Datasets:

OpenCoder-LLM
/

opc-fineweb-math-corpus

Dataset card Data Studio Files Files and versions Community

Split (1)

train · 5.24M rows

url stringlengths 14 5.47k	tag stringclasses 1 value	text stringlengths 60 624k	file_path stringlengths 110 155	dump stringclasses 96 values	file_size_in_byte int64 60 631k	line_count int64 1 6.84k
https://www.coursehero.com/file/6040437/Atwhatanglewithrespecttothelinejoiningthestarting-andfinishingpointsshouldsheswim/	math	This preview shows page 1. Sign up to view the full content. Unformatted text preview: trates this relationship? 4. (2 points) An object, tied to a string, moves in a circle at constant speed as shown. The direction of its velocity and acceleration at point W is: a) →, ↓ b) →, ↑ c) ←, ↓ d) ←, ↑ e) ←, ← 5. (2 points) A girl wishes to swim across a river to a point directly opposite as shown. She can swim at 2 m/s in still water and the river is flowing at 1 m/s. At what angle θ with respect to the line joining the starting and finishing points should she swim? a) 30° b) 45° c) 60° d) 63° e) 90° 6. (2 points)You deserve to have an easy question on this exam because: a) You are awesome. b) You actually came to take the exam. c) You love Big Bang Theory as much as Dorina does. d) You have to tolerate Dorina in class. 7. A time dependent force F = ( −3) i + 2t j (in N), is exerted on a 2 kg object initially at rest. a) Calculate the magnitude of the acceleration of the object at t = 2 seconds. (4 points) b) Calculate the x and y components of the velocity at t = 2 seconds. (4 points) c) Calculate the magnitude and direction of the object’s velocity at t = 2 se... View Full Document - Spring '10	s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560285001.96/warc/CC-MAIN-20170116095125-00303-ip-10-171-10-70.ec2.internal.warc.gz	CC-MAIN-2017-04	1,238	4
https://cholaempire.com/how-to-measure-52-grams.html	math	MASS-VOLUME EQUIVALENTS OF COMMON CHEMICAL SOLIDSShare on: Volume and temperature measurements can easily be used for many materials, but when using weight ... All weights were measured in grams. .... C76H52O46. Chapter 1 Chemistry and Measurements - Bakersfield College Scientists use the metric system of measurement and have adopted a modification of the metric ... Mass, Gram (g) and Kilogram (kg). 1 kg = 1000 g ..... Page 52 ... Chem 11.Chapter 1.12-8-11.dch.pdf Weights, Measures, and Conversion Factors for Agricultural - USDA Factors for converting domestic and metric weights and measures commonly used for .... 52. 42. Fruits, dehydrated (low moisture): Relationship between farm and .... 1 gram (g). = 1 000 milligrams. 10 grams. = 1 dekagram (dag). 10 dekagrams. Standard drink measures in Europe - rarha ascertain to determine the number of grams of alcohol in standard drinks across .... pure alcohol, 52% more alcohol than the US standard drink size (12 g). WP5 Background paper Standard drink measures HRB.pdf math for nursing and allied health - Delta College Sample Problem Proportion is often used to calculate a dosage. ..... Sample problem: How many grams of drug will 100 mL of a 10% solution ..... 52 gtts/min. 15. math for nursing and allied health.pdf THE METRIC SYSTEM mass, measured in grams (g); and. • temperature ... length, commonly measured in inches (in), feet (ft), yards and miles;. • time, commonly ... 52 weeks = 1 yr. Alcohol Measures and Units - Cleave Books Measures & Units ... measures used in other countries, and a set of on-screen ..... 38 Units. 36 Units. 34 Units. 32 Units. 44 Units. 42 Units. 40 Units. 52 Units. Units of Measure Codes - The Produce Traceability Initiative Unit of Measure Codes for Use With ... Use the following codes to identify units of measure (UoM) when customizing the PTI-provided ... Grams Per Cubic Centimetre ...... Z52. Usage (e.g. in laundry, 24 usage). Usage (e.g. in laundry, 24 usage). The Metric System Appendix Metric Units of Measurement A.1 The gram (the unit of weight, about the weight of a regular paper clip). 4. ..... umn with an appropriate measure in the second column. 52. i. A letter-sized sheet. REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52 Can I measure in length with a metric ruler, volume with a metric beaker, and .... is water and a sample of the substance contains 52 grams of water, what is the. Problem Set 9 - MIT OpenCourseWare (c) In (b), how many people in total would you need to measure to bring the width ... significantly less than 52-grams and some weighed significantly more than ... Stovetop Yama Brewing Tip Sheet - Sweet Maria's Home The instructions tell you to measure coffee using the scoop provided, which is ... measure either by weight (32 grams for the 5 cup Yama; 52 grams for 8 cup) or ... Conversion Tables, Formulas and Suggested Guidelines - Maine.gov Table No. Page. 1. Equivalents for liquid measure (volume) . ... Fertilizer weight as measured by standard pot size . ... (or grams in 1 liter) and vice versa . 4.5 Metric Measurement - CCBC Faculty Web different system of measures known as the metric system. The metric ... It bases all measures on powers of 10. .... Convert 3.52 kilograms (kg) to grams (g). MiddleChapter 3, Lesson 1: What is Density? - Middle School Students determine the density of each cube and identify the sub- stance the cube is ... Have students use any balance that can measure in grams. Metric ruler . Determining Museum Storage Equipment Needs - National Park Determining the specialized storage equipment needed to ... Conserve 0 Gram 4/ l 1, Determining Museum. Storage ... determine how many will fit into the 52% “-. Determining Amounts of Fertilizer for Small Areas - College of Example: Determine the amount of ammonium sulfate needed by a 1,000 .... Phosphorus Sources. 18-46-0 (DAP†) 11-52-0 (MAP‡) 0-46-0 (TSP¶) 16-20-0- 13S§. Grade 5 Mathematics Annotated 2014 State Test - EngageNY measures the intended standards and sample student responses representing each possible score point. ...... A box contains 512 grams of cereal. ..... The student may have thought that 52 inches was equal to 5 feet 2 inches and calculated 6 ft. View/Open - Oregon State University samples to measure seed moisture: a Koster tester, a microwave oven, and a convection oven. You will ... cool then measure the dry weight…7.9 grams for the dry weight. If you choose to use the ... This one is 52 grams. To calculate the seed ... Video transcript EM 9030.pdf?sequence=5 Instructor Training Manual: Teaching Math in Context measure ingredients using measuring spoons and grams; a third station that includes ...... 2-52. Culinary Math. Answers for Handouts:, continued. Cornbread.	s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540488620.24/warc/CC-MAIN-20191206122529-20191206150529-00354.warc.gz	CC-MAIN-2019-51	4,752	44
http://www.e-booksdirectory.com/details.php?ebook=6550	math	The CRing Project: a collaborative open source textbook on commutative algebra by Shishir Agrawal, et al. Publisher: CRing Project 2011 Number of pages: 493 The CRing project is an open source textbook on commutative algebra, aiming to comprehensively cover the foundations needed for algebraic geometry at the level of EGA or SGA. It is a work in progress. The present project aims at producing a work suitable for a beginning undergraduate with a background in elementary abstract algebra. Download or read it online for free here: by Thomas J. Haines - University of Maryland Notes for an introductory course on commutative algebra. Algebraic geometry uses commutative algebraic as its 'local machinery'. The goal of these lectures is to study commutative algebra and some topics in algebraic geometry in a parallel manner. by Francis Sowerby Macaulay - Cambridge University Press Many of the ideas introduced by F.S. Macaulay in this classic book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring'. by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay These notes give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are: Hilbert basis theorem, primary decomposition of ideals in noetherian rings, Krull intersection theorem. This wikibook is intended to give an introduction to commutative algebra; i.e. it shall comprehensively describe the most important commutative algebraic objects. The axiom of choice will be used, although there is no indication that it is true.	s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315865.44/warc/CC-MAIN-20190821085942-20190821111942-00197.warc.gz	CC-MAIN-2019-35	1,688	13
http://mathhelpforum.com/statistics/95370-probability-problem-help.html	math	There are 2 red balls and 4 yellow ones in a box. a) if a ball is drawn and replaced,and a second ball is drawn,what is the probability that the first ball is red and the second ball is yellow? b)What is the probability that the balls will be red and yellow combination in any order? a) total no. of balls =6 Are my answers correct because I doubt it ?	s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122167.63/warc/CC-MAIN-20170423031202-00132-ip-10-145-167-34.ec2.internal.warc.gz	CC-MAIN-2017-17	352	5
https://theoriginsofthefuture.com/ponentes/index.php?id=3&lng=en	math	"Im a Mathemagician, it means that I combine my love of math and magic to do something I name Matemagics." What is the square root of 78,308? This may seem like a simple mathematic equation, but if we dont have access to a 10-digit calculator, finding the answer may take a little more time. This is where Mathematics professor, Arthur Benjamin, comes in. He can solve this equation in just a few seconds using only his mind. He can also make an accurate guess of the month and day in which you were born. How does he do it? With Mathemagic, his astonishing combination of magic and math. Benjamin is a human calculator, and represents the multiple possibilities of the brain. Benjamin is professor of Mathematics, specializes in combinatorics and is professor at Harvey Mudd College. He is the first mathematician to have been featured on the Colbert Report and The Mathematical Association of America distinguished him for teaching in 1999 and 2000. He also filmed a series of The Teaching Company lectures called The Joy of Mathematics, Discrete Mathematics and The Secrets of Mental Math.	s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00377.warc.gz	CC-MAIN-2021-21	1,092	5
http://journals.plos.org/plosone/article/figure?id=10.1371/journal.pone.0020728.g002	math	Entrepreneurs, Chance, and the Deterministic Concentration of Wealth In simulations with , % and all 100,000 individuals starting with wealth of 1 at time zero, the lower portion of the wealth distribution is represented by the blue line at time , the red line at time , and the black line at time . Circles indicate the median wealth and diamonds indicate the mean wealth. Note that mean wealth increases much faster than median wealth, while in this case the modal wealth, identified by the peaks of the curves, decreases. Over time, an increasing portion of the population has wealth greater than 20 units (0.01% of the population, 1%, and 18% at , 12, and 31, respectively), which is not depicted because it falls beyond the right boundary of the graph.	s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818695113.88/warc/CC-MAIN-20170926070351-20170926090351-00390.warc.gz	CC-MAIN-2017-39	757	2
