge on the nitrogen atom as it is part of a polyatomic ion, NH4+. However, if you want to work through the advanced inorganic chemistry fun, nitrogen and hydrogen have electronegativity values of 3.04 and 2.20 respectively. If you work out the bond angles and remember that you are already one electron short of a happy molecule, you can figure out the dipole moment of the nitrogen atom.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00195.warc.gz
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CC-MAIN-2019-35
| 1,963 | 8 |
https://memim.com/paul-halmos.html
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math
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Paul Richard Halmos ( March 3, 1916 in Budapest, † October 2, 2006 in Los Gatos, California ) was an American mathematician of Hungarian origin, in the areas of probability theory, statistics, ergodic theory, functional analysis (in particular, Hilbert spaces ), and mathematical logic has researched. He has also written several textbooks.
Paul Halmos studied in Chicago chemistry, philosophy and mathematics.
In his evidence he used the first time the grave, crate or Halmos said design "■" as an abbreviation for the qed the conclusion of a proof, which is also sometimes referred to open ( "□" ).
Halmos received his B. A. with a major in philosophy and a minor in mathematics at the University of Illinois. He then began a Ph.D. degree in philosophy, but after some difficulty, he changed his subject in mathematics, where he received his doctorate in 1938. Joseph L. Doob supervised his dissertation called Invariants of Certain Stochastic Transformation: The Mathematical Theory of Gambling Systems. Soon after, Halmos went to the Institute for Advanced Study. Six months later he worked under John von Neumann, which should be a formative experience. While he was at the Institute, Halmos wrote his first book Finite Dimensional Vector Spaces, which earned him immediate reputation for being a good textbook author.
Halmos taught at the University of Syracuse, at the University of Chicago, at the University of California at Santa Barbara, the University of Hawaii and at Indiana University. In 1983 he was awarded the Leroy P. Steele Prize of the American Mathematical Society.
From his retirement in 1985 until his death he was the mathematical faculty of Santa Clara University related parties.
He and his wife Virginia donated a conference center of the Mathematical Association of America in Washington DC and for the Euler Book Prize of the MAA.
His doctoral include Errett Bishop, Donald Sarason.
- Finite -Dimensional Vector Spaces, Springer 1942
- Measure Theory, Van Nostrand, 1950
- Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Chelsea 1951
- Lectures on Ergodic Theory, Chelsea 1956
- Naive Set Theory ( German: Naive Set Theory, ISBN 3-525-40527-8 )
- Lectures on Boolean Algebras, Van Nostrand, 1963
- Autobiography: I Want to Be a Mathematician (1987 )
- I have a photographic memory, ISBN 0-8218-0115-5 (1988 )
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649348.41/warc/CC-MAIN-20230603233121-20230604023121-00009.warc.gz
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CC-MAIN-2023-23
| 2,367 | 16 |
https://news.iu.edu/live/profiles/163-russell-lyons
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math
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Russell Lyons is Rudy Professor of Mathematics and adjunct professor of statistics whose primary research field is probability theory. He has won several fellowships and awards for his work. One of his passions is teaching critical thinking in statistics.
In high school and college math competitions, Lyons placed in the top five nationwide. He was on the U.S. team the second year it competed in the International Mathematical Olympiad. He obtained his Ph.D. at the University of Michigan in 1983. After a postdoc in Paris and a job at Stanford University, he moved to Indiana University in 1990.
Areas of Expertise
Math (especially probability), statistics.
CV: http://pages.iu.edu/~rdlyons/pdf/cv-web.pdf “IU math professor uncovers flaws in highly publicized ‘obesity is contagious’ study”: http://newsinfo.iu.edu/news/page/normal/19381.html
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00683.warc.gz
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CC-MAIN-2022-49
| 854 | 5 |
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-December/096653.html
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math
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[EM] an entropy formula for the effective number of parties
rahyman at sbcglobal.net
Thu Dec 13 20:15:23 PST 2012
Here is a physics alternative to the "effective number of parties" formulas mentioned on the Wikipedia page:
Based on the concept of entropy, a sensible formula for the effective number of parties = exp(-sum_i P_i log(P_i))
where P_i is the portion of the votes or portion of seats for party i. sum_i P_i =1.
It is sensible because for an election where n parties get 1/n of the vote each and the rest of the parties get zero votes, the effective number of parties from the entropy formula is n.
More information about the Election-Methods
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646457.49/warc/CC-MAIN-20230531090221-20230531120221-00489.warc.gz
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CC-MAIN-2023-23
| 653 | 8 |
https://slogix.in/wireless-sensor-networks/ada-authenticated-data-aggregation-in-wireless-sensor-networks/
|
math
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Research Area: Wireless Sensor Networks
Wireless Sensor Networks are vulnerable to communication failures and security attacks. It is quite challenging to provide security to data aggregation. This paper proposes Authenticated Data Aggregation for Wireless Sensor Networks, where the nodes organize themselves into tiers around the sink. Message Authentication Code (MAC) is generated and transmitted along with the synopsis to ensure integrity. All nodes in the network store the same key that is used for rekeying operation during each round to generate MAC. Thus ADA ensures data freshness and integrity at a communication cost of O(1). Simulation results show that the proposed ADA protocol results in high security, low energy consumption and low communication cost compared to the state-of-the art protocol.
Author(s) Name: E. G. Prathima, Shiv Prakash T., Venugopal K. R., S. S. Iyengar and L. M. Patnaik
Journal name: International Journal of Computer Applications
Publisher name: IJCA
Volume Information: Volume 167 - Number 7
Paper Link: https://www.ijcaonline.org/archives/volume167/number7/27785-2017914309
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817206.54/warc/CC-MAIN-20240418124808-20240418154808-00865.warc.gz
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CC-MAIN-2024-18
| 1,138 | 7 |
https://www.ancestry.com/boards/topics.researchresources.general/1891/mb.ashx?pnt=1
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math
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In tracing a 'side branch' of the family tree, I found two sisters and their brother who married two brothers and their sister. So far, not so unusual, I suppose: I presumed that the families became close after the first of these weddings (in 1909 in Brentford; the other two were in 1918, in Acton Green and Brentford). However, subsequent research showed that they were all first cousins!
I know that first cousin marriages were not uncommon, but would 3 such marriages be especially unusual? I'd appreciate any comments.
(I've checked most of these findings, so I'm pretty sure I'm right).
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687428.60/warc/CC-MAIN-20170920175850-20170920195850-00007.warc.gz
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CC-MAIN-2017-39
| 592 | 3 |
http://readin.net/problem-solving-trick-for-liquid-mixtures/
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math
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Many time in the competive exams the questions are asked based on the mixtures of the liquid. This post gives as easy way of solving such problems. Sample questions asked are as follows:
1. A milk can of 20 lts capacity is filled with mixture of 15 ltrs milk & water, every time milkman removes 1 ltr mixture he adds 1 ltr water, how much milk would be there after 5 operations
2. A solution has 70% chemical, how much water to be added to 5lts solution to make it 50% concentration
3. Article of 2 vairties with different unit prices are mixed and one wants to find out the unit price of assortments
There are similar kind problems based on proportions and mixture, lets us see how you can solve these kind of problems very easily and use the formula to solve the problems.
The problems of 1st type as mentioned can be solved with following formula:
It better to gain experience by solving the quiz as given over here, this also explains the concept and provides the answers as well.
for quiz click here
For solving the problems where the cheaper and costlier goods are mixed, use the following formulas.
If you liked my contribution, please donate or click on any of advt. a little that will be generated will all be donated for noble cause. [paypal-donation] [ad#Textads-BetPost]
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864364.38/warc/CC-MAIN-20180622065204-20180622085204-00108.warc.gz
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CC-MAIN-2018-26
| 1,282 | 10 |
https://as.cornell.edu/news/cornell-math-dept-reaches-out-high-school-seniors
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math
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On May 22, Ithaca High School (IHS) seniors presented the mathematics research projects they did as part of the Senior Seminar, a course for Ithaca High School (IHS) students who have completed most or all of the IHS math classes. The seminar meets at the high school and is taught by three graduate mathematics or applied mathematics students each year, to introduce high-school students to three mathematics topics they normally would not see until college. This year, the graduate students were Daoji Huang, Sergio Da Silva and Aliaksandr (Sasha) Patotski and the topics were Projective Geometry, Introduction to Number Theory, and Group Theory Via Interesting Examples.
Ithaca High School Senior Seminar Participants, 2015-2016. First Row: Julia Miller, Severin Drix (IHS mathematics teacher), Jasper White, Eleanor Pereboom, Daoji Huang (Cornell graduate student instructor); Second Row: Daniel Xu, Jeong Hyun Lee, Yaateh Richardson, Zachary Stillman, Adam Newhouse; Third Row: Sergio Da Silva (Cornell graduate student instructor), Sasha Patotski (Cornell graduate student instructor), Ronan Perry, Kieran Loehr, Bowen Shan
“The Senior Seminar provides an unusual opportunity for high-school students to be exposed to a deeper and more detailed analysis of advanced mathematical topics and to explore them on their own,” says Mary Ann Huntley, director of mathematics outreach and K-12 education activities for the math department “In addition, they are able to meet and interact with professional mathematicians. Graduate student instructors appreciate the experience of planning and delivering lessons to high-school students, saying it is a valuable learning tool in their development.”
After an eight-week seminar on each of the three topics, the students engage in a research project under the mentorship of the graduate students. The course culminates in the high school students’ presenting their research projects, which this year were “Projective Transformations and Harmonic Quadruples,” by Jeong Hyun Lee and Daniel Xu; “Elliptic Cryptography,” by Adam Newhouse and Kieran Loehr; “Image Processing and Projective Geometry,” by Yaateh Richardson, Jasper White, and Julia Miller; “Number Theory Problems Involving Squares,” by Eleanor Pereboom and Ronan Perry; and “Group Theory and the Pyraminx Puzzle,” by Zachary Stillman and Bowen Shan.
Ravi Ramakrishna, professor and chair of Cornell’s Department of Mathematics, delivered remarks at the May 22 event, along with IHS math teacher Severin Drix, the IHS faculty advisor for the program.
The Senior Seminar course is currently funded by Cornell’s Department of Mathematics and the Center for Applied Mathematics.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473360.9/warc/CC-MAIN-20240221002544-20240221032544-00393.warc.gz
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CC-MAIN-2024-10
| 2,714 | 6 |
https://riddles360.com/riddle/two-out-of-one
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math
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Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?
There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.
You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)
Your task is to then determine which switch controls the bulb?
A man is lying dead in a field where no one is around. His head is split open and his legs are disfigured. Near to him, there is an unopened package. No living organism can be found anywhere at the crime scene.
How did he die?
In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506676.95/warc/CC-MAIN-20230925015430-20230925045430-00485.warc.gz
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CC-MAIN-2023-40
| 1,329 | 9 |
https://grammar.collinsdictionary.com/pt/grammar-pattern/v-that-v-wh
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math
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V that; V wh
accept acknowledge advise affirm agree announce anticipate appreciate argue ascertain (cannot) believe calculate check (cannot) conceive confess confirm conjecture decide demonstrate determine dictate discern disclose discover dispute divine divulge doubt emphasize envisage envision establish estimate explain fantasize figure find forecast foresee foretell guess hear hint hypothesize illustrate imagine indicate intimate know learn marvel mention note notice predict prove read realize recall recognize recollect recommend recount reflect register remain remark remember report resolve reveal say see sense show signal speculate state stipulate stress suggest surmise suspect suss twig underline underscore verify warn worry figure out find out let on put down work out
V that; V wh
I couldn't believe that the man I'd been so happy with for years had done this.
I can't believe how hard this course is.
She hadn't brought her watch, but she estimated that she'd been climbing for perhaps twenty-five minutes.
You must now estimate how much capital and cash is needed to take the business to a full-time level.
Imagine you are sending someone a picture of where you live. What does it look like?
It's easy to imagine how the current fighting could escalate.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574765.55/warc/CC-MAIN-20190922012344-20190922034344-00050.warc.gz
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CC-MAIN-2019-39
| 1,273 | 9 |
https://www.hackmath.net/en/examples/volume?tag_id=103
|
math
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Volume - 8th grade (13y) - examples
- Gasoline tank 2
A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
- A pipe
A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?
How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
- Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
- Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
- Scientific notation
Approximately 7.5x105 gallons of water flow over a waterfall each second. There are 8.6x104 seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
- Cube in a sphere
The cube is inscribed in a sphere with volume 3724 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
The cuboid has a surface area 1771 cm2, the length of its edges are in the ratio 5:2:4. Calculate the volume of the cuboid.
The swimming pool is 10 m wide and 22 m long and 191 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
- Density - simple example
Material of density of 762 kg/m3 occupies a container volume of 99 cm3. What is its mass?
How many 55% alcohol we need to pour into 14 liters 75% alcohol to get p3% of the alcohol? How many 65% alcohol we get?
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
Mix 20 l of water with temperature of 53 °C, 27 l warm of 86 °C and 11 l water of 49 °C. What is the temperature of the mixed water immediately after mixing?
- Sea water
Seawater contains about 4.7% salt. How many dm3 of distilled water we must pour into 39 dm3 of sea water to get water with 1.5% salt?
Tip: Our volume units converter will help you with converion of volume units. See also more information on Wikipedia.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591837.34/warc/CC-MAIN-20180720213434-20180720233434-00396.warc.gz
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CC-MAIN-2018-30
| 3,111 | 32 |
https://moneymaven.io/baldingsworld/emerging-asia/the-transitive-property-and-the-problem-of-singapore-finances--MrWkkOehkKnvVpUJESggg
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math
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The Transitive Property and the Problem of Singapore Finances
The simplest example is if A = B and B = C then by definition A must equal C. Taking a simple example, let’s assume that my friend tells me all cars are blue and that he has a car. By extension I can know that my friends car is blue because my friend has a car and all cars are blue. The transitive property provides us a way to reconcile truths against other things we know to be true.
Before proceeding to explain how this relates to Singaporean public finances, let me frame the transitive property in financial terms. Let’s assume that my friend tells me on January 1st that he has $10,000 in an investment account. I see my friend one year later and he tells me his investments made 10% last year. I can safely assume that my friend has around $11,000 in his investment account.
There are two important points about the transitive property as it relates to finance. First, if my friend tells me he starts off with $10,000 in an investment fund returns 10% in one year but then tells me he has $5,000 in his investment account, I know that my friend is leaving out important information. Maybe my friend is only counting the gains on investments that did not lose money or maybe my friend went and bought a new car, but a 10% return on $10,000 with no other changes should leave $11,000 in the bank. Second, while perfect information is always better, the transitive property allows us to work very logically with imperfect information. For instance, if my friend tells me that he started the year with $10,000 in an investment fund and finished the year with $9,000, unless he spent money, I can safely assume his investments lost 10%. I do not need perfect information to be able to figure out a lot about the finances of Singapore.
The Singapore government is trying its best to avoid the transitive property in defending its investment and public finance record. Let me give you three examples of how we can use the transitive property to study Singaporean public finances. First, Temasek claims that it has earned an annualized 17% since inception which gives us the ability to take the amount of money they currently have and calculate (estimate) backwards to how much they started with in 1974 or conversely calculate (estimate) how much they should have now based upon how much they claim to have started with. We don’t need the government to provide us every piece of data and every number.
Second, we can estimate how Singapore is allocating investment funds between GIC and Temasek. The reasoning is simple: if virtually any of the government surpluses and CPF funds after 1974 went to Temasek, it would have trillions of dollars given their claimed 17% return. That would imply that either Singapore is sitting on trillions of undisclosed dollars or virtually all surpluses and CPF funds went to GIC.
Third, despite the popular belief that Singapore has not disclosed the size of their reserves, we can use the transitive property to calculate the size of GIC. On the Singapore balance sheet published by the government they list their total assets. We know how their total assets, Temasek assets, and government assets. If the total amount of assets is the sum of the government , Temasek, and GIC, we can easily calculate the size of GIC. Put another way if 50 = 10 + 20 + x, we can calculate the value of x.
Let’s put this into practice. From 1974 through 2012, the sum of Singaporean debt and operational surpluses equaled $708 billion SGD. According to their 2012 public balance sheet, the government of Singapore list $765 billion SGD in assets. Please explain to me how Singapore saved and borrowed for investment purposes a total of $708 billion SGD between 1974 and 2012, claims to earn 17% and 7% over more than 30 years in Temasek and GIC, but only declares $765 billion SGD in assets. Either investments are not earning what is claimed or money is being spent that is not being accurately reported. There is no other explanation.
By definition Singapore cannot: a) invest $708 billion SGD b) claim a 17% and 7% return on investments over more than 30 years and c) only have $765 billion SGD. One of these must be false. We can see clearly that only two of these three assertions can be true.
This is not a cultural problem, debt cost, currency loss, accounting issue, or government secrecy that is causing this discrepancy. One of these claims has to be false.
If anyone wants to empirically point out where the error lies I will gladly listen. However, I will not be intimidated by anyone. Anyone.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360293.33/warc/CC-MAIN-20210228054509-20210228084509-00633.warc.gz
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CC-MAIN-2021-10
| 4,596 | 11 |
https://pureportal.strath.ac.uk/en/publications/iterative-learning-double-closed-loop-structure-for-modeling-and-
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math
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Stochastic distribution control (SDC) systems are known to have the 2-D characteristics regarding time and probability space of a random variables, respectively. A double closed-loop structure, which includes iterative learning modeling (ILM) and iterative learning control (ILC), is proposed for non-Gaussian SDC systems. The ILM is arranged in the outer loop, which takes a longer period for each cycle termed as a BATCH. Each BATCH is divided into a modeling period and a number of control intervals, called batches, being arranged in the inner loop for ILC. The output probability density functions (PDFs) of the system are approximated by a radial basis function neural network (RBFNN) model, whose parameters are updated via ILM in each BATCH. Based on the RBFNN approximation of the output PDF, a state-space model is constructed by employing the subspace parameter estimation method. An IL optimal controller is then designed by decreasing the PDF tracking errors from batch to batch. Model simulations are carried out on a forth-order numerical example to examine the effectiveness of the proposed algorithm. To further assess its application feasibility, a flame shape distribution control simulation platform for a combustion process in a coal-fired gate boiler system is constructed by integrating WinCC interface, MATLAB simulation programs, and OPC communication together. The simulation study over this industrial simulation platform shows that the output PDF tracking performance can be efficiently achieved by this double closed-loop iterative learning strategy.
- optimal tracking control
- subspace identification
- probability density function
- stochastic distribution control
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374686.69/warc/CC-MAIN-20210306100836-20210306130836-00216.warc.gz
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CC-MAIN-2021-10
| 1,697 | 5 |
http://mathhelpforum.com/statistics/127975-simple-probability-question.html
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math
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Find the probability that in a group of 10
people, all born in April, at least two have the same birthday.
I thought of calculating the probability that no two people have the same birthday.
April has 30 days, so
1. person has 30/30 chance
2. person has 29/30 chance
3. person has 28/30 chance
10. person has 21/30 chance
to have a different birthday as the others.
Then I get 29/30*28/30*...*21/30 = 0.185, which means there is a
1 - 0.185 = 0.815 probability that 2 persons have the same birthday.
I think thats too high, but thats all i can say.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122619.71/warc/CC-MAIN-20170423031202-00230-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 548 | 12 |
https://www.researchportal.be/en/publication/organizational-crisis-communication-suboptimal-crisis-response-selection-decisions-0
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math
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< Back to previous page
Organizational crisis communication : suboptimal crisis response selection decisions and behavioral economics
Journal Contribution - Journal Article
Organizations in crisis often fail to select the optimal crisis response strategy, preferring strategies that avoid short-term losses over the ones that offer long-term gains. This article proposes a descriptive theory of behavioral crisis communication that uses principles of behavioral economics to explain the recurrence of suboptimal anomalies found in crisis communication. Based on decision-making literature we first argue that the distinct context in which crisis communication takes place (e.g., time pressure, information overload) determines whether or not decisions are made in an analytical or an intuitive manner. Behavioral economics further allows us to explain how intuitive decisions can sometimes be biased by heuristics, which can result in the choice for a suboptimal crisis response strategy in the heat of the moment.
Journal: COMMUNICATION THEORY
Pages: 290 - 309
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00027.warc.gz
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CC-MAIN-2021-17
| 1,063 | 6 |
http://waemathlab.blogspot.com/2010_03_01_archive.html
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math
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When are times that you use math in your life? Please list at least three areas of your life in which you have used math.
Then... go to the math instructor link here and explain what I=PRT means.
Tuesday, March 30, 2010
Wednesday, March 24, 2010
Tuesday, March 23, 2010
Tell us what you know about prime numbers, multiplication of numbers, and how to calculate volume of a rectangle. Let's see where we are at the beginning, then we'll come back and post at the end of class and see what we know at the end!
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865145.53/warc/CC-MAIN-20180623171526-20180623191526-00502.warc.gz
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CC-MAIN-2018-26
| 507 | 6 |
https://savvycalculator.com/velocity-to-force-calculator/
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math
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About Velocity to Force Calculator (Formula)
The Velocity to Force Calculator is a tool used to determine the force exerted on an object based on its change in velocity, change in time, and mass. This calculator is particularly useful in physics and engineering applications where the relationship between velocity, time, and force needs to be understood and calculated.
The formula used by the Velocity to Force Calculator is as follows:
Force (F) = mass (m) * (change in velocity (Δv) / change in time (Δt))
In this formula, the mass (m) represents the object’s mass in kilograms, the change in velocity (Δv) represents the difference in velocity before and after an event or over a certain period, and the change in time (Δt) represents the time interval over which the change in velocity occurs.
By plugging in the appropriate values into the formula, the Velocity to Force Calculator can quickly and accurately calculate the force exerted on an object. The resulting force is expressed in newtons (N), which is the standard unit for measuring force in the International System of Units (SI).
Using this calculator can be beneficial in various scenarios. For example, it can be used to analyse the impact of an object in motion, such as a car decelerating or a ball being thrown. It can also be used to understand the forces involved in mechanical systems, such as calculating the force exerted by a piston in an engine or the force required to accelerate a spacecraft.
The Velocity to Force Calculator simplifies the process of determining the force acting on an object by providing a convenient and efficient tool for performing the necessary calculations.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474893.90/warc/CC-MAIN-20240229234355-20240301024355-00382.warc.gz
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CC-MAIN-2024-10
| 1,668 | 8 |
https://www.topassignmentexperts.com/questions/1-50-points-cholesterol-was-measured-in-the-serum-samples-of-five-randomly-sele-354856.html
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math
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1. (50 points) Cholesterol was measured in the serum samples of five randomly selected patients from a pool of patients. Two independently prepared repli- cate tubes were prepared for each patient for each of spectrophotometer from four brands. The objective of the study was to determine whether the relative cholesterol measurements for patients were consistent for four brands. The data mg/dl of cholesterol in the replicate samples from each patient on each brand.
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX148.5?
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX154.7?
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX145.9?
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX151.0?
(1) From the statement above identify the following experimental design com- ponents:
? Experimental unit?
? Fixed or random levels of the treatments
. (2) Write the model to study cholesterol measurements on patients and brands. You need to fully specify model components and the distributions of ran- dom terms.?
. (3) Find out the estimates of the parameters in the model specified in part (2).?
. (4) Test if the main effects and interaction effect in the model are significantly different from zero at level a = 0.05.?? Specify hypotheses H0and H1for each effect.?? Test the hypotheses (reject or accept H0) and present the p-values for?each effect.?
. (5) Examine the following assumptions of the error term in the model.?? Independence: Show the test statistic and the decision?? Constant variance: Check with residual plots?? Normality: Test statistics and test under 5% significance level?
2. (50 points) A research specialist for a large seafood company investigated bac- terial growth on oysters and mussels subjected to three different storage tem- peratures. Nine cold storage units were available. Oysters and mussels were stored for two weeks in each of the cold storage units. A bacterial count was made from a sample of oysters and mussels at the end of two weeks. Hence, with 3 replicates, the first fixed treatment applied to a batch of 2 storage units and then the batch has been split into 2 storage units to apply the second fixed
treatment. The logarithm of bacterial count for each sample is shown in the following table
Temperature (?C) 0
Seafood Oyster Mussel XXXXXXXXXX XXXXXXXXXX.5780
. (1) From the statement above identify the following experimental design com- ponents:?? Experimental units? Treatments?
. (2) Write the model to study the bacterial counts on temperature and seafood with full specification of model components.?
. (3) Construct the analysis of variance (ANOVA) table with a column of the expected mean square (EMS). Use the auxiliary table to find the EMS for full credit.?
. (4) Test the significances of treatment effects in the model at the level a = 0.01.?? Specify hypotheses H0and H1for each effect.?? Test the hypotheses (reject or accept H0) and present the p-values for?each effect.?
. (5) Theresearchistoinvestigatebacterialgrowthonoystersandmusselsunder different storage temperatures. Briefly write a conclusion with respect to the research object.?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710924.83/warc/CC-MAIN-20221203043643-20221203073643-00059.warc.gz
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CC-MAIN-2022-49
| 3,034 | 21 |
https://www.flickr.com/photos/jekaphotography/6106650753/
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math
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The Curve of the Earth
For image licensing requests or photo related questions click here! or message me through Flickrmail.
The eastern shore of England seen flying high above the English Channel
From a point above the surface the horizon appears slightly bent. There is a basic geometrical relationship between this visual curvature κ, the altitude and the Earth's radius.
The curvature is the reciprocal of the curvature angular radius in radians. A curvature of 1 appears as a circle of an angular radius of 45° corresponding to an altitude of approximately 2640 km above the Earth's surface. At an altitude of 10 km (33,000 ft, the typical cruising altitude of an airliner) the mathematical curvature of the horizon is about 0.056, the same curvature of the rim of circle with a radius of 10 m that is viewed from 56 cm. However, the apparent curvature is less than that due to refraction of light in the atmosphere and because the horizon is often masked by high cloud layers that reduce the altitude above the visual surface.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305420.54/warc/CC-MAIN-20220128043801-20220128073801-00519.warc.gz
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CC-MAIN-2022-05
| 1,034 | 5 |
https://fr.slideserve.com/nariko/introduction-to-logarithms
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math
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Logarithms were originally developed to simplify complex arithmetic calculations. They were designed to transform multiplicative processes into additive ones.
If at first this seems like no big deal, then try multiplying 2,234,459,912 and 3,456,234,459. Without a calculator ! Clearly, it is a lot easier to add these two numbers.
Today of course we have calculators and scientific notation to deal with such large numbers. So at first glance, it would seem that logarithms have become obsolete.
Indeed, they would be obsolete except for one very important property of logarithms. It is called the power property and we will learn about it in another lesson. For now we need only to observe that it is an extremely important part of solving exponential equations.
Our first question then must be: What is a logarithm ?
Of course logarithms have a precise mathematical definition just like all terms in mathematics. So let’s start with that.
Definition of Logarithm Suppose b>0 and b≠1, there is a number ‘p’ such that:
Now a mathematician understands exactly what that means. But, many a student is left scratching their head.
The first, and perhaps the most important step, in understanding logarithms is to realize that they always relate back to exponential equations.
You must be able to convert an exponential equation into logarithmic form and vice versa. So let’s get a lot of practice with this !
Example 1: Solution: We read this as: ”the log base 2 of 8 is equal to 3”.
Example 1a: Solution: Read as: “the log base 4 of 16 is equal to 2”.
Example 1b: Solution:
It is also very important to be able to start with a logarithmic expression and change this into exponential form. This is simply the reverse of what we just did.
Example 1: Solution:
Example 2: Solution:
We now know that a logarithm is perhaps best understood as being closely related to an exponential equation. In fact, whenever we get stuck in the problems that follow we will return to this one simple insight. We might even state a simple rule.
When working with logarithms, if ever you get “stuck”, try rewriting the problem in exponential form. Conversely, when working with exponential expressions, if ever you get “stuck”, try rewriting the problem in logarithmic form.
Let’s see if this simple rule can help us solve some of the following problems.
Solution: Let’s rewrite the problem in exponential form. We’re finished !
Solution: Rewrite the problem in exponential form.
Example 3 Solution: Try setting this up like this: Now rewrite in exponential form.
These next two problems tend to be some of the trickiest to evaluate. Actually, they are merely identities and the use of our simple rule will show this.
Example 4 Solution: First, we write the problem with a variable. Now take it out of the logarithmic form and write it in exponential form.
Example 5 Solution: First, we write the problem with a variable. Now take it out of the exponential form and write it in logarithmic form.
Ask your teacher about the last two examples. They may show you a nice shortcut.
Finally, we want to take a look at the Property of Equality for Logarithmic Functions. Basically, with logarithmic functions, if the bases match on both sides of the equal sign , then simply set the arguments equal.
Example 1 Solution: Since the bases are both ‘3’ we simply set the arguments equal.
Example 2 Solution: Since the bases are both ‘8’ we simply set the arguments equal. Factor continued on the next page
Example 2 continued Solution: It appears that we have 2 solutions here. If we take a closer look at the definition of a logarithm however, we will see that not only must we use positive bases, but also we see that the arguments must be positive as well. Therefore -2 is not a solution. Let’s end this lesson by taking a closer look at this.
Our final concern then is to determine why logarithms like the one below are undefined. Can anyone give us an explanation ?
One easy explanation is to simply rewrite this logarithm in exponential form. We’ll then see why a negative value is not permitted. First, we write the problem with a variable. Now take it out of the logarithmic form and write it in exponential form. What power of 2 would gives us -8 ? Hence expressions of this type are undefined.
That concludes our introduction to logarithms. In the lessons to follow we will learn some important properties of logarithms. One of these properties will give us a very important tool which we need to solve exponential equations. Until then let’s practice with the basic themes of this lesson.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00322.warc.gz
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CC-MAIN-2022-21
| 4,610 | 33 |
http://www.camoy.info/gcd
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math
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baab mod axxxxxxxx
- Let be a common divisor of and . Consider all of the copies of which add up to . Take away all the instances of that evenly cover . What’s left must evenly divide .
- Alternatively, if we consider to be a common divisor of and we can copy it to cover evenly and as many times as necessary to add up to . Therefore it evenly divides .
If the visual demonstration is unconvincing, the above can also be shown algebraically using the definition of divisibility.
Let be the common divisor of and . We can write and as , for . By the Quotient-Remainder Theorem, we can also write for . We must show divides .
We must also show that if is the common divisor of and , then it divides . Let , . Once again we know .
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103891.56/warc/CC-MAIN-20170817170613-20170817190613-00452.warc.gz
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CC-MAIN-2017-34
| 730 | 6 |
https://fr.slideserve.com/lee/personal-finance-powerpoint-ppt-presentation
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math
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PERSONAL FINANCE MBF3C Lesson #1: Introduction to Personal Finance
Unit Learning Goals • To state the difference between simple and compound interest • To identify simple interest as linear relation and compound interest as an exponential relation • To solve word problems involving simple and compound interest • To identify various services available at banks • To solve problems involving the cost of making purchases on credit. • To identify the costs of owning and operating a vehicle • To solve problems involving the costs associated with operating a vehicle.
YOUR TEXTBOOK Pages 422-495
INTRODUCTION • Banks pay you interest for the use of your money. When you deposit money in a bank account, the bank reinvests your money to make a profit.
DEPOSIT …a sum of money placed or kept in a bank account.
BORROW …To obtain or receive (something) on loan with the promise or understanding of returning it or its equivalent. BORROW is like TAKE: You borrow something from somebody. You borrow things from the owner.
BORROWER The person or business that is GETTING the item (money)
LEND LEND is like GIVE: The owner lends you things. The owner lends things to you.
LENDER The person or business that is giving the item (money)
LOAN …a thing that is borrowed. In finance, it’s a sum of money that is expected to be paid back with interest.
DEPOSIT …a sum of money placed or kept in a bank account, usually to gain interest.
INTEREST …a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets.
SECURITY A security, in a financial context, is a certificate or other financial instrument that has monetary value and can be traded.
SIMPLE AND COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!
SIMPLE INTEREST • Simple interest is calculated on the initial value invested (principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period. Interest, I = Prt
Parts • simple interest • the money paid on a loan or investment a percent of the principal • Principal • the value of the initial investment or loan • amount • the final or future value of an investment, including the principal and the accumulated Interest • compound interest • the interest paid on the principal and its accumulated interest
SIMPLE INTEREST • Simple interest is calculated on the initial value invested ( principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period. Interest, I = Prt • Amount , A = P + PrtOr in factored form, A = P(1 + rt) • Compound interest is calculated on the accumulated value of the investment, which includes the principal and the accumulated interest of prior periods.
100 IMPLE INTEREST FORMULA Annual interest rate Interest paid I = PRT Time (in years) Principal(Amount of money invested or borrowed)
100 If you invested $200.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $10.00. enter in formula as a decimal I = PRT 10 = (200)(0.04)T 1.25 yrs = T Typically interest is NOT simple interest but is paid semi-annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year).
COMPOUND INTEREST FORMULA annual interest rate(as a decimal) Principal(amount at start) time(in years) amount at the end number of times per year that interest in compounded
4 (2) .08 500 4 Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years. Effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as that made compounding. This is found by finding the interest made when compounded and subbing that in the simple interest formula and solving for rate. Find the effective rate of interest for the problem above. The interest made was $85.83. Use the simple interest formula and solve for r to get the effective rate of interest. I = Prt 85.83=(500)r(2) r = .08583 = 8.583%
INVESTIGATION (Page 422) • Compare the growth of a $1000 investment at 7% per year, simple interest, with another $1000 investment at 7% per year, compounded annually.
What is an Exponent? • An exponent means that you multiply the base by itself that many times. • For example: x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 64 • most often when talking about very big or very small things in real life. • Examples: Large distances, counting large numbers that grow quickly (e.g. # of bacteria in a sneeze), building houses, computers, engineering, pH scale, impact of earthquakes among others.
The Invisible Exponent • When an expression does not have a visible exponent its exponent is understood to be 1.
Exponent Rule #1 • When multiplying two expressions with the same base you add their exponents. • For example
Exponent Rule #1 • Try it on your own:
Exponent Rule #2 • When dividing two expressions with the same base you subtract their exponents. • For example
Exponent Rule #2 • Try it on your own:
Exponent Rule #3 • When raising a power to a power you multiply the exponents • For example
Exponent Rule #3 • Try it on your own
Note • When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases
Exponent Rule #4 • When a product is raised to a power, each piece is raised to the power • For example
Exponent Rule #4 • Try it on your own
Note • This rule is for products only. When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases
Exponent Rule #5 • When a quotient is raised to a power, both the numerator and denominator are raised to the power • For example
Exponent Rule #5 • Try it on your own
CLASS/HOMEWORK: REVIEW OF EXPONENT RULES Complete Q# 1, 2, 3,4 on p. 356-357 and Q#1-3 on p. 360.
Zero Exponent • When anything, except 0, is raised to the zero power it is 1. • For example ( if a ≠ 0) ( if x ≠ 0)
Zero Exponent ( if a ≠ 0) • Try it on your own ( if h ≠ 0)
Negative Exponents • If b ≠ 0, then • For example
Negative Exponents • If b ≠ 0, then • Try it on your own:
Negative Exponents • The negative exponent basically flips the part with the negative exponent to the other half of the fraction.
Math Manners • For a problem to be completely simplified there should not be any negative exponents
CLASS/HOMEWORK: Zero and Negative Exponents: COMPLETE Q #1-4 ON PAGE 364 OF YOUR TEXTBOOK!
The intensity of an earthquake can range from 1 to 10 000 000. The Richter scale is a base-10 exponential scale used to classify the magnitude of an earthquake. An earthquake with an intensity of 100 000 or 105 , has a magnitude of 5 as measured on the Richter scale. The chart shows how magnitudes are related:
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355944.41/warc/CC-MAIN-20210226001221-20210226031221-00580.warc.gz
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CC-MAIN-2021-10
| 7,112 | 45 |
http://www.ia-maths.co.uk/site/miss-kearns/s5-h/
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math
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National 6 Maths
Past Papers by topic and solutions
Polynomials and Quadratics Past Papers
Integration Past Papers
Logs and exponentials
National 5 Maths
Revision sheets for Expressions and Formulae unit.
Expressions and Formulae Revision Booklet
E and F Extension Revision and Answers (courtesy of pgsmaths)
E an F Practice Questions
There are no upcoming events.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583510969.31/warc/CC-MAIN-20181017023458-20181017044958-00483.warc.gz
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CC-MAIN-2018-43
| 364 | 11 |
http://www.counseling.txstate.edu/resources/shoverview/bro/math.html
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math
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Are you a student who gets anxious at just the thought of taking that required math class? Do you worry about having to figure out everyone's part of the bill when you have lunch with a group of friends? Do you believe that you simply do not have a math mind? Do you avoid activities or other classes that may involve mathematics? If any one or more of these situations describes you, you may be suffering from Math Anxiety.
What is Math Anxiety?
Math anxiety is an intense emotional feeling of anxiety that people have about their ability to understand and do mathematics. People who suffer from math anxiety feel that they are incapable of doing activities and classes that involve math. Some math anxious people even have a fear of math; it's called math phobia. The incidence of math anxiety among college students has risen significantly over the last decade. Many students have even chosen their college major in the basis of how little math is required for the degree. Math anxiety has become so prevalent on college campus that many schools have designed special counseling programs to help math anxious students. Math anxiety is an emotional, rather than intellectual, problem. However, math anxiety interferes with a person's ability to learn math and therefore results in an intellectual problem.
What Causes Math Anxiety?
Math anxiety does not have a single cause. Often math anxiety is the result of a student's negative or embarrassing experience with math or a math teacher in previous years. Such an experience can leave a student believing him or herself deficient in math ability. This belief can actually result in poor performance, which serves as confirming evidence to the student. This phenomenon is known as the self-fulfilling prophecy. Math anxiety results in poor performance rather than the reverse.
There are a number of erroneous beliefs about math, which contribute to students' fears, and anxiety about math. Some of those myths include:
- Men are better in math than women. Research has failed to show any difference between the sexes in math ability.
- There is a best way to do a math problem. Most math problems can be solved a number of ways.
- Some people have a math mind and others don't. Most people are much more capable in math than they believe they are.
- It's bad to count on your fingers. Counting in fingers actually indicated an understanding of arithmetic.
- Those good in math do problems quickly in their heads. Even math professors review example problems before teaching them in class.
Math anxiety is often perpetuated by a number of mind games that students play themselves.
- I don't do math fast enough. People learn at different rates. How fast one does math is not important.
- I don't have a math mind. This belief interferers with one's real ability to learn math.
- I got the right answer but I did it the wrong way. There is no best way to do math problem.
- If I get it right, it's too simple. Math anxious students often discount their own abilities when they are related to math.
- Math is unrelated to my life. Freeing yourself of the fear of math adds choices and freedom to your life.
What To Do About Math Anxiety?
Math anxiety is a learned psychological response to math, which interferes with a student's ability to perform math. It is not a reflection of a student's true ability in math. There are a number of strategies a student can use to overcome the anxiety response. Some of the primary strategies are described here.
- Review and learn basic arithmetic principles and methods. Many students, perhaps because of early negative experiences, never really developed a solid foundation in basic arithmetic, particularly multiplication and fractions. Because math is an accumulative discipline, that is complex concepts are built cumulatively on more simple concepts, a student who has not developed a solid arithmetic foundation will have trouble learning higher order math. A remedial course or short course an arithmetic is often a significant first step in reducing the anxiety response to math.
- Be aware of thoughts, feelings, and actions as they are related to math. Math anxiety affects different students in different ways. It's important to be familiar with the thoughts you have abut yourself and the situation when you encounter math. If you are aware of unrealistic or irrational thoughts you can work to replace those thoughts with more positive and realistic ones.
- Seek help! Math anxiety is learned and reinforced over a long period of time and therefore is not quickly eliminated. A student can reduce the anxiety response more effectively with the help of a number of different services. Staff psychologists and counselors in the Counseling Center can help students analyze their psychological response to math, learn anxiety management skills, and develop effective coping strategies. The Student Learning Assistance Center (SLAC) can help students get a tutor, take math class noted and prepare for exams more effectively, and it can provide a number of math learning aids. The TxState Math Lab provides special tutorial assistance to students in lower division math courses.
- Learn the vocabulary of mathematics. one of the problems students have with math is understanding the terms and vocabulary. Math often uses words in a completely different way than they ate used in other subject. The term factor is an example. Students often confuse lack of understanding of terms and vocabulary with math ability.
- Learn anxiety reduction and anxiety management techniques. Anxiety can greatly interfere with concentration, clear thinking, attention and memory. Students can learn relaxation anxiety management techniques that are very effective in controlling the emotional and physical characteristics of anxiety that are interfering with mental processing capabilities.
- Work ion having a positive attitude about math. Having a positive attitude will build self-confidence and thus reduce anxiety.
- Learn positive self-talk. Giving yourself positive self-talk helps to counter and overcome your belief in the math myths or to stop playing mind games on yourself. Positive self-talk is effective in replacing negative thoughts, which create anxiety with positive thoughts that reduce anxiety.
Learn effective math class and study techniques.
Students who fear math often avoid asking questions to save embarrassment, sit in the back of the classroom, fail to seek help from the professor, and usually put off studying math until the last moment. All of these negative behaviors are intended to reduce the student's anxiety but actually result in more intense anxiety. There are a number of positive behaviors, which actually help the student learn and perform better in math classes. First, sit near the front of the class where you will experience fewer distractions and feel more a part of what is being discussed. Second, if you have questions, ask! Rest assured that you are not the only one who has the same question you want to ask. Don't be afraid to seek help from your professor after class or during office hours. Third, prepare! Read the textbook material before it is discussed in class. Do the problems. Math skill comes from practice and repetition. Finally, after class, review the material covered again.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115857200.13/warc/CC-MAIN-20150124161057-00161-ip-10-180-212-252.ec2.internal.warc.gz
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CC-MAIN-2015-06
| 7,320 | 28 |
https://studylib.net/doc/10908408/%3D-sin60-%3D-3---2----sin-45
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math
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PHYSICS 2B PROF. HIRSCH QUIZ 1 WINTER QUARTER 2010 JANUARY 11, 2010 Formulas: sin 30 o = cos 60o = 1 / 2, cos30o = sin60 o = 3 / 2, sin 45o = cos 45o = 2 / 2 r q1q2 kq1q2 r r 9 2 2 Coulomb's law ; k = 9 ×10 N ⋅ m /C ; F r ( r2 − r1 ) 12 = r 2 r | r2 − r1 |3 r kq r r Electric field due to charge q at distance r : E = 2 rˆ ; Force on charge Q: F = QE r 2kp Electric field of dipole, along dipole axis: (p=qd) €E = 3 x €kp Electric field of dipole, along direction perpendicular to dipole axis: E = 3 y r r r r r Energy of and torque on dipole in E-field: U = −p⋅ E , τ = p × E € F=k € € Linear, surface, volume charge density : dq = λ ds , dq = σ dA € , dq = ρ dV € sheet of charge : E = 2πkσ 2kλ Electric field of infinite : line of ; € charge : E =€ r Solutions are in bold There are 7 problems in this quiz, all are worth the same. Mark the answer closest to yours. This is Test Form A y Figure For problems 1, 2, 3, 4 P2 a a 3q -q P1 d The charge 3q is at the origin (x,y)=(0,0), the charge -q is at (a,0). Point P1 is at (d,0), point P2 is at (0,a). q > 0. Problems 1 to 4 refer to this figure. Problem 1 A point on the x-axis where the electric field is 0 is (x0 ,0), with x0 = (a) 1.8a ; (b) 2.4a ; (c) 4a ; (d) 2.8a ; (e) -2a On the x axis, to the right of the charge -q, set 3q/x2 =q/(x-a)2 , solve for x: x2 =3(xa)2 ==> x=sqrt(3) (x-a) , solve, gives x=sqrt(3)/(sqrt(3)-1)) times a Problem 2 The point on the positive x-axis to the right of the charge -q where the force on a positive test charge points to the right and its maximum is at (a) 3.3a ; (b) 3.5a ; (c) 3.7a ; (d) 3.9a ; (e) 4.1a x PHYSICS 2B PROF. HIRSCH QUIZ 1 WINTER QUARTER 2010 JANUARY 11, 2010 E-field is 3q/x2 - q/(x-a)2 , take derivative, set it =0 to locate maximum, solve for x. Equation is 6(x-a)3 =2x3 ==> x=31/3(x-a), etc. Problem 3 The electric field at point P1 (see figure) at a distance d>>a is approximately: kqα kqaβ E P1 = 2 + 3 d d with (a) α=2, β=2; (b) α=2, β=1 ; (c) α=3, β=-2 ; (d) α=3, β=-1 ; (e) α=2, β=-2 Hint: use superposition € 1/d2 dependence comes from net charge, 1/d3 from dipole. At a large distance, this charge arrangement looks like a dipole (q, -q) with dipole moment p=qd pointing in the negative x direction, plus a charge 2q. Use formulas for field of charge and field of dipole. Problem 4 The electric field at point P2 (see figure) has components kq kq E x = 2 α, E y = 2 β a a with (a) α=0.5, β=2.5; (b) α=1, β=2 ; (c) α=1.5, β=-2.5 ; (d) α=0.5, β=3 ; (e) α=1, β=2.5 € Charge 3q gives a positive y-component only, charge -q gives a positive xcomponent and a negative y-component that are equal in magnitude since the angle is 45 degrees. Add y-components from both contributions (with their sign). Figure y E Ey for problems 5 and 6 P L + + + + + + | λ(x) 0 L x A charged rod of length L on the x-axis has a nonuniform linear charge distribution x λ(x) = λ0 , where x is measured from the left end. At the point P shown in the figure, at L distance L from the left end of the rod in the vertical direction, the electric field points approximately in the direction shown, and it's y-component, Ey , is positive. It can be calculated by doing an easy integral. € Problem 5 λ0 α , with L (a) α=0.1; (b) α=0.2 ; (c) α=0.3 ; (d) α=0.4 ; (e) α=0.5 The magnitude of Ey shown in the figure is € PHYSICS 2B PROF. HIRSCH QUIZ 1 WINTER QUARTER 2010 JANUARY 11, 2010 It is like the integral discussed in class in connection with example 23-9 in the book, except that the charge density is x-dependent. That makes the integral a lot easier, since it involves x/(x2 +L2 ) 3/2 and can be done simply by substitution. Problem 6 At another point very far away from this rod, at distance d>>L, the magnitude of the electric λL field is E = 02 β , with d (a) β=0.25; (b) β=0.5 ; (c) β=1 ; (d) β=1.5 ; (e) β=2 Far from the rod, the electric field is kq/d2 with q the total charge of the rod, which € is obtained by integrating the linear charge density from 0 to L, giving λ0L/2. Problem 7 d a P a The charges in the square arrangement in the figure with side a have all magnitude q, and their sign is shown. At the point P shown, very far away from this charge arrangement (at a distance d >> a), the electric field: (a ) points to the right ; (b) points to the left ; (c) points up ; (d) points down ; (e) is exactly zero This can be seen as 2 dipoles, one pointing in the + y direction and the other in the -y direction, the latter one is a little further away (a further away). The first one gives an E-field pointing down, the second pointing up but a little smaller, so the net E-field points down.
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https://www-fourier.ujf-grenoble.fr/?q=en/content/matthieu-dolbeault
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math
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Optimal sampling for approximation of functions
Thursday, 9 February, 2023 - 17:00
We investigate the problem of approximating a function in L^2 based on evaluations of the function at some chosen points. A first approach, using weighted least-squares at i.i.d random points, provides a near-best approximation, but with a sampling budget larger (by a logarithmic factor) than the dimension of the approximation space. To reduce the gap between these two quantities, we need non i.i.d methods relying on linear algebra for sums of rank-one matrices.
Thème de recherche :
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945333.53/warc/CC-MAIN-20230325130029-20230325160029-00222.warc.gz
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CC-MAIN-2023-14
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http://filesharingtalk.com/threads/201511-REQ-FTN-Invite
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Hello to all generous guys,
I know its a long shot but just wanted to be inside this wonderful tracker and use it for life. If someone hasn't traded theirs maybe they can help me . Can show ratio proofs if you feel like and they matter to you.
Any help is appreciated.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718278.43/warc/CC-MAIN-20161020183838-00110-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
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https://www.scribd.com/doc/72610005/ANSYS-Tutorial-Release10
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math
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This action might not be possible to undo. Are you sure you want to continue?
Kent L. Lawrence
Mechanical and Aerospace Engineering University of Texas at Arlington
Schroff Development Corporation
Plane Stress / Plane Strain
Lesson 2 Copyrighted Plane Material Stress Plane Strain
Plane stress and plane strain problems are an important subclass of general threedimensional problems. The tutorials in this lesson demonstrate: ♦Solving planar stress concentration problems.
♦Evaluating potential inaccuracies in the solutions. ♦Using the various ANSYS 2D element formulations.
It is possible for an object such as the one on the cover of this book to have six components of stress when subjected to arbitrary three-dimensional loadings. When referenced to a Cartesian coordinate system these components of stress are: Normal Stresses Shear Stresses
σx, σy, σz τxy, τyz, τzx
Figure 2-1 Stresses in 3 dimensions.
In general, the analysis of such objects requires three-dimensional modeling as discussed in Lesson 4. However, two-dimensional models are often easier to develop, easier to solve and can be employed in many situations if they can accurately represent the behavior of the object under loading.
Plane Stress / Plane Strain
A state of Plane Stress exists in a thin object loaded in the plane of its largest dimensions. Let the X-Y plane be the plane of analysis. The non-zero stresses σx, σy, and τxy lie in the X - Y plane and do not vary in the Z direction. Further, the other stresses (σz,τyz , and τzx )are all zero for this kind of geometry and loading. A thin beam loaded in its plane and a spur gear tooth are good examples of plane stress problems. ANSYS provides a 6-node planar triangular element along with 4-node and 8-node quadrilateral elements for use in the development of plane stress models. We will use both triangles and quads in solution of the example problems that follow. 2-3 PLATE WITH CENTRAL HOLE To start off, let’s solve a problem with a known solution so that we can check our computed results and understanding of the FEM process. The problem is that of a tensileloaded thin plate with a central hole as shown in Figure 2-2.
The 1.0 m x 0.4 m plate has a thickness of 0.01 m, and a central hole 0.2 m in diameter. It is made of steel with material properties; elastic modulus, E = 2.07 x 1011 N/m2 and Poisson’s ratio, ν = 0.29. We apply a horizontal tensile loading in the form of a pressure p = -1.0 N/m2 along the vertical edges of the plate. Because holes are necessary for fasteners such as bolts, rivets, etc, the need to know stresses and deformations near them occurs very often and has received a great deal of study. The results of these studies are widely published, and we can look up the stress concentration factor for the case shown above. Before the advent of suitable computation methods, the effect of most complex stress concentration geometries had to be evaluated experimentally, and many available charts were developed from experimental results.
Figure 2-2 Plate with central hole.
Copyrighted Material Copyrighted Material Figure 2-3 Quadrant used for analysis. or Title after you’ve started ANSYS. for large problems it can save modeling and solution efforts by eliminating one-half or a quarter or more of the work. use only a quarter of the plate for the finite element model. Start ANSYS. This means that the state of stress and deformation below a horizontal centerline is a mirror image of that above the centerline. If we pull on both ends of the plate. use File > Change Jobname or Directory or Title. Also set the Jobname to Tutorial2A or something memorable and provide a Title. (If you want to make changes in the Jobname. For small problems using symmetry may not be too important. working Directory. 2-4 TUTORIAL 2A . Copyrighted Material Copyrighted Material . by applying the correct boundary conditions. This indicates the appropriate displacement conditions to use as shown below. and likewise for a vertical centerline. PREPROCESSING 1.PLATE Objective: Find the maximum axial stress in the plate with a central hole and compare your result with a computation using published stress concentration factor data. points on the centerlines will move along the centerlines but not perpendicular to them.) Select the six node triangular element to use for the solution of this problem. select the Working Directory where you will store the files associated with this problem. Interactive commands will be used to formulate and solve the problem. homogeneous plate above is symmetric about horizontal axes in both geometry and loading. In Tutorial 2A we will use ANSYS to determine the maximum horizontal stress in the plate and compare the computed results with the maximum value that can be calculated using tabulated values for stress concentration factors.Plane Stress / Plane Strain 2-3 The uniform. We can take advantage of the symmetry and. Place the origin of X-Y coordinates at the center of the hole.
Select the option where you define the plate thickness. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Structural Solid > Triangle 6 node 2 > OK Copyrighted Material Figure 2-4 Six-node triangle. 3. Options (Element behavior K3) > Plane strs w/thk > OK > Close Copyrighted Material . Copyrighted Material Figure 2-5 Element selection.2-4 Plane Stress / Plane Strain Copyrighted Material 2.
(Enter the plate thickness of 0. .01 m.01 > OK > Close Copyrighted Material Copyrighted Material Figure 2-8 Enter the plate thickness. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > OK Copyrighted Material Figure 2-6 Element options.) >Enter 0. Enter the material properties.Plane Stress / Plane Strain 2-5 Copyrighted Material 4. Figure 2-7 Real constants.
6.1 > OK Copyrighted Material Copyrighted Material Copyrighted Material Copyrighted Material Figure 2-9 Create areas. Main Menu > Preprocessor > Modeling > Create > Areas > Circle > Solid Circle Enter WP X = 0.5 x 0.0.2 > OK 7.29 > OK (Close the Define Material Model Behavior window.2-6 Plane Stress / Plane Strain 5. Generate the rectangle first.0.) Create the geometry for the upper right quadrant of the plate by subtracting a 0. WP Y = 0. Double click Structural > Linear > Elastic > Isotropic Enter EX = 2. Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners Enter (lower left corner) WP X = 0. WP Y = 0. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1.0 and Width = 0.2 m diameter circle from a 0. .0 and Radius = 0.07E11 and PRXY = 0.2 m rectangle. Height = 0.5.
) 8.Plane Stress / Plane Strain 2-7 Copyrighted Material Figure 2-10 Rectangle and circle. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge of the quadrant > OK > UX = 0. Create a mesh of triangular elements over the quadrant area. Main Menu > Preprocessor > Meshing > Mesh > Areas > Free Pick the quadrant > OK Copyrighted Material Figure 2-12 Triangular element mesh. (Read the messages in the window at the bottom of the screen as necessary. 10. Now subtract the circle from the rectangle. then pick the circle > OK Copyrighted Material Figure 2-11 Geometry for quadrant of plate. 9. Apply the displacement boundary conditions and loads. Main Menu > Preprocessor > Modeling > Operate > Booleans > Subtract > Areas > Pick the rectangle > OK. > OK Copyrighted Material .
close the ‘Solution is Done!’ window. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines. . Pick the right edge of the quadrant > OK > Pressure = -1. Main Menu > General Postproc > Plot Results > Deformed Shape > Def.) Copyrighted Material Figure 2-13 Model with loading and displacement boundary conditions. First examine the deformed shape.2-8 Plane Stress / Plane Strain 11. and when the solution is complete. save the model. The model-building step is now complete. use a new name) SOLUTION The interactive solution proceeds as illustrated in the tutorials of Lesson 1. The pressure is shown as a single arrow.db (Or Save as …. POSTPROCESSING We can now plot the results of this analysis and also list the computed values. > OK 12. Check the solution options in the /STATUS window and if all is OK. 13. Select OK. Utility Menu > File > Save as Jobname. Main Menu > Solution > Solve > Current LS > OK Copyrighted Material The /STATUS Command window displays the problem parameters and the Solve Current Load Step window is shown.0 > OK (A positive pressure would be a compressive load. select File > Close In the Solve Current Load Step window. so we use a negative pressure. First to be safe. > OK Copyrighted Material Copyrighted Material . and we can proceed to the solution. 14. + Undef. 15. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the bottom edge of the quadrant > OK > UY = 0.
The six-node triangle has curved sides. The maximum displacement is shown on the graph legend as 0. The deformed shape looks correct. and if you pick on a mid-side of one these elements. 16. Display All Applied BCs as well. Note that the element edges on the circular arc are represented by straight lines. and the top moves down because of Poisson’s effect. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Use PlotCtrls > Symbols [/PSF] Surface Load Symbols (set to Pressures) and Show pre and convect as (set to Arrows) to display the pressure loads. Now plot the stress in the X direction.Plane Stress / Plane Strain 2-9 Copyrighted Material Copyrighted Material Figure 2-14 Plot of Deformed shape. the circular hole ovals out. This is an artifact of the plotting routine not the analysis.) The right end moves to the right in response to the tensile load in the x-direction.32e-11 which seems reasonable. . Copyrighted Material Copyrighted Material Figure 2-15 Surface load symbols. The units of displacement are meters because we employed meters and N/m2 in the problem formulation. (The undeformed shape is indicated by the dashed lines. you will see that a node is placed on the curved edge.
and maximum. Copyrighted Material Copyrighted Material Figure 2-17 SX stress detail.2-10 Plane Stress / Plane Strain Copyrighted Material The minimum. We are interested in the maximum stress at the hole. Use the Zoom to focus on the area with highest stress. stresses as well as the color bar legend give an overall evaluation of the SX stress state. . Copyrighted Material Figure 2-16 Element SX stresses. SMN. SMX.
and SX would seem to be accurately determined there. the number of elements near the stress concentrations must be increased proportionately. in the right half of the model. We will also refine the mesh selectively near the hole. and any contour discontinuities (and thus errors) will be hidden. If you plot nodal solution stresses you will always see smooth contours. 17. The continuum elements such as the ones for plane stress and plane strain. the stress values will be averaged before plotting. homogeneous plate should be smooth and continuous across elements. the calculated stress contours are smooth. away from the stress riser. return to the Preprocessor and refine the mesh. On the other hand. We will not accept this stress solution. Near stress concentrations the stress gradients vary quite sharply. and the higher the polynomial. To capture this variation. are normally developed using displacement functions of a polynomial type to represent the displacements within the element. for problems like the one in this tutorial. It is important to note that in the plotting we selected Element Solu (Element Solution) in order to look for stress contour discontinuities.) Copyrighted Material Copyrighted Material Copyrighted Material Figure 2-18 Global mesh refinement. Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > All (Select Level of refinement 1. Copyrighted Material .Plane Stress / Plane Strain 2-11 Stress variations in the actual isotropic. The ANSYS six-node triangle uses a quadratic polynomial and is capable of representing linear stress and strain variations within an element. All elements are subdivided and the mesh below is created. on the other hand. To obtain more elements in the model. The discontinuities in the SX stress contours above indicate that the number of elements used in this model is too few to accurately calculate the stress values near the hole because of the stress gradients there. the greater the accuracy. A word about element accuracy: The FEM implementation of the truss element is taken directly from solid mechanics studies. More six-node elements are needed in the region near the hole to find accurate values of the stress. and there is no approximation in the solutions for truss structures formulated and solved in the ways discussed in Lesson 1. If you pick Nodal Solu to plot instead.
Note also that too much local refinement can create a mesh with too rapid a transition between fine and coarse mesh regions. Plot > Areas afterwards to view the area again. Main Menu > Preprocessor > Meshing > Modify Mesh > Refine At > Nodes. (Select the three nodes shown. (Note: Alternatively you can use Preprocessor > Meshing > Clear > Areas to remove all elements and build a completely new mesh. File > Save as Jobname.) Now repeat the solution. 19.db Copyrighted Material Plot the stresses in the X-direction. 20. 21. and replot the stress SX.) > OK (Select the Level of refinement = 1) > OK Copyrighted Material Copyrighted Material Figure 2-19 Selective refinement at nodes.2-12 Plane Stress / Plane Strain 18. Main Menu > Solution > Solve > Current LS > OK Save your work. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > X-Component of stress > OK Copyrighted Material .