https://mathshistory.st-andrews.ac.uk/Biographies/Sintsov/	math	Dmitrii Matveevich Sintsov Viatka (now Kirov), Russia BiographyDmitrii Matveevich Sintsov was born in Viatka (sometimes written as Vyatka) which was a large city in western Russia and the administrative centre of the Kirov Province. The change of name of this city to Kirov did not happen until 1934 when it was renamed after the Soviet official Sergey M Kirov. He attended the Third Kazan High School, graduating with the Gold Medal in 1886. Later in the year in which he graduated from the High School, he began his studies at Kazan University, graduating in 1890. This University, the result of one of the many reforms of the Emperor Alexander I, was founded in 1805, and was famed in mathematics by having Lobachevsky as its rector from 1827 to 1846. By the time Sintsov began his university studies he was already convinced that mathematics was the topic for him to concentrate on, and he became a member of the mathematics section of the Physics and Mathematics Faculty of the university. His lecturers in mathematics were A V Vasil'ev, F M Suvorov, V V Preobrazhenskii and P S Nazimov. He also took courses in astronomy with D I Dubyago. Sintsov's first research was on Bernoulli functions of fractional order and he carried this out while taking his fourth year undergraduate courses. His paper on the topic was published in the Notices of the Kazan Physics and Mathematics Society in 1890. This was a remarkable piece of work for a student at this stage in his undergraduate studies and it earned him a Gold Medal. Although Sintsov's interests moved away from the areas of his first scientific investigations, nevertheless he did undertake further research into Bernoulli functions and published further papers on this topic near the beginning of his career. Having made such an excellent start to his research, his "esteemed teacher" Aleksandr Vasil'evich Vasil'ev (1853-1929) recommended that he continue his studies at the University of Kazan with the aim of qualifying as a High School teacher. He spent three years, from the beginning of February 1891 to the beginning of February 1894, taking the necessary courses to obtain his teaching qualification. During this period he was being advised on research topics by Vasil'ev and, following his advice, he wrote his Master's Thesis The Theory of Connexes in Space in Connection with the Theory of First Order Partial Differential Equations. I A Naumov explains in :- The German mathematician A Clebsch was the first to investigate the theory of connexes in the period 1870-1872. He considered plane connexes i.e., plane geometrical objects, where the point-straight line combination was chosen as the basic element of the plane. Such connexes are termed ternary. Clebsch constructed the geometry of a ternary connex and applied it to the theory of ordinary differential equations.Sintsov was appointed to the staff of Kazan University and taught there from 1894 to 1899. After leaving Kazan, Sintsov taught at the Odessa Higher Mining School, then, in 1903, he was appointed to Kharkov University where he taught until his death in 1946. He took a leading role in the development of mathematics at Kharkov University and, for many years, he was President of the Kharkov Mathematical Society. This Society is one of the early mathematics societies, being founded in 1879. Following Vladimir Andreevich Steklov's presidency from 1902 to 1906, Sintsov took over as President, and held the position until his death forty years later :- Through Sintsov's initiative, the Kharkov Mathematical Society was deeply involved in the improvement of mathematical education in the schools of the Kharkov region. Sintsov also put considerable effort into maintaining the Kharkov Mathematical Society mathematical library which is still one of the most complete mathematical libraries in the Ukraine.Sintsov had an outstanding research record, and published 267 works during his long and productive scientific and teaching career. Of course through his many years of research his interests varied but the main areas on which he worked were the theory of conics and applications of this geometrical theory to the solution of differential equations and, perhaps most important of all, the theory of nonholonomic differential geometry. I A Naumov writes :- His classical work on the theory of connexes, of which he was one of the founders, and on nonholonomic differential geometry are well known far beyond the frontiers of our country.The book in which the articles (written by Ja P Blank who was a student of Sintsov) and appear, contains a selection of the Sintsov's major works on nonholonomic geometry. These were first published during the years 1927-1940 and include: A generalization of the Enneper-Beltrami formula to systems of integral curves of the Pfaffian equation Pdx + Qdy + Rdz = 0 (1927); Properties of a system of integral curves of Pfaff's equation, Extension of Gauss's theorem to the system of integral curves of the Pfaffian equation Pdx + Qdy + Rdz = 0 (1927); Gaussian curvature, and lines of curvature of the second kind (1928); The geometry of Mongian equations (1929); Curvature of the asymptotic lines (curves with principal tangents) for surfaces that are systems of integral curves of Pfaffian and Mongian equations and complexes (1929); On a property of the geodesic lines of the system of integral curves of Pfaff's equation (1936); Studies in the theory of Pfaffian manifolds (special manifolds of the first and second kind) (1940) and Studies in the theory of Pfaffian manifolds (1940). At Kharkov University, Sintsov created a school of geometry which became the leading school in this field in the Ukraine and has continued to flourish through the years still today being a leading centre. There he studied the geometry of Monge equations and he introduced the important ideas of asymptotic line curvature of the first and second kind. In 1903 he published two papers on the functional equation , now called the 'Sintsov equation,' which are discussed by Detlef Gronau in . He writes:- Sintsov gave in 1903 an elegant proof of its general real solution, which has the form , where q is an arbitrary function in one variable. ... [Sintsov] was the first who gave (in two papers ... in 1903) elementary simple proofs of its general real solutions. But before, it was Moritz Cantor who proposed these equations (there are two equations). In his journal 'Zeitschrift fur Mathematik und Physik,' ... he published [a note on them] in 1896. Cantor quotes these equations as examples of equations in three variables which can be solved by the method of differential calculus due to Niels Henrik Abel. ... The proof of Sintsov is much simpler and elegant.Sintsov also took an interest in the history of mathematics and one of the major projects which he undertook in this area was the detailed study of the work of previous mathematicians at Kharkov University. This work provides a fascinating account of the development of mathematics there from the founding of the university in 1805. The Ukrainian Academy of Sciences honoured Sintsov by electing him to membership on 22 February 1939. - I A Naumov, Dmitrii Matveevich Sintsov (his life and scientific and pedagogical work) (Kharkov University Press, 1955). - Ja P Blank, D M Sintsov (1867-1946), in Ja P Blank, D Z Gordevskii, A S Leibin and M A Nikolaenko (eds.), D M Sintsov, Papers on nonholonomic geometry (Kiev, 1972), 4-8. - Dmitrii Syntsov, Encyclopedia of Ukraine (Toronto-Buffalo-London, 1993). - D Gronau, A remark on Sincov's functional equation, Notices of the South African Mathematical Society 31 (1) (2000), 1-8. - List of the scientific works of D M Sintsov, in Ja P Blank, D Z Gordevskii, A S Leibin and M A Nikolaenko (eds.), D M Sintsov, Papers on nonholonomic geometry (Kiev, 1972), 286-293. - I A Naumov, Dmitrii Matveevich Sintsov on the 100th anniversary of his birth (Ukrainian), Ukrainskii Matematicheskii Zhurnal 20 (2) (1968), 232-237. - I A Naumov, Dmitrii Matveevich Sintsov on the 100th anniversary of his birth, Ukrainian Mathematical Journal 20 (2) (1968), 208-212. - I V Ostrovskii, Kharkov Mathematical Society, European Mathematical Society Newsletter 34 (December, 1999), 26-27. Additional Resources (show) Written by J J O'Connor and E F Robertson Last Update April 2009 Last Update April 2009	s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100762.64/warc/CC-MAIN-20231208144732-20231208174732-00623.warc.gz	CC-MAIN-2023-50	8,360	22
https://www.numbersaplenty.com/3010225	math	3010225 has 9 divisors (see below), whose sum is σ = 3743467. Its totient is φ = 2401240. The previous prime is 3010219. The next prime is 3010279. The reversal of 3010225 is 5220103. The square root of 3010225 is 1735. It is a perfect power (a square), and thus also a powerful number. It can be written as a sum of positive squares in only one way, i.e., 1083681 + 1926544 = 1041^2 + 1388^2 It is not a de Polignac number, because 3010225 - 219 = 2485937 is a prime. It is a super-2 number, since 2×30102252 = 18122909101250, which contains 22 as substring. It is a Duffinian number. 3010225 is a lucky number. It is an unprimeable number. It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 8502 + ... + 8848. Almost surely, 23010225 is an apocalyptic number. 3010225 is the 1735-th square number. 3010225 is the 868-th centered octagonal number. It is an amenable number. 3010225 is a deficient number, since it is larger than the sum of its proper divisors (733242). 3010225 is an frugal number, since it uses more digits than its factorization. 3010225 is an evil number, because the sum of its binary digits is even. The sum of its prime factors is 704 (or 352 counting only the distinct ones). The product of its (nonzero) digits is 60, while the sum is 13. The cubic root of 3010225 is about 144.3886268005. Adding to 3010225 its reverse (5220103), we get a palindrome (8230328). The spelling of 3010225 in words is "three million, ten thousand, two hundred twenty-five".	s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100184.3/warc/CC-MAIN-20231130094531-20231130124531-00013.warc.gz	CC-MAIN-2023-50	1,535	24
https://www.jiskha.com/display.cgi?id=1252773072	math	posted by muffy . Shelby can paint a room in 4 hours. Zoe can paint the same room in 7 hours. How long will it take them to paint the room if they work together? If they start 9:30a.m., and want to see a movie that is playing 45 minutes from their house and starting 12:00 p.m., will they make it on time? If they can make it, how early are they? If they will be late, how late will they be? Please let me know if I am correct. First I took the average of 4 and 7 and got 5.5 hours. So they can both paint the room in 5.5 hours. Next, If they start at 9:30 they will finish at 3:00 Next if they have to leave 45 minutes early to get to a 12:00 show, they should leave at 11:15. Next, therefore, they will be 3:45 minutes late for the 12:00 show. You cant trust the average always. I assume you are using a rate equation, Consider in 28 hours, shelby can paint 7, and Zoe can paint 4. So the combined rate = (7+4 rooms)/28 hrs= 11/28 rooms/hr Now the time to paint one room time= amount/rate= 1room/(11/28 room/hr) time= 1*28/11 hrs= 2.54hrs= 2hrs 33min If they start at 9:30, then they finish about three min after noon. Check my thinking and calculations. Now on your thinking... Using the average 5.5hrs per room, but BOTH are working, that is the average for each, so time for both together would be 5.5/2= 2.75hrs, which is not 28/11 hrs (2.545hrs). SO don't use the average, throw away that thinking, it wont work. Thank you soooooooo much, you are a great teacher! I truly understand!	s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806979.99/warc/CC-MAIN-20171123214752-20171123234752-00429.warc.gz	CC-MAIN-2017-47	1,490	16