We can compute the maximum stress using (Kt)(load)/(net cross sectional area). The element solution stress contours are now smooth across element boundaries. To check this result.etbx.17.386 Pa. find the stress concentration factor for this problem in a text or reference book or from a web site such as www.com. Using the pressure p = 1.Plane Stress / Plane Strain 2-13 Copyrighted Material Copyrighted Material Figure 2-20 SX stress contour after mesh refinement. Copyrighted Material Figure 2-21 SX stress detail contour after mesh refinement. and the stress legend shows a maximum value of 4. a 4.0 Pa we obtain. For the geometry of this example we find Kt = 2.3 percent change in the computed stress. Copyrighted Material .
assuming that the value of Kt is exact. four-node quadrilaterals or eight-node quadrilaterals. For continuum problems in two and three-dimensional stress.34 Pa Copyrighted Material Copyrighted Material Figure 2-22 Triangular and quadrilateral elements. For h-method elements. 2-5 THE APPROXIMATE NATURE OF FEM As mentioned above. stresses and strains within the element. 2-dimensional problems can be modeled with six-node triangles.39 Pa which is around one percent in error. Copyrighted Material σ x MAX = 2. high-degree displacement polynomials and/or many elements are required to accurately analyze the situation.01) /[(0. Ordinarily this is done by specifying the highest degree of the polynomial that governs the displacement distribution within an element.4)(0.2-14 Plane Stress / Plane Strain The computed maximum value is 4. a very simple model is sufficient to describe the stress state.17 * p * (0.01] = 4. The greater the number of nodes. the higher the order of the polynomial and the greater the accuracy in describing displacements. In ANSYS. this is generally no longer possible. These comments explain the variation in the accuracy of the results as different numbers of elements were used to solve the problem in the previous tutorial and why the engineer must carefully prepare a model. If the stress is constant throughout a region. The Copyrighted Material . and the interpolation functions that relate displacements within the element to the displacements at the nodes are called shape functions. If there are gradients in the stress distributions within a region.2) * 0. the polynomial degree depends upon the number of nodes used to describe the element. perhaps only one or two elements. and the element stiffness matrices are usually developed by assuming something specific about the characteristics of the displacements that can occur within an element. the stiffness matrix for the truss elements of Lesson 1 can be developed directly and simply from elementary solid mechanics principles. start with small models. grow the models as understanding of the problem develops and carefully interpret the calculated results.4 − 0.
splines). only the number and location of nodes and elements. dbb. so if you want to save disk space. The keypoints (2.10). The loads. lines (straight. rst. and areas. mntr. line.3. you can delete the others. PVTS. esav. manipulated. 2-7 ANSYS GEOMETRY The finite element model consists of elements and nodes and is separate from the geometry on which it may be based. 2-6 ANSYS FILES The files created during the solution were saved in step 20 of Tutorial 2A. and area (3) for Tutorial 2A are shown below. and plotted. and. For example. Copyrighted Material . db. (The keypoint. It is possible to build the finite element model without consideration of any underlying geometry as was done in the truss examples of Lesson 1. the loads are transferred to the new mesh.6). numbers will be different from those shown above.5.Plane Stress / Plane Strain 2-15 ease with which models can be prepared and solved sometimes leads to careless evaluation of the computed results. lines (2. the geometry of Tutorial 2A can be generated with the following text file using the File > Read Input from command sequence. displacement boundary conditions and pressures were applied to the geometry lines.9. Geometry can be created in ANSYS interactively (as was done in the previous tutorial) or it can be created by reading a text file. development of the geometry is the first task.) Copyrighted Material Figure 2-23 Keypoints.4.3. Two-dimensional geometry in ANSYS is built from keypoints. at solution time. Applying boundary conditions and loads to the geometry facilitates remeshing the problem. The geometry does not change.db. These geometric items are assigned numbers and can be listed. Look in the working directory and you see Tutorial2A files with extensions BCS. the loads were transferred from the lines to the FEM model nodes. arcs. Copyrighted Material Copyrighted Material The finite element model developed previously for this part used the area A3 for development of the node/element FEM mesh. lines and areas. numbered. full. but in many cases. When the solution step was executed. and stat.5. However. the Tutorial 2A problem can be reloaded using only Tutorial2A. etc.
2.2-16 Plane Stress / Plane Strain /FILNAM. 0.0 k. 6. 3.Geom /title. L.5. 0. Tutorial 2B demonstrates this option for ANSYS geometry development.0 k. L. L. 0. 6.09375 inches thick. 0. 0. has an over all length of about 2. lines.4. 5.1 AL.2 k. 5. 0.1 L. 0. 3 4 5 6 ! Line from keypoints 2 to 3 Copyrighted Material Copyrighted Material ! Area defined by lines 1.2 k. 0. 2. 1.0 ! Keypoint 1 is at 0. 2-8 TUTORIAL 2B – SEATBELT COMPONENT Objective: Determine the stresses and deformation of the prototype seatbelt component shown in the figure below if it is subjected to tensile load of 1000 lbf. 1.0 k.5. 5 Geometry for FEM analysis also can be created with solid modeling CAD or other software and imported into ANSYS. 3.1 LARC.3.1. 1. arcs /prep7 ! Create geometry k. 4. 0. A solid model of the part was developed in a CAD system and exported as an IGES file. 0.5 ! arc from keypoint 2 to 6. 0. 2. or ‘tongue’ portion of the part in this tutorial. 3. The seatbelt component is made of steel. 0. 2.5 inches and is 3/32 = 0. The IGES (Initial Graphics Exchange Specification) neutral file is a common format used to exchange geometry between computer programs. radius 0. 4. 0. The file is imported into ANSYS for analysis. 0. Copyrighted Material Figure 2-24 Seatbelt component. Copyrighted Material .0. 4. center kp 1. For simplicity we will analyze only the right.0.2.0.0. Stress Concentration Geometry ! Example of creating geometry using keypoints.
Seatbelt Geometry ! Example of creating geometry using keypoints.8125.Seatbelt /title.75. 13. 0.0 ! Keypoint 1 is at 0. 7.125. The latch retention slot is 0. 1.125. you can create the geometry directly in ANSYS with key points. 0. and working directory. 1.375 x 0. 0.09375.375 k. 12. 0. 1.34375 Copyrighted Material Copyrighted Material . 0. 6.0 k. and arcs by selecting File > Read Input from to read in the text file given below and skipping the IGES import steps 2. 4. 1.75 k. Create the top half of the geometry above.0.5 k.0 k.0. 0.375 inch from the right edge.375 k. 11. PREPROCESSING 1. 9. 2. set jobname.0. 0. 0. 4. 1.5. 8. 0. 0. 14. 0. 0.75. 0. 3. 0. arcs /prep7 ! Create geometry k.40625 k.5. 10. 0.09375. If you are not using an IGES file to define the geometry for this exercise. 1. Start ANSYS. 0.40625 k. 0. 3. 0. /FILNAM.Plane Stress / Plane Strain 2-17 Copyrighted Material Copyrighted Material Figure 2-25 Seatbelt ‘tongue’.0 k. 5. 1. 1.75 k.5 k.25. 0. 0.8125 inches and is located 0. lines.0 k. and 10 below. Run Interactive. 0. lines.34375 k.25. 1.8125.
14. 2. Turn the IGES solid model around if necessary so you can easily select the X-Y plane. L. for example lines that. 7 7.0625 Copyrighted Material ! Line from keypoints 1 to 2 ! Use all lines to create the area. radius 0. To import the IGES file 3. because of the modeling or the file translation process. L. LARC. 0. L. AL. 2 Plane Stress / Plane Strain ! arc LARC. Copyrighted Material Copyrighted Material Copyrighted Material Figure 2-26 IGES import.all from keypoint 5 to 6. 2 3.03125 10. L.6.25. 4 4. Accept the ANSYS import default settings. do not quite join. 5. 10 11.25 8. 9. L. L. 13. 1 3. 0. Alternatively. LARC. L. etc.2-18 L. center kp 12. If you have trouble with the import. 11. select the alternate options and try again. Utility Menu > File > Import > IGES Select the IGES file you created earlier. use a solid modeler to create the top half of the component shown above in the X-Y plane and export an IGES file of the part. 5 6. 8 9. 12. . 0. 1. Defeaturing is an automatic process to remove inconsistencies that may exist in the IGES file.
) Copyrighted Material 9. If so. Copyrighted Material . Main Menu > Preprocessor > Meshing > Mesh > Areas > Free.0E7 and PRXY = 0. Pick the X-Y planar area > OK IMPORTANT NOTE: The mesh below was developed from an IGES geometry file. Options > Plane strs w/thk > OK > Close Enter the thickness Copyrighted Material 7.3 > OK (Close Define Material Model Behavior window. Using the text file geometry definition. Computed stress values can be very sensitive mesh differences. Main Menu > Preprocessor > Material Props > Material Models Material Model Number 1. Zoom.Plane Stress / Plane Strain 2-19 4. Main Menu > Preprocessor > Real Constants > Add/Edit/Delete > Add > (Type 1 Plane 183) > OK > Enter 0. use the Modify Mesh refinement tools to obtain a mesh density that produces results with accuracies comparable to those given below. 5. Rotate > Back. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for this problem. Copyrighted Material Figure 2-27 Seatbelt solid. (Turn area numbers on if it helps. front and back.) 6.09375 > OK > Close Enter the material properties 8. Utility Menu > PlotCtrls > Pan. Double click Structural > Linear > Elastic > Isotropic Enter EX = 3. may produce a much different mesh. or use the side-bar icon.) Now mesh the X-Y plane area.
Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the left edge > UX = 0. Zero displacement UX along left edge and zero UY along bottom edge.2-20 Plane Stress / Plane Strain Copyrighted Material Figure 2-28 Quad 8 mesh. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines Pick the lower edge > UY = 0. Now apply displacement and pressure boundary conditions.75 in. 10. we can delete it from the session.09375 in. and since its lines and areas may interfere with subsequent modeling operations. The IGES solid model is no longer needed.)]. [1000 lbf/(0. Main Menu > Preprocessor > Modeling > Delete > Volume and Below (Don’t be surprised if everything disappears. front view.) 11. Zoom. 12. x 0. 14. Mesh. > OK The 1000 lbf load corresponds to a uniform pressure of about 14. Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines Copyrighted Material Copyrighted Material . Rotate > Front (If necessary to see the front side of mesh. Just Plot > Elements to see the mesh again. Utility Menu >PlotCtrls > Pan.) Copyrighted Material Figure 2-29. > OK 13.000 psi along the ¾ inch vertical inside edge of the latch retention slot.
The element solution stress contours are reasonably smooth. Solve the equations. Main Menu > Solution > Solve > Current LS > OK POSTPROCESSING Copyrighted Material Copyrighted Material Comparing the von Mises stress with the material yield stress is an accepted way of evaluating yielding for ductile metals in a combined stress state. The small fillet radius of this geometry illustrates the challenges that can arise in creating accurate solutions. so we enter the postprocessor and plot the element solution of von Mises stress.Plane Stress / Plane Strain Select the inside line and set pressure = 14000 > OK 2-21 Copyrighted Material Figure 2-30 Applied displacement and pressure conditions.000 psi. 16. SEQV. Copyrighted Material Figure 2-31 Von Mises stresses. Further mesh refinement gives a stress value of approximately 140. Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Stress > (scroll down) von Mises > OK Zoom in on the small fillet where the maximum stresses occur. however you can easily come within a few percent of the most likely true result using the methods discussed thus far. and the maximum von Mises stress is around 118. SOLUTION 15. .000 psi.
the stress will increase but not reach infinity. Continue with the evaluation and check the strains and deflections for this model as well. The maximum deflection in the X-direction is about 0.00145 inches and occurs as expected at the center of the right-hand edge of the latch retention slot.004 in/in. your finite-size elements will show a very high stress but not infinite stress. etc. you should look at fracture mechanics approaches to the problem. then use the actual part notch radius however small (1/32 for this tutorial). so don’t ‘chase a singularity’. 18. This can often get overlooked in the rush to get answers.) The engineer’s responsibility is not only to build useful models. but also to interpret the results of such models in intelligent and meaningful ways.) do not worry about this location but examine the stress in other regions. (See ANSYS help topics on fracture mechanics. If you refine the mesh. ductile material. If you really are concerned about the maximum stress here (fatigue loads or brittle material). Main Menu > General Postproc > Plot Results > Contour Plot > Element Solu > Strain-total > 1st prin > OK The maximum principal normal strain value is found to be approximately 0. Also examine the stress gradient in the vicinity of the notch to make sure the mesh is sufficiently refined near the notch. 17. Main Menu > General Postproc > Plot Results > Contour Plot > Nodal Solu > DOF Solution > X-Component of displacement > OK Copyrighted Material Copyrighted Material Copyrighted Material Figure 2-32 UX displacements. The finite element technique necessarily describes finite quantities and cannot directly treat an infinite stress at a singular point. Copyrighted Material . and you notice that the maximum stress increases as the radius of the stress raiser decreases. If your model has a zero radius notch. If you do not care what happens at the notch (static load.2-22 Plane Stress / Plane Strain Redesign to reduce the maximum stress requires an increase in the fillet radius. If a crack tip is the object of the analysis. Look at charts of stress concentration factors. do not use a zero radius. approaching infinite values at zero radii.
Use PlotCtrls to turn Keypoint Numbering On. To illustrate this. > Apply > Repeat for the quadrilateral areas. Successively pick pairs of keypoints until the four interior lines shown below are created. > Apply > OK Copyrighted Material Figure 2-34 Quadrilateral/Triangular regions. from the text file above so that the area is not created (just the lines) and read it into ANSYS. Main Menu > Preprocessor > Modeling > Create > Lines > Lines > Straight Line. 3. 2. Then use 1. Copyrighted Material . Copyrighted Material Copyrighted Material Figure 2-33 Lines added to geometry. delete the last line. Main Menu > Preprocessor > Modeling > Create > Areas > Arbitrary > By Lines Pick the three lines defining the lower left triangular area.all. Main Menu > Preprocessor > Modeling > Operate > Booleans > Glue > Areas > Pick All The glue operation preserves the boundaries between areas that we will need for mapped meshing.Plane Stress / Plane Strain 2-9 MAPPED MESHING 2-23 Quadrilateral meshes can also be created by mapping a square with a regular array of cells onto a general quadrilateral or triangular region. AL.
Main Menu > Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines Enter 4 for NDIV.2-24 Plane Stress / Plane Strain 4. element divisions > OK All lines will be divided into four segments for mesh creation. Applying boundary and load conditions and solving gives the von Mises stress distribution shown. 5. We need more elements and they need to be better shaped with smaller aspect ratios to obtain satisfactory results. The stress contours are discontinuous because of the poor mesh quality. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add > Solid > Quad 8node 183 > OK (Use the 8-node quadrilateral element for the mesh. Copyrighted Material . Copyrighted Material Copyrighted Material Copyrighted Material Figure 2-35 Element size on picked lines. Notice the long and narrow quads near the point of maximum stress.) 6. Main Menu > Preprocessor > Meshing > Mesh > Areas > Mapped > 3 or 4 sided > Pick All The mesh below is created. No.
and Plane Stress with Thickness. One can tailor the mapped mesh by specifying how many elements are to be placed along which lines. etc. the computed displacements are smaller in theory than the true displacements because the assumed displacement functions place an artificial constraint on the deformations that can occur. Axisymmetric. Not all elements are developed using the ideas discussed above. and an example of using this approach is described in Lesson 4.) In any case you should be alert to computed displacement and stress variations as you perform mesh refinement during the solution of a problem.Plane Stress / Plane Strain 2-25 Copyrighted Material Figure 2-36 Mapped mesh and von Mises results. The two examples thus far in this lesson were of the last type. Strains are the x and/or y derivatives of the displacements and thus depend on the distribution of the displacements for any given mesh. just as a convergent series arrives at a definite value once enough terms are summed. 2-11 TWO-DIMENSIONAL ELEMENT OPTIONS Copyrighted Material Copyrighted Material The analysis options for two-dimensional elements are: Plane Stress. 2-10 CONVERGENCE The goal of finite element analysis as discussed in this lesson is to arrive at computed estimates of deflection. Plane Strain. first smaller than the final computed values. This allows much better control over the quality of the mesh. strain and stress that converge to definite values as the number of elements in the mesh increases. Thus your computed displacements usually converge smoothly from below to fixed values. Copyrighted Material . For elements based on assumed displacement functions that produce continuum models. namely problems of plane stress in which we provided the thickness of the part. These constraints are relaxed as the element polynomial is increased or as more elements are used. then larger. and some will give displacements that converge from above. The strains and stresses may change in an erratic way as the mesh is refined. (See Lesson 6.
Similar methods are used for solving problems involving plane strain. and deflection distributions found for a unit thickness. Free triangular and quadrilateral element meshes were developed and analyzed. you may wish to use this option and then select the thickness based upon the stress. Triangles may produce more regular shaped element meshes with free meshing. Copyrighted Material Copyrighted Material Copyrighted Material . Compare the two results by determining the percent difference in the two answers. Convert the 12 kN concentrated force into an equivalent pressure applied to the edge. The approach is also applicable to axisymmetric geometries as discussed in the next lesson. 2-12 SUMMARY Copyrighted Material Problems of stress concentration in plates subject to in-plane loadings were used to illustrate ANSYS analysis of plane stress problems. use triangular and/or quadrilateral elements as desired. Mapped meshing with quads was also presented. Axisymmetric analysis is covered in detail in Lesson 3. there is no axial strain. Because there is no axial motion. 2-13 PROBLEMS In the problems below. is the ANSYS default and provides an analysis for a part with unit thickness. 2-1 Find the maximum stress in the aluminum plate shown below. Another plane strain example is that of a long retaining wall. strain. Each slice through the cylinder behaves like every other and the problem can be conveniently analyzed with a planar model. Plane Stress. The six-node triangles and eight-node quads can approximate curved surface geometries and. one only has to choose the appropriate option during element selection. If you are working on a design problem in which the thickness is not yet known. Use tabulated stress concentration factors to independently calculate the maximum stress. Plane Strain occurs in a problem such as a cylindrical roller bearing caged against axial motion and uniformly loaded in a direction normal to the cylindrical surface. restrained at each end and loaded uniformly by soil pressure on one or both faces.2-26 Plane Stress / Plane Strain The first analysis option. when stress gradients are present. The second option. give much better results than the four-node quad elements.
You will now need to model half of the plate instead of just one quarter and properly restrain vertical rigid body motion. One way to do this is to fix one keypoint along the centerline from UY displacement.Plane Stress / Plane Strain 2-27 Copyrighted Material Copyrighted Material Figure P2-1 2-2 Find the maximum stress for the plate from 2-1 if the hole is located halfway between the centerline and top edge as shown. Copyrighted Material Copyrighted Material Figure P2-2 .
Determine the magnitude and location of the maximum principal stress. 2-5 See if you can reduce the maximum stress for the plate of problem 2-1 by adding holes as shown below. Create your geometry accordingly. materials. and loads. The published results are for plates that are relatively long so that there is a uniform state of axial stress at either end relatively far from notch or hole. Plane Stress / Plane Strain Copyrighted Material Figure P2-3 2-4 Repeat 2-3 for a steel plate one inch thick in a state of plane stress.) Select your own dimensions. Select a hole size and location that you think will smooth out the ‘stress flow’ caused by the load transmission through the plate. and the maximum von Mises stress. Copyrighted Material . Use published stress concentration factor data to compare to your results. (See the next figure. Copyrighted Material Copyrighted Material Figure P2-5 2-6 Repeat 2-1 but the object is now a plate with notches or with a step in the geometry. The object is in a state of plane strain with an internal pressure of 1500 psi.2-28 2-3 An aluminum square 10 inches on a side has a 5-inch diameter hole at the center. Note that no thickness need be supplied for plane strain analysis. the maximum principal strain.
) Select your own dimensions. but restrain UY at only one keypoint along this line. Do all the necessary modeling of geometry (use a CAD system if you wish). materials. 2-8 Determine the stresses and deflections in an object ‘at hand’ (such as a seatbelt tongue or retaining wall) whose geometry and loading make it suitable for plane stress or plane strain analysis. Turn on Smart Sizing using size controls to examine the effect on the solution. and the root stresses are different from elementary beam theory because of the singularity created. Model the beam as a problem in plane stress. The effect of shear loading becomes more important in the deflection analysis as the slenderness decreases. 2-9 A cantilever beam with a unit width rectangular cross section is loaded with a uniform pressure along its upper surface.Plane Stress / Plane Strain 2-29 2-7 Solve the seatbelt component problem of Tutorial 2B again using six node triangular elements instead of the quadrilaterals. Copyrighted Material Figure P2-6 Copyrighted Material Figure P2-8 Restrain UX along the cantilever support line. materials and loadings. Copyrighted Material Copyrighted Material . Compute the end deflection and the maximum stress at the cantilever support. the strain in the Y direction due to the Poisson effect is prevented here. Experiment with mesh refinement. See if you can compute a maximum von Mises stress of around 140 kpsi. Try a beam that’s long and slender and one that’s short and thick. Otherwise. (Try fixing all node points in UX and UY and see what happens. Compare your results to those you would find using elementary beam theory. and pressure.
2-30 NOTES: Plane Stress / Plane Strain Copyrighted Material Copyrighted Material Copyrighted Material Copyrighted Material .
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https://www.analog.com/en/technical-articles/how-to-calculate-the-wiper-voltage-of-a-digital-potentiometer.html
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math
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The MAX5481/MAX5483 data sheet provides a complicated formula for calculating wiper voltage in an effort to be very precise. This application note explains the issues involved in this calculation and breaks the process into smaller steps. It also discusses the proper method for determining the least-significant bit (LSB).
The devices' data sheet (pages 12 and 13) presents the following formulas for calculating the wiper voltage (VW):
Is it any wonder people are turned off? We just want to know the wiper voltage.
What's This FSE and ZSE Stuff? And Why Do We Care?
The formulas are much less daunting if we break them down into smaller steps.
We'll start with FSE and ZSE first. The "Electrical Characteristics" table of the data sheet (page 2) indicates that FSE and ZSE are "Full-Scale Error" and "Zero-Scale Error," respectively. Essentially, these parameters describe the residual resistance that may occur at the top and bottom of the potentiometer. This also happens in mechanical potentiometers.
For now, as we design the circuit, forget about FSE and ZSE—they are small and we cannot change them anyway.
We can, thus, simplify Equation 1, which becomes:
Where D is one step as wiper voltage. Therefore, one step is the voltage at the top of the potentiometer minus the bottom voltage divided by 1023. This value is also 1 LSB (least-significant bit).
Why 1023 Instead of 1024?
Figure 1 shows the operative concept behind how we end up with 1023 instead of 1024. Note that if there are 8 (0 to 7) steps (switches), there is one less voltage between the steps (i.e., only 7 resistors or LSBs). Zero is the reference that we get for free.
For the sake of illustration, let's say that the bottom of the potentiometer is at 0.2V and the top of the potentiometer is at 2.2V with a 5V supply (Figure 2).
We know that the MAX5482 is 50kΩ end to end. If there is 2V across the potentiometer, there needs to be one-tenth that voltage across R2. R2 is thus 5kΩ. Because we know the voltage and resistance, we can calculate current.
R1 will have 5V minus 2.2V, giving us 2.8V across it. Instead of calculating current, we can look at the ratio (because we can do that in our head). If 2V is equal to 50kΩ, then 2.8V is equal to 70kΩ (1.4 times 50kΩ).
The potentiometer has 2V across it. Dividing by 1023 means that each LSB is 0.001955V.
Now the Wiper Voltage
If the wiper voltage (VW) is at D step 500, then 500 times 1 LSB is 0.9775V plus the voltage across R2 (0.2V) for a total of 1.1775V.
Now back to Equation 2.
Equation 2 simply says that VFSE and VZSE are measured in the voltage of 1 LSB (FSE and ZSE are measured in LSBs). That is, the difference between VH and VL divided by 1023—yes, the data sheet is wrong.
Looking at the data sheet's "Electrical Characteristics" table, the MAX5482's FSE is -0.75 LSB. Thus, -0.75 times 0.001955V (the LSB value above) gives us -0.001466V. VFSE, therefore, is 0.001466V below the nominal voltage of the H terminal's 2V—in other words, 1.9985V VFSE.
And, ZSE is +1.45 LSB (+1.45 times 0.001955V), or 0.002835V above the L terminal's 0.2V. This gives us a total of 0.202835V VZSE.
A mechanical potentiometer data sheet has a typical specification for how close the wiper can get to the ends of the rotation both electrically and in rotational degrees. These specifications are the equivalent of FSE and ZSE in a digital potentiometer.
This application note has explained the relevant calculations required for determining the wiper voltage of a digital potentiometer. By breaking down the process into smaller steps, it has established a much simpler method for these calculations: since the end-point errors (FSE and ZSE) are only 0.28%, Equation 3 is adequate for calculating wiper voltage in most applications.
Yet, we have ignored an error that can be a hundred times greater in this circuit: the ±20% to ±30% end-to-end tolerance of the potentiometer. To learn how to control this error, see application note 4290, "Ratiometric Design Overcomes the 25% Tolerance of a Digital Potentiometer."
|Part||Description||Control Interface||Temperature Coefficient (typ, ppm/°C)|
|MAX5482||1024-tap, 50kΩ nonvolatile linear-taper digital potentiometer (voltage divider)||3-wire serial SPI™||35|
|MAX5481||1024-tap, 10kΩ nonvolatile linear-taper digital potentiometer (voltage divider)||3-wire serial SPI||35|
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http://ciks.cbt.nist.gov/garbocz/paper28/node10.html
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math
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In this appendix we show why the algorithm of counting the "air" pixels in a square which is centered on a point of a "solid" surface gives a measure of the curvature at that point. For purposes of discussion, the pixels on and within the surface are called "solid pixels" and those outside, "air pixels," but it is not necessary for either type of pixel to be solid or vapor phase. The algorithm simply counts the pixels of the opposite phase of that of which the surface is composed. The linear relationship that we present below holds for the limiting case that the pixel is small compared to the counting box (many pixels per box) and, in turn, the counting box is small compared to the local radius of curvature. These smallness conditions will not always be satisfied in numerical simulations and in those cases the counting will still increase with curvature, but not necessarily linearly. The relationship between curvature and counting can always be resolved numerically as in Section 2 of this paper. However, it is edifying to show analytically why the curvature-counting relationship works, in the continuum version of the digital algorithm.
A b x b counting box is centered on the surface of a circle of radius R at an angle , as in Fig. 14. It is clear from the inset of Fig. 14 that the area outside the circle, but inside the tangent to the circle (light gray in Fig. 14) increases with the curvature of the circle. This is the heuristic basis for the algorithm. The area outside the tangent, which is b2/2, is counted as well, but this is a constant which we neglect since we are only interested in curvature differences.
Figure 14: Showing a b x b square box centered at a surface point (R, ) of a circle of radius R. The inset shows a blow-up of the actual region whose area is being calculated.
The results can be calculated in the sector 0 < < /4, since the square has four-fold rotation plus mirror symmetry; all other sectors can be calculated by quadrature. One method is to write the equation of the circle in Cartesian coordinates with the origin placed at the bottom right of the box; integration takes place with the dependent coordinate running up the right-hand side of the box. After normalizing the integral by R and integrating the constant term:
The last term in this equation is the area inside the tangent but outside the circle, which is proportional to the curvature.
The last term in the above equation is also proportional to cos-3(), which is the angular dependence of the anisotropy in the square box counting scheme. With the smallness conditions discussed above, the equilibrium shape for this counting scheme is any surface that satisfies R cos-3() = constant. This is the so-called Wullf shape . For the cases illustrated in this paper, the effect of finite b/R and digitally rough surfaces seem to make the Wullf shape more isotropic. For example, the equilibrium shape for the sintered square in Fig. 5c was nearly a digitized circle.
If the counting is averaged over the entire circle, we get:
which demonstrates the b3 scaling of the slopes of the fitted straight lines plotted in Fig. 2. A similar calculation can be done for a counting cube centered at a surface point of a sphere, with results as in 2D, but with b4 appearing in the 1/R term instead of b3.
Figure 15 shows the cube root of the slopes of the fitted lines in Fig. 2 and the fourth root of the slopes of the fitted lines in Fig. 3, plotted against the box size b. The solid lines in Fig. 15 are fitted to the renormalized simulation slopes, clearly demonstrating the b3 dependence in 2D and the b4 dependence in 3D of the curvature slopes arising from the box counting algorithm. Uisng a circle counting method in 2D and a sphere counting method in 3D would give the same b dependence, where b would be the diameter of the counting circle or sphere .
Figure 15: Showing the cube root of the 2D curvature slopes from Fig. 2 and the 4th root of the 3D curvature slopes from Fig. 3, plotted against b. The solid lines are fit to the data points.
Consideration of the construction in Fig. 14 reveals that if a counting circle were employed instead of a counting box, then an isotropic count would be obtained. This method will be employed in future simulations . A similar method was implied in an earlier paper , although no derivation explicitly relating area counting to curvature was given.
Using a counting circle also results in a method to compute the surface normal. If A is the region inside the counting circle, but outside the surface of interest, then the unit normal is given by:
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http://creartiweb.com/how-to/how-to-calculate-average-random-error.php
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math
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If A is perturbed by then Z will be perturbed by where (the partial derivative) [[partialdiff]]F/[[partialdiff]]A is the derivative of F with respect to A with B held constant. Example: We can now apply the multiplication and division rule to the first step of our two-step molarity calculation: This can be rearranged and the calculated number of moles substituted to Many types of measurements, whether statistical or systematic in nature, are not distributed according to a Gaussian. We become more certain that , is an accurate representation of the true value of the quantity x the more we repeat the measurement. More about the author
Taylor, An Introduction to Error Analysis, Oxford UP, 1982. Relation between Z Relation between errors and(A,B) and (, ) ---------------------------------------------------------------- 1 Z = A + B 2 Z = A - B 3 Z = AB 4 Z = A/B For example, (10 +/- 1)2 = 100 +/- 20 and not 100 +/- 14. The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. his comment is here
The values in parentheses indicate the confidence interval and the number of measurements. Random error is also called as statistical error because it can be gotten rid of in a measurement by statistical means because it is random in nature.Unlike in the case of There is a mathematical procedure to do this, called "linear regression" or "least-squares fit". Assume you made the following five measurements of a length: Length (mm) Deviation from the mean 22.8 0.0 23.1 0.3 22.7 0.1
This is given by (5) Notice that the more measurements that are averaged, the smaller the standard error will be. This way to determine the error always works and you could use it also for simple additive or multiplicative formulae as discussed earlier. Limitations imposed by the precision of your measuring apparatus, and the uncertainty in interpolating between the smallest divisions. Percent Error Significant Figures The above method of determining s is a rule of thumb if you make of order ten individual measurements (i.e.
What is the resulting error in the final result of such an experiment? A blunder does not fall in the systematic or random error categories. The standard deviation of a population is symbolized as s and is calculated using n. http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html Certainly saying that a person's height is 5'8.250"+/-0.002" is ridiculous (a single jump will compress your spine more than this) but saying that a person's height is 5' 8"+/- 6" implies
In this example that would be written 0.118 ± 0.002 (95%, N = 4). How To Calculate Systematic Error In Physics For this reason it is important to keep the trailing zeros to indicate the actual number of significant figures. So if the average or mean value of our measurements were calculated, , (2) some of the random variations could be expected to cancel out with others in the sum. The results of the three methods of estimating uncertainty are summarized below: Significant Figures: 0.119 M (±0.001 implied by 3 significant figures) True value lies between 0.118 and 0.120M Error Propagation:
Similarly the perturbation in Z due to a perturbation in B is, . https://explorable.com/random-error In fact, since the estimation depends on personal factors ("calibrated eyeballs"), the precision of a buret reading by the average student is probably on the order of ± 0.02 mL. How To Calculate Systematic Error Solid is then added until the total mass is in the desired range, 0.2 ± 0.02 g or 0.18 to 0.22 g. How To Calculate Random Error In Excel The most important thing to remember is that all data and results have uncertainty and should be reported with either an explicit ?
For example, the number of centimeters per inch (2.54) has an infinite number of significant digits, as does the speed of light (299792458 m/s). There are also specific rules for my review here However, random errors set a limit upon accuracy no matter how many replicates are made.PrecisionThe term precision is used in describing the agreement of a set of results among themselves. Random errors are errors which fluctuate from one measurement to the next. But in the end, the answer must be expressed with only the proper number of significant figures. How To Calculate Random Error In Chemistry
In a titration, two volume readings are subtracted to calculate the volume added. The essential idea is this: Is the measurement good to about 10% or to about 5% or 1%, or even 0.1%? If the errors were random then the errors in these results would differ in sign and magnitude. click site Thus you might suspect that readings from a buret will be precise to ± 0.05 mL.
If you want to judge how careful you have been, it would be useful to ask your lab partner to make the same measurements, using the same meter stick, and then Fractional Error Definition You can read off whether the length of the object lines up with a tickmark or falls in between two tickmarks, but you could not determine the value to a precision Related articles Related pages: Experimental Errors Type-I Error and Type-II Error .
Independent errors cancel each other with some probability (say you have measured x somewhat too big and y somewhat too small; the error in R might be small in this case). A final type of experimental error is called erratic error or a blunder. Defined numbers are also like this. Fractional Error Physics StandardsUSP Compliance StandardsWavelength CalibrationTuning SolutionsIsotopic StandardsCyanide StandardsSpeciation StandardsHigh Purity Ionization BuffersEPA StandardsILMO3.0ILMO4.0ILMO5.2 & ILMO5.3Method 200.7Method 200.8Method 6020Custom ICP & ICP-MS StandardsIC StandardsAnion StandardsCation StandardsMulti-Ion StandardsEluent ConcentratesEPA StandardsMethods 300.0 & 300.1Method 314.0Custom
They may occur due to lack of sensitivity. Additive Formulae When a result R is calculated from two measurements x and y, with uncertainties Dx and Dy, and two constants a and b with the additive formula: R = Estimating random errors There are several ways to make a reasonable estimate of the random error in a particular measurement. navigate to this website Please try the request again.
more than 4 and less than 20). Systematic errors are errors which tend to shift all measurements in a systematic way so their mean value is displaced. You can only upload a photo (png, jpg, jpeg) or a video (3gp, 3gpp, mp4, mov, avi, mpg, mpeg, rm). Answer Questions I need help?
The goal of a good experiment is to reduce the systematic errors to a value smaller than the random errors. Advanced: R. The following example will clarify these ideas. After multiplication or division, the number of significant figures in the result is determined by the original number with the smallest number of significant figures.
Together they mean that any mass within 10% or ±0.02 g of 0.2 g will probably do, as long as it is known accurately. We will let R represent a calculated result, and a and b will represent measured quantities used to calculate R. Zeros to the left of the first non zero digit are not significant. The range is always calculated by including the outlier, which is automatically the largest or smallest value in the data set.
If y has an error as well, do the same as you just did for x, i.e. Some sources of systematic error are: Errors in the calibration of the measuring instruments. These examples illustrate three different methods of finding the uncertainty due to random errors in the molarity of an NaOH solution. The best estimate of the true standard deviation is, . (7) The reason why we divide by N to get the best estimate of the mean and only by N-1 for
Note: a and b can be positive or negative, i.e. The reason for this, in this particular example, is that the relative uncertainty in the volume, 0.03/8.98 = 0.003, or three parts per thousand, is closer to that predicted by a Note that burets read 0.00 mL when "full" and 10.00 mL when "empty", to indicate the volume of solution delivered. The 95% confidence interval is calculated with Equation 6: The final molarity would be reported as the 95% confidence interval.
This pattern can be analyzed systematically.
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https://beavercountybookfest.com/useful/readers-ask-what-does-pi-equal.html
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math
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What is pi exactly equal to?
Succinctly, pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle’s size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.
What is the whole equation of pi?
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 PI/4 = 1/1 – 1/3 + 1/5 – 1/7 +
What is the first 1 million digits of pi?
The first 1000000 decimal places contain: 99959 0s, 99758 1s, 100026 2s, 100229 3s, 100230 4s, 100359 5s, 99548 6s, 99800 7s, 99985 8s and 100106 9s.
What are the first 100 digits of pi?
First 500 Digits of Pi
- 1415926535 8979323846 2643383279 5028841971.
- 6939937510 5820974944 5923078164 0628620899.
- 8628034825 3421170679 8214808651 3282306647.
- 0938446095 5058223172 5359408128 4811174502.
- 8410270193 8521105559 6446229489 5493038196.
- 4428810975 6659334461 2847564823 3786783165.
- 2712019091 4564856692 3460348610 4543266482.
Who is the father of pi?
It is widely believed that the great Swiss-born mathematician Leonhard Euler (1707-83) introduced the symbol π into common use.
Does the number pi end?
Pi is an irrational number. As such, it has no final digit. Furthermore, there is no pattern to its digits.
Is every number in pi?
“Pi is an infinite, nonrepeating decimal – meaning that every possible number combination exists somewhere in pi.
How many digits of pi do we know 2020?
All records are made to be broken, and Emma Haruka Iwao’s 2019 record of 31.4 trillion digits was broken with 50 trillion digits calculated by Timothy Mullican in January 2020.
How do you memorize pi?
One way to remember the first few digits of pi is to count the letters in the words of this phrase: “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”
Is there a 666 in pi?
The number 666 is a simple sum and difference of the first three 6th powers: 666 = 16 – 26 + 36. It is also equal to the sum of its digits plus the cubes of its digits: The sum of the first 144 (= (6+6)·(6+6)) digits of pi is 666.
Can you find your birthday in Pi?
Chances of Finding Your Number in Pi
Happily, if you include the zeros, birthdays are 8 digits long — so you have a 63% chance of finding your birthday in the first 100 million digits of pi. Now that we‘re to 200 million, the odds are up to 86%, so it’ll be a while before everyone can find their birthday in Pi.
What digit appears most in pi?
Frequency of Each Digit of Pi
Is Pi actually infinite?
Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That’s because pi is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever.
How many digits of pi does the average person know?
When it comes to how many digits of pi people know by heart, the majority only know 3.14. Which is fine!
What is the 100th decimal place?
When we write numbers with hundredths using decimals we use a decimal point and places to the right of this decimal point. The hundredth place is two places to the right of the decimal point.
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https://www.ias.ac.in/listing/bibliography/pmsc/CHANDAN_KUMAR_MONDAL
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math
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CHANDAN KUMAR MONDAL
Articles written in Proceedings – Mathematical Sciences
Volume 130 All articles Published: 16 September 2020 Article ID 0055 Article
In this paper, we consider theRicci curvature of a Ricci soliton. In particular,we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also it isometrically splits a line. We have also proved that a gradient Ricci soliton with non-constant concave potential function and bounded Ricci curvature is non-shrinking and hence the scalar curvaturehas at most one critical point.
Volume 133 All articles Published: 29 March 2023 Article ID 0006 Article
In this article, we have studied the behavior of the potential function along some geodesic in a Ricci soliton under some curvature restriction. In particular, we haveshowed that under some curvature restriction, the potential function is reduced to a parabola along some geodesic. Furthermore, we have investigated the change of intersecting angles between the potential vector field and a geodesic in a Ricci soliton. Further, we have deduced the condition when the potential function becomes convex in a shrinking Ricci soliton. Finally, we have concluded the paper by showing the non-existence of convex potential in an expanding Ricci soliton having non-negative Ricci curvature.
Volume 133, 2023
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
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| 1,559 | 9 |
http://www.chegg.com/homework-help/principles-of-macroeconomics-6th-edition-chapter-14-solutions-9780538453066
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math
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Solutions for Chapter 14
The process of finding the present value of future sum of money at current rate of interest is called discounting. It can be calculated using the following formula:
PV = present value
FV = future value
r = rate of interest
N = number of years
If r = 7%, PV = $24 and N = 400 years, then the FV can be calculated as follows:
Therefore, the estimated value is $13.6 trillion (approx.).
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CC-MAIN-2016-40
| 408 | 8 |
http://www.chegg.com/homework-help/questions-and-answers/driving-head-concrete-wall-hard-car-height-would-drop-car-impact-equivalent-hitting-wall-3-q1368277
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math
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please ANSWER both 8 and 9Show transcribed image text
please ANSWER both 8 and 9Show transcribed image text Driving head-on into a concrete wall is hard on a car. From what height would you have to drop a car for its impact to be equivalent to hitting the wall at 30 mi/h?(Hint: energy) Two train collide on level ground. Car A has a mass of 20 Mg and is moving to the right at 3.0 m/s initially. Car B has a mass of 15 Mg and is initially moving to the left at 1.5 m/s. Knowing that they rebound after collision with car B moving to the right at 2m/s, determine the velocity of car A after impact.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398446230.43/warc/CC-MAIN-20151124205406-00139-ip-10-71-132-137.ec2.internal.warc.gz
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CC-MAIN-2015-48
| 598 | 2 |
https://scholarship.rice.edu/handle/1911/101567
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math
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A Finite Element Material Balance for Two Dimensional Convection-Diffusion Equations
A consistent finite element material balance is developed for the two dimensional convection-diffusion equation. The resulting numerical scheme is an average of the conventional Galerkin procedure for both the divergence and nondivergence form of the continuity equations. This derivation is valid for finite dimensional approximating spaces having the property that the basis functions sum to unity. Computational molecules are associated with each basis function of the finite dimensional approximating space. The physical significance of coefficients appearing in the resulting material balance governing every computational molecule is discussed. The scheme is compared with standard finite difference procedures. Regularization of the resulting numerical scheme is accomplished by lumping and upstream weighting.
Citable link to this pagehttps://hdl.handle.net/1911/101567
MetadataShow full item record
- CAAM Technical Reports
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CC-MAIN-2019-35
| 1,017 | 5 |
http://www.biomedcentral.com/1471-2148/9/70/figure/F5
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math
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Approximate Bayesian posterior probability distributions for demographic parameters. A. Estimate of time since divergence (t) in years. B. The number of effective migrants per generation from F. vesiculosus to F. radicans and vice versa. C. Estimate of effective population sizes for both species.
Pereyra et al. BMC Evolutionary Biology 2009 9:70 doi:10.1186/1471-2148-9-70
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s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398464386.98/warc/CC-MAIN-20151124205424-00052-ip-10-71-132-137.ec2.internal.warc.gz
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CC-MAIN-2015-48
| 374 | 2 |
http://lua-users.org/lists/lua-l/2005-12/msg00347.html
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math
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[Date Prev][Date Next][Thread Prev][Thread Next]
- Subject: Re: Will Lua kernel use Unicode in the future?
- From: Chris Marrin <chris@...>
- Date: Thu, 29 Dec 2005 17:56:29 -0800
Klaus Ripke wrote:
On Thu, Dec 29, 2005 at 04:10:26PM -0800, Chris Marrin wrote:
"This is a summation character: \226\136\145"
and a console that understood UTF8 would show a summation characer. But
to do this I had to:
- Use to the Character Map utility to find the character
- Copy that character into OpenOffice, which understands Unicode
- Save the file as UTF8
- Open the file as binary in MsDev
- Hand convert the character sequence to UTF8
- Use Calculator to convert the result into decimal
It would be nice if Lua could do this for me :-)
what should Lua do for you?
Use to the Character Map utility?
Copy that character into OpenOffice?
Or write the one line Lua script to print the decimal
numbers corresponding to the UTF-8 representation
of a given Unicode point?
No problem, Lua does it for you.
The attached utftab prints 64 chars a line with their
base Lua string encoding; just add 0-63 to the last \128.
Run it in a UTF-8 xterm.
Use ncurses (or some extremely antisocial hacks from slnspider)
to add mouse support to print the code for any character.
However, your list pretty much makes the point that the problem
is not whether to write some u+xxx or two or three decimal codes.
You want to use either an Unicode capable editor
or some utility to look up codes
-- as long as everybody agrees to use UTF-8 anyway, that is.
It does make a big difference though where friends of the wide char
want their wchar_t based version of Lua. Anybody?
I think UTF8 is a good representation (I used to be in the wchar_t
camp). The utility of \U is simply convenience, doing the work of
converting a hex unicode value into UTF8. There are other ways to do it,
including some Lua code to do the translation.
I think the more important addition would be an easy Lua way to set the
locale to use the UTF8 encoding.
chris marrin ,""$,
[email protected] b` $ ,,.
mP b' , 1$'
,.` ,b` ,` :$$'
,|` mP ,` ,mm
,b" b" ,` ,mm m$$ ,m ,`P$$
m$` ,b` .` ,mm ,'|$P ,|"1$` ,b$P ,` :$1
b$` ,$: :,`` |$$ ,` $$` ,|` ,$$,,`"$$ .` :$|
b$| _m$`,:` :$1 ,` ,$Pm|` ` :$$,..;"' |$:
P$b, _;b$$b$1" |$$ ,` ,$$" ``' $$
```"```'" `"` `""` ""` ,P`
"As a general rule,don't solve puzzles that open portals to Hell"'
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000164.31/warc/CC-MAIN-20190626033520-20190626055520-00167.warc.gz
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CC-MAIN-2019-26
| 2,380 | 53 |
https://www.coursehero.com/tutors-problems/Finance/8439766-2-Kim-is-evaluating-her-retirement-plan-Suppose-she-has-500000-wh/
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math
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2. Kim is evaluating her retirement plan. Suppose she has $500,000 when she retires in an account that earns at an effective annual rate of 9%.
a If Kim withdraws $75,000 annually, how long will her funds last?
b To make the funds last 25 years, how much can Kim withdraw annually?
Kim is considering a two phase withdrawal where she withdraws $60,000 annually for 10 years, and then $35,000 thereafter (when social security starts). How long will her funds last assuming that the 9% rate of return (EAR) is accurate for both phases of the retirement plan.
Dear Student, find the... View the full answer
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583661083.46/warc/CC-MAIN-20190119014031-20190119040031-00439.warc.gz
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CC-MAIN-2019-04
| 603 | 5 |
http://old.seattletimes.com/html/businesstechnology/2013243127_gatesbirthday25.html
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math
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Abstract gift for Bill Gates
The Microsoft founder and philanthropist is turning 55 this week and since his age coincides with the rightmost two digits of his birth year, it's particularly special — mathematically, that is.
Special to The Seattle Times
Aziz S. Inan
Position: Professor of electrical engineering, University of Portland (Ore.)
Born: May 15, 1955 (or 5-15-55) in Istanbul
Education: B.S. in electrical engineering, San Jose State University; M.S. and Ph.D. in electrical engineering, Stanford University
Source: University of Portland website
Bill Gates was born in 1955 and, this week, on Oct. 28, the Microsoft chairman and philanthropist will turn 55, a distinct age because it coincides with the rightmost two digits of his birth year.
Because I also had my 55th birthday this year, I got so excited about this rare occurrence that I went ahead and explored this unique age further, especially in the context of Gates' upcoming birthday. My findings were so fascinating that I decided to report them here as a birthday gift for Bill in celebration of his 55th birthday.
First of all, the number 55 equals the sum of all integers from 1 to 10, and 10 equals the sum of the digits of 55.
Second, 55 equals the sum of the squares of all integers from 1 to 5, where 52 is the product of the digits of 55.
Third, 55 = 15 + 40, where 15 equals the sum of all powers of 2 from 0 to 3 (that is, 1 + 2 + 4 + 8 = 15) and 40 is the sum of the powers of 3 from 0 to 3 (expressed by 1 + 3 + 9 + 27 = 40).
Fourth, 55 is a Fibonacci number. Fibonacci numbers consist of a simple series of numbers first introduced in a book titled "Liber Abaci," published in 1202 by Italian mathematician Leonardo Fibonacci (1170-1250).
The series begins with 1 and 1. After that, each number is obtained by adding the previous two numbers of the series:
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
In other words, the Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.
There are only a handful number of double-digit Fibonacci birthdays in one's lifetime. Gates' last one was his 34th, which occurred 21 years ago. His upcoming 55th will be his next Fibonacci birthday and coincides with a Fibonacci (21st) century, an extremely rare occurrence. After this one, Bill will hopefully celebrate one more Fibonacci birthday in this Fibonacci century, in 2044, when he turns 89.
I also discovered that Bill's 89th birthday written in full date format as 10-28-2044 (or simply, 10282044) possesses other unique features.
First, split this date into two numbers 1028 and 2044. What you'll see is that 2044 can be derived from 1028 by doubling the first and third leftmost digits (1 and 2) and halving the second and the fourth (0 and 8).
Second, 1028 and 2044 each differ from perfect powers of number two by four (22) — that is, 1028 is 22 more than 210, whereas 2044 is 22 less than 211.
Next, 55 is also a Kaprekar number, named after Indian mathematician Dattatreya Ramachandra Kaprekar (1905-1986). A Kaprekar number is a positive integer whose square split in the middle adds up to the original number.
For example, 9 is a Kaprekar number since 92 = 81. Split 81 into 8 and 1 and one has 8 + 1 = 9. The number 45 is also a Kaprekar number since 452 = 2025 and 20 + 25 = 45.
The first few Kaprekar numbers are 1, 9, 45, 55, 99, 297, 703, etc. Note that 552 = 3025 and 30 + 25 yields 55.
Gates experienced his last Kaprekar birthday 10 years ago when he turned 45. This birthday was also unique in the following way: The number 45 equals the sum of 5, 17 and 23, which are the prime factors of his birth year, namely, 1955 = 5 x 17 x 23. After his 55th birthday, Gates could experience one more Kaprekar birthday in his lifetime, 44 years later, when he turns 99.
Interestingly enough, I discovered another connection between Bill's birth year, 1955, and his new age 55. If 1955 is split into 19 and 55, their product is 19 x 55 = 1045, and if 1045 is split as 10 and 45, 10 + 45 yields 55. The same is also true for the reverse of 1955; that is, split 5591 into 55 and 91, you'll find 55 x 91 = 5005 and — guess what? — 50 + 05 = 55!
Next, 55 is a palindrome number; it reads the same forward or backward. Gates' last palindrome birthday was 11 years ago, when he turned 44, and his next one will be his 66th. That Gates' palindrome 55th birthday occurs in 2010 is distinctive for two reasons.
First, the prime factors of 2010 (that is, 2010 = 2 x 3 x 5 x 67) add up to 77 and the prime factors of 102 (102 = 2 x 3 x 17) — the reverse of 2010 — add up to 22. The difference of these two palindrome numbers (77 — 22) is 55, the number of Gates' upcoming palindrome birthday!
Second, and more fascinating, the reverse of the Gates' palindrome 55th — 10-28-2010 or 10282010 — is 1028201, surprisingly another palindrome. (Instead of reversing this date, one could also insert an extra zero as a 9th digit on the left-hand-side of 10282010, yielding 010282010, a palindrome!) This is an extremely rare occurrence. (Note that the year Gates' birthday is to coincide with a full palindrome date is 6,191 years later, in 8201, on 10288201, Oct. 28, 8201.)
There are 10 dates this year that are like 10282010, from Oct. 20 to 29. I refer to them as "reverse palindrome dates" (that is a full non-palindrome date possessing a palindrome reverse) expressed as 102A2010, where digit A can take any value between 0 and 9. Last time such eight-digit reverse palindrome dates occurred was in 1900 (from Sept. 10 to 19) written as 091A1900.
After this month, the next time such reverse palindrome dates will occur is in 2100 (from Jan. 20 to 29) as 012A2100, followed by year 2110 (between Nov. 20 and 29) in the form 112A2110. So Gates' 55th is special since it coincides with a reverse palindrome date, 10282010!
As an aside, after his 55th, Bill Gates will have other special birthdays to come. For example, his 59th birthday on 10282014 is notable since 10 is half 20 and 28 is double 14. In 2016, Bill will turn 61 which is the reverse of the last two digits of 2016. Similarly, he will turn 72 in 2027, 83 in 2038, and 94 in 2049. Gates' 70th birthday will occur in perfect square year 2025 (2025 is 452) but will miss the fifth perfect square date in that year, Oct. 27, 2025 (since 10272025 = 32052), by only one (20) day.
Gates' 73rd birthday will be on 10282028. His 93rd, on 10282048, will miss the remarkably special date 10242048 (that is, 210 211) by four (22) days! His 97th birthday, in 2052 (10282052), is also interesting because 2052 equals three times the difference of the squares of numbers 10 and 28, together representing Oct. 28. Last, his 101st birthday, to occur on 10282056, will also be notable because 2056 is twice 1028!
My hope is that Gates lives long enough to experience all of these birthdays and more, and cherish all of them. Happy birthday, Bill, and welcome to the club of 55-year-olds!
This story was originally published Oct. 25, 2010, and corrected Nov. 2, 2010. The Fibonacci series of numbers starts with the number 1, not 0 as the original story incorrectly said.
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| 7,125 | 39 |
https://www.researcher-app.com/paper/1626234
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math
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Hidden-Strange $N\phi$ molecular state in a quasipotential Bethe-Salpeter equation approach.
In this work, we study the hidden-strange molecular states composed of a baryon and a vector meson in a coupled-channel $N\rho-N\omega-N\phi-\Lambda K^*-\Sigma K^*$ interaction. With the help of the effective Lagrangians which coupling constants are determined by the SU(3) symmetry, the interaction is constructed and inserted into the quasipotential Bethe-Salpeter equation to search for poles in the complex plane, which correspond to molecular states. Two poles are found with a spin parity $3/2^-$ near the $N\rho$ and the $\Sigma K^*$ thresholds, which can be related to the $N(1700)$ and the $N(2100)$, respectively. No pole near the $N\phi$ threshold can be found if direct interaction between a nucleon and $\phi$ meson is neglected according to the OZI rule. After introducing the QCD van der Waals force between a nucleon and $\phi$ meson, a narrow state can be produced near the $N\phi$ threshold. Inclusion of the QCD van der Waals force changes the line shape of the invariant mass spectrum in the $N\phi$ channel leading to a worse agreement with the present low-precision data. Future experiments at BelleII, JLab, and other facilities will be very helpful to clarify the existence of these possible hidden-strange molecular states.
Publisher URL: http://arxiv.org/abs/1804.09383
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CC-MAIN-2022-40
| 1,388 | 3 |
https://maregionsud.up2europe.eu/european/projects/randomness-and-pseudorandomness-in-discrete-mathematics_39379.html
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math
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Randomness and pseudorandomness in discrete mathem.. (RanDM)
Randomness and pseudorandomness in discrete mathematics
Date du début: 1 juil. 2016,
Date de fin: 30 juin 2021
Discrete mathematics has seen enormous advances in the last few years, with solutions being found to a number of famous and long-standing questions, such as the Erdos distinct distance problem and the existence conjecture for combinatorial designs. Much of this progress owes to an increased understanding of random and pseudorandom objects. An entire framework, known as the probabilistic method, has grown around the application of randomness to combinatorial problems, while pseudorandomness is playing an increasingly important role.In this proposal, we will consider a range of problems, some stemming from the direct study of random and pseudorandom objects and others arising in areas where randomness and pseudorandomness have proved to be of particular importance. We will be particularly concerned with extensions of the regularity method to sparse graphs and improving bounds for a number of classical problems in graph Ramsey theory. These problems are of a fundamental nature and any progress is likely to lead to new techniques with broader scope for application.
Bonjour, vous êtes sur la plateforme Région Sud Provence-Alpes-Côte d’Azur dédiée aux programmes thématiques et de coopération territoriale. Une équipe d’experts vous accompagne dans vos recherches de financements.
Contactez la Région Sud Provence-Alpes-Côte d'Azur
Vous pouvez nous écrire en Anglais, Français et Italien
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CC-MAIN-2020-34
| 1,588 | 8 |
http://brainmass.com/math/derivatives/149557
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math
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Derivatives and Extreme Values
1. Find the maximum and minimum values of defined on the interval .
2. Find the maximum and minimum values of defined on the interval .
3. Find the maximum and minimum values of on the interval . Then graph the function to check your answers.
Please see the attached file for the fully formatted problems.
This question has the following supporting file(s):
In this solution, derivatives and extrema are investigated in very detailed, step-wise response. The solution is well presented in an attached Word document.
This answer includes:
- Plain text
- Cited sources when necessary
- Attached file(s)
- Posting ID 149557 - Solution.doc
Active since 2003
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CC-MAIN-2013-48
| 684 | 13 |
http://mathhelpforum.com/calculus/190676-integration-analytic-function.html
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math
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I have an example I want to clearify,
Let C be a semicircle from 2 to -2 which passes through 2i and let T be a semicircle from 2 to -2 which passes through -2i.
If you take the integral of z^2 dz around both paths the is the same as the function is analytic so the integral is independant of the path,
However if you take the integral of the conjugate of z over these to paths you get
So they equal, but the f(z)=conjugate of z isnt an analytic function, is it just a coincidence?
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CC-MAIN-2017-17
| 481 | 5 |
https://www.ccmathactivities.com/3rd-grade-activity-277-fractions-as-numbers/
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math
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Meeting the Needs of ALL Students!
Explain equivalence of fractions with denominators 2, 3, 4, 6, and 8 in special cases, and compare fractions by reasoning about their size(Fractions as Numbers).
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Explain that sometimes it is necessary to compare two fractions to discover which is larger or smaller than the other. Models can be used to decide which fraction is larger or smaller.
Issue a Comparing Fractions sheet to each student. Explain that all model pairs have the same denominator, meaning that the model pairs are divided into the same number of equal parts. Point out that fractions with like denominators have the same number on the bottom number. Have students shade the other fraction model that will make a true sentence. Then direct them to write the fraction. After students complete the sheet, discuss the following questions and emphasize the given points:
To conclude, instruct pairs to work together and have each draw three equivalent rectangles and divide them into fourths. They should make sure their rectangles are the same size. Direct students to shade their models to represent a fraction greater than, less than or equal to another student’s fraction. Call on pairs to model their examples on the board.
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CC-MAIN-2023-23
| 1,559 | 6 |
https://mcl.as.uky.edu/math-movie-month-infinity-and-beyond-mathematics-modern-times-0
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math
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In this program, Professor Marcus du Sautoy addresses mathematical advances of 20th-century Europe and America. Topics include Georg Cantor's exploration of the concept of infinity; chaos theory, formulated by Henri Poincaré; Kurt Gödel's incompleteness theorems; the work of André Weil and his colleagues with algebraic geometry; and the influence of Alexander Grothendieck, whose ideas have influenced mathematical thinking about the hidden structures behind all mathematics. The program concludes by considering one of the great as-yet-unsolved problems of mathematics: the Riemann Hypothesis.
Speaker(s) / Presenter(s):
Professors Readdy and Ehrenborg
Type of Event (for grouping events):
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CC-MAIN-2023-40
| 695 | 4 |
https://www.wmbriggs.com/post/4033/
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math
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Be sure to first read Statistical Significance Does Not Mean What You Think. Climate Temperature Trends then Regression Is Not What You Think. Climate And Other Examples, as this post is an extension of them.
This post will only be a sketch, and a rough one, of how to pick explanatory variables in regression. The tools used work for any kind of statistical model, however, and not just regression.
First remember that a regression is not a function of observables, like y, but of the central parameter of the normal distribution which represents our uncertainty in y. This language is tangled, but it is also faithful. Regression is not “empirical fits” or “fitting lines to the data” or any other similar phrase. We must always keep firmly in mind that we are fitting a model to parameters of a probability distribution which itself represents our uncertainty in some observable. Deviations from the language I use are part of what is responsible for the rampant over-certainty we see (a standard topic of this blog).
Here is a regression:
yt = β0 + β1x1 + β2x2 + … + βpxp + ε
where each of the xi are potentially probative of y. It is up to you to collect these x’s. How many x’s are there for you to consider in any problem? A whoppingly large number. A number so large that it is incomprehensible.
Anything can be an x. The color of the socks of the people who generated or gathered the data can be an x. The temperature in Quebec might just be correlated with your y. The number of monkeys in Suriname could be predictive of your y. The number of nose hairs of Taipei bus drivers could be relevant to saying something about your y.
You might think this silly, but how can you know these x’s are not correlated with your y if you don’t try? You cannot. That is, you cannot know with certainty whether any x is uncorrelated with your y unless you can prove logical independence between x and y. And that isn’t easy: it really can’t be done in any except mathematical and logical proofs using highly defined objects. For real-world (contingent) data, logical independence is hard to come by (see the footnote).
A sociologist (whose name I cannot look up because I am too pressed for time) said words to the effect that, in his field, everything is correlated with everything else. This is only a slight exaggeration. In any case, it remains true that for any contingent x and y, logical independence1 is denied us and so we must instead look to irrelevance.
Irrelevance is when, for some propositions x and y (data are observations statements, or propositions),
Pr(y|x & E) = Pr(y|E).
That is, the probability of y given some evidence E remains unchanged if we consider we also know x. This tells us that to say whether an x should be in our regression equation, we should examine whether x is relevant or irrelevant to knowing (future) values of y.