https://mechanika.ktu.lt/index.php/Mech/article/view/32035	math	Robot Workspace Optimization based on Monte Carlo Method and Multi Island Genetic Algorithm Keywords:Monte Carlo; multi island genetic algorithm: workspace; optimization Workspace analysis is an indispensable part of robot research. The workspace volume is an important factor to measure the working ability of parallel robot. In order to maximize the workspace of parallel robot, this paper solves the workspace of robot by using Monte Carlo method, and obtains that the workspace volume is 2.142×106 mm3, which is optimized by the multi Island genetic algorithm in the global optimization algorithm. After optimization, the workspace volume increases to 8.25×106 mm3, the volume of workspace before and after optimization is increased by 3.85 times. The influence of various structural parameters of the parallel robot on the workspace volume is analyzed and studied. It is obtained that the rod length ratio of the connecting rod and the driving rod has the greatest influence on the workspace volume, followed by the ratio of the center angle of the long and short sides, and the radius of the moving platform has the least influence. Furthermore, the influence of single parameter on the workspace volume is analyzed. When other parameters remain unchanged, the maximum workspace volume can be achieved when the rod length ratio of connecting rod and driving rod is 1.25, or the ratio of center angle of long and short sides is 1.53.	s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506623.27/warc/CC-MAIN-20230924055210-20230924085210-00273.warc.gz	CC-MAIN-2023-40	1,440	3
https://studylib.es/doc/8815475/metodologia-para-el-dise%C3%B1o-de-bobinas-de-bitter	math	Journal of Manufacturing Processes 16 (2014) 551–562 Contents lists available at ScienceDirect Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro Technical Paper Bitter coil design methodology for electromagnetic pulse metal processing techniques Oleg Zaitov a,∗ , Vladimir A. Kolchuzhin b a b Belgian Welding Institute, Technologiepark 935, B-9025 Zwijnaarde, Belgium Chemnitz University of Technology, Department of Microsystems and Precision Engineering, Reichenhainerstrasse 70, D-09126 Chemnitz, Germany a r t i c l e i n f o Article history: Received 2 March 2014 Received in revised form 2 June 2014 Accepted 15 July 2014 Available online 22 August 2014 Keywords: Bitter coil Magnetic pulse welding Design methodology a b s t r a c t Electromagnetic pulse metal processing techniques (EPMPT) such as welding, forming and cutting have proven to be an effective solution to speciﬁc manufacturing problems. A high pulse magnetic ﬁeld coil is a critical part of these technologies and its design is a challenging task. This paper describes a Bitter coil design using a newly developed methodology for a simpliﬁed analytical calculation of the coil and complementary ﬁnite element models (FE) of different complexity. Based on the methodology a Belgian Welding Institute (BWI) Bitter coil has been designed and tested by means of short circuit experiments, impedance and B-ﬁeld measurements. A good agreement between the calculated and the experimental design parameters was found. © 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 1. Introduction In a certain range of thicknesses and materials combinations EPMPT are more competitive than of the same name conventional manufacturing methods. However a wide industrial use of the technologies is limited, partly due to a lack of compact engineering guidelines for a coil design. The main purpose of the present work is to develop such guidelines for a pulsed Bitter coil. Different types of coils categorized by Furth et al. can be used for EPMPT. On the basis of an analysis of manufacturing techniques, principal design solutions and performance characteristics of the above-named coils described by Lagutin and Ozhogin one can conclude that within tubular applications the Bitter coils have high reliability, manufacturability and maintainability. These are the key characteristics for an industrial implementation of the coils and factors which deﬁned our choice to develop the calculation methodology for them. The coil is an assembly of the alternating conducting and insulating discs, each with a radial slit as shown in Fig. 1. The contact between the disks is realized due to their overlap. The Bitter coils can be used with ﬁeldshapers (FS). Unfortunately a joint analytical treatment of the coil and a FS is hugely limited. However the FS can be partially taken into account, but in ∗ Corresponding author. Tel.: +33 630775462. E-mail addresses: [email protected] (O. Zaitov), [email protected] (V.A. Kolchuzhin). order to be brief in this article we are focused on the calculation methodology for the direct acting Bitter coil. The coil design is a complex task and mainly includes the determination of appropriate coil materials, sizes, the electromagnetic parameters such as an inductance, a resistance and the B-ﬁeld as well as thermal and stress loadings. Most publications dedicated to the high magnetic coil design deal with pulsed coils having constant current density distribution which is according to Kratz and Wyder approximately realized in multi-layer multi-turn coils. Some of the relevant publications within the constant current density coils design are represented below. Wood et al. proposed an approach to a material selection for such a coil. Knoepfel suggested a methodology to calculate main electromagnetic parameters of the coil: the inductance, the resistance and the central ﬁeld. Similar methodology to ﬁnd the main design parameters of the coil and its strength was proposed by Dransfeld et al. . A relatively precise and complete design of the coil can be fulﬁlled in software developed by Vanacken et al. . The pulsed Bitter coils have the current density distribution which is approximately in inverse proportion to the inner radius and therefore the above-mentioned publications become irrelevant in the present case. Nevertheless methods of ﬁnding single design parameters of the pulsed Bitter coils are found in specialized literature. For example, the inductance of the Bitter coil can be calculated using a method proposed by Grover . Knoepfel suggested a formula to ﬁnd the central ﬁeld of the coil. Moreover, the most comprehensive physical and mathematical interpretations of the general design principles and different calculation techniques of http://dx.doi.org/10.1016/j.jmapro.2014.07.008 1526-6125/© 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 552 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 known. Ideally the ﬁeld distribution law in the gap coil-WP must be speciﬁed based on demands of an application. A step-by-step explanation of the scheme is represented below. Initial data for calculation: 1. Demanded parameters of the ﬁeld: an amplitude magnetic ﬁeld in the centre of the gap coil-WP Bmax and the rise time of the ﬁeld are given. 2. A WP geometry characterized by an outer radius r0 , a wall thickness r and a work area length l as well as WP material properties represented by the conductivity , the heat conductivity , the speciﬁc heat capacity c, the yield strength y and the mass density m are known. 3. Pulse generator data such as the storable energy W, the maximum current amplitude I0 , the short circuit frequency f0 , the inductance Li and the resistance Ri are convenient to know for a simulation of a current pulse but this information is not obligatory and can be speciﬁed later during the design process. Fig. 1. A principal construction of the Bitter coil: 1 – Bitter plate, 2 – connecting lead, 3 – contact, 4 – current path, 5 – ﬂange, 6 – insulator. the design parameters of the pulsed Bitter coils are given by Kratz and Wyder . Despite a sufﬁcient, mainly academically orientated theoretical knowledge on the pulsed Bitter coils design, a simpliﬁed but complete industrial design methodology does not exist. The fact has prompted us to rework a thorough academic approach into a compact, industry-friendly methodology of the analytical calculation of the pulsed Bitter coil. This has been done by analysing an applicability of theoretical models describing electromagnetic, strength and thermal parameters of the coil and adjusting them to the present coil embodiment. A principal novelty of the methodology is that every design parameter is modiﬁed by asymmetry factors reﬂecting real geometry of the coil. An implementation of the asymmetry factors and a frequency-dependent resistance has improved precision of the methodology. Moreover several supporting FE models have been developed aiming to partly verify the analytical approach and to get a deeper insight into the design parameters. As it will be shown further the methodology of the analytical calculation is an effective tool for deﬁning the main design parameters. Furthermore each step of the methodology can be fulﬁlled on a paper. Finally short circuit experiments, impedance and B-ﬁeld measurements have been used for a veriﬁcation purpose. A list of the symbols used in this article and the corresponding meanings is represented in Table 1. 