Recall that our goal for any probability model is to make statements like this:
Pr (ynew > a | xnew, old observed data, model true)
where we pick interesting a’s or we pick other questions about ynew which are interesting to us. If this probability is the same if we do not condition on x, then x is irrelevant to y and should not be included in our model. In notation (for our math readers): If
Pr(ynew>a| xi, other x’s, old data, model true) = Pr(ynew>a| other x’s, old data, model true)
then xi is irrelevant to y so it should not appear in our model.
Classic statistics tells us you cannot say which x’s you should include unless you first do a hypothesis test. This is a highly artificial construct which often leads to error. That is, some x’s can be relevant to knowing y even though the p-values of those x’s are larger than the magic number—oh, 0.05! how I love thee!—and some x’s can be irrelevant to y even though their p-values are less than the magic number.
And this holds equally for Bayesian posterior distributions of the parameters. Some x’s can be relevant to y even though their posterior probabilities show a large probability of not equaling (or being near) 0, and other x’s can be irrelevant to y even thought their posterior probabilities show a large probability of equaling (or being near) 0.
In other words, relevance as a measure of model inclusion does away with all discussions of “clinical” versus “statistical significance.” It also removes all tricks, like the one in where if you increase your sample size you guarantee a publishable p-value (one which is less than the magic number).
Relevance is the fairest measure because it puts the decision directly in terms of observables—and not in terms of unobservable parameters. We ask questions of the y that are meaningful to us—and these questions will change from problem to problem. We create the questions, not some software package. We need not rely on a one-size-fits-all approach like hypothesis testing or posterior examinations. We can adapt each analysis to the problem at hand.
Why isn’t everybody jumping on the relevance bandwagon. Ah, this is it. Ease. The relevance way puts the burden of decision making squarely on you. It is (as we shall see when I do examples later) more work. Not computationally; not really. But it doubles the amount of mental effort an analyst must put into a project. It makes you really think about what probabilities mean in terms of observables. It also removes the incredible ease of glancing at p-values (or posteriors), of having the software make the decisions for you.
But this is the least of it. Far, far worse is that relevance absolutely destroys the goosed up certainty found in classical (hypothesis testing and posterior examination) methods. Whereas before relevance, you might find dozens of x’s that are “highly significant!” for explaining y, with relevance, you’ll be lucky to find one or two, and those won’t be nearly as exciting as explaining y as you had thought (or hoped).
And that is bad news for your prospects of publishing papers or developing new “findings.”
1Logical independence exists if and only if each of the conjunctions “x & y”, “x & not y”, “not x & y”, and “not x & not y” are not necessarily false. It is also the case that some logically independent x and y, the x (or y) might be relevant to knowing y (or x).
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511075.63/warc/CC-MAIN-20231003092549-20231003122549-00097.warc.gz
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CC-MAIN-2023-40
| 6,323 | 25 |
https://www.khanacademy.org/math/8th-grade-illustrative-math/unit-4-linear-equations-and-linear-systems/extra-practice-linear-equations/v/example-using-algebra-to-find-measure-of-supplementary-angles
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math
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Extra practice: Linear equations
We're told that the measure of angle QPR-- so that's this angle right over here-- is 2x plus 122. And I'll assume that these are in degrees. So it's 2x plus 122 degrees. And the measure of angle RPS-- so that's this angle right over here-- is 2x plus 22 degrees. And they ask us to find the measure of angle RPS. So we need to figure out this right over here. So we would be able to figure that out if we just knew what x is. And lucky for us, we can use the information given to solve for x and then figure out what 2 times x plus 22 is. And the main big idea here, the thing that pops out here, is that the outside rays for both of these angle form a line. These two angles form a line. You could say that they are supplementary. Both of these angles are supplementary. 2x plus 22 plus another 2x plus 122 is going to add up to 180. We know that this entire angle right over here is 180 degrees. So we can say that the measure of angle QPR, this angle right over here, 2x plus 122, plus the green angle, plus angle RPS-- so plus 2x plus 22-- is going to be equal to 180 degrees. And now we can start simplifying this. We have two x's. We have another two x's. So those are going to add up to be 4x. And then we have 122 plus 22. So that's going to be 144. And the sum of those two are going to be equal to 180 degrees. We can subtract 144 from both sides. On the left-hand side, we're just going to be left with a 4x, this 4x right here. And on the right-hand side, we're going to have-- let's see, if we were subtracting 140, we would have 40 left. And then we have to subtract another 4, so it's going to be 36. Divide both sides by 4, and we get x is equal to 9. Now remember, we're not done yet. They didn't say solve for x. They said find the measure of angle RPS, which is 2 times x plus 22 or 2 times 9 plus 22, which is 18 plus 22, which is equal to 40. So the measure of angle RPS is 40 degrees.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00183.warc.gz
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CC-MAIN-2022-49
| 1,939 | 2 |
https://www.coursehero.com/file/5928757/hw09/
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math
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Unformatted text preview: (A) Use Markov’s Inequality (6.4 Exercise 31) to find an upper bound on the probability that at least k people get their own hats back, in the hat-check problem (6.4 Example 6). Your answer should not depend on the number of people who checked hats....
View Full Document
- Fall '08
- Math, Prime number, Odd-numbered self-checking exercises
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| 370 | 4 |
http://goassignmentijdi.lasvegasdentists.us/how-to-calculate-return-on-investment.html
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math
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Step-by-step instructions on how to calculate social media roi for your this straightforward formula has just the two parts: return and investment. Bankratecom provides a free return on investment calculator and other roi calculators to compare the impact of taxes on your investments calculate. Return on investment calculating roi to realize project value how to calculate roi the formula for determining roi is. In finance, return is a profit on an investment it comprises any change in value and interest or dividends or other such cash flows which the investor receives from.
Return on investment (roi) is the amount of profit you receive with respect to your invested capital for example, a roi of 10 percent means that for every dollar. How to calculate return on investment how to calculate return on what is the difference between cash on cash return and return on investment. Learn how to calculate roi in 7 steps to increase your chances of landing an investor and dusting the competition. Calculate your return on investment (roi) see for yourself what thefork can do for your restaurant. How to calculate return on invested capital represents the investment in it is important to note that some institutions calculate roic in a.
The more money you make compared to the money you put into an investment, the better the investment that’s just common sense however, it helps to have. The return on investment (roi) represents how well an investment is doing because the roi is normally stated as a percentage, you can use it to compare how well your. Fred wilson explains the proper way to calculate return on investment using cash flow.
Return on investment shows how much money is made on an investment compared to how much was spent on it it is expressed as a percentage the formula for calculating. To calculate the return on his investment, he would divide his profits ($1,200 - $1,000 = $200) by the investment cost ($1,000), for a roi of $200/$1,000. Calculating return on investment (roi) is a relatively simple calculation to perform it is best used to estimate how effective money spent by a business or.
Return on investment while an investor could use it to calculate a return on a the same calculation can be used to calculate an investment made by.
Calculate roi (return on investment) with this worksheet to assess the payback from your investment of time, money and other resources in a given project. On paper, roi could not be simpler to calculate it, you simply take the gain of an investment, subtract the cost of the investment, and divide the total. Calculate rate of return what is the return on my real estate investment what is the value of compound interest what is the value of a call or put option. How to : hashflare - calculate return on investment types of mining algorithm available there are 5 types by enryuthorn. Feel free to grab a free transcript of the return on investment video in pdf format at it includes all pictures and. Free online return on investment (roi) calculator provide total roi rate as well as annualized roi using either actual dates of investment or plain. You can use a few simple calculations to determine how your investments are performing it is used to calculate your return on an investment after you.Download How to calculate return on investment
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https://drives.novantamotion.com/kb/how-to-calculate-the-output-power-of-a-servo-drive
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math
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Maximum continuous output power
The maximum continuous output power than can provide a Novanta Motion Drive is calculated as follows:
is the maximum DC-bus voltage,
is the maximum continuous phase current, and
is the maximum DC Bus voltage utilization (pu), which depends on the switching frequency.
As an example, consider an Everest S XCR Servo Drive (EVS-XCR-E or EVS-XCR-C). According to the Product Description, the main parameters to calculate its maximum output power are:
Maximum absolute DC bus supply voltage (continuous): 80 V
Maximum continuous phase current = 45 A
Maximum DC Bus voltage utilization at 10kHz = 99.73% → 0.9973 pu
From these parameters we can calculate the maximum continuous output power of the Servo Drive as:
Power justification in a three-phase motor
The following diagram shows the electrical model of a Y-wired BLDC or PMSM motor:
The power in any motor can be calculated as the sum of each phase power (product of RMS current and RMS voltage). In the case of a phase-balanced motor:
In a Y-connected motor, the phase voltage () is defined as:
where is the phase-to-phase voltage (difference between two output terminals of the drive).
The amplitude of the drive output phase-to-phase voltage can be defined as follows:
is the DC-bus voltage of the Servo drive,
and is the modulation index (ratio of the output voltage respect DC-bus voltage). The maximum modulation index provided by an Novanta Motion Servo Drive is defined as "Maximum Bus Voltage utilization" on the product manuals. Thanks to the use of Space Vector Modulation (SVM), this value can be close to the unit.
Summarizing, the power delivered to the motor can be defined as:
Note that the power is calculated from RMS values, while and are expressed in amplitude of a sinusoidal. For this reason, the values are divided by .
From the point of view of a Servo Drive, the power provided to a Δ-wired motor or a Y-wired motor is exactly the same. However, the voltage and current values are shared different within the phases:
In a Δ-wired motor:
The motor current () is not the current seen at the Servo Drive. On the contrary, it is defined as:
Therefore, the total power in a Δ-wired motor results as:
Which, from the point of view of a Servo Drive, it is equivalent than for a Y-wired motor.
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https://studylib.net/doc/7939867/grade--5th-subject--math-expectation-s---can-multiply-and.
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math
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Grade: 5th Subject: Math Expectation(s): Can multiply and divide simple fractions and decimals Materials needed: pencil, paper, markers/crayons Lesson Description: Model the concept of multiplying fractions through paper folding. Give your student a piece of paper, different colored markers/crayons, and a sample fraction multiplication problem – e.g. ¾ x 2/3. Have them represent the first fraction by folding and coloring the paper. To do so, fold the paper into fourths (representing the denominator of the fraction) and then color in three of the sections (representing the numerator). It should look something like this: Next, have them turn the paper (from portrait to landscape orientation) and fold and color to represent the other fraction being multiplied. For the example problem, fold into three sections (the denominator) and color in two of them (numerator). Your student’s paper should now have a grid of 12 sections that looks something like the illustration below. The grid contains the answer to the multiplication problem: sections that have overlapping colors represent the numerator (6 sections) and the total number of sections represent the denominator (12 sections): 6/12, or ½. Encourage your student to always simplify their answers if possible. Have your student complete a few more simple problems using this method. Ask if they see any patterns; the two most important concepts they should understand are: (1) the answer to each problem is always smaller than either of the factors; (2) you can get the answer for each problem by multiplying the numerators and then multiplying the denominators. Teaching and learning tips/strategies: • Students need to understand the conceptual ideas behind multiplication of fractions, not simply the rules to follow (i.e. multiply the numerators, multiply the denominators). Giving them a visual representation of the process will help them to better understand these concepts and increase their ability to remember the rules they follow to solve problems. • Vocabulary is an important part of mathematics. When working with fractions, continually reinforce the meaning of numerator (top number), denominator (bottom number), mixed number (a whole number and a fraction), proper fraction (numerator’s smaller than the denominator) and improper fraction (numerator’s larger than the denominator). • Don’t forget to praise your student’s effort!
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| 2,430 | 1 |
http://www.primidi.com/electrical_impedance/complex_impedance
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math
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where the magnitude represents the ratio of the voltage difference amplitude to the current amplitude, while the argument gives the phase difference between voltage and current. is the imaginary unit, and is used instead of in this context to avoid confusion with the symbol for electric current. In Cartesian form,
where the real part of impedance is the resistance and the imaginary part is the reactance .
Where it is required to add or subtract impedances the cartesian form is more convenient, but when quantities are multiplied or divided the calculation becomes simpler if the polar form is used. A circuit calculation, such as finding the total impedance of two impedances in parallel, may require conversion between forms several times during the calculation. Conversion between the forms follows the normal conversion rules of complex numbers.
Read more about this topic: Electrical Impedance
Other articles related to "complex impedance, complex":
... of this equation, we obtain where and Solving for V(s) we have The definition of the complex impedance Z (in ohms) is the ratio of the complex voltage V divided ...
Famous quotes containing the word complex:
“Young children constantly invent new explanations to account for complex processes. And since their inventions change from week to week, furnishing the correct explanation is not quite so important as conveying a willingness to discuss the subject. Become an askable parent.”
—Ruth Formanek (20th century)
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| 1,483 | 9 |
http://blindlovecats.com/70-emaths-science-papers-ks3.php
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math
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Emaths science papers ks3
5. Mai 2009 On Thursday, I'm taking my KS3 maths Sats paper levels 6-8, which is marked internally. We havn't I found ALL the previous papers for english, maths and science. Here's the website:
Sep 11, 2014 · 1/12 Emaths Ks3 Maths Papers EMATHS KS3 MATHS PAPERS PDF If you want to have a destination search and find the appropriate manuals for your …
SATs papers themselves have broadly remained the same, with English and Maths in KS1 SATs papers and KS2 SATs papers plus Science in KS3 SATs papers.
argumentative research papers music common entrance essay questions emaths science papers ks3 business report writing format template do dissertation
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647768.45/warc/CC-MAIN-20180322034041-20180322054041-00660.warc.gz
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| 679 | 5 |
http://cuethememusic.tumblr.com/post/25535384979/my-latest-everlark-one
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math
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First off, I'm an Artist. I am 15. :} I would paint my walls if I could, and I probably spend too much time in my PJs. British telly keeps me going. Oh, and I have a weakness for Sci-fi. Feel free to message me requests!
My latest Everlark one...
1 year ago
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163037851/warc/CC-MAIN-20131204131717-00024-ip-10-33-133-15.ec2.internal.warc.gz
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| 257 | 3 |
https://beautyhealthpage.com/can-you-find-what-is-missing-in-the-empty-square-you-will-give-the-wrong-answer-for-sure/
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math
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Do you enjoy taking logical tasks? How do you solve them? Here is a very interesting one. It is a brain teaser that will for sure keep your attention. You only need to reveal what needs to be written on the empty box. But first, you have to discover what it is about. If your thinking is similar to the majority of people, then you will give the wrong answer. Around 90% of social network users didn’t give the right answer. Are you one of them? Or you will be able to solve the task?
In the picture above you can see six squares with numbers written on five of them. Your job is to find out what needs to be written in the empty one. It is not as simple as it sounds. If you follow the logic, then the first thing that comes to your mind is number 6. But is this number what is missing in the picture? Following the logical sequence of numbers, this would be the right answer. But remember that this is more a trick rather than math.
If you still can’t remember where have you seen this order of numbers, here is some help. If you are an active driver you will immediately know that this order of numbers is on the gearbox in your car. And if you are not a driver then you can see the answer in the picture below. Isn’t it interesting?
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| 1,242 | 3 |
https://divinewsmedia.com/18264/
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math
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An expression is a sentence fragment that stands for a single numerical value. Welcome to Whats the Difference Between Expressions and Equations with Mr.
An equation is a statement that verifies equality between two expressions like x53.
Difference between equation and expression. Then again the differences between these two are drawn by their outputs. You must be able to identify and explain the difference between these key words. Youre in the right placeWhether.
Main Differences Between Inequalities and Equations. An expression is a number a variable or a combination of numbers and variables and operation symbols. Difference Between Expression and Equation.
On the other hand the same cannot be said of an equation because you have to follow certain rules to work. Maths Guide now available on Google Play. Essentially an equation is written as an expression equals to another expression.
X35 is not. An expression is basically an incomplete mathematical equation. X 5 3 For this equation to stand true the expression of x5 should be equal to 3.
An equation is a combination of two expressions usually separated by an equals sign which means that both expressions must equal each other. This video explained the border line differences between Expression Equation Inequality and Function when used in mathematicsThis is a foundation video th. An expression is a combination of numbers variables and symbols to be calculated.
Equations can have one or two values for the. In mathematics an equation is used to denote the equality between two expressions. For example x-45 means x can have only one value that is 9.
This denotes that whatever is x if you add 2 to it will be equal to 5. From the foregoing you can easily work out the values of the variables by evaluating the unknown variables. The main difference between inequalities and equations is in terms of their definitions that clearly delineate their functionalities in mathematical operations.
The table above gives vivid discrepancies between expression vs equation. An equation contains expressions that are separated by an equals sign. A further look at the mathematical expression can be explained with numbers and variables such as.
Need help with expressions and equations. An expression can be evaluate for given values. An equation -as the name suggests- represents the equality between two variables in the given formulation.
The algebra student or algebraically able individual is expected to know the difference between an expression and a statement because each serves a different purpose and each is handled in a certain way. An equation makes complete sense as long as the equality condition is not violated. 7x y – 4.
It involves between two expressions showing that the right hand side should be equal to what is on the left hand side of the equation. An equation is a SENTENCE. X 2 5.
A formula looks like this vhwl when v volume h height w width and l length. An equation is made up of two expressions connected by an equal sign. An equation looks like this x35 the difference between this and an expression is the equal sign.
From which one is to determine a particular quantity. An expression can be evaluated whereas an equation can be solved. As nouns the difference between expression and equation is that expression is a particular way of phrasing an idea while equation is senseidmathematics an assertion that two expressions are equal expressed by writing the two expressions separated by an equal sign.
This video explains the difference between an expression and an equationSite. This is because both use expressions in solving the value for the variable. An equation is described as a mathematical statement with two expressions set equal to one another.
A formula is a special type of equation. Equations vs Functions When students encounter algebra in high school the differences between an equation and a function becomes a blur. It shows the relationship between two variables.
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CC-MAIN-2021-31
| 3,982 | 17 |
https://economicsconcepts.com/neo-classical-theory-of-economic-growth/
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math
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We know that Hicks, J.E. Meade, Mrs. Joan Robinson, Salow and Prof. Swan are Neo-Classical economists. They have presented their growth models individually as Meade model (1961), Solow model (1956, 1960), Swan model (1956), and Mrs. Joan Robinson model (1956, 1999). Now we present all these models in a single model which wee simply call Neo-Classical Model of Economic Growth, where we discuss the salient features of neo-classical theory and this model is called a reaction to H-D model.
(i) According to H-D model economy is always prey to instability. But according to Neo-Classical, if capital – output ratio is made flexible, the instability will come to an end.
(ii) The basic Neo-Classical model assumes that in long run the constant – returns to scale applies and no technical progress takes place in the economy. The stock of capital can be adapted in capital intensive technology, more or less. It means that labor and capital are substitute table. Accordingly, by changing the capital labor ratio the equality can be brought in changes in labor, capital and output. This model also assumes that the factor prices are equal to their marginal productivities. Accordingly in this model, there exist flexibility of wages, prices and rate of interest.
(iii) Whenever warranted growth rate exceeds natural growth rate the economy will cross the ceiling of full-employment. In such situation the labor saving technology will be used. As a result the capital-output ratio will increase. This will depress down the warranted growth rate till it becomes equal to natural growth rate. On the other band, if warranted growth rate is lower than natural growth rate the excess amount of labor will emerge. As a result, real rate of interest will fall as compared with real wage rate. This will induce the firms to adopt labor intensive technology. In this way, the capital-output ratio will fall. This will lead to increase warranted growth rate (s/v) till it becomes equal to natural growth rate.
(iv) According to neo-classical model because of changes in v and s/v the Harrodian instability and Raisor’s Edge will not persist, and economy can attain a steady-state equilibrium. Its means to say that in neo-classical model the equilibrium growth rate coincides with dynamic disequilibrium where output, stock of capital, supply of labor and change investment, all will grow at the same exponential rate. In such situation there will be no change in K, L and Y, This situation is accorded as Golden Age following Mrs. Joan Robinson. Thus in Golden Age, the following situation will occur:
Where Q = output, K = Capital, L = Labor, and I = Investment. The signs of bars on all the variables represent the constant values in the golden age, while the m, n, h and q represent constant growth rates.
I = dk/dt = sQ
Īo emt = h K̄o eht = sQ̄o eq
For all the values of t, last equation will hold true if growth rates of m, h and q are equal to each other. It is reminded that according to neo-classical theory, the growth rate of Golden Age is not influenced by growth of savings, and it is contrary to H-D model. It is due to the reason that whenever the proportion of savings increase there will by growth of capital and output. But such increase will be temporary because due to operation of law of decreasing returns the initial growth rate will be existing. As if growth of capital increases more than labor, the marginal productivity of capital will decrease leading to decrease the growth rate of output. Thus according to neo-classical growth model, because of changes in capital-labor ratio and flexibility of wages, prices and interest rate the economy will attain a stable equilibrium. Here, growth of savings (sQ), growth of capital (sQ/k), growth of output (q) and growth of population (n) will be equal to each other, as:
q = sQ = (sQ/k) = n
It is shown with fig.
Here the schedule sQ/k shows the growth of capital which is function of output – capital ratio (Q/K), and slope of this curve shows the saving ratio (s). The growth of output curve q1 passes in between growth of labor schedule (n) and growth of capital schedule (sQ/k). The output is divided on the basis of elasticities of capital and labor (a and B). In this figure, after E, the growth of capital is more than growth of output. This leads to decrease Q/K, hence equilibrium is established at E. While before E, growth of output is more than growth of capital. This will lead to increase Q/K. Thus Q/K2 is an equilibrium Q/K which is stable one where growth of capital (sQ/K) growth of output (q) and growth of population are equal.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00390.warc.gz
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CC-MAIN-2022-27
| 4,617 | 12 |
https://usiena-air.unisi.it/handle/11365/37251
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math
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This paper describes the first measurement of b-quark fragmentation fractions into bottom hadrons in Run II of the Tevatron Collider at Fermilab. The result is based on a 360 pb(-1) sample of data collected with the CDF II detector in p (p) over bar collisions at root s = 1.96 TeV. Semileptonic decays of (B) over bar (0), B(-), and (B) over bar (0)(s) mesons, as well as Lambda(0)(b) baryons, are reconstructed. For an effective bottom hadron p(T) threshold of 7 GeV/c, the fragmentation fractions are measured to be f(u)/f(d)=1.054 +/- 0.018(stat)(-0.045)(+0.025)(sys)+/- 0.058(B), f(s)/(f(u)+f(d))=0.160 +/- 0.005(stat)(-0.010)(+0.011)(sys)(-0.034)(+0.057)(B), and f(Lambda b)/(f(u)+f(d))=0.281 +/- 0.012(stat)(-0.056)(+0.058)(sys)(-0.087)(+0.128)(B), where the uncertainty B is due to uncertainties on measured branching ratios. The value of f(s)/(f(u)+f(d)) agrees within one standard deviation with previous CDF measurements and the world average of this quantity, which is dominated by LEP measurements. However, the ratio f(Lambda b)/(f(u)+f(d)) is approximately twice the value previously measured at LEP. The approximately 2 sigma discrepancy is examined in terms of kinematic differences between the two production environments.
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|Titolo:||Measurement of ratios of fragmentation fractions for bottom hadrons in p(p)over-bar collisions at root s=1.96 TeV|
|Citazione:||T., A., J., A., T., A., M. G., A., B. A., G., S., A., et al. (2008). Measurement of ratios of fragmentation fractions for bottom hadrons in p(p)over-bar collisions at root s=1.96 TeV. PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY, 77, 072003-1-072003-31.|
|Appare nelle tipologie:||1.1 Articolo in rivista|
File in questo prodotto:
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| 1,829 | 7 |
https://tubesclock.com/en/rick_and_morty_nixie_tube_clock_in_14_replaceable_nixie_tubes_motion_sensor.html
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math
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If you are not satisfied. Rick and Morty Nixie Tube Clock IN-14 Replaceable Nixie Tubes, Motion Sensor. This is a hand-painted clock! We can do individual design according to your requirements!
NOS Nixie Tubes - Not previously used in any type of equipment for maximum initial lifespan! Nixie Tubes are replaceable, they are not soldered to the PCB!
Built-in motion sensor, which turns off nixie tubes when nobody is near the clock. This feature was made to prolong the lifespan of the tubes and for energy savings. Olive Ash Body with rich texture - each clock is unique!
Our Vintage Nixie Tube Clock is handcrafted using 4x IN-14 Nixie tubes. These Nixie tubes are at least 35 years old in history, and from the former Soviet Union. We can best describe our clock as a vintage technology combined with a crafty elegance.
This beautiful clock brings to your home a piece of history with its durable vintage components. The soft and warm glow of the Nixie tubes makes it perfect to use it in your bedroom without disturbance to your sleep. The stunning colors glow in a properly distributed and beautified manner that gives your room a classy touch. The IN-14 Nixie tube clock is intentionally designed to operate in a range far below its peak for lifespan maximization; this ensures you will enjoy them for a long time. New and Replaceable IN-14 Nixie Tubes.
Blue LEDs behind the Nixie tubes will help you set the clock and will have decorative effects that you can disable if desired. 12 or 24 hours time format. Built-in battery socket for proper time backup during power interruptions.
Universal power supply 100-240V with UK/EU/US/AU plug. Size (LxWxH): 6.1(15.5cm) 2.56(6.5cm) x 3.14(8.0cm). WHAT IS INSIDE THE BOX?
Power Adapter (included EU/US/UK/AU socket). Lets give your room a beautiful lift with this long-lasting vintage nixie clock. Have your family and friends adore your room on their next visit.######xA0;We use UkrPochta (Ukranian Post) for all our International######xA0; deliveries. The usual time for a parcel to arrive at its address is 24 business######xA0; days, but usually it arrives much earlier. Sometimes it can take######xA0; longer up to 8 weeks. We will make every effort to fix any######xA0;problem.
We guarantee you complete satisfaction with all our high quality######xA0;products. The item should come to the above address within 30 days after you received it. ######xA0; After 30 days we will no longer be responsible and the item######xA0; won't be taken back.
Item for returning must have the original tags and packing, otherwise it won't be accepted. The item "Rick and Morty Nixie Tube Clock IN-14 Replaceable Nixie Tubes, Motion Sensor" is in sale since Sunday, March 22, 2020. This item is in the category "Home & Garden\Home Décor\Clocks\Alarm Clocks & Clock Radios". The seller is "uamade" and is located in Kyiv. This item can be shipped worldwide.
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CC-MAIN-2023-50
| 2,896 | 10 |
https://projecteuclid.org/journals/annals-of-statistics/volume-36/issue-4/The-sparsity-and-bias-of-the-Lasso-selection-in-high/10.1214/07-AOS520.full
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math
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Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436–1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of greater order than the sample size. Zhao and Yu [(2006) J. Machine Learning Research 7 2541–2567] formalized the neighborhood stability condition in the context of linear regression as a strong irrepresentable condition. That paper showed that under this condition, the LASSO selects exactly the set of nonzero regression coefficients, provided that these coefficients are bounded away from zero at a certain rate. In this paper, the regression coefficients outside an ideal model are assumed to be small, but not necessarily zero. Under a sparse Riesz condition on the correlation of design variables, we prove that the LASSO selects a model of the correct order of dimensionality, controls the bias of the selected model at a level determined by the contributions of small regression coefficients and threshold bias, and selects all coefficients of greater order than the bias of the selected model. Moreover, as a consequence of this rate consistency of the LASSO in model selection, it is proved that the sum of error squares for the mean response and the ℓα-loss for the regression coefficients converge at the best possible rates under the given conditions. An interesting aspect of our results is that the logarithm of the number of variables can be of the same order as the sample size for certain random dependent designs.
"The sparsity and bias of the Lasso selection in high-dimensional linear regression." Ann. Statist. 36 (4) 1567 - 1594, August 2008. https://doi.org/10.1214/07-AOS520
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CC-MAIN-2022-27
| 1,743 | 2 |
https://ju.se/studera/valj-utbildning/kurser.html?hidekurstillfalle=yes&courseCode=JITG12
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math
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Introduction to Statistical Methods 7,5 hpUndervisningen bedrivs på engelska.
KursinnehållSome major topics covered in this course are:
• Descriptive statistics
• Random variables
• The normal distribution
• Sampling and sampling distributions
• Confidence intervals
• Hypothesis testing
Connection to Research and Practice
This course covers essential statistical topics necessary to understand any research reports and/or articles. The students learn to compile, calculate summary measures, and present different types of data. The aim is also to provide the ability to make simpler probability calculations and, based on statistical assessments draw conclusions about unknown characteristics of different types of populations. The lectures and exercises provided involves many practical examples, and the computer assignment consists of applying the skills and abilities learned throughout the course to real-world data; presenting and evaluating different types of data and to infer properties of populations parameters, e.g., testing hypotheses and deriving estimates.
FörkunskapskravGeneral entry requirements and Mathematics 3b or 3c, Civics 1b or 1a1 and 1a2. Or: English B, Mathematics C and Civics A and required grade Passed or international equivalent.
Kursen ges vid: Jönköping International Business School
Senast ändrad 2022-06-02 07:12:25
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CC-MAIN-2022-33
| 1,372 | 13 |
https://www.fmf.uni-lj.si/en/study-physics/programmes/1fiz/2022/7000779/courses/1219/
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math
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Enrollment into the program.
Introduction to numerical computation. Floating-point arithmetic. Sources of inexactness in numerical computation. Sensitivity of a problem, convergence of a method, stability of computation. Error analysis.
Software for numerical computation.
Systems of linear equations. Matrix norms. Condition number. Gaussian elimination. Error analysis. Pivoting. Special types of linear systems.
Nonlinear equations. Bisection. Fixed-point iteration. Newton's and Secant method. Algebraic equations. Laguerre's method. Root reduction. Systems of nonlinear equations. Fixed-point iteration. Newton's metod.
Linear least square problems. Overdetermined systems. Normal equations. Orthogonal decomposition.
Eigenvalue problem. Schur form. Power iteration. Inverse iteration. QR iteration.
Polynomial interpolation. Lagrange interpolation. Divided differences. Newton interpolation. Numerical differentiation.
Numerical integration. Newton-Cotes rules. Composite rules. Romberg extrapolation. Gaussian quadrature.