2. Methodology of the analytical calculation The analytical approach can only be applied to the coil having cylindrical symmetry, which means that there is no change in geometry when rotating about one axis, and when magnetoresistance phenomenon, eddy currents, plastic deformations and thermal stresses are neglected. Additionally the ﬁeld at each instant of time is calculated as the static ﬁeld of the coil with a certain current density. With the limitations stated above the methodology can be schematically represented in Fig. 2. The present scheme assumes an approach to the coil design provided that the demanded magnetic ﬁeld in the gap coil-WP, its rise time, WP geometry and parameters of the pulse generator are Material assignment. An insulating material represented by allowable working temperatures, dielectric and ultimate compression strengths, and a coil material described by the conductivity , the heat conductivity , the speciﬁc heat capacity c, the ultimate tensile strength UTS and allowable working temperatures initial Ti and ﬁnal Tf must be deﬁned. Maximum ﬁeld in the gap coil-WP. It is known that the maximum achievable ﬁeld in the gap coil-WP (FS-WP) must be at least 40 Tesla and the rise time must not exceed 25 s for the most of welding applications. Using an efﬁciency coefﬁcient introduced by Wilson and Srivastava one can connect the ﬁelds in the gaps coil-FS and FS-WP. Coil geometry value assignment. An inner radius r1 is deﬁned by the WP outer radius r0 and an insulation gap g which is typically 0.75–1.5 mm, a nominal length of the coil l0 is determined by the work area length of the WP l, while an outer radius r2 , thicknesses of a turn and the insulation between the turns h, as well as the asymmetry parameters ϕ, , of the turns can be deﬁned using the parameters of the existing prototypes or arbitrarily. Finally a nominal number of turns N can be estimated. Auxiliary calculations. These are calculations of two form-factors of the coil ˛ and ˇ reﬂecting relations between the sizes of the coil, an “effective” number of turns allowing to transform the asymmetrical real to the ideally symmetrical coil, the skin depth characterizing an attenuation of electromagnetic waves in a conductor, the demanded current in the coil, a so-called ﬁlling factor describing a structure of conducting and insulating regions in the total cross-section and the material integral connecting physical properties of the coil material with an amplitude ﬁeld and a pulse length. Design limitations. The maximum achievable ﬁeld in the coil is mainly limited by two factors. The ﬁrst is the mechanical strength of the coil depending on the ultimate tensile strength UTS of the coil material, its geometry and a distribution of the current density in it. The second factor is the thermal one and is determined by the thermal physical properties of the coil material, its geometry, the distribution of the current density in the coil, the allowable temperature range and the demanded pulse length. Both factors have to be considered in conjunction and the strongest factor deﬁning the maximum achievable ﬁeld must be selected. Finally the demanded ﬁeld in the gap coil-WP Bmax and the maximum achievable ﬁeld B0 are compared and a decision is made according to the scheme. Inductance of the coil. Geometrical parameters of the coil such as the inner r1 and the outer r2 radiuses, the length lcoil , the effective number of turns and a self-inductance factor (˛,ˇ) depending on the coil geometry and the current density distribution in the coil determine the inductance of the coil Lcoil . O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 553 Table 1 List of symbols. Symbol Unit Description Symbol Unit Description Bmax B0 r0 r l c y m W I0 f0 Li Ri UTS Ti Tf r1 r2 ı j jth L R U H E T T s mm mm mm MS/m W/m·K J/kg·K MPa kg/m3 J A kHz nH mOhm MPa K K mm mm mm mm A/m2 A/m2 nH mOhm V A/m V/m Maximum demanded ﬁeld in the gap coil-WP Maximum achievable ﬁeld in the gap coil-WP Rise time of the ﬁeld WP outer radius WP wall thickness WP work area length Electrical conductivity Heat conductivity Heat capacitance Yield strength Density Discharge energy Maximum current amplitude of a generator Short circuit frequency of the generator Inner inductance of the generator Inner resistance of the generator Ultimate tensile strength Allowable initial temperature Allowable ﬁnal temperature Inner radius of the coil Outer radius of the coil Thickness of a turn Skin depth Stress-determined current density Thermally-determined current density Equivalent inductance of the coil and the WP Equivalent resistance of the coil and the WP Discharge voltage H-ﬁeld Electric ﬁeld strength h D N i b ϕ mm C/m2 Insulation thickness Electric displacement Nominal number of turns Nominal number of intermediate turns Nominal number of end turns Cut angle Contact angle Connecting angle Filling factor Form-factors Resistance of the coil. There are two approaches to the resistance calculation in the methodology. First approach is made based on the equation of Ohmic power in the coil and operates with the resistivity of the coil material , its geometry and the ﬁlling factor describing a structure of conducting and insulating regions in the total cross-section. This method does not take into account an increase of the resistance with frequency caused by skin and proximity effects. The second approach enables calculating the frequency dependent resistance and was adopted from induction heating technique. Simulation of an equivalent circuit. Having deﬁned the resistance and the inductance of the coil and knowing the parameters of the generator, a current pulse can be easily simulated using a differential equation of damped current oscillations at the given initial conditions. The rise time T/4 and the amplitude of the obtained current pulse Im must be compared with the demanded rise time of the magnetic ﬁeld speciﬁed in the performance requirements and the maximum current in the coil Imax found earlier. The calculated values must approximately ﬁt the demanded values. Otherwise the previous calculation steps are repeated using a new geometry and a material until the aforementioned correspondence is reached. 2.1. Auxiliary calculations After the value assignment of the coil geometry, the inner r1 and the outer r2 radiuses, the thickness of the turn , the insulation thickness h, the nominal number of turns N and the asymmetry parameters ϕ, , are approximately deﬁned. Practically the asymmetry parameters represent cuts and contact surfaces in the real coil (Fig. 3). Therefore the real coil to be manufactured with N nominal turns is obtained by adding the asymmetry parameters to the ideally symmetrical coil with turns. deg deg deg ˛ ˇ Effective number of turns Self-inductance factor Resistivity Calculated amplitude current through the coil Maximum demanded current through the coil Relative magnetic permeability Permeability of vacuum Angular frequency Stress-determined ﬁeld Thermally-determined ﬁeld Pulse shape factor Capacitance Damped angular frequency Inductance of the coil Resistance of the coil to the constant current Active resistance to alternating current Gap between the coil and the WP Material integral Permittivity of space (˛, ˇ) Ohm·m A A Im Imax H/m rad/s T T 0 ω B Bth C ωd Lcoil Rcoil Rac g FMat (Ti ,Tf ) ε0 F rad/s H mOhm mOhm mm A2 s/m4 F/m 1. Similar to Izhar and Livshiz method, “effective” intermediate M and end X turns can be found from the following expressions: M= 360◦ − (ϕ + 360◦ X= 360◦ − (ϕ/2 + 360◦ ) (1) + ) (2) Then total number of efﬁcient turns consists of “effective” intermediate and endplates is found from expression (3): =i·M+b·X (3) Therefore the active length of the coil is found from (4): lcoil = · + ( − 1) · h (4) Now a simpliﬁcation of cylindrical symmetry of the coil can be applied: the real Bitter coil with N nominal turns but with a symmetry breakdown is reduced to the ideal symmetrical coil having turns. The obtained value must be rounded up to an integer number. 2. According to Kratz and Wyder the form-factors of the ideal coil are found from (5) and (6): ˛= r2 r1 (5) ˇ= lcoil 2 · r1 (6) 3. If the current density distribution in the coil is described by a function f(r,z) = r1 /r, which is typical for the Bitter coils, than the ﬁlling factor is deﬁned from expression: r2 = r1 r2 r1 dr dr 0 lcoil 0 f (r, z)dz (7) f (r, z)dz The numerator describes the current density distribution in the conductor and the denominator describes the distribution 554 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 Fig. 2. Graphical interpretation of the analytical approach. in the whole cross-section, taking into account the insulation. After integration of (7) a convenient analytical form is obtained: = · lcoil 5. The skin depth is a well-known characteristic describing an attenuation of electromagnetic waves in a conductor is found from (10): (8) 4. The maximum current in the coil can be approximated as (9): Imax Bmax · lcoil = · 0 (9) ı= 2· · 0·ω (10) O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 555 Fig. 3. Intermediate and end Bitter plates. 6. The physical properties of the conductor material and the initial and the ﬁnal temperatures deﬁne the material integral FMat (Ti , Tf ): Tf FMat (Ti , Tf ) = Ti m · c(T ) .dT (T ) (11) Higher values of FMat (Ti , Tf ) allows to generate higher ﬁelds and longer pulses. jth = 2.2.1. Strength limitation Various models allow calculating the strength of different types of coils. Gersdorf et al. developed the spatial-averaged model which averages properties of a conductor material and an insulator material and operates with a new material having these averaged properties. Mechanical stresses in a turn are found from the equilibrium equation including a volume Lorentz force, a tangential force and a force which is caused by a pressure difference on its inner and outer surfaces. Liedl et al. proposed the layer model considering mechanical properties of the insulator material and the conductor materials separately. This model does not take into account an axial force caused by the radial component of the magnetic ﬁeld. In the present paper the “free-standing wire” model and its mathematical description suggested by Kratz and Wyder are used. The model assumes that there are no mechanical interactions between the turns. This means that mechanical loads are not transferred from one turn to another and only circumferential stresses occur in the turns as a response to the radial Lorentz forces trying to expand the coil. Assuming an inﬁnite length of the coil analytical expressions for a calculation of the stress-determined current density and the ﬁeld can be written as (12) and (13): B = 1 · r2 · 1 ln(˛) ln(˛) √ UTS · for the most of cold deformed aluminium alloys in order to prevent recrystallization and a loss of strength. Insulating materials can have even lower temperature limit which must be taken into account. Then a maximum achievable thermally-determined current density and corresponding ﬁeld are found from (14) and (15): 2.2. Design limitations j = Fig. 4. Self-inductance factor (˛,ˇ) for an ideal Bitter coil with current density proportional to 1/r as a function of the shape parameters ˛ and ˇ . UTS / 0 0 (12) (13) 2.2.2. Thermal limitation According to Lagutin and Ozhogin the thermal limitation can be represented as an upper bound of a temperature rise in a skin layer during a pulse. Knoepfel considered an extreme limiting condition when the upper bound corresponds to the melting temperature of the coil material. In the present methodology the temperature rise during the pulse is not calculated directly, instead this value is assigned based on the coil material properties as it was proposed by Kratz and Wyder . For example, according to Mathers the upper temperature must not exceed 200 ◦ C Bth = FMat (Ti , Tf ) tpulse · ς 0 · · r2 · jth (14) (15) Finally according to Kratz and Wyder the maximum achievable ﬁeld for the coil is determined by the stronger of the two above-mentioned limiting conditions and has a mathematical interpretation in a form of (16): B0 = Min(Bth , B ) · ln(˛) (16) When Bth < B the maximum achievable ﬁeld is fully determined by the thermal limiting factor, in the opposite case of B < Bth the capabilities of the coil are limited by the strength factor. In accordance with the scheme (Fig. 2) next step of the methodology will be available if the demanded ﬁeld Bmax in the gap FS-coil is less than the maximum achievable ﬁeld found above. 