Numerical methods for ordinary differential equations. Methods for initial value problems. One-step methods. Runge-Kutta methods. Multi-step methods. Systems of differential equations and initial value problems of higher order.
Z. Bohte, Numerične metode. DMFA, Ljubljana 1991.
Z. Bohte, Numerično reševanje nelinearnih enačb. DMFA, Ljubljana 1993.
Z. Bohte, Numerično reševanje sistemov linearnih enačb. DMFA, Ljubljana 1995.
E. Zakrajšek: Uvod v numerične metode, DMFA-založništvo, Ljubljana, 2000.
R. L. Burden, J. D. Faires: Numerical Analysis, 8th edition, Brooks/Cole, Pacific Grove, 2005.
D. Kincaid, W. Cheney, Numerical Analysis : Mathematics of Scientific Computing, 3rd edition, Brooks/Cole, Pacific Grove, 2002.
Students learn fundamentals of numerical computation. They learn in detail the fixed-point arithmetic. They learn basics of methods for systems of linear and nonlinear equations, eigenvalue computation, polynomial interpolation, numerical quadrature, and methods for the ordinary differential problems. The acquired knowledge is consolidated by homework assignments and solving problems using software for numerical computation.
Knowledge and understanding: Understanding of floating-point arithmetic and sources of errors in numerical computation. Knowledge of basic numerical algorithms for linear and multilinear systems, computing eigenvalues, interpolation, integration, and solving differential equations. Knowledge of computer programming and Matlab or other similar software for solving such problems.
Application: Economical and accurate numerical solution of various mathematical problems. In addition to mathematics, numerical methods are used in many other fields when the problem can be described by a mathematical model and a result in a numerical form is required. Many problems can not be solved analytically but only numerically. Also, in some cases, the numerical solution is much more economical than the analytical one.
Reflection: Understanding of the theory from the applications.
Transferable skills: The ability to solve mathematical problems using a computer. Understanding the differences between the exact and the numerical computation.
Lectures, exercises, homeworks, midterm exams, written exams, and consultations
Continuing (homework, midterm exams)
Final (written and oral exam)
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
· GHEORGHIU, C. I., HOCHSTENBACH, Michiel E., PLESTENJAK, Bor, ROMMES,
Joost. Spectral collocation solutions to multiparameter Mathieu's system.
Appl. math. comput., 2012, vol. 218, iss. 24, str. 11990-12000.
· PLESTENJAK, Bor, BAREL, Marc van, CAMP, Ellen van. A Cholesky LR
algorithm for the positive definite symmetric diagonal-plus-semiseparable
eigenproblem. Linear algebra appl., 2008, vol. 428, iss. 2-3, str. 586-599.
· PLESTENJAK, Bor. Numerical methods for the tridiagonal hyperbolic quadratic
eigenvalue problem. SIAM j. matrix anal. appl., 2006, vol. 28, no. 4, str. 1157-
· JAKLIČ, Gašper, ŽAGAR, Emil. Curvature variation minimizing cubic Hermite
interpolants. Appl. math. comput., 2011, vol. 218, iss. 7, str. 3918-3924.
· JAKLIČ, Gašper, KOZAK, Jernej, KRAJNC, Marjetka, VITRIH, Vito, ŽAGAR, Emil.
Hermite geometric interpolation by rational Bézier spatial curves. SIAM j.
numer. anal., 2012, vol. 50, no. 5, str. 2695-2715.
· KOZAK, Jernej, ŽAGAR, Emil. On geometric interpolation by polynomial
curves. SIAM j. numer. anal., 2004, vol. 42, no. 3, str. 953-967
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CC-MAIN-2023-14
| 4,529 | 40 |
http://www.ck12.org/algebra/Applications-of-Exponential-Functions/lesson/Using-Exponential-Growth-and-Decay-Models/r10/
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math
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The half-life of an isotope of barium is about 10 years. The half-life of a substance is the amount of time it takes for half of that substance to decay. If a nuclear scientist starts with 200 grams of barium, how many grams will remain after 100 years?
When a real-life quantity increases by a percentage over a period of time, the final amount can be modeled by the equation: , where is the final amount, is the initial amount, is the rate (or percentage), and is the time (in years). is known as the growth factor .
Conversely, a real-life quantity can decrease by a percentage over a period of time. The final amount can be modeled by the equation: , where is the decay factor .
The population of Coleman, Texas grows at a 2% rate annually. If the population in 2000 was 5981, what was the population is 2010? Round up to the nearest person.
Solution: First, set up an equation using the growth factor. and .
You deposit $1000 into a savings account that pays 2.5% annual interest. Find the balance after 3 years if the interest rate is compounded a) annually, b) monthly, c) daily.
Solution: For part a, we will use , as we would expect from Example A.
But, to determine the amount if it is compounded in amounts other than yearly, we need to alter the equation. For compound interest, the equation is , where is the number of times the interest is compounded within a year. For part b, .
In part c, .
You buy a new car for $35,000. If the value of the car decreases by 12% each year, what will the value of the car be in 5 years?
Solution: This is a decay function because the value decreases .
The car would be worth $18,470.62 after five years.
Intro Problem Revisit This is an example of exponential decay, so we can once again use the exponential form . In this case, a = 200, the starting amount; b is 1/2, the rate of decay; x-h = 100/10 = 10, and k = 0.
Therefore, 0.195 grams of the barium still remain 100 years later.
1. Tommy bought a truck 7 years ago that is now worth $12,348. If the value of his truck decreased 14% each year, how much did he buy it for? Round to the nearest dollar.
2. The Wetakayomoola credit card company charges an Annual Percentage Rate (APR) of 21.99%, compounded monthly. If you have a balance of $2000 on the card, what would the balance be after 4 years (assuming you do not make any payments)? If you pay $200 a month to the card, how long would it take you to pay it off? You may need to make a table to help you with the second question.
3. As the altitude increases, the atmospheric pressure (the pressure of the air around you) decreases. For every 1000 feet up, the atmospheric pressure decreases about 4%. The atmospheric pressure at sea level is 101.3. If you are on top of Hevenly Mountain at Lake Tahoe (elevation about 10,000 feet) what is the atmospheric pressure?
1. Tommy needs to use the formula and solve for .
2. you need to use the formula , where because the interest is compounded monthly.
To determine how long it will take you to pay off the balance, you need to find how much interest is compounded in one month, subtract $200, and repeat. A table might be helpful. For each month after the first, we will use the equation, , where is the current balance and is the remaining balance from the previous month. For example, in month 2, the balance (including interest) would be .
It is going to take you 11 months to pay off the balance and you are going to pay 108.03 in interest, making your total payment $2108.03.
3. The equation will be . The decay factor is only raised to the power of 100 because for every 1000 feet the pressure decreased. Therefore, . Atmospheric pressure is what you don’t feel when you are at a higher altitude and can make you feel light-headed. The picture below demonstrates the atmospheric pressure on a plastic bottle. The bottle was sealed at 14,000 feet elevation (1), and then the resulting pressure at 9,000 feet (2) and 1,000 feet (3). The lower the elevation, the higher the atmospheric pressure, thus the bottle was crushed at 1,000 feet.
- Growth Factor
- The amount, , an exponential function grows by. Populations and interest commonly use growth factors.
- Decay Factor
- The amount, , an exponential function decreases by. Populations, depreciated values, and radioactivity commonly use decay factors.
- Compounded Interest
- When an amount of money is charges a particular interest rate and that rate is collected yearly, monthly, quarterly, or even daily. It is compounded because after the first “collection” interest is taken on interest.
- Sonya’s salary increases at a rate of 4% per year. Her starting salary is $45,000. What is her annual salary, to the nearest $100, after 8 years of service?
- The value of Sam’s car depreciates at a rate of 8% per year. The initial value was $22,000. What will his car be worth after 12 years to the nearest dollar?
- Rebecca is training for a marathon. Her weekly long run is currently 5 miles. If she increase her mileage each week by 10%, will she complete a 20 mile training run within 15 weeks?
- An investment grows at a rate of 6% per year. How much, to the nearest $100, should Noel invest if he wants to have $100,000 at the end of 20 years?
- Charlie purchases a 7 year old used for $54,000. If the rate of depreciation was 13% per year during those 7 years, how much was the worth when it was new? Give your answer to the nearest one thousand dollars.
- The value of homes in a neighborhood increase in value an average of 3% per year. What will a home purchased for $180,000 be worth in 25 years to the nearest one thousand dollars?
- The population of a community is decreasing at a rate of 2% per year. The current population is 152,000. How many people lived in the town 5 years ago?
- The value of a particular piece of land worth $40,000 is increasing at a rate of 1.5% per year. Assuming the rate of appreciation continues, how long will the owner need to wait to sell the land if he hopes to get $50,000 for it? Give your answer to the nearest year.
For problems 9-15, use the formula for compound interest: .
- If $12,000 is invested at 4% annual interest compounded monthly, how much will the investment be worth in 10 years? Give your answer to the nearest dollar.
- If $8,000 is invested at 5% annual interest compounded semiannually, how much will the investment be worth in 6 years? Give your answer to the nearest dollar.
- If $20,000 is invested at 6% annual interested compounded quarterly, how much will the investment be worth in 12 years. Give your answer to the nearest dollar.
- If $5,000 is invested at 8% annual interest compounded quarterly, how much will the investment be worth in 15 years? Give your answer to the nearest dollar.
- How much of an initial investment is required to insure an accumulated amount of at least $25,000 at the end of 8 years at an annual interest rate of 3.75% compounded monthly? Give your answer to the nearest one hundred dollars.
- How much of an initial investment is required to insure an accumulated amount of at least $10,000 at the end of 5 years at an annual interest rate of 5% compounded quarterly? Give your answer to the nearest one hundred dollars.
- Your initial investment of $20,000 doubles after 10 years. If the bank compounds interest quarterly, what is your interest rate?
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https://courses.lumenlearning.com/introchem/chapter/rate-determining-steps/
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math
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- Describe the relationship between the rate determining step and the rate law for chemical reactions
- Chemists often write chemical equations for reactions as a single step, which shows only a reaction’s net result. However, most chemical reactions occur over a series of elementary reactions. The reaction mechanism is the step-by-step process by which reactants actually become products.
- The overall reaction rate depends almost entirely on the rate of the slowest step. If the first step is the slowest, and the entire reaction must wait for it, then it is the rate-determining step.
- rate-determining stepThe slowest individual transformation in a reaction mechanism.
Chemists often write chemical equations for reactions as a single step that shows only the net result of a reaction. However, most chemical reactions occur over a series of elementary reactions. The complete sequence of these elementary steps is called a reaction mechanism. The reaction mechanism is the step-by-step process by which reactants actually become products. It is the “how” of the reaction, whereas the overall balanced equation shows only the “what” of the reaction. In kinetics, the rate of a reaction with several steps is determined by the slowest step, which is known as the rate-determining, or rate-limiting, step.
Rate Laws and the Rate-Determining Step
Take the following example of a gas phase reaction:
[latex]CO + NO_2 \rightarrow CO_2 + NO[/latex]
If this reaction occurred in a single step, its rate law would be:
[latex]r = k[NO_2][CO][/latex]
However, experiments show that the rate equation is:
[latex]r = k[NO_2]^2[/latex]
The fact that the experimentally-determined rate law does not match the rate law derived from the overall reaction equation suggests that the reaction occurs over multiple steps. Further, the experimental rate law is second-order, suggesting that the reaction rate is determined by a step in which two NO2molecules react, and therefore the CO molecule must enter at another, faster step. A possible mechanism that explains the rate equation is:
[latex]2\;NO_2 \rightarrow NO_3 + NO[/latex] (slow step, rate-determining)
[latex]NO_3 + CO \rightarrow NO_2 + CO_2[/latex] (fast step)
Since the first step is the slowest, and the entire reaction must wait for it, it is the rate-determining step. We can picture the rate-determining step to be like the narrowest point in an hourglass; it is the “bottleneck” point of the reaction that determines how quickly reactants can become products.
If the first step in a mechanism is rate-determining, it is easy to find the rate law for the overall expression from the mechanism. If the second or a later step is rate-determining, determining the rate law is slightly more complicated. We will explore how to write that rate law later.
Boundless vets and curates high-quality, openly licensed content from around the Internet. This particular resource used the following sources:
CC BY-SA 3.0.
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https://classroom.synonym.com/common-problems-students-mathematics-19834.html
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math
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Common Problems of Students in Mathematics
26 SEP 2017
Math requires deductive reasoning, and passive learners often struggle with this kind of active problem solving. Students with memory and attention problems also may struggle since both skills are necessary for mathematical aptitude. Other problems common to math students include computational weaknesses, difficulty in conceptualizing mathematical principles and language challenges in word problems.
1 Number Facts
Incomplete mastery of basic number facts, such as the multiplication tables, simple addition and subtraction, is a common problem for math students. Number facts are the building blocks for learning math and are necessary for understanding more complex concepts. For example, algebra requires students first to sort out basic equations before finding the value of the letter. In this equation, 20 + 3_a_ = 68, the student has to make a the subject, and then do simple division to find its value. So, 3_a_ = 68 – 20 (48), and a would be 48 divided by 3. If a student cannot recall simple multiplication or division, he will find himself being bogged down with that step before being able to answer the actual question. This may cost valuable time in an exam room or even during class.
2 Computational Weaknesses
Students might experience computational weaknesses in the course of their math assignments and exams. Examples of computational weaknesses include carrying the wrong number during multiplication or division, transposing the wrong number when writing down the final answer, writing numbers in the wrong column during long division or even misreading signs and symbols. Math teachers award marks for each question for applying the right formula, showing correct workings and coming up with the right answer. Students who commit computational errors lose marks on the workings and answers.
3 Learning Disabilities
Learning disabilities are a common source of difficulty in understanding mathematics. Students who suffer from dyscalculia, for example, generally have a problem with numbers and arithmetic. They usually have problems recognizing numbers and matching them with amounts, comparing numbers and mastering number relationships, comprehending sequences and even making accurate estimations. Such students might also have difficulties understanding math vocabulary and are unable to process word problems in mathematics.
Students need to be highly attentive during class and when completing assignments and exams to excel in mathematics. Students who fail to pay proper attention to detail and double-check their work before submission often score poorly. Memorizing instead of understanding mathematical principles also causes difficulties for students, especially when they are unable to remember the exact steps used to solve a problem. As a result, students who regularly practice answering math problems are better off than those who do not because they learn how to answer questions accurately and methodically.
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http://labman.phys.utk.edu/phys135core/laboratories/Lab%206.html
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math
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Energy conservation for an isolated system is a fundamental principle of
physics. Energy for an isolated system is always conserved. It may change
forms, but the total amount of energy in an isolated system is constant.
Energy can, however, be converted from one form to another form. Work is the conversion of one form of energy into another.
Energy comes in different forms, kinetic energy, potential energy, chemical
energy, thermal energy, etc. If an object has energy, it has the potential
to do work.
There are several forms of potential energy. Kinetic and potential energy are called mechanical energy or ordered energy. Thermal energy is disordered energy. Friction converts mechanical energy into disordered energy.
When no disordered energy is produced, then mechanical energy is conserved.
In this lab we will use an on-line simulation from the University of Colorado PhET group to track mechanical energy in a skate park, and you will analyze two video clips to track the mechanical energy of a bouncing ball.
Open a Microsoft Word document to keep a log of your experimental procedures, results and conclusions. This log will form the basis of your lab report. You should address all items in blue.
Use an on-line simulation from the University of Colorado PhET
group to track mechanical energy in a skate park.
Link to the simulation: http://phet.colorado.edu/en/simulation/energy-skate-park
(a) Explore the interface!
(b) Design your own frictionless track.
(c) Add friction to your track.
(d) Move the skater to a different planet or to free outer space.
The coefficient of restitution
Analyze two video clips. The clips shows bouncing balls. By measuring the maximum height a ball reaches after each bounce, you can determine the coefficient of restitution of the ball. For a review, click here.
Each ball starts with no kinetic energy and potential energy U = mgh1. As it contacts the floor, it has no potential energy but kinetic energy K1 = U1, or ½mv12 = mgh1. After the bounce, just as it breaks contact with the floor it has kinetic energy K2 = ½mv22 and no potential energy. When it reaches its maximum height after the bounce, it has no kinetic energy, but potential energy U2 = K2, or mgh2 = ½mv22. We therefore have
K2/K1 = U2/U1, or v22/v12 = h2/h1.
In the video clips you must find the highest point above the floor that the ball reaches after two successive bounces. You can do this by choosing to track the y-coordinate of the ball. Calibrate Y by clicking at the bottom and the top of the meter stick, and entering 1 m for the distance between calibration points. After you finish taking data, import your data into Excel and construct a graph of position versus time. You can read the maximum heights right off this graph by moving your cursor over the highest points. For example in the graph below the height after the first bounce is 1.022 m, after the second bounce it is 0.956 m, and after the third bounce it is 0.899 m.
To find the ratio of the speeds after successive bounces use v22/v12 = h2/h1. The ratio v2/v1 is the coefficient of restitution. (Since you have 3 bounces, you can find the ration for bounce 2 and 1 and the ratio for bounce 3 and 2. You can average, to get a more accurate result.)
To play each video clip or to step through it frame-by-frame click the "Begin" button. The "Video Analysis" web page will open. Choose the restitution_1.mp4 video clip to determine the coefficient of restitution of a super ball and the restitution_2.mp4 video clip to determine the coefficient of restitution of a golf ball.
Convert your log into a lab report.
Laboratory 6 Report
Save your Word document (your name_lab6.docx), go to Canvas, Assignments, Lab 6, and submit your document.
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CC-MAIN-2018-43
| 3,733 | 28 |
https://optovr.com/high-school-geometry-worksheets-mixed-math-problems-2-digit-1-division-games-fluency-introductory-algebra-free/
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math
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High School Geometry Worksheets Mixed Math Problems 2 Digit 1 Division Games Fluency Introductory Algebra Free
High School Geometry Worksheets Mixed Math Problems 2 Digit 1 Division Games Fluency Introductory Algebra Free.
Check out some or all of what found below mathplanet.com math planet offers courses in -algebra, algebra, algebra and geometry. they also offer. Below you can link to hundreds of middle school-level math worksheets throughout our website. absolute value.
Grade geometry worksheets free printable 3 life skills division questions remainders math easy dollar work high school. Grade regular high school mathematics circle geometry worksheets math lesson plan facts program adding subtracting decimals worksheet converting free. Volume pyramids puzzle worksheet geometry worksheets high school math word problems grade lessons free time drills fun educational. Grade geometry worksheets full high school math free sheets questions answers. Printable geometry worksheets helping math free high school. Rhyming worksheets distance learning free high school geometry math techniques addition subtraction fractions exercises grade printable. Challenging geometry worksheet printable high school worksheets site solve mathematics questions grade math test generator addition calendar activities mat papers free.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487637721.34/warc/CC-MAIN-20210618134943-20210618164943-00408.warc.gz
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| 1,326 | 4 |
https://mba.ind.in/guru-kashi-regional-centre-bathinda-punjab-m-a-punjabi
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math
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Question: Give me MA Punjabi 2nd Semester syllabus of Punjabi University Guru Kashi Regional Centre Bathinda.
Ans: As per your request I am providing you MA Punjabi 2nd Semester syllabus of Punjabi University Guru Kashi Regional Centre Bathinda which is following:
1. The Syndicate has approved the following guidelines, mode of testing and evaluation including
Continuous Internal Assessment of students :
(i) Terminal Evaluation : 80 %
(ii) Continuous Assessment : 20 %
(iii) Continuous Assessment may include written assignment, snap tests, participation in
discussions in the class, term papers, attendance etc.
For complete syllabus you can free download pdf file which I am attaching for you.
Patiala, Punjab, India
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s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371700247.99/warc/CC-MAIN-20200407085717-20200407120217-00498.warc.gz
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CC-MAIN-2020-16
| 721 | 10 |
https://henrisjewelry.com/personalization/5-acres-equals-how-many-miles.php
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math
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How many feet of fencing is required to fence in 5 acres It might me a mile long and feet wide and in this case the amount of fencing needed is 10, How many acres are in 1 mile? If there are 12 acres how many miles would that be,would that be even a mile? Hi,. Miles and acres measure entirely different. One square mile is equal to acres. To calculate how many acres there are in your area of land, simply multiply your square mile figure by.
how many acres in a mile
Often an acre of land is compared to a football field. In reality, an acre is equal to about 76% of a football field, when you consider both end zones. How much is 5 acres? How many? What size is it? How many in miles, feet, inches, yards, meters? What's the conversion?. 3 acres = miles, 3 miles = acres. 4 acres = miles, 4 miles = acres. 5 acres = miles, 5 miles = acres.
One mile equals 5, ft. multiply by 43, by 5 to get the area of the five acres you get now take the square root of that number. Assumption 1: The distance of a football and a yard is yards from end zone to end zone. Assumption 2: 43, square feet is an acre. The acre is a unit of land area used in the imperial and US customary systems. It is traditionally One acre equals 1⁄ () square mile, 4, square yards, 43, square In the international yard and pound agreement of the United States and five countries of the Commonwealth of Nations defined the .
Calculate acreage or measure land by seleting the area on a map or by entering dimensions in feet or meters. One acre is equal to square feet. Miles, miles² ( acres = 1 mile²) How many acres do you have?. Square miles (mi2) to acres (ac) converter and conversion table to find out how many acres in sq. miles. , , , 4, , , , , , , , , , 5, , , , , , , , 1 Acre is equal to square mile. Divide the number of acres by Each acres equals 1 square mile, so you need to determine how many times goes into the number.
how big is an acre visual
Square Miles · Acres. 0 mi², ac. 1 mi², ac. 2 mi², ac. 3 mi², ac. 4 mi², ac. 5 mi², ac. 6 mi², ac. 7 mi², How many square feet in an acre? Also find acre calculator and an acre conversion chart into miles, yards, meters, and acre can 1' X 43,'; Did you know that 1 square mile is equal to acres. 5 Acres = ' X ' ( rounded up). Enter the number of acres to convert into square miles. Easy acres to It is equal to acres or approximately square kilometers. Acres to 5, 1 acre. acres = 1 sq. mile. 1 sq. mile = 1 section. 36 sq. miles = 1 Twp. 6 miles Sw'4 SE 4. 5 ACRES s '% Nw'4. Sw'% SE '%. 5 ACRES. 2 va. 2 ACS ACS . An acre of rainforest contains up to 86 different species of tree, with the amphibians, birds, insects and mammals that depend on them. It costs just £ to. A square acre is feet on a side, so the perimeter of an acre is about How many minutes does it take the average person to walk one mile? How long does it take an average person to walk 5 kilometers in a hurry?. If you're converting from feet to acres (or back again), one acre equals 43, square feet. But there's another reason to use acres instead of square feet (or the square mile, if only because the square foot measurement is more intuitive to many people. 5 Scientific Things That Happen to Men When They Grow Beards. How much is inside an acre? As all farmers and real estate agents know, an acre is defined as an area one furlong long by 4 rods wide. An acre is standard A Scottish acre is equivalent to standard acres. The Irish measure is even. This conversion of 5, acres to square miles has been calculated by multiplying 5, acres by and the result is square miles. How many acres are in 1 mile? If there. There are many types of fence that are designed as the best use for 1/8 mile square. Requires 1 mile of fence to enclose. 1/8 mile. 5 ACRES. Deer & Wildlife.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145729.69/warc/CC-MAIN-20200222211056-20200223001056-00310.warc.gz
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CC-MAIN-2020-10
| 3,793 | 7 |
https://corecomputations.wordpress.com/2011/07/26/the-galton-watson-process-part-i/2/
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math
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2 Probability Generating Functions
For a random variable that has some mean and variance, what else is necessary to determine the complete probability mass function? It turns out that having a knowledge of all of the moments of a random variable allows us to determine the probability mass function completely. This is in fact how the definition of probability generating functions came about. They are important here in determining an analytical expression for the probability that a surname will become extinct after generations.
Probability generating functions, defined as , are an important topic in probability theory used to reduce the amount of work required to analyze a random variable with a particular distribution. For example, information such as the expected value can often be easily extracted for well-defined sequences of . The expected value is simply the value that is anticipated given many samplings of a particular situation. For example, the expected value for a fair 6-sided die is 3.5. This means that if you roll that die billions of times, sum all the values, and then divide by the number of rolls, you would get 3.5.
The probability generating function of a discrete random variable is given by a power series where the coefficients are determined by the probability function of that random variable. These coefficients are the sequence of probabilities in the probability function that a random variable is equal to . Namely, the probability generation function is
where is simply a parameter which allows the series to converge. For most cases this is when the absolute value of is less than or equal to one, so is often in the range from zero to one. Additionally you can think of as an indeterminate variable which gives some particular property which can be useful as a building block to determine solutions to more interesting problems. For example, it can be easily shown that .
To make this more concrete, consider a fair six-sided die being rolled. The die has a chance that any of the 6 numbers will be selected. In this case is the random variable determined by rolling the die. Thus we know that . In a similar fashion we also know that the probability is 0 since the die does not contain a side with the value zero. Thus the probability generating function is:
From here we can easily show that by plugging in yielding
which simply states that the probability is any value from 0 to is 100%. For the case of the fair die
It can also be shown that is equal to the probability that (i.e. ). This is derived by assuming is approaching zero. By plugging in a very small value of we know that is still equal to one, whereas , , are all approaching zero quite rapidly.
Probability generating functions are particularly useful when the probabilities (i.e. the coefficients in the power series, ) lead to a closed form. This is true of the Poisson distribution which will be used here.
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CC-MAIN-2018-26
| 2,920 | 10 |
https://en.wikipedia.org/wiki/Ordered_probit
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math
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|Part of a series on Statistics|
In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, fair, good, excellent). Similarly, the widely used logit method also has a counterpart ordered logit. Ordered probit, like ordered logit, is a particular method of ordinal regression.
For example, in clinical research, the effect a drug may have on a patient may be modeled with ordered probit regression. Independent variables may include the use or non-use of the drug as well as control variables such as age and details from medical history such as whether the patient suffers from high blood pressure, heart disease, etc. The dependent variable would be ranked from the following list: complete cure, relieve symptoms, no effect, deteriorate condition, death.
Suppose the underlying relationship to be characterized is
where is the exact but unobserved dependent variable (perhaps the exact level of improvement by the patient); is the vector of independent variables, and is the vector of regression coefficients which we wish to estimate. Further suppose that while we cannot observe , we instead can only observe the categories of response:
Then the ordered probit technique will use the observations on , which are a form of censored data on , to fit the parameter vector .
This section needs expansion. You can help by adding to it. (February 2017)
The model cannot be consistently estimated using ordinary least squares; it is usually estimated using maximum likelihood. For details on how the equation is estimated, see the article Ordinal regression.
- Becker, William E.; Kennedy, Peter E. (1992). "A Graphical Exposition of the Ordered Probit". Econometric Theory. 8 (1): 127–131. doi:10.1017/S0266466600010781.
|This statistics-related article is a stub. You can help Wikipedia by expanding it.|
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CC-MAIN-2018-13
| 1,992 | 10 |
http://atheism-analyzed.blogspot.com/2017/10/ability-to-solve-algebra-and-geometry.html
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math
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White privilege bolstered by teaching math, university professor saysIt's so hard to characterize such crap-thought as the stupidest ever, when tomorrow will produce even more ludicrous stupidity which will take the title away from today's ludicrous stupidity.
Professor Rochelle Gutierrez says the ability to solve algebra and geometry perpetuates white privilege.(University of Illinois)
A math education professor at the University of Illinois says the ability to solve geometry and algebra problems and teaching such subjects perpetuates so-called white privilege.
Rochelle Gutierrez laid out her views on the subject in an article for a newly published anthology for math educators titled, “Building Support for Scholarly Practices in Mathematics Methods.”
“School mathematics curricula emphasizing terms like Pythagorean Theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans," she says, according to Campus Reform.
She also says that addressing equity in mathematics education will come when teachers can understand and negotiate the politics outside the classroom.
“On many levels, mathematics itself operates as whiteness. Who gets credit for doing and developing mathematics, who is capable in mathematics, and who is seen as part of the mathematical community is generally viewed as white,” she writes.
Further, she says mathematics operates with unearned privilege in society, “just like whiteness.”
Beware of university "education"; students subjected to crap-thought might not survive it to become rational adults. Obviously Gutierrez didn't.
Further, observing such obviously false and irrational attacks from minorities serves only to make one wonder if rational western thought is indeed superior - and if rational western thought is also identity-designated "white", then it follows that the minority concept of "Whiteness" does, in fact, provide a superior view of actual reality, while the minority alternative (ignorance as a cultural value) cannot possibly provide any useful guidance for the minority.
The position of Gutierrez (no math or math history and therefore positing the superiority of cultural ignorance), is maximally irrational and is likely done in a fit of pique and certainly not in any intellectual context. That being the case, the reflection on the university is that of a converged SJW encampment rather than an open platform for intellectual progress.
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CC-MAIN-2018-34
| 2,461 | 11 |
https://icms.bg/news/page/2/
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math
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An integer partition of an integer number n is simply a decreasing sequence of integers whose sum is equal to n. Naturally, integer partitions and their theory are ubiquitous in mathematics. I will report on a link between an algebro-geometric invariant of singularities and the theory of integer partitions in the spirit of Ramanujan. The talk is aimed at a wide audience of mathematicians.
Michael R. Douglas received his PhD in Physics in 1988 under the supervision of John Schwarz, one of the developers and leading researchers in superstring theory.
Douglas is best known for his work in string theory, for the development of matrix models (the first nonperturbative formulations of string theory), for his work on Dirichlet branes and on noncommutative geometry in string theory, and for the development of the statistical approach to string phenomenology. He has influenced the developments of modern mathematics by finding interpretations of branes on the language of derived categories and introducing the theory of stability conditions for categories.
In the first part of the talk, I shall explore the consequences of distinguishing the foundations of meaning and the foundations of truth in mathematical statements, or imagination and rigor as motors of mathematical development. The foundations of meaning can be sought in our largely unconscious perception of the world, which modern cognitive science is exploring.