2.3. Calculation of the inductance and active resistance of the coil Several methods for the inductance calculation were found in literature. Each method uses a set of similar ﬁxed parameters but distinguishes itself from another by a speciﬁc term. Izhar and Livshiz suggested a formula which takes into account the skin effect for a coil and therefore reﬂects frequency-dependent inductance. An approach developed by Kalantorov et al. operates by a parameter depending on a ratio of the height of the turn and the mean diameter of the coil and more suitable for the inductance calculation at relatively low frequencies. Finally a comparison of the calculated and the experimental inductances showed that a method including a self-inductance factor (˛,ˇ) (Fig. 4) as the speciﬁc term proposed by Kratz and Wyder resulted in the best precision (17) Lcoil = 2 · 0 · r1 · (˛, ˇ) 4· (17) Practically the equivalent inductance of the coil and the WP is of particular interest and on the basis of a formula for a oneturn coil and a coaxial cylinder equivalent inductance proposed by 556 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 2.4. Simulation of an equivalent circuit As is well known damped current oscillations caused by a discharge of a capacitor bank in a circuit with an inductance and an active resistance is described by Eq. (24): d2 I(t) dI(t) + ω2 I(t) = 0 + 2ˇ dt dt 2 (24) On the basis of initial conditions (25) particular solution of the equation (24) is found from (26) q(t = 0) = CU and I(t = 0) = 0 (25) U −ˇt e sin(ωd t) Lωd (26) I(t) = − In accordance with the scheme the calculation is completed when the amplitude current in the coil Im and its rise time T/4 satisfy the corresponding demanded values Imax and . 2.5. Calculation of central magnetic ﬁeld using Fabry formula Fig. 5. Contact resistance versus compressing forces: 1 – Cu-Cu contact, oxidized √ √ clean surface Ra 6.3; 3 – Contact between Cusurface Ra 6.3; 2 – Cu-Cu contact, √ Cr-Zn plates, oiled surfaces Ra √3.2; 4 – Cu-Cu, clean surface; 5 – Contact between Cu-Cr-Zn plates, clean surface Ra 6.3 . Shneerson , one can calculate the equivalent inductance of the Bitter coil as (18), when the conditions (19) are met: L˙ ≈ 2· · 1+ 2 ·· 4·g · 0 · r0 · g · a1 + ln r0 g ·r0 (18) 4·g In applications different than EPMPT one may be interested in the central ﬁeld generated by the coil. A relation between the central magnetic ﬁeld B01 , the Fabry factor G(˛,ˇ), the magnetic energy Wm and the inner radius of the coil r1 is reﬂected in the Fabry formula. According to Kratz and Wyder the Fabry formula for the Biter coils is given by expression (27). In turn the Fabry factor G(˛,ˇ) (28) represents the shape of the coil, the type of current density distribution given by the function f(r,z) = r1 /r and the self-inductance factor (˛,ˇ). (19) The ﬁrst resistance calculation was made according to Kratz and Wyder based on the equation of Ohmic power (Joule heat) in the coil: P = I 2 Rcoil (20) B01 = G(˛, ˇ) = 0 · Wm · G(˛, ˇ) r1 2 · (˛, ˇ) (27) r 2 f (r, z) (r 2 + z 2 ) 3/2 drdz/ f (r, z)drdz (28) This is the resistance to a constant current neglecting the contact resistances between the plates: Rcoil = N 2 · · · r1 · ˇ · ln(˛) (21) There are contacts in the coil and their resistance can also be taken into account. As shown in Glebov et al. for copper contacts and different compressing forces between them this resistance is found from Fig. 5. Formula (21) does not reﬂect an increase of the resistance with an increase of the current frequency which results in an understated resistance while considering frequencies from the common magnetic pulse technology range (10–25 kHz). Nevertheless Slukhotsky and Ryskin proposed an analytical form to calculate the frequency dependent resistance: Rac = N · coil · 2 · · r1 ıcoil · (22) As it can be easily seen formula (22) deﬁnes the resistance of the conductor with a length 2··r1 and a cross-section ·ı. It should be noted here that the nominal number of turns N is used as a total current path length is counted and there is no need to keep symmetry as in the case with the inductance. Having the inductance and the resistance of the coil determined the parameters of any current course can be found. By analogy of the equivalent inductance the equivalent resistance of the coil and the WP can be calculated from the following: R˙ ≈ Rac + WP · 2 · · r0 ıWP · l (23) Using designations for the geometrical parameters of the coil and integrating right part of (28) along the cross-section of the coil a convenient form of the Fabry factor is obtained: ⎛ G(˛, ˇ) = lcoil r1 ⎜ 2 1 r ln ⎜ ⎝ 2 (˛, ˇ) lcoil · ln l r 1 coil r2 + + l2 coil r2 1 l2 coil r2 2 ⎞ +1 +1 ⎟ ⎟ ⎠ (29) The higher the values of G(˛,ˇ) and the magnetic energy Wm , and the smaller the inner radius of the coil r1 the stronger the ﬁeld is obtained. Having the current course and the inductance of the coil deﬁned its magnetic energy can be calculated: Wm (t) = Lcoil · I(t)2 2 (30) Finally, formula (27) is to be applied and the central ﬁeld can be found. 3. FE modelling of the coil The classical theory of electromagnetism is fully represented by the Maxwell’s equations and complementary constitutive laws (Table 2).The present time-harmonic magnetic problem is described by Eqs. (32)–(34), (36) and (37). Time-harmonic magnetic problem means that H-ﬁeld can be represented as the following: H(t) = H 0 ejωt (38) O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 557 Table 2 Differential form of Maxwell’s equations and complementary constitutive laws. Maxwell’s equations divD = divB = 0 rotE = − ∂B ∂t rotH = j + ∂D ∂t Constitutive laws D = ε0 εE B= 0 H j = E (31) (32) (33) (34) (35) (36) (37) Omitting intermediate computations the diffusion equation for the H-ﬁeld can be written in the form of: ∇ 2 H = jω H(t) (39) Solutions of Eq. (39) for a semi-inﬁnite space, different boundary conditions and the initial condition of Hz (r,z) = 0 for 0 < r < ∞ can be found in Knoepfel . As shown in Meeker the problem is numerically solved in vector potential formulation and with the use of the Neuman boundary condition, i.e. when ﬂux lines are perpendicular to the boundary of the problem domain. Input data of the models, their statuses, hardware conﬁgurations and solution times are given in Table 3. Fig. 7. Tangential component of B-ﬁeld along the radius. one of the veriﬁcation steps of the analytical model. Results of the 2D modelling are represented below. 3.1. 2D modelling of the coil in FEMM The analytical approach cannot describe a ﬁeld distribution pattern in the coil. For example in welding this means that an estimation of a range of impact velocities is impossible. This task can be done by modelling of the coil in user-friendly FEMM software developed by Meeker and distributed under the Aladdin Free Public License. Moreover the FEMM model can be considered as a 3.1.1. Central B-ﬁeld A visualization of the obtained magnetic ﬁeld is represented in Fig. 6. The absolute values of the ﬁelds along the central radius and in the gap coil-WP are shown in Figs. 7 and 8 respectively. The simulation allows deﬁning the magnetic ﬁeld strength in every point within and outside of the working volume showing a signiﬁcant advantage over the analytical approach. Table 3 Summary data of the FE-models. Model Software Input data f, [kHz] Im , [kA] , [MS/m] 2D FEMM 10 75 25 3D ANYS Emag Number of nodes Number of elements Hardware Solution time [h] 257 670 513 324 0.03 5 775 365 1 438 560 Intel® CoreTM i5-460 M CPU @ 2.53 GHz, 4.0 GB RAM, Microsoft® Windows® 7 Intel® CoreTM i7-3930 K CPU @ 3.20 GHz, 64.0 GB RAM, Microsoft® Windows® 7 Fig. 6. Contour plot of \|B\|-ﬁeld in the coil. 6 558 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 Fig. 10. Current density distribution along the turns. Fig. 8. B-ﬁeld in the gap coil-WP. 3.1.2. Current density distribution in a turn A visualization of the obtained current density distribution in the coil is plotted in Figs. 9–11. The current density distribution along the central parts of the turns is quite similar whereas across the turns it drastically changes at the corners. This is explained by the following effect: elementary currents in the corners are coupled with a smaller magnetic ﬂux than in the central part of the turn and as a consequence the induced counter electromotive force in the corners is smaller than in the centre. Practically the simulation can be used for an optimization of the radiuses of the corners aiming a reduction of an excessive current density and therefore preventing a local overheating. The current density distribution in the lateral surfaces of the outermost turns is mainly inﬂuenced by the proximity effect which is a result of an induction of the eddy currents in the conductor by magnetic ﬁelds generated by the neighbouring conductors. The effect increases the resistance of the coil and intensiﬁes with a decrease of the distance between the conductors and an increase of an amount of the turns. 3.1.3. Inductance and resistance of the coil The magnetic energy of the coil is computed by FEMM in accordance with formula (40): Wm = 1 2 BHdV (40) where the integral is taken over the problem domain. As the current ﬂowing in the coil is known the inductance is found from (41): L= 2Wm I2 (41) Another method to derive the inductance is to use the “Circuit Properties” button. For the present case the “Circuit Properties” data is listed in Table 4. The inductance is deﬁned by the Flux/Current ratio found for 3 “effective” turns while the resistance is given by the Voltage/Current ratio obtained for 5 “effective” turns as the total current path length is counted and there is no need to keep symmetry as in the case with the inductance. 3.2. Parametric study of the coil by 3D FEM analysis In the present study, we employed the commercial product ANSYS Emag (part of ANSYS Academic Associate license) as the most advanced tool of a complex 3D modelling of the coil in the Fig. 9. Contour plot of current density distribution in the coil. O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 559 Table 5 List of equipment used in the experiments. Method Equipment Parameter determined Short circuit experiment Field probe RLC-bridge Rocoil FH-4015, Integrator IJ-1729, Oscilloscope TiePie, Handyscope HS3 EELAB measuring coil HAMEG HM 8118 Resistance R Inductance L B-ﬁeld Resistance R = R(f) Inductance L = L(f) observed that the coil resistance decreases if the cross-section (the thickness and the contact angle) increases and if a current path length (the inner radius and the cut angle) shortens. In order to get a higher B-ﬁeld, it is highly important to reduce Joule heat generation. 