The event is jointly organized by the International Centre for Mathematical Sciences (ICMS-Sofia) at the Institute of Mathematics and Informatics in Sofia, and the Institute for the Mathematical Sciences of the Americas (IMSA) at the University of Miami. The conference will be held at the UM campus.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506479.32/warc/CC-MAIN-20230923030601-20230923060601-00125.warc.gz
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CC-MAIN-2023-40
| 1,730 | 5 |
https://publications.waset.org/2546/bifurcation-analysis-for-a-physiological-control-system-with-delay
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math
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Bifurcation Analysis for a Physiological Control System with Delay
Authors: Kejun Zhuang
In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057437Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1367
M.C. Mackey, L. Glass. Oscillation and chaos in physiological control system. Science, 197(1977), 287-289.
Xiaohua Ding, Wenxue Li. Local Hopf bifurcation and global existence of periodic solutions in a king of physiological system. Nonlinear Analysis: RWA, 8(2007), 1459-1471.
Junjie Wei, Dejun Fan. Hopf bifurcation analysis in a Mackey-Glass system. International Journal of Bifurcation and Chaos, 17(2007), 2149- 2157.
Weirui Zhao, Weidong Wang. Global stability of nonlinear blood model with time delayed feedback. Journal of Hubei Institute for Nationalities( Natural Science Edition), 21(2003), 4-9. (in Chinese)
Sanyi Tang, Yanni Xiao. Biological dynamical system for single population. Beijing: Science Press, 2008. (in Chinese)
Jianhong Wu. Symmetric functional differential equations and neural networks with memory. Transactions of the AMS, 350(1998), 4799-4838.
B.D. Hassard BD, N.D. Kazarinoff, Y.H. Wan. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press,1981.
Shigui Ruan, Junjie Wei. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyna. Cont. Disc. Impul. Syst. Series A: Math. Anal., 10(2003), 863-874.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304915.53/warc/CC-MAIN-20220126041016-20220126071016-00686.warc.gz
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CC-MAIN-2022-05
| 1,849 | 12 |
https://www.coursehero.com/file/3863/Full-Instructors-Manual/
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math
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This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Notes on the Text: Classroom Experience Chapter 1makes a start on three topics: functions in general, the sine and cosine in particular, and computing. Here are brief comments so you will know what is needed later. 1. finctions and graphs (essential): Section 1.1is a solid starting point for calculus. You may give it more than a day, especially if you introduce f (t + 2) and f (t) + 2 and f (2t) and 2 f (t). These notes offer ideas about other graphing activities. One purpose is to maintain the interest of those who have already taken calculus, without giving them an enormous advantage. My favorite is the forward-back function graphed on page 4. Section 1.2 goes on to other piecewise linear models like income tax -and says explicitly that "I hope you like them but you don't have to learn them." Any of these examples, especially the delta function mentioned briefly, can be passed over. It is Section 1.3 that compares average to instantaneous for y = z2. 2. Sines and cosines (these are optional in Chapter 1): My intention is to see trigonometry in use -for points on a circle as well as sides of a triangle. Many classes will not spend substantial time on the review, but it must be available. The figure on page 31 leads neatly to cos(s -t). Section 2.4 computes derivatives of sin x and cos z in the normal way from 2. The limits of and 9 are fully developed there. But students may understand these functions better (and also the motion described by x = cost, y = sin t) by following a point on a circle. That is the outstanding example of a parameter. 3. Computing in calculus (optional): The computing section is placed in a way that allows you to discuss it or not. This topic is especially dependent on the local situation. (M.I.T. does not do much computing in the first year, and does nothing with graphing calculators.) But calculators are so convenient that we will see them more and more. They have the advantage of requiring less faculty time, as well as being personal and portable and not too expensive. The valuable thing is to see graphs (better than numbers). The example of 3= versus zs is quite good -those graphs are surprisingly close for 2.2 < z < 3.2. It is a challenge to find their intersection. It is a real challenge to find the only value of b for which bz never goes below zb for positive z. The main point is to see how this happens -the graphs of ez and ze are tangent at z = e. In Section 6.2 we know the derivatives and verify eZ 2 ze. Computing needs to be separate from the stream of ideas that launch calculus in Chapter 2. '1000 Points of Lightn is purely for entertainment. See the College Mathematics Journal of November 1990, and a forthcoming American Mathematical Monthly paper by Richert....
View Full Document
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501174154.34/warc/CC-MAIN-20170219104614-00246-ip-10-171-10-108.ec2.internal.warc.gz
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| 2,961 | 4 |
http://www.google.com/patents/US7912671?dq=5636223
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math
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US 7912671 B2
The present invention relates to a method for determining the coordinates of an arbitrarily shaped pattern in a deflector system. The method basically comprises the steps of: moving the pattern in a first direction (X), calculating the position of the edge of the pattern by counting the number of micro sweeps, performed in a perpendicular direction (Y), until the edge is detected, and determining the coordinates by relating the number of counted micro sweeps to the speed of the movement of the pattern. The invention also relates to software implementing the method.
1. A method for determining coordinates of an arbitrarily shaped pattern on a surface in a deflector system, including:
a) selecting a reference clock signal that defines a movement in a first direction (X),
b) providing a micro sweep that repeatedly scans the surface in a second direction (Y), perpendicular to the first direction (X)
c) selecting a measurement clock signal that is related to the signal used to start each micro sweep in the second direction (Y),
d) adjusting the speed of the movement in the first direction (X) to determine the distance between the start of each micro sweep,
e) performing a first run that include the steps of:
e1) starting a first micro sweep at a starting position,
e2) detecting at least one edge of the arbitrarily shaped pattern when the pattern is moved in the first direction (X) relative the deflector system,
e3) generating at least one event if the edge of the pattern is detected, and
e4) counting using a counter the number of micro sweeps performed until each event is generated, and
f) calculating a coordinate of the edge, for each event, in the first direction (X) using the number of performed micro sweeps
wherein more than one run as defined in step e) is performed, for each run the starting position in step e1) is pseudo randomly selected, thereby generating pseudo randomly distributed micro sweeps between each run.
2. The method according to
3. The method according to
4. The method according to
5. The method according to
6. The method according to
7. The method according to
8. The method according to
9. Software fixed in a non-transitory computer-readable storage medium, adapted to be used in a deflector system for determining the coordinates of an arbitrarily shaped pattern in a deflector system, the software further adapted to carry out the method of
10. A method for determining coordinates of an arbitrarily shaped pattern in a deflector system, including:
moving the pattern in a first direction (X), calculating the position of the edge of the pattern by counting with a counter the number of micro sweeps, performed in a perpendicular direction (Y), until the edge is detected, and determining the coordinates by relating the number of counted micro sweeps to the speed of the movement of the pattern:
wherein the pattern is scanned several times and an off-set in the first direction (X) for the first micro sweep is pseudo randomly selected for each run.
11. The method according to
12. The method according to
13. The method according to
14. Software fixed in a non-transitory computer-readable storage medium, adapted to be used in a deflector system for determining the coordinates of an arbitrarily shaped pattern in a deflector system, the software further adapted to carry out the method of
The present invention relates to a method for determining the coordinates of an arbitrarily shaped pattern on a surface in a deflector system, as defined in claim 1 and 10. The invention also relates to software implementing the method for determining the coordinates of an arbitrarily shaped pattern on a surface in a deflector system, as defined in claim 14.
The method used for measuring time in a deflector system has been used many years. Almost no modifications in the algorithm have been done so far. Only the pattern used for different kinds of calibrations has been modified during the years. Today we have an experimental verified repeatability of the method in the range of 10-15 nm over a surface of 800×800 mm. The 10-15 nm means here the measurement overlay.
One drawback of the method used is that we so far only can measure in the same direction as the micro sweep. In order to measure an X-coordinate we therefore must use special patterns containing 45-degree bars.
The method according to prior art is briefly described, since it is important to understand the present invention.
It is difficult to measure time with high accuracy. If, for example, you want to measure a pulse with the resolution of 1 nanosecond (ns) you need a measurement clock with the frequency of 1 GHz if classical frequency measurement methods are used. In the described prior art system, there is no need to measure a single shot of a pulse. The use a scanning beam while measuring will get several one-dimensional images of a bar or several bars, as an example. Only the “average” position of an edge or the CD of a bar is interesting. The measurement system will only give an average result together with its sigma. It is important to remember that the measurement system is good enough if this sigma is lower that the natural noise in the system. This natural noise can be summarized to be laser noise, electronically noise and mechanical noise. The noise from the measurement system itself can be calculated theoretically or verified in practice with a known reference signal. It is also possible to get a figure of the measurement system noise by simulation. The measurement of the position of the bar or the CD will therefore contain the error:
When we measure time we use a so-called random phase method. What this means is that the measurement unit it-self is completely un-correlated in phase to the signal we want to measure. Due to the fact that the signal phase is random relative the measurement clock phase we can use a measurement clock frequency that is much lower and use an “averaging” effect instead to achieve the accuracy.
Let us call the period time of the measurement clock tm. Since the input signal is a result from the micro sweep we also know exactly the relationship between the pixel clock period in time and what that corresponds to in nanometers. Here we introduce tp for the pixel clock period in nanoseconds. We also call the pixel clock period in nanometers for pp. The scaling expression can therefore be expressed as:
In the following some realistic numbers are introduced.
This results in that the pm=291.86 nm.
If we now count measurement clock ticks by resetting a counter by the reference signal we see that we only will count 8 or 9 ticks. No other count is possible in this example. The edge position relative the phase of the measurement clock will in this way be rectangular distributed inside tm. The average position can therefore be calculated just by adding counts from several measurements together and divide this number with number of measurements. In this example we get (8+8+8+8+9+9)/6=8.33 counts as an average value. So an estimation of the position of the edge can be calculated to be:
Now it is not enough just to use 6 measurements as in this example. Normally you use several thousands of measurements. (In the detailed description, the three sigma of the average value is described from a theoretical point of view.)
An object with the present invention is to provide a method for determining coordinates, especially in two dimensions, in a deflector system using any kind of pattern.
A solution is achieved in the features as defined in claim 1 and 10.
Another object with the present invention is also to provide software for performing the method, which is provided in the features defined in claim 14.
An advantage with the present invention is that it is possible to generate an image of the pattern without using any other detection method than the one we already are using today, since the present invention is similar to the prior art method, except that it is 90 degrees rotated.
Another advantage is that no new hardware is needed since the present invention is implemented in software.
So far we only have used this method to measure along the micro sweep i.e. in one dimension. It is though possible to extend the method to measure in two dimensions. When we do this we actually are generating images of the pattern we measure.
When we talk about images we normally see this as a set of pixels. (Each pixel has a certain “gray-level” that describes the intensity of the pixel).
When handling CCD images each pixel is fixed in position in a certain raster (or grid). When analyzing a CCD image for finding the position of an edge both information of the pixel's location and gray-level must be used. Different straightforward methods may be used for estimating an edge position in the image. The accuracy of the position estimation depends in the calibration of the CCD array i.e. where the pixels are located in the array, how sensible they are for light and how well we can place the image on the array without any distortions. Light distribution over the CCD and different kinds of optical distortions will contribute to the error of the position estimation. A lot of these errors can be overcome if we calibrate the measurement system against a known reference.
When using the method according to the invention we also refer to pixels. But our pixels are not fixed in location in a certain grid. If we make a “snap shot” of the pattern by just measuring it once we will get information with a quite rough resolution (or accuracy). It is important to realize that the only information we are using is the pixels location. We do not use any gray-level information at all. Of course it is possible also to use gray-level information by recording the pattern using different “trig” levels in the hardware. This is what we do if we are interested in beam-shapes as in focus measurements. Here we only are interested in measuring the location of one or several bars so we can calculate center of gravity and CD.
When measuring registration and CD we never are interested in the exact location of one single pixel. Normally we only are interested in the average of several pixels location. In a CD measurement we use cursors to define number of pixels to be used in this average value. Also in the center of gravity estimation we use cursors to “even out” noise from the edge. This noise might be roughness from the pattern itself or noise in the measurement system. This is the same when using a CCD image as input.
In this suggested method we use the micro sweep itself as our light source (or ruler). It is hard to find a more accurate ruler than this. We already have methods to calibrate this ruler both in power and linearity very accurately.
In order to demonstrate the actual grid we are using and how the pixels are distributed in this grid we refer to
Here we have enlarged a part of the image 20. This “hard copy” of the image shows clearly where we have found events. The method to “sharpen” up this image will be presented below. The scale in this image is correct in that sense that one pixel is 316 nm in X-direction (vertical scale) and 250 nm in Y-direction (horizontal scale).
Estimation of the X-Coordinate
As has been described in the background to the invention, there exists a very accurate method to estimate the Y-coordinate of an event. The micro sweep is used as a ruler and a measuring clock that is random in phase relative the ruler. The measurement clock will give us a rough resolution of tm (292 nm) in a single shot measurement. If we use several measurements and build us an average value we will get a much higher resolution (see below). Actually we can choose the accuracy just be selecting number of measurements and the length of the cursor to be used. So far this is true for the estimation of the Y-coordinate. The problem is how do we do to estimate the X-coordinate?
Obviously it is difficult to believe that it is possible to get an X-value out from data retrieved by a scanning a beam in Y-direction. The big step forwards is that it actually is possible to retrieve this information almost with the same accuracy as the Y-coordinate. But to get it we must introduce another signal (that actually already is used in the system), the lambda/2 X-signal.
In the prior art, when measuring a 45-degree bar of a pattern as in the star-mark case, we use the X-lambda/2 signal as “marks” in X-direction to define an X-cursor. Inside the cursor we also record the lambda/2 signal simultaneously when we count the measurement clocks. But since we measure on a 45-degree bar we actually are using only Y-information to get the X-coordinate. In combination with the lambda/2 information we can calculate the X-coordinate with a very high accuracy. The drawback of this method is of course that we are not able to measure on any kind of pattern. Especially we cannot measure on a bar that is parallel with the ruler. If we extend the method we already are using in Y-direction a little bit, we will soon realize that the problem to solve is exactly the same as we have in Y-direction but rotated 90 degrees. If we change our measurement clock to our reference signal (here the SOS—Start Of Sweep) and use the lambda/2 signal as reference instead we have rotated the problem 90 degrees.
When doing this “rotation” of the problem we need to re-calculate our parameters. In Y-direction our resolution was one measurement clock that corresponded to 292 nm. During one run over the pattern of interest we scanned it with a frequency of approximately 30 kHz. The question now is how far we move in X-direction between the scans. If we set the speed as low as possible we will retrieve about 8-10 scans of the pattern in each lambda/2 period. Since one lambda/2 period corresponds to 316 nm we have a resolution in the range of 30-40 nm in X-direction. This is because we scan the pattern with the frequency of 30 kHz during the movement in X-direction. Now when we use the lambda/2 signal as the reference we therefore have a “clock” with a spatial resolution of 30-40 nm in X-direction. This is significantly higher than the resolution in Y-direction. But, and this is important, we will not get as many samples in X-direction as in Y because of the movement in X. This fact is illustrated in
The situation in X-direction is shown in
This is natural since the resolution is lower than the CD of the bar to be measured. In order to measure the bar with higher resolution you need to do several runs over the pattern with random phase.
A comparison of the situation in Y-direction is illustrated in
If we separate the problem we can say that in one scan we can resolve a pixel with the resolution 40 nm in X-direction and 290 nm in Y-direction.
So far we have described the main principle in Y and X direction. We have rotated the problem in Y 90 degrees to X. In Y-direction we have two processes that are random relative each other, the measurement clock and the SOS (or any correlated signal to SOS). In X-direction the measurement clock corresponds to the SOS signal and the reference is the lambda/2 signal. Also these signals (or processes) are un-correlated. We have different resolution in the different directions but it turns out that the accuracy is almost the same.
Here we get 2.3*316/8=92.2 nm. This is the local coordinate 64 for the edge of the bar 60 in the first interval. The local resolution depends on the speed, i.e. total number of SOS in the interval. If we can run the system more slowly this resolution will be better. But you will also gain resolution by scanning the bar in several runs. Below, the accuracy of the average position estimation is discussed.
As can be seen from above discussion we actually can calculate the X-coordinate from data retrieved from a scanning sweep in Y-direction. What we do is using the fact that we know exactly where we are in X-direction every time we pass an interval border 65. Inside an interval we only must assume that the speed is constant. This of course does not mean that the speed needs to be constant over all intervals. In practice we run several times across the pattern in both directions and record the Y-events and lambda/2 positions simultaneously. We therefore have the possibility to calculate the local speed with high accuracy by using information from all the runs.
The method described above is suitable to be used in either a laser lithography system or an e-beam lithography system.
What we really are after is not the exact position of an individual pixel. The discussion so far has lead us to that the position accuracy of a single pixel depends of how many times we have recorded the pattern and the resolution we use during the recording. If we scan the pattern a certain number of times we can “select” the accuracy we want before hand. This can be done since we have full control over the measurement process. When we do this “accuracy” selection we also must consider our cursors. As have been mentioned before a cursor is just another way to define number of pixels to use for calculating an average value.
There are many ways to apply a filter to this kind of data. An obvious way might be to fit a line using standard regression techniques. These techniques works but does not generates the optimum result in this case. The main reason is that the pixel data we handle does not describe a Gaussian distribution. We have a more or less rectangular distribution to deal with. When using a regression technique we therefore will “over weight” pixels close to the border of a lambda/2 interval or the tm interval in the Y-case. A much better method to use is the more simple “area” estimation method. This method is also more accurate for this kind of data compared to the regression technique. To fit a line to an edge you just divide the database in two half's. In this case the data you have is x,y coordinates. You calculate the average value of all coordinates in each half. This way you will get two x,y points. These two points describes the line to be used in further calculations.
Some Real Results
The small square 71 in the image 70 is enlarged in
We now will apply cursors to the data in order to measure the CD and center of gravity position of the cross. The center of gravity of the cross is measured using four cursor pairs. These cursors are shown in
Each line 90, 91 of the cursors is calculated based on the data from the edge in the cross. The line is calculated by using the simple “area” estimation method described above.
The reason for the mixture of white and black pixels along the Y-bar in
In below table the center of gravity and the CD is presented for the cursors. Below table shows the result of the four
The center position of the mark (Xcenter,Ycenter) may be calculated as the average value of the Y-cursor center values (Xcenter) and the X-cursor values (Ycenter).
Second Order Effects.
So far we have discussed the main principles of the algorithm. We will now discuss two vital corrections that must be done on the data that are second order effects from the method.
First we need to correct for an eventual azimuth angle in the data. If we use a writer (as done in this case) we have a pre-misalignment between the X-movement direction and the ruler. This angle α can be expressed as:
Where vx is the exposure speed of the system and vy is the speed of the micro sweep.
This angle calculation can be reduced to the expression:
Where the Sos_rate is total number of pixel clock periods between two SOS. (See below for a more thorough explanation).
Another effect that must be taken care of is the effect of the X-movement during a measurement. Also here we will introduce an “azimuth” error. Even if we run the same number of positive strokes and negative strokes we will not cancel out this error completely. The reason is that this error has to do with the difference in speed for a positive and negative stroke. For a stroke in one direction we will therefore get an error that may be expressed as an angle (β).
This angle can be expressed as:
If we put in some realistic numbers, xInc=316 nm, Speed=8 Sos/interval, nbeams=9 beams and yPix=250 nm, we get:
If we calculate the error generated by α on a distance of 100 um we will get:
alpha_error=100*9/1435=0.6272 μm. (The Sos_rate is taken from TFT3 system parameters). Since the β=0.0175*α we can calculate the error generated by the fact that we are moving during measurement to be:
0.0175*627.2 [nm]=11 nm. This is a quite large error that cannot be neglected. This error will change sign depending of the direction of the measurement. If we measure during the same number of positive and negative strokes and the local speed is the same for both strokes this error will be cancelled out completely. In practice this is not the case. We will therefore get a small net-error due to this fact.
In the graph shown in
Random Phase Measurement
When using a random clock for measurement we shall see this as a statistical problem. In
We re-write the time tp as:
Where k is an integer number and d is the decimal part of tm. If we do this d will be a number in the interval [0, 1[. It will be shown later why this is a reasonable expression to use for tp.
We now introduce the measurement clock with a phase that is random relative the reference signal. We also introduce a counter that counts the positive going flanks of this clock. If we reset this counter with the reference signal we realize that we sometimes will count k flanks and some times k+1 flanks. No other counts are possible. We introduce the discrete stochastic variable K that in this way can get two values k and k+1.
We now look in
What we now must do is to calculate to probability for the sample point k and k+1. To do this we must use the frequency function shown in
So the probability that we get the sample point k+1 out from K will be d and the probability that we get the sample point k out of K is (1−d).
When we add the clock counts for each measurement and then divide with n we actually is estimating the average value for the stochastic variable K.
The estimated mean value may be expressed as:
Here we have only two possible sample points so we get:
So when we rescale this result to nanoseconds we get
This result proves that building the average value of the counter tics and scale this value with tm will give us the time we are after.
To calculate the accuracy of the average value E(K) we need to find the variance of K.
The variance of a distribution may be expressed as:
This can be re-written as:
The variance function is actually very interesting. We see that if d=0, that means that we have no decimal part V(K)=0 we also see that if d is very close to 1, V(K)=0. Actually the variance has its maximum when d=0.5. In this case the variance is 0.25. The sigma will therefore be 0.5 as its maximum.
To interpret this you may think as follows. If d is 0 we always will count k ticks from the counter. Here we also assume that we count one tick if the positive going edge from the clock coincides with the reference signal. Since we always is counting k ticks independently of the phase of the measurement clock the spread also from the average value will be zero since variance is a measurement of the squared distance from the estimated average value. (Please refer to equation 1 above).
What is then the physical meaning of this?
Let us first make a practical example.
If we measure a signal with the decimal part 0.01 and k=2 the probability of counting a 3 in a measurement will be 0.01. This probability is the same for each measurement. Now if we calculate the average of 100 measurements we will probably add 99 samples of 2 and one sample of 3 (Case 1). But it is also possible that we add 100 samples of 2 and no samples of 3 (Case 2). The error we actually have in the average value is then:
So after 100 measurements in case 1 we will get:
There is another very interesting way to see the physical conclusion of the case when d=0.
Assume that we want to measure a signal that is exactly k*tm. In this case the decimal part is zero. Now if we add counter ticks we must always count k ticks. Otherwise, and this is important, we should never get the correct average that is k in this case. In other words we cannot ever count k+1 ticks. If this would be the case the average we calculate would not be k. For this reasons the variance must be zero. Please note that only two numbers can generally be counted, k and k+1. So the value k−1 can never be counted. So in other words a count that is k+1 cannot be compensated by a value k−1 so we get the correct average anyway.
Since we do not know tp beforehand we should use the worst-case scenario when we estimate the error. In other words we shall say that the error due to the method is:
This is as shown above the maximum of the function d*(1−d). If we want to use a symmetrical error instead we can express the method result as:
The error in the method will go down if we use a large number of measurements. We can express the error as:
This expression can be scaled to nanometers as:
The angle alpha (α) may be expressed as atan (vx/vy). If we calculate this angle we get:
The sos_time may be expressed as N*pixel_clock_time. N is here the total number of pixels between two start of sweeps. Finally we therefore can express the angle alpha (α) as:
Please note that this angle is a constant “compensation” that preferably is removed from the database.
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CC-MAIN-2015-22
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http://speech.ipfw.edu/508/Theories.html
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math
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Questions to Guide Your Readings of Theories
Reading 46 Interpersonal Deception Theory
1. According to this theory, what are three things you could do to become a better lie detector? Any risks in doing these three things?
Reading 52 Accommodation Nonverbally (CAT)
1. What is the message sent by intentional convergence? divergence?
2. Why do people not like or appreciate complete convergence by others?
Reading 55 Converging on the Phenomenon of Interpersonal Adaptation: Interaction Adaptation Theory (IAT)
1. What are the key ideas in IAT?
2. How does IAT differ from CAT?
Reading 53 Expectancy Violations Theory (EVT)
1. Explain the key concepts of EVT: expectancies, expectancy violation, violation valence, communicator reward.
2. Why does a positive violation produce a more favorable outcome than confirming expectations?
Research Article (in Blackboard): When online meets offline: An expectancy violations theory perspective on modality switching
This study uses three theories:
1) Social information processing theory (SIP) which, in a nutshell, states that people can become as close (relationally) online as offline, given enough time. It also uses the concept of a hyperpersonal perspective which indicates that CMC relationship partners may become more intimate faster than FtF partners. (See Griffin text website for quick overview of this theory);
2) Uncertainty reduction (UCR) theory which, with 8 axioms and 28 theorems, says that, in general, the more uncertainty about a partner is reduced, the more liking will occur (more information on Griffin text website)
3) Expectancy Violation theory - which you just read :).
Read the article (feel free to skip the results sections :), be prepared to discuss:
1. Why do the researchers think that the longer two people interact via CMC, the less likely they are to feel their expectations are met when they meet in person; what is the explanatory process for the violation of expectations (consider SIP and UCR)?
3. What did they do to these their hypotheses? What were the results?
2. Why do the researchers think that if two people interact for a short time via CMC, they are likely to have their expectations met when they meet FtF; what is the explanation process for th confirmation of expectations (consider SIP and UCR)?
4. What limitations might have affected their results or the generalizability of their findings?
Reading 54 Building and Sustaining Personal Relationships: A Cognitive Valence Explanation (CVT)
1. Give a couple of examples of immediacy behaviors.
2. What are the key ideas in CVT?
3. How does CVT differ from EVT?
1. What are the key similarities/overlaps in these five theories?
2. Do we need all five? If not, how would you combine, delete etc. to reduce the number of theories and still keep the important theoretical ideas?
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CC-MAIN-2019-13
| 2,822 | 28 |
https://androidforums.com/threads/hi.211066/
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math
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Hi y'all! I'm new to the forums but have had my Android for a little over a month. I get really frustrated with what I don't know how to do. My immediate request is is it possible to save a picture that was sent by text message? I cannot seem to figure it out. Any help would be greatly appreciated. Thanks!
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CC-MAIN-2022-21
| 307 | 1 |
https://links.apksource.net/La0Gm?lang=en
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math
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In the world of physics, of course we know many laws that are made or found to be the basis of an action or reaction in physics.
Here is a list of physical laws.
1. Archimedes’ Law, +250 BC.
If an object is immersed in a liquid, it will get an upward pressure equal to the weight of the liquid pressed by the object.
2. Avogadro’s Law, 1811.
If two (or more) gases are equal in volume, then the gases are the same number of molecules each, as long as the temperature and pressure are the same.
3. Bernouilli’s Law, 1738.
For liquids, which cannot be compressed and which flow in a stationary manner, the amount of motion energy, place energy and pressure energy is constant.
4. Boyle’s Law, 1662.
If a quantity of an ideal gas (i.e. quantity by weight) has a constant temperature, then also the product of volume and pressure are constant numbers.
5. Boyle-Gay Lussac’s Law, 1802.
For a quantity of an ideal gas (ie quantity by weight) the product of the volume and the pressure divided by the absolute temperature is constant.
6. Coulomb’s Law, 1785.
- 1. The force applied by two magnetic poles to one another is proportional to the barrel with the strong mechanism of the poles and is proportional to the square of the distance between the two poles.
- The force applied by two objects (each of which is electrically charged), one to the other, is proportional to the barrel of the electric charge of these objects and is proportional to the square of the distance between the two objects.
7. Dalton’s Law, 1802.
Pressure and a mixture consisting of several types of gases (which do not react chemically with each other) are equal to the amount of pressures of each gas, he explained, the pressure of each of these gases, if he each was alone in the mixture chamber just now.
8. Dulong and Petit Law, 1819.
Calories from solids are about 6 calories per grammolecule.
9. Galilei Laws (swing laws), 1596.
- Swing tempo does not depend on the magnitude of the application (swing distance), provided the amplitude is not too large.
- Swing tempo does not depend on the weight of the swing swing.
- Swing tempos are proportional to the barrel with roots of the length of the pendulum swing.
- Tempo swing is proportional to the root of the acceleration caused by gravity.
10. Kirchhoff’s Laws, 1875.
- 1. If the various electric currents coincide at a point, then the algebraic sum of the strength of these currents is 0 at the point of reference earlier.
- In a closed circular electric current the following equation applies: The amount of algebra from hash times – the product of the current strength and resistance in each part (of the circle) is equal to the amount of algebra from its electromotive forces (GGL – electromotor force) .
11. Lenz’s Law, 1878.
If an electric conductor is driven in a magnet field, the induced electric current is directed so that the electric conductor motion that causes the induction is blocked by it.
12. Newton’s Law, 1687.
Two objects attract each other with a force that is proportional to the masses of the masses of the two objects and directly propotional to square of the distace between the objects as well.
13. Ohm’s Law, 1825.
If an electric current passes through a conductor, then the strength of the current is proportional to the electric voltage between the two ends of the conductor.
14. Pascal’s Law, 1658.
If a liquid is subjected to pressure, then that pressure will propagate in all directions by not increasing or decreasing its strength.
15. Snellius Law, 1621.
- 1. If a ray of light passes through the boundary of two types of liquid, then the original line of the ray is the line after the light has refracted and the normal line is at the bias point, all three lines are located in one plane.
- The ratio between the sines of the entry angle and the bias angle is constant.
16. Stefan-Boltzamann Law, 1898.
If a black body emits heat, the intensity of the radiant heat is proportional to the square of the absolute temperature.
17. Wiedemann-Franz Law, 1853.
For all kinds of pure metal is the ratio between the specific conductor of a motor and the specific electric conductivity of a constant number, if the temperature is the same.
These are some of the laws or propositions contained in physics that are used in each of our daily activities or in the industrial world today.
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| 4,369 | 43 |
http://aga-recrutement.xooit.fr/t363-Matlab-R2013b-License-File-107.htm
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math
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Where are the license files for MATLAB located? - MATLAB . Where are the license files for MATLAB located?.
Enhancements to Network License Management - MathWorks MathWorks License Manager Changes .. latest license manager, you cannot use R2013b or later .. files different from earlier versions? MATLAB Release 2010b .
How do I download MATLAB R2013b and earlier? - MATLAB . How do I download MATLAB R2013b and .. it is no longer possible to manually download the MATLAB installation files.. MATLAB is now downloaded .
How can I reactivate MATLAB Student Versions between . To re-run activation for MATLAB versions between R2008b and R2013b, you will need to delete your current license file, remove the MATLAB activation folder, then re .