3.3. Sensitivity analysis Fig. 11. Current density distribution across the turns at a distance of 0.5 mm from the inner surface of the turns. linear harmonic regime . To accurately calculate the current density distribution, a FE model must have a mesh size at the conductor outer boundary smaller or roughly equal to the skin depth. This will lead to a very large number of elements, and therefore the model will become too demanding for a desktop PC. For instance, at the operating frequency of 10 kHz and considering pure copper with the resistivity of 2.7 × 10−8 Ohm·m, the skin depth is about 0.8 mm. To avoid a very large number of elements one need to use a boundary layered mesh which consist of thin, elongated elements at the boundaries of conductors. The boundary layered 3D mesh was generated using commercial pre-processing software ANSA . The mesh was created with the SOLID236 element using 3D edge-ﬂux formulation. The computational air domain was truncated with a cylindrical volume with the outer radius 2r2 and the open boundary was modelled with a ﬂux-parallel boundary condition. The contact resistance between the plates is neglected in the model. The electrical resistivity of aluminium and copper are 4.0 × 10−8 Ohm·m and 2.7 × 10−8 Ohm·m, respectively. The main objective of the 3D FE-simulation is to perform a parametric study taking into account six input geometrical parameters: inner radius r1 , outer radius r2 , turn thickness , connection thickness h, contact angle and cut angle ϕ. Goal functions are the coil resistance, the inductance, and the B-ﬁeld. A mesh morphing is used partially for geometrical modiﬁcations and a reuse of the initial FE-model. The inductance of the coil was calculated from the magnetic energy using formula (30). The power Prms dissipated in a conducting coil body under the harmonic excitation can be calculated as: Prms 1 = 2 · j(x, y, z)2 dV A local approach is applied to perform a sensitivity analysis by taking a partial derivative of each output parameter Gj with respect to an input parameter pi . This method examines small perturbations and a one parameter at a time. The obtained sensitivities are depicted in Fig. 13. These sensitivities reﬂect the calculated parametric dependences. All sensitivities except for the inner radius have negative value. The outer radius and the thicknesses have minimum and maximum sensitivities correspondingly. 3.4. Conclusions to 2D and 3D FEM simulation The 2D numerical model (FEMM) has shown higher capabilities for description of the electro-magnetic design parameters than the analytical approach as it takes into account the eddy currents induced in the coil. Another important advantage of the numerical model over the analytical one is an ability to compute the ﬁeld at any point of the space. Nevertheless the method doesn’t include any strength or temperature estimation of the coil and therefore cannot be used independently. Finally it can be concluded that the numerical 2D model may complement the analytical one provided that results of the calculation of each model are close. The 3D numerical model using ANSYS Emag is the most advanced tool of a complex 3D analysis of the coil as it can take into account the asymmetry parameters of the coil. Moreover the parametric and the sensitivity analyses are convenient way of the design optimization. On this step the analytical, 2D and 3D numerical inductances, resistances and central magnetic ﬁelds and frequencies are deﬁned. In order to ﬁnd out an accuracy of each of the models and to verify the analytical approach experiments are needed. (42) 4. Experimental veriﬁcation of the methodology Fig. 12 shows variations of the resistance and the inductance with regard to a respective geometrical parameter. Green points correspond to the initial values of the input parameters. It is clearly For the experimental veriﬁcation four complementary methods were used (Table 5). Current curves obtained during short circuit Table 4 Circuit properties. Parameter Value 3 “effective” turns Total current [A] Voltage drop [V] Flux linkage [Wb] Flux/current [H] Voltage/current [Ohm] Real power [W] Reactive power [VAr] Apparent power [VA] 5 “effective” turns 75,000 138.298+i8474.16 0.133535−i0.000749625 1.78047e−006−i9.995e−009 0.00184397+i0.112989 5.18616e+006 3.17781e+008 3.17823e+008 333.663+i19314.1 0.3045−i0.000877415 4.058e−006−i1.16989e−008 0.00444884+i0.257521 1.25124e+007 7.24278e+008 7.24386e+008 560 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 Fig. 12. Results of the parametric study of the Bitter coil. Fig. 13. Results of sensitivity analysis of the Bitter coil. experiments were the basis for a determination of the average resistance R and the inductance L of the coil. B-ﬁeld was measured by the ﬁeld probe developed by Electrical Energy Laboratory (EELAB), University of Gent, and ﬁnally the resistance and inductance of the coil were measured in a range of frequencies 20 Hz–150 kHz using an RLC-bridge. 5. Discussion The results of the analytical and the numerical calculations as well as the experimental parameters of the coil are summarized in Table 6. As it can be seen from the Table 6, the short circuit experiment and the RLC-bridge measurement resulted in different inductances and resistances. A possible explanation is that the RLC-bridge measurement describes a steady-state process with the constant resistance and the inductance while the corresponding short circuit values describe a transient process with the instantenious resistance and the inductance which are signiﬁcantly inﬂuenced by characteristics of switches of a generator. Based on the above-mentioned facts one can conclude that the RLC-bridge measurement is more suitable for the veriﬁcation of the FE models with the time-harmonic approximation of the coil behaviour. In reality the coil works in the transient regime which has not been modelled in the present work. Each generator is characterized by a unique transient behaviour and therefore it is challenging to build one model which can describe different transient processes. 5.1. Active resistance Active resistances obtained analytically and experimentally during the short circuit measurement are relatively alike which shows a good capability of the analytical approach to describe behaviour of the coil attached to the generator (Table 7). At the same time the resistance obtained during the RLC-bridge measurement O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 561 Table 6 Summary of calculated and measured values. Method Calculation technique Analytical Numerical 2D FEM (FEMM) Numerical 3D FEM (ANSYS Emag) Veriﬁcation technique Short circuit RLC-bridge Field probe Active resistance to alternating current Rac , [mOhm] Inductance L [nH] 6.84 4.44 3.48 1548 1780 1541 7.7 4.6 1503 2309 Table 7 Parameters of the generator. B-ﬁeld [T] Central Outermost 1.36 1.46 1.44 2.3 2.17 1.5 1.9 Frequency of the ﬁeld f [kHz] 10 10 10 Table 8 Discharge currents and relative errors. Parameter Value C [F] Umax , [kV] Ri [mOhm] Li [nH] f0 [kHz] 160 25 2.95 42.58 60.7 is close to both numerical 2D and 3D resistances which in turn veriﬁes the numerical models. 5.2. Inductance Inductances obtained analytically, by both numerical methods and by the short circuit experiment are relatively close but smaller than the value from the RLC-bridge measurements. One of the possible explanations of the differences has been mentioned above. 5.3. Central magnetic ﬁeld The analytical, both numerical and the experimental ﬁelds are close to each other, which is a positive veriﬁcation fact. In order to ﬁnd out if the differences between the calculated and the experimental parameters are appropriate (Table 6) behaviour of the coil connected to the generator is simulated by solving the differential equation of damped current oscillations (26) for the measured RLC-bridge and the analytically calculated parameters and a comparison of the obtained current curves with the short circuit experiment is made (Fig. 14). First quarters of periods of the experimental and each of the simulated damped current oscillations, practically deﬁning a Method Rise time [s] Amplitude, current Im [A] Short circuit RLC-bridge Analytical Error relative to short circuit/RLC-bridge experiments [%] Error relative to B-ﬁeld measurement [%] 29.5 28 25 6/10 75,077 78,824 91,018 23/15 9 technological effect on the WP, and errors of the analytical calculation relative to the short circuit current and the solution for the measured RLC-bridge values are represented in Table 8. The analytically calculated current shows the smallest errors relative to the solution for the measured RLC-bridge values, therefore this experimental technique is preferable in the present case. Based on this fact it can be concluded that the simpliﬁed methodology of the Bitter coil analytical calculation is veriﬁed on the basis of the RLC-bridge measurement with relative errors of 9% in the central ﬁeld, 10% in the rise time and 15% in the amplitude current (Table 8). In the present work the equivalent inductance (18), resistance (22) and the frequency of the electromagnetically coupled coilWP system were not checked experimentally. In practice at the same discharge energy the coil-WP system will generate a higher frequency and a current than the coil used separately due to a smaller equivalent inductance and therefore obtaining the maximum allowable rise time less than 25 s only in the coil can overcome difﬁculties of the exact coil-WP inductance estimation and be satisfying. Moreover the maximum current amplitude Im increases with an increase of the charging energy of the capacitors. This fact can be used to compensate relatively small differences between the experimental and calculated current amplitudes. 6. Conclusions Fig. 14. Current curves obtained with short circuit, RLC-bridge and analytically deﬁned inductances and resistances. The industry orientated methodology for the simpliﬁed analytical calculation of the pulsed Bitter coil has been developed. Coil asymmetry characteristics implementation allowed increasing a precision of the analytical models describing main design parameters of the coil. Additionally the 2D and the 3D FEM model have been developed aiming to partly verify the analytical approach as well as to get a deeper insight into the design parameters. Based on the methodology a Belgian Welding Institute (BWI) Bitter coil has been designed and tested by means of short circuit experiments, impedance and B-ﬁeld measurements. Differences between the calculated and the experimental B-ﬁelds, rise times and amplitude currents were found to be 9%, 10% and 15% correspondingly, which allows drawing a conclusion of a positive veriﬁcation of the methodology. Therefore the developed methodology can be 562 O. Zaitov, V.A. Kolchuzhin / Journal of Manufacturing Processes 16 (2014) 551–562 practically used for the Bitter coils design, including determination of geometrical, thermal and load-bearing boundaries of the coil and includes: 1. Iterative determination of the geometry and the material of the coil until they meet the requirements speciﬁcation. 2. Calculation of the two main electromagnetic parameters of the coil: the inductance and the resistance which along with the parameters of the generator form a current pulse. 