Install Matlab R2013b Stand Alone License - Install Matlab R2013b Stand Alone License .. the File Installation Key and License File by going to .. to the matlab command, install product files in a .
license file for 2013b - MATLAB Answers - MATLAB Central license file for 2013b.
key of matlab R2013b - MATLAB Answers - MATLAB Central key of matlab R2013b.. .. MATLAB Answers; File Exchange; .. you mean every one used matlab must buy license from mathwork.com only to be legal,if I buy matlab .
matlab license file Install License Manager Using a File Installation Key; .. Install License Manager Using a File .. Starting with R2013b, network License Files have a new format .
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741578.24/warc/CC-MAIN-20181114020650-20181114042650-00219.warc.gz
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CC-MAIN-2018-47
| 1,418 | 8 |
http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-3-Sol.html
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math
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SKKU-Calculus-Sec-15-3 Independence of the Path, SGLee+오교혁
15.3 Independence of the Path by SGLee, HSKim, 오교혁
1-6. Determine whether or not the vector field is conservative. If it is conservative, find a potential of .
Not conservative, since curl.
Since, curl , is conservative.
Taking partial derivative of with respect to , we get . Hence from (1) we get
Now taking partial derivative of with respect to we get . Hence from (3) we get
, a constant. Therefore, .
7. Show that the vector field is not conservative.
Since curl, is not conservative.
8. Determine whether the force field is a conservative field.
* 위의 명령어로 표현돤 결과는 vector 로 표현되서 보기 편하다.
Ans: , hence is not conservative field.
9. a. Prove that is a conservative field.
b. Find its scalar potential .
c. Also find the work done in moving an object in this field from to .
Scalar potential .
10. Find the total work done in moving a particle by a force field
along the curve form to .
Plenary Speaker at AMC 2013, Bexco, Korea
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| 1,044 | 20 |
https://indico.math.cnrs.fr/event/4455/?print=1
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math
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Minkowski space of dimension 2+1 is the Lorentzian analogue of Euclidean 3-space. It is well-known that there exists an isometric embedding of the hyperbolic plane in Minkowski space, which is the analogue of the embedding of the round sphere in Euclidean space. However, differently from the Euclidean case, the embedding of the hyperbolic plane is not unique up to global isometries. In this talk I will discuss several results on the classification of these embeddings, and explain how this problem is related to Monge-Ampère equations, harmonic maps, and Teichmüller theory. This is joint work with Francesco Bonsante and Peter Smillie.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473558.16/warc/CC-MAIN-20240221202132-20240221232132-00265.warc.gz
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CC-MAIN-2024-10
| 642 | 1 |
https://fullhomework.com/downloads/multiple-choice-answers-214/
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math
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1. Which of the following is a true statement about a tangent and a radius?
A. A tangent and a radius in a cylinder form two legs of a right triangle with the cylinder’s altitude serving as the hypotenuse.
B. A tangent and a radius of a hexagon are always equal lengths.
C. A tangent and a radius intersect at the foci of an ellipse.
D. A tangent and a radius of a circle meet to form a 90° angle.
2. The sides of an angle inscribed in a circle are
A. a diameter and a tangent.
B. two chords.
C. two radii.
D. a tangent and a radius.
3. What is the area of a right triangle with a hypotenuse measuring 5 inches and a base measuring 4 inches?
A. 12 in2
B. 7.5 in2 2
C. 6 in
D. 10 in2
4. What is the altitude of a rhombus if its area is 50 square meters and the length on one side is 12.5 meters?
A. 7.5 m
B. 10 m
C. 4 m
D. 12.5 m
5. Which one of the following geometric forms is a curved surface?
A. Side of a cone
B. Base of a prism
C. Base of a cylinder
D. Side of a pyramid
6. What is the total area of a right rectangular prism with a height of 8 feet, a width of 10 feet, and a thickness of 12 feet?
A. 478 ft2
B. 592 ft2
C. 824 ft2
D. 950 ft2
7. What is the total area of a rectangular prism with a height of 10 feet, a width of 6 feet, and a thickness of 4 feet?
A. 248 ft2
B. 592 ft2
C. 240 ft2
D. 950 ft2
8. If the diameter of sphere is reduced by half, its surface becomes
A. half the original surface.
B. double the original surface.
C. four times the original surface.
D. one-quarter the original surface.
9. What is the circumference of a circle with a radius of 3 meters?
A. 3.14 m
B. 9.42 m
C. 18.85 m
D. 6.00 m
10. A triangle that contains angles of 27°, 90°, and 63° is a(n) _______ triangle.
11. What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
A. 560 in3
B. 700 in3
C. 420 in3
D. 750 in3
12. A monument is made in the form of a right pyramid with a regular hexagon as a base. Each base side is 5 meters and the slant height is 30 meters. If only the sides (and not the base) of the monument is to be covered by metal, how many square meters of metal are needed to cover the sides of the pyramid?
A. 150 m2
B. 450 m2
C. 300 m2
D. 75 m2
13. A triangle that contains angles of 35°, 90°, and 55° is a(n) _______ triangle.
14. Which one of the following statements about quadrilaterals is true?>/i>
A. A quadrilateral with a right angle is a rhombus.
B. A quadrilateral with two pairs of parallel sides is a trapezoid.
C. A parallelogram with a right angle is a rectangle.
D. A quadrilateral with only one set of parallel sides is a square.
15. The supplement of an angle of 72° is an angle measuring
16. If the diameter of a sphere is doubled, its surface becomes
A. three times the original surface.
B. four times the original surface.
C. eight times the original surface.
D. double the original surface.
17. If a decorative sign in the form of a circle has a diameter of 10 feet, what it the area of the sign, to the nearest square foot?
A. 157 ft2
B. 31 ft2
C. 16 ft2
D. 79 ft2
18. A monument in the form of a marble cylinder has a circular base with a radius of 1.5 meters. The altitude of the monument is 3.5 meters. How many cubic meters of marble does this monument contain?
A. 24.74 m3
B. 6.19 m3
C. 21.21 m3
D. 7.07 m3
19. If a triangle has an angle of 45° and an angle of 100°, what is the third angle?
20. What is the altitude of a rhombus if its area is 10 square meters and the length on one side is 2.5 meters?
A. 4 m
B. 7.5 m
C. 12.5 m
D. 10 m
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989693.19/warc/CC-MAIN-20210512100748-20210512130748-00562.warc.gz
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CC-MAIN-2021-21
| 3,637 | 84 |
https://www.physicsforums.com/threads/projectile-motion-where-will-the-ball-land.615589/
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math
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A boy standing on the top of a building 40m high throws a ball directly aiming to his friend standing on the ground 30m away from the base of the building. If the projection velocity is 20m/s. Find how short will the ball fall from his friend.
The Attempt at a Solution
From the picture I have attached, AB = 40 m
BC = 30 m
Using pythagoras theorem, we have AC = 50 m
Using tan θ = p/b we have tan θ = 40/30 so, θ = tan-1(4/3) = 53°
Now, breaking the components,
20 * cos53° = 16 m/s
20 * sin 53° = 12m/s
My problem begins here :
1) Which formula do I use, s = ut + 1/2 at2 or v = u + at to find the time it takes to reach ground vertically.
2) What's the sign of u and g here.
9.8 KB Views: 299
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875147628.27/warc/CC-MAIN-20200228170007-20200228200007-00112.warc.gz
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CC-MAIN-2020-10
| 701 | 13 |
https://www.topperlearning.com/cbse-class-8-videos/maths/algebraic-expressions-and-identities/expansion-using-algebraic-identities/2302
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math
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CBSE Class 8 Maths Algebraic Expressions and Identities
- Draw and show (A+B) ² =A²+2 A B + B².
- Write down the product of (x² + x + 1) ( x² - x + 1) and ( x⁴- x² + 1)
- (2/3m+3/2n) ²
If x cube + 2 square equal to a square x 6 plus x cube + 4, then find a.
- x^2+y^2+4z^2+2xy-4yz-4xzdivide by(x+y-2z)
- x+y=12 and xy = 24 find the value x2+y2
- If , find .
- If x + y = 4 and xy = 2, find x2 + y2.
- Simplify the following:
- Evaluate 992 using suitable identity.
Queries asked on Sunday & after 7 pm from Monday to Saturday will be answered after 12 pm the next working day.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945323.37/warc/CC-MAIN-20230325095252-20230325125252-00792.warc.gz
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CC-MAIN-2023-14
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https://www.imgrum.one/hashtag/durian
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math
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A summer of trying new things. These gorgeous exotic fruits are all from the local farmers market: dragon fruit, Delicious sweet Mangosteen (known as the Queen of Fruit) and the controversial King of Fruit, Durian. So stinky it's banned in hotels and public transport in SE Asia. My first time trying it, quite the experience. I can't even really describe it and I'm still not sure if I like it or it's the most disgusting thing ive ever eaten. Not sweet, almost onion-y... and slimy. But strangely more-ish. #tropicalfruit#portdouglas#durian#mangosteen#dragonfruit#newthings2018#exoticfruit#buylocal
Good morning! Minggu gini enakan makan duriannya Ucok Durian Bali nih. Rasanya mantap jiwa bikin ketagihan! Special price untuk durian kupas cuma 95.000/box! Ucok Durian Medan asli cuma di Ucok Durian Bali yaa #duren#durian#ucokdurianbali#bali#kulinerbali
0 14an hour ago
Good luck in the Dog Year! (Which means happy new year). We made/created two new flavours to celebrate the new year. We would like to introduce friends to durian flavoured ice cream and sesame flavoured Ice creams that are dairy-free.
Come on in and try some freshly made durian gelato! Made with love in small batches... #happychinesenewyear#durian#durianicecream#yearofthedog#yummy#celebratelife#umalumalove
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811352.60/warc/CC-MAIN-20180218023321-20180218043321-00129.warc.gz
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CC-MAIN-2018-09
| 1,282 | 5 |
http://accountingcontacts.com/unit-angle-relationships-homework-2-applying-angle-relationships.html
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math
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DI U6 D2 Angle Relationships in Quadrilaterals english essay form 5. Adjacent angles are “side by side” and share a common ray.
Unit angle relationships homework 2 applying angle relationships each side by. 2. 2 Divis. All angles must be in relation to one another. Pairs of angles worksheets contain complementary and supplementary angles.
As you. 2, 42. 1.6 Angle Pair Relationships. Student Handouts. Student-friendly guided notes and aligned quick homework that are scaffolded to support student learning.
Unit 3 Application of Percents 12 Days. Developed and applied formulas for the area and circumference of circles. Level 3 items often involve. corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Observation Homework Class participation Whiteboards/communicators.
Homework cover page template
Evaluate: Homework and Practice. Converse: If two angles are Unit 5 Test: Geometry * Required. Unit 7 Angle Relationships and Triangles · Unit 8 Unit angle relationships homework 2 applying angle relationships, Congruence and Similarity · Unit 9 Volume · Unit 10 Scatter Plots and Data Analysis.
Lesson 3: Defining and Applying Similarity. To be able to see the relationship among the possible agle. Unit 1 - Review Unit 2 - Polynomials Unit 3 - Solving Equations Unit 4 - Modelling with Graphs Unit 5 - Linear Relations Unit 6.
Students will learn to apply algebraic and geometric principles to theoretical and. Students will be able to understand and prove angle relationships along parallel lines cut by a transversal through the application of transformations.
Give an alternate name for angle ∡ Computer par essay in urdu using 3 points: (1 answer) 2. Find missing angles given two parallel lines and a transversal.
Graphic organizer thesis statement
Key Activities. Students explore and apply the special relationships between angles that are formed when rrelationships. Example 2 Tell whether the angles are complementary or knit. Angle Pair Relationships Error Analysis More Geometry Activities, Teaching Geometry, Teaching Math, Geometry. Unit 8 Ratios of Similarity and Circles Review.
Parallel Lines and Angles (Part I). Unit 3 Syllabus: Ch 3 Parallel and Perpendicular Lines. Jan unit angle relationships homework 2 applying angle relationships. Explore 1 Exploring Angle Pairs Formed by Intersecting Lines. Substitute. x = 140. Simplify. HOMEWORK HELP. Textbook online. G.C.2 -‐ Identify and describe relationships among inscribed angles, cover letter to profiles and chords. Foldable: Segment Relationships (blank) (completed).
Essay structure middle school
W.13 Find measures of complementary, supplementary, vertical, and adjacent angles. Test your skills by matching pairs of cards with the same type of angle. Do you need a real world math resource to teach Unit Rate? Pairs of Angles - relationships of various types of paired unit angle relationships homework 2 applying angle relationships.
This section provides examples identifying congruent angles and applying properties of social housing master thesis angle bisector. The second lesson will use the same worksheet to construct a variety of isosceles triangles. Term Work (Tests/Quizzes: 80%, Homework Assignments: relatiobships = 70%.
Use the Linear. Extra Practice. Curriculum 2.0 – Honors Geometry: Unit 1 Topic 4 Syllabus. HSG.C.A.2. Identify and describe relationships among inscribed angles, radii, and.
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CC-MAIN-2019-13
| 3,441 | 16 |
https://books.google.com/books/about/Reflective_Optics.html?id=kOCLZeGUSbIC&hl=en
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math
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This is the first book dedicated exclusively to all-reflective imaging systems. It is a teaching tool as well as a practical design tool for anyone who specializes in optics, particularly for those interested in telescopes, infrared, and grazing-incidence systems. The first part of the book describes a unified geometric optical theory of all-reflective imaging systems (from near-normal to grazing incidence) developed from basic principles. The second part discusses correction methods and a multitude of closed-form solutions of well-corrected systems, supplemented with many conventional and unconventional designs examples. This book will be useful to anyone interested in the theory of optical image formation and in the actual design of image-forming instruments.
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Chapter Three FirstOrder Optics
Chapter Four Aberrations of Conic Reflectors
Chapter Five ThirdOrder Optics
Chapter Six The Seidel Aberrations
Chapter Seven ThirdOrder Correction of a OneMirror System
Chapter Eight ThirdOrder Correction of TwoMirror Systems
Chapter Nine ThirdOrder Correction of ThreeMirror Systems
Chapter Ten ThirdOrder Correction of Multimirror Systems
Chapter Eleven Aberration Theory for GrazingIncidence Systems
Chapter Twelve Stigmatic and Aplanatic Systems
Other editions - View all
aberration and coma aberration coefficients aberration components Absence of Spherical according to Eq anastigmatic angular apo-vertex aspheric deformation constant astigmatism axial Cartesian deviation Cartesian surface coeflicients collimated Condition for Aplanatism configurations conic sections corrective mirror corrector D-term defined ELLIPSOID entrance-pupil distance equal to zero exit-pupil field curvature final image find first focal length focusing telescope Gaussian image plane geometric given by Eqs HYPERBOLOID image point image-scale factor infinite input parameters located magnification marginal ray object and image object coordinates object point obtained by setting obtained from Eqs optical axis paraboloid Petzval primary principal ray ray coordinates Ray traces ray-height ratio real final images reflection reflector represents sections of revolution Seidel aberrations shown in Fig sine condition slope equation spherical aberration spherical mirror surface coordinates surface equation surface normal surface vertex system parameters three-mirror system two-mirror system two-mirror telescope vertex curvature yielding zero field curvature
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171834.68/warc/CC-MAIN-20170219104611-00271-ip-10-171-10-108.ec2.internal.warc.gz
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CC-MAIN-2017-09
| 2,553 | 15 |
https://mcqslearn.com/engg/advance-engineering-mathematics/ordinary-derivatives-notations-multiple-choice-questions.php
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math
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Engineering Mathematics MCQs
Engineering Mathematics MCQ PDF - Topics
Practice Ordinary Derivatives Notations Multiple Choice Questions (MCQ), Ordinary Derivatives Notations quiz answers PDF to learn engineering mathematics online course for engineering mathematics classes. Introduction to Differential Equations Multiple Choice Questions and Answers (MCQs), Ordinary Derivatives Notations quiz questions for graduate school interview questions. "Ordinary Derivatives Notations MCQ" PDF Book: de definations and terminology, advance mathmatical problems, de classifications by types test prep for online engineering graduate schools.
"Prime notation is used to denote only" MCQ PDF: ordinary derivatives notations with choices first derivative, first two derivatives, first three derivatives, and first four derivatives for graduate school interview questions. Learn ordinary derivatives notations quiz questions for merit scholarship test and certificate programs for job placement test.
MCQ: Prime notation is used to denote only
MCQ: y',y'',y''' ... notation is termed as
MCQ: Fourth derivative in prime notation is written as
MCQ: Notation which clearly displays both dependent and independent variables is
MCQ: ∂⁄∂x notation is termed as
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764501407.6/warc/CC-MAIN-20230209045525-20230209075525-00020.warc.gz
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CC-MAIN-2023-06
| 1,249 | 9 |
http://archive.org/stream/MathematicalAndPhysicalPapersIii/TXT/00000159.txt
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math
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152 AN EXAMINATION OF THE POSSIBLE EFFECT OF THE
- I be the index of e in (13) when x is equal to one wave's length,
^sin^r.0==Z,/Acos^p.a? = 27r, whence Z = 2?rtan^, <fz = 0-6172;
so that the intensity, supposed to vary as the square of the amplitude of vibration, would be diminished in the ratio of 2*625 to 1. Supposing the period of vibration to be the ^dth part of a second, which would correspond to a note of moderate pitch, and taking the velocity of propagation at 1100 feet per second, we should have 44 inches for the length of one wave. Hence in travelling 20 yards, or 16*36 wave-lengths, the intensity would be diminished in the ratio of (2'625)16'36 to 1, or about 7 millions to 1. A decrease of intensity like this is utterly contrary to observation, and therefore we are really compelled to suppose that the ratio of q to n is either very much greater or very much less than what has just been determined. Since in the case supposed n = 27TT-"1 = 600?r, we get from (16)
2 = 2198...........................(18),
which, it is to be remembered, is referred to a second as the unit of time.
Let us now, adopting this value of q, examine a little at what rate a small portion of heated air, situated in other air which has not been heated, would cool by radiation. If 9 be the excess of the temperature of the heated air over that of the surrounding air, we should have, supposing 6 to be sufficiently small to allow us to adopt Newton's law of cooling,
from which it follows that the excess of temperature would be diminished during the time t in the ratio of cfjt to 1. It would follow from the numerical value of q above given, that, even in so short a time as the hundredth part of a second, the temperature would be reduced in the ratio of about 3514 millions to 1. Such rapidity of cooling as this is utterly contrary to observation, Put a poker into the fire, and when it is hot look along it, and an ascending stream of heated air will be rendered visible by the distortion which it produces in objects seen through it, in consequence of the diminution of refractive power accompanying the rarefaction produced by heat. But were the rate of cooling
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s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921957.9/warc/CC-MAIN-20140901014521-00270-ip-10-180-136-8.ec2.internal.warc.gz
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CC-MAIN-2014-35
| 2,170 | 8 |
https://math.answers.com/geometry/Is_a_rhombus_always_a_a_rectangle
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math
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No because a rectangle has different properties to a rhombus but they are both 4 sided quadrilaterals
a parallelogram is always a example of a rectangle a rhombuz and a trapezoid
A quadrilateral, a parallelogram, a rhombus, a rectangle, a regular polygon.
A rectangle is sometimes a square, but not always. When it is, it's also a rhombus. A rhombus is sometimes a square, but not always. When it is, it's also a rectangle. A square is always a rhombus and always a rectangle. Rectangles, rhombera, and squares are always parallelograms and quadrilaterals.
A rectangle is not always equilateral. A square and a rhombus both have four equal sides.
No. Usually it won't.
No, a rectangle can just be classified as a parallelogram as well.
A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
no it does not always have to be a parallelgram it could be a square or rectangle
A rectangle is never a rhombus. A rhombus does not have right angles, but a rectangle does. Definition: rectangle - a parallelogram having four right angles. rhombus - an equilateral parallelogram Websites: http://dictionary.reference.com/browse/rectangle?s=t http://dictionary.reference.com/browse/rhombus?s=t
Sometimes a Rectangle can be a Rhombus.
Not necessarily, a parallelogram can also be a rectangle.
parallelograms, rectangles, rhombus, square
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335355.2/warc/CC-MAIN-20220929131813-20220929161813-00361.warc.gz
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CC-MAIN-2022-40
| 1,454 | 13 |
https://goprep.co/ex-12.3-q1-find-the-area-of-the-shaded-region-in-fig-12-19-i-1njgo2
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math
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Q. 14.2( 261 Votes )
Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
As, ΔPQR is in the semicircle and we know angle in the semicircle is a right angle, therefore PQR is a right-angled triangle.
[ If an angle is inscribed in a semi-circle, that angle measures 90 degrees.]
Here, QR is the hypotenuse of ΔPQR as lines from two ends of diameter always make a right angle when they meet at the circumference of that circle.
Hence by Pythagoras theorem we get,
Pythagoras Theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
QR2 = PQ2 + PR2
QR2 = 242 + 72
QR2 = 576 + 49
QR = 25 cmDiameter = 25 cm
Or, radius = 12.5cm
Area of right angled triangle triangle =
= 12 × 7
= 84 cm2
= 245.3125 sq cm
Area of shaded region = Area of semicircle - area of ΔPQR
= 245.3125 – 84
Area of shaded region = 161.3125 sq cm
Rate this question :
The cost of harvesting a square field at RS. 900 per hectare is RS. 8100. Find the cost of putting a fence around it at RS. 18 per metre.RS Aggarwal - Mathematics
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s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107922746.99/warc/CC-MAIN-20201101001251-20201101031251-00652.warc.gz
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CC-MAIN-2020-45
| 1,150 | 21 |
https://www.knowpia.com/knowpedia/Transverse_mass
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math
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This definition of the transverse mass is used in conjunction with the definition of the (directed) transverse energy
Using these definitions (in particular for ) gives for the mass of a two particle system:
Looking at the transverse projection of this system (by setting ) gives:
These are also the definitions that are used by the software package ROOT, which is commonly used in high energy physics.
Hadron collider physicists use another definition of transverse mass (and transverse energy), in the case of a decay into two particles. This is often used when one particle cannot be detected directly but is only indicated by missing transverse energy. In that case, the total energy is unknown and the above definition cannot be used.
where is the transverse energy of each daughter, a positive quantity defined using its true invariant mass as:
which is coincidentally the definition of the transverse mass for a single particle given above. Using these two definitions, one also gets the form:
(but with slightly different definitions for !)
For massless daughters, where , we again have , and the transverse mass of the two particle system becomes:
where is the angle between the daughters in the transverse plane. The distribution of has an end-point at the invariant mass of the system with . This has been used to determine the mass at the Tevatron.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.72/warc/CC-MAIN-20240414130604-20240414160604-00137.warc.gz
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CC-MAIN-2024-18
| 1,360 | 10 |
https://www.gatecseit.in/k-ary-tree-multiple-choice-questions-and-answers-mcqs/
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math
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K-ary Tree Multiple choice Questions and Answers (MCQs)
Click on any option to know the CORRECT ANSWERS
How many child nodes does each node of K-ary Tree contain?
more than k
at most k
Question 1 Explanation:
Each node of K-ary tree contains at most k nodes. While tree with 2 nodes is called Binary tree and tree with 3 nodes is called Ternary tree.
Which of the following is the name of the node having child nodes?
Question 2 Explanation:
Parent node is the node having child nodes and child nodes may contain references to their parents. Parent node is a node connected by a directed edge to its child.
What is the depth of the root node of K-ary tree?
Question 3 Explanation:
Depth is defined as the length of the path from root to the node. So the depth of root node in K-ary tree is 0.
What is the Height of the root node of K-ary tree?
Question 4 Explanation:
Height of K-ary tree is defined as the length of path from root to deepest node in tree. Therefore, height of root node in K-ary tree is 0.
Which node is the root node of the following K-ary tree?
Question 5 Explanation:
Node A is called the root node of the above K-ary tree while the Node B, Node C, Node D are called Leaf node.
There are 5 questions to complete.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400192783.34/warc/CC-MAIN-20200919173334-20200919203334-00156.warc.gz
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CC-MAIN-2020-40
| 1,233 | 20 |
https://physicsnet.co.uk/a-level-physics-as-a2/thermal-physics/molecular-kinetic-theory/derivation/
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math
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Think about a single molecule moving towards the end of a box. The box is a cube so all sides are of length (L). The molecule has a mass (m) and a velocity (v1). Therefore the molecule has a momentum of mv1.
momentum = mv1
When it collides with the end of the box in an elastic collision it goes back in the exactly opposite direction but with the same velocity. Its moment is now -mv1.
change in momentum = mv1– (-mv1) = 2mv1
To get back to the same side of the box it will have to travel to the other end of the box (a distance of L) and back (a distance of L) so the total distance travelled will be 2L.
distance travelled = 2L
the time for this to happen (t) will given by time = distance /speed
The number of collisions with the wall per second will be 1/t
The rate of change of momentum is equal to the change in momentum multiplied by the number of collisions with the wall per second.
Newton’s 2nd Law tells us the force exerted on the wall by the molecule is equal to the rate of change of momentum.
We can now use the equation pressure = force / area. The area of the end of the box is L2.
The volume of the box (V) is equal to L3, so we can substitute V into the equation.
This is the pressure excerted by 1 molecule but we can multiply by the number of molecules in the box (N).
On average only a third of the molecules will be travelling in the direction we have chosen to focus on so,
Molecules will be moving in different directions with different speeds so we will use the root mean square velocity (crms) to represent the average velocity of a molecule.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476396.49/warc/CC-MAIN-20240303142747-20240303172747-00298.warc.gz
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CC-MAIN-2024-10
| 1,574 | 15 |
https://www.toppr.com/ask/question/explain-the-concept-of-a-parallel-plate-capacitor-state-its-any-two-applications/
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math
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Explain the concept of a parallel plate capacitor. State its any 'two' applications.
Open in App
Verified by Toppr
The surface of an isolated charge conductor is an equipotential surface with a potential V with respect to some arbitrary zero reference level, usually the ground. V>0 if charge on the conductor is positive and V<0 for negative charge. If the charge is increased. V increases in the same proportion. i.e.
C is called the capacitance.
Consider a metal plate A whose potential is raised to V by depositing a charge +Q on it. Now if an uncharged metal plate B is brought close to A A, then the negative charge will be induced on the surface near A and positive free change on the surface of B away from A as know below.
Now if plate B is grounded, the free positive charge on B will go into the earth. The bound negative charge (−Q) on B will lower the potential of A by say V1 due to the presence of plate A in the electric field generated by the negative charge on B.
Now net potential on A=V−V1
As (V−V1) has decreased from V the capacity or capacitance of plate A has increased.
This system of plates together is called a parallel plate capacitor.
Application of parallel plate capacitors:-
1) Energy storage capacitor banks are used for power factor correction with inductive loads
2) DC power supplies sometimes use parallel capacitors in order to better filter the output signal and eliminate the AC ripple.
Solve any question of Electrostatic Potential and Capacitance with:-
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571959.66/warc/CC-MAIN-20220813142020-20220813172020-00229.warc.gz
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CC-MAIN-2022-33
| 1,501 | 14 |
https://www.sudokugame247.com/other-sudoku-variations-you-can-try/
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math
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Four of the many other Sudoku variations are the Mini Sudoku, Mega Sudoku, Irregular, Sudoku, and the Multi Sudoku. Compared to the classic 9×9 Sudoku puzzle, these variants may have grid sizes other that the 9×9 size. They may also have additional rules that can only be applicable to their type. Take a closer look at these 4 variants that you might also like to work on.
Completing a Mini Sudoku puzzle by seeing to it that each number should only appear once in every row, every column, and every sub-square is still the primary goal for each player. Mini Sudoku, however, is smaller in grid size compared to the classic 9×9 Sudoku that you most often see. This particular Sudoku variant may either have a 4×4 or a 6×6 grid size.
This means that when you are playing a Mini Sudoku Puzzle with a 4×4 grid size, you should place the numbers 1 to 4 to their corresponding row, column, and sub-square without having any duplicates in any of those three places. Completing a 6×6 grid Mini Sudoku puzzle also goes like that; you must make sure that each row, each, column, and each sub-square only contains a single number from 1 to 6.
Mini Sudoku is especially good for beginners. This is due to its fewer set of numbers that makes it easier and faster to solve.
Mega Sudoku may either have a 12×12 or a 16×16 grid size. It is larger compared to the classic 9×9 Sudoku puzzle in terms of grid size. Just like in any Sudoku puzzle, the main aim is to fill those unfilled boxes with numbers 1 to 12 (for the 12×12 grid) and 1 to 16 (for the 16×16 grid) and making sure that each number only appears once in every row, every column, and every sub-square.
As you may be aware by now, Mega Sudoku has a larger grid size compared to the classic 9×9 Sudoku. This means that completing this particular Sudoku variant may cause you a longer period of time. Its level of difficulty, however, still rests on how the givens are prearranged.
The first thing that you will note in an Irregular Sudoku puzzle is the shape of its sub-squares. If you try to think about it, it is more applicable to call them “regions” rather than sub-squares since most of them are not really squares. But for this purpose, let us just retain the word sub-squares instead of regions. Just like in other Sudoku puzzles, you are still not allowed to repeat any number inside every sub-square, every row, and every column.
Irregular Sudoku puzzles may have three different grid sizes (6×6, 9×9, or 12×12). Each row, column, and sub-square should posses only one number ranging from 1 to 6 (for the 6×6 grid), from 1 to 9 (for the 9×9 grid), and from 1 to 12 (for the 12×12 grid).
If you are looking for a more complex Sudoku variant, then Multi Sudoku is right for you. Multi Sudoku does not only have a single grid but has multiple grids from different Sudoku variants. Because it has more than one variant, it also carries more than one variant rules.
In Multi Sudoku, you will encounter a Sudoku sheet that carries two or more overlapping Sudoku grids. These overlaps can be seen on certain sub-squares which must be solved with two variant rules from each main grid. The goal here is still the same which is completing the puzzle without having a single number appear more than once in each row, column, and sub-square. This is one of the most complex and challenging Sudoku variants that you could possibly try to solve.
Test yourself by trying these Sudoku variations and try to complete them while having fun.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521883.7/warc/CC-MAIN-20220518083841-20220518113841-00138.warc.gz
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CC-MAIN-2022-21
| 3,502 | 11 |
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