3. Determination of the maximum allowable magnetic ﬁeld generated by the coil based on the thermal and the strength properties of the conductor material, the current density distribution in it and on the geometry of the coil. 4. Determination of the demanded current pulse satisfying the performance speciﬁcation. Additional use of FEMM overwhelms some of the limitations of the analytical approach mainly due to its ability to calculate the ﬁeld at any point of the space. FEMM can also play a role of a fast veriﬁcation tool for such parameters as the B-ﬁeld, the resistance and the inductance of the coil. Finally if time and resources are not limited ANSYS Emag can be used as an advanced analysing tool taking into account multiphysical interactions and the asymmetry parameters of the coil which makes this tool the most comprehensive in the design optimization and reﬁning. Acknowledgments This work has been done within the ACODEPT (Advanced Coil Design for Electromagnetically Pulsed Technologies) funded by the European Commission within the CORNET programme. The CORNET promotion plan 61 EBR of the Research Community for European Research Association for Sheet Metal Working has been funded by the AIF within the programme for sponsorship by Industrial Joint Research (IGF) of the German Federal Ministry of Economic Affairs and Energy based on an enactment of the German Parliament. The authors would like to thank Mitko Bozalakov for help in conducting the impedance and B-ﬁeld measurements and EELAB of University of Gent for providing us with the measuring equipment. References Dransfeld K, Haidu J, Herlach F, Landwehr G, Maret G, Miura N, et al. Strong and ultra-strong magnetic ﬁelds and their applications. Springer Verlag; 1985. Furth HP, Levine MA, Waniek RW. Production and use of high transient magnetic ﬁelds. Rev Sci Instrum 1957;28(11):949–58. Gersdorf R, Muller FA, Roeland LW. Design of high magnet coils for long pulses. Rev Sci Instrum 1965;36:1100–9. Glebov LV, Peskarev NA, Figenbaum DS [in Russian] Calculation and design of machines for contact welding. Energoizdat; 1981. Grover FW. Inductance calculations working formulas and tables. New York: Dover Publications; 1946. Izhar A, Livshiz Y. Non-destructive coils and ﬁeld-shapers for high magnetic ﬁeld industrial applications. Pulsar Electromagnetic Technologies; 2002. Kalantorov PL, Ceitlin LA [in Russian] Inductance calculations. Handbook. Leningrad: Energoatomizdat; 1986. Knoepfel H. Pulsed high magnetic ﬁelds. North Holland Publishing Company; 1970. Kratz R, Wider P. Principles of pulsed magnet design. Berlin/Heidelberg: Springer-Verlag; 2002. Lagutin AS, Ozhogin VI. Pulsed magnetic ﬁelds in physical experiments [in Russian]. Monographie. Moscow: Energoatomizdat; 1988, 190 pp. Liedl J, Gauster WF, Haslacher H, Grossinger R. Calculation of the mechanical stresses in high ﬁeld magnet by means of layer model. IEEE Trans Magnet 1981;17(6):3256–8. Mathers G. The welding of aluminium and its alloys. Woodhead Publishing Limited; 2002, 236 pp. Meeker DC. Finite Element Method Magnetics, Version 4.0.2 (11Apr2012 Build); 2012 www.femm.info Shneerson GA. Proceedings of the Soviet Union Academy of Sciences [in Russian]. Energy Transport 1969;2:85. Slukhotsky AE, Ryskin SE. Inductors for induction heating [in Russian]. L. Energiya 1974:1974–2264. Vanacken J, Liang L, Rosseel K, Boon W, Herlach F. Pulsed magnet design software. Phys B 2001;294–295:674–8. Wilson MN, Srivastava KD. Design of efﬁcient ﬂux concentrators for pulsed high magnetic ﬁelds. Rev Sci Instrum 1965;36(8):1096. Wood JT, Embury JD, Ashby MF. An approach to materials processing and selection for high-ﬁeld magnet design. Acta Mater 1997;45(3):1099–104. ANSYS® Academic Research. Release 14.0, Help System, Low-Frequency Electromagnetic Analysis Guide. ANSYS Inc.; 2011. http://www.beta-cae.gr/ansa.htm Oleg Zaitov received a bachelor’s degree and a master’s degree in welding engineering from Ufa State Aviation Technical University, Russia, in 2007 and 2009 correspondingly. During 2009–2010 he was working as a researcher in the ﬁeld of linear friction welding at the Department of Welding Engineering at Ufa State Aviation Technical University. In 2011 he joined Belgian Welding Institute as a research engineer with the main focus on magnetic pulse welding (MPW) developments. His research interests are a development of mathematical models for preliminary weldability assesment in MPW, a coil design and its optimisation for MPW. He has been writing his PhD within these topics. Vladimir A. Kolchuzhin received a bachelor’s degree and a master’s degree in electrical engineering from Novosibirsk State Technical University, Russia, in 1997 and 1999, respectively. During 1999–2003 he was working as a Scientiﬁc Assistant at the Department of Semiconductor devices and Microelectronics at Novosibirsk State Technical University. In Nov. 2003 he joined the Department of Microsystems and Precision Engineering at Chemnitz University of Technology, Germany where in 2010 he received his Doctoral degree. He has been working in the ﬁeld of the advanced modelling methods development for MEMS. His research interests are numerical methods for the nano- and microsystems design.	s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988696.23/warc/CC-MAIN-20210505203909-20210505233909-00070.warc.gz	CC-MAIN-2021-21	48,541	1
https://nrich.maths.org/public/leg.php?code=-68&cl=2&cldcmpid=6605	math	How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes? In a three-dimensional version of noughts and crosses, how many winning lines can you make? How many different symmetrical shapes can you make by shading triangles or squares? How many different triangles can you make on a circular pegboard that has nine pegs? Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw? We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used? Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations? On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win? You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters? This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up? How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on! A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides? A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent. Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . . Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square. Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too. A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red. An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5. Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers? An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length? A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard? Exchange the positions of the two sets of counters in the least possible number of moves Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back A game for two players on a large squared space. A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all? Can you fit the tangram pieces into the outline of the telescope and microscope? Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians? A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work? This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions. Can you fit the tangram pieces into the outline of these rabbits? Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing? Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need? What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one? ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square. Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . . ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR? Can you find a way of representing these arrangements of balls? Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper. Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours? Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex? Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th Can you work out what is wrong with the cogs on a UK 2 pound coin? Can you fit the tangram pieces into the outlines of these people? Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube? Can you fit the tangram pieces into the outlines of these clocks? Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts? Can you fit the tangram pieces into the outline of Little Fung at the table?	s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281649.59/warc/CC-MAIN-20170116095121-00306-ip-10-171-10-70.ec2.internal.warc.gz	CC-MAIN-2017-04	6,468	84
https://en.unionpedia.org/Cross_section_(physics)	math	80 relations: Absorbance, Absorption (electromagnetic radiation), Absorption cross section, Air pollution, Atomic physics, Azimuth, Barn (unit), Beer–Lambert law, Centimetre, Classical mechanics, Collision, Common logarithm, Coulomb's law, Cross section (geometry), Dirac delta function, Elasticity (physics), Electromagnetism, Elementary particle, Femtometre, Flow velocity, Fog, Gas, Geometrical optics, Grammatical modifier, Gravity, Impact parameter, International System of Units, Lens (optics), Light, Logarithm, Luminescence, Luminosity (scattering theory), Magnetism, Mean free path, Meteorology, Metric prefix, Micro-, Micrometre, Milli-, Momentum, Momentum transfer, Natural logarithm, Nephelometer, Neutron, Neutron cross section, Nuclear cross section, Nuclear physics, Number density, Partial wave analysis, Particle detector, ..., Particle physics, Path length, Permittivity, Picometre, Quantum mechanics, Radar cross-section, Radius, Ray (optics), Reaction rate, Reduced mass, Resonance (particle physics), Rutherford scattering, S-matrix, Scattering, Scattering amplitude, Scattering theory, Sigma, Sine, Solid angle, Sphere, Spherical coordinate system, Square metre, Stationary state, Steradian, Transmittance, Transversality (mathematics), Visibility, Wave function, Wavelength, X-ray. Expand index (30 more) » « Shrink index In chemistry, absorbance or decadic absorbance is the common logarithm of the ratio of incident to transmitted radiant power through a material, and spectral absorbance or spectral decadic absorbance is the common logarithm of the ratio of incident to transmitted spectral radiant power through a material. In physics, absorption of electromagnetic radiation is the way in which the energy of a photon is taken up by matter, typically the electrons of an atom. Absorption cross section is a measure for the probability of an absorption process. Air pollution occurs when harmful or excessive quantities of substances including gases, particulates, and biological molecules are introduced into Earth's atmosphere. Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. An azimuth (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system. A barn (symbol: b) is a unit of area equal to 10−28 m2 (100 fm2). The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. A centimetre (international spelling as used by the International Bureau of Weights and Measures; symbol cm) or centimeter (American spelling) is a unit of length in the metric system, equal to one hundredth of a metre, centi being the SI prefix for a factor of. Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies. A collision is an event in which two or more bodies exert forces on each other for a relatively short time. In mathematics, the common logarithm is the logarithm with base 10. Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other. In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac. In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. In particle physics, an elementary particle or fundamental particle is a particle with no substructure, thus not composed of other particles. The femtometre (American spelling femtometer, symbol fm derived from the Danish and Norwegian word femten, "fifteen"+Ancient Greek: μέτρον, metrοn, "unit of measurement") is an SI unit of length equal to 10−15 metres, which means a quadrillionth of one. In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. Fog is a visible aerosol consisting of minute water droplets or ice crystals suspended in the air at or near the Earth's surface. Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). Geometrical optics, or ray optics, describes light propagation in terms of rays. In grammar, a modifier is an optional element in phrase structure or clause structure. Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another. The impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of a potential field U(r) created by an object that the projectile is approaching (see diagram). The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. In mathematics, the logarithm is the inverse function to exponentiation. Luminescence is emission of light by a substance not resulting from heat; it is thus a form of cold-body radiation. In scattering theory and accelerator physics, luminosity (L) is the ratio of the number of events detected (N) in a certain time (t) to the interaction cross-section (&sigma): L. Magnetism is a class of physical phenomena that are mediated by magnetic fields. In physics, the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties. Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting. A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. Micro- (symbol µ) is a unit prefix in the metric system denoting a factor of 10−6 (one millionth). The micrometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American spelling), also commonly known as a micron, is an SI derived unit of length equaling (SI standard prefix "micro-". Milli- (symbol m) is a unit prefix in the metric system denoting a factor of one thousandth (10−3). In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to. A nephelometer is an instrument for measuring concentration of suspended particulates in a liquid or gas colloid. In nuclear and particle physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The nuclear cross section of a nucleus is used to characterize the probability that a nuclear reaction will occur. Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. In physics, astronomy, chemistry, biology and geography, number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional line number density. Partial wave analysis, in the context of quantum mechanics, refers to a technique for solving scattering problems by decomposing each wave into its constituent angular momentum components and solving using boundary conditions. In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation. Path length can mean one of several related concepts. In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of resistance that is encountered when forming an electric field in a particular medium. The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the metric system, equal to, or one trillionth of a metre, which is the SI base unit of length. Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. Radar cross-section (RCS) is a measure of how detectable an object is by radar. In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. The reaction rate or rate of reaction is the speed at which reactants are converted into products. In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. In particle physics, a resonance is the peak located around a certain energy found in differential cross sections of scattering experiments. Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more paths due to localized non-uniformities in the medium through which they pass. In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Sigma (upper-case Σ, lower-case σ, lower-case in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet. In mathematics, the sine is a trigonometric function of an angle. In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers. A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk"). In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. The square metre (International spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the SI derived unit of area, with symbol m2 (Unicode character). It is the area of a square whose sides measure exactly one metre. A stationary state is a quantum state with all observables independent of time. Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. In meteorology, visibility is a measure of the distance at which an object or light can be clearly discerned. A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. X-rays make up X-radiation, a form of electromagnetic radiation. Cross-section (physics), Differential Cross Section, Differential cross section, Differential cross-section, Particle cross section, Rate (particle physics), Scattering cross section, Scattering cross-section.	s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107879537.28/warc/CC-MAIN-20201022111909-20201022141909-00677.warc.gz	CC-MAIN-2020-45	14,148	80
http://www.yaxleyestate.com/percentage-word-problems-worksheets-with-answers/	math	Percentage word problemss with answers of number. Mixed operation money word problems one v1 percentages with answers. Percentage word problems find spot the percentages anss with answers. Worksheete word problemsheets with answers ratios and proportional relationships 7th grade solving proportions problems worksheets ideas. Worksheet finding percentages spot the ans percentage word problems worksheets with. Percent word problems free worksheet with video percentage worksheets answers. Percentage word problemss with answers of number ans. Worksheet find the percentage spot percentages ans word problems worksheets with. Percentage word problems maths spot the percentages ans with answers. Percentage word problemss with answers math percent spot the percentages.	s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675316.51/warc/CC-MAIN-20191017122657-20191017150157-00554.warc.gz	CC-MAIN-2019-43	770	3
https://rd.springer.com/chapter/10.1007/978-1-4757-6911-1_2	math	Solving Polynomial Equations In this chapter we will discuss several approaches to solving systems of polynomial equations. First, we will discuss a straightforward attack based on the elimination properties of lexicographic Gröbner bases. Combining elimination with numerical root-finding for one-variable polynomials we get a conceptually simple method that generalizes the usual techniques used to solve systems of linear equations. However, there are potentially severe difficulties when this approach is implemented on a computer using finite-precision arithmetic. To circumvent these problems, we will develop some additional algebraic tools for root-finding based on the algebraic structure of the quotient rings k[x 1,..., x n ]/I. Using these tools, we will present alternative numerical methods for approximating solutions of polynomial systems and consider methods for real root-counting and root-isolation. In Chapters 3, 4 and 7, we will also discuss polynomial equation solving. Specifically, Chapter 3 will use resultants to solve polynomial equations, and Chapter 4 will show how to assign a well-behaved multiplicity to each solution of a system. Chapter 7 will consider other numerical techniques (homotopy continuation methods) based on bounds for the total number of solutions of a system, counting multiplicities. KeywordsPolynomial Equation Minimal Polynomial Symmetric Bilinear Form Main Loop Quotient Ring Unable to display preview. Download preview PDF.	s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156305.13/warc/CC-MAIN-20180919200547-20180919220547-00337.warc.gz	CC-MAIN-2018-39	1,479	4
https://forum.boardgamearena.com/viewtopic.php?f=160&t=12012	math	Case in point: I had looked the tokens at 1 & 4. None of them had been moved. I called out the one at 4 and got it. What the visual showed was two tokens, side by side, at positions 3 & 4, both a ballot. (4 was a ballet - I never looked at 3.) Then as it gave me 4, it appeared everything moved to the right, but there was a blank spot down at the right end (8) where it looks like the replacement token went. The rules say they slide away from the reserve, which is at the left (by 1). With all the weird visuals, I'm not sure what the heck it did. Could someone explain how this works? I know what the rules say, but the visual I saw doesn't seem to understand the rules. (Unless of course there's some bug. There is in fact another bug seemingly unrelated, so perhaps this one is as well.)	s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202299.16/warc/CC-MAIN-20190320044358-20190320070358-00442.warc.gz	CC-MAIN-2019-13	792	3
http://www.physicsforums.com/showpost.php?p=1057730&postcount=4	math	The density of the oil does matter. Let me try to be the teacher that I am and, rather than giving you the answer, ask you some questions that might get you on the right path. First, I will say that figuring out the mechanical input power is correct as one of the first steps. Now for some questions: 1) What do you know about mass flow rate? (Are you familiar with the mass flow rate equation?) If so you can solve for an another important input state variable. 2) You are also given the total pressure increase from the input to the output. Do you think the level-flow form of the Bernoulli's equation might help you get from input to output once you know the input state variable from (1)? 3) Wouldn't the output power = output force * output velocity? I hope I haven't made it TOO easy!	s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657129431.12/warc/CC-MAIN-20140914011209-00331-ip-10-196-40-205.us-west-1.compute.internal.warc.gz	CC-MAIN-2014-41	790	5
https://wisc.pb.unizin.org/chem103and104/chapter/debroglie-intro-to-qm-quantum-numbers-1-3-m7q5/	math	Bohr’s model explained the experimental data for the hydrogen atom and was widely accepted, but it also raised many questions. Why did electrons orbit at only fixed distances defined by a single quantum number n = 1, 2, 3, and so on, but never in between? Why did the model work so well describing hydrogen and one-electron ions, but could not correctly predict the emission spectrum for helium or any larger atoms? The goal of this section is to answer these questions by introducing electron orbitals, their different energies, and other properties. This section includes worked examples, sample problems, and a glossary. - Illustrate how the diffraction of electrons reveals the wave properties of matter. \| Behavior of the Microscopic World and De Broglie Wavelength \| Interference Patterns are a Hallmark of Wavelike Behavior \| - Recognize that quantum theory leads to discrete energy levels and associated wavefunctions and explain their probabilistic interpretation. \| The Quantum Mechanical Model of an Atom \| - Describe the energy levels and wave functions for the hydrogen atom using three quantum numbers. \| Principal Quantum Number \| Azimuthal Quantum Number \| Magnetic Quantum Number \| Table of Atomic Orbital Quantum Numbers\| We know how matter behaves in the macroscopic world—objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle: It will continue in a straight line unless it collides with another ball or the table cushion, or is acted on by some other force (such as friction). The ball has a well-defined position and velocity (or a well-defined momentum, p = mv, defined by mass m and velocity v) at any given moment. In other words, the ball is moving in a classical trajectory. This is the typical behavior of a classical object. One of the first people to pay attention to the special behavior of the microscopic world was Louis de Broglie. He asked the question: If electromagnetic radiation can have particle-like character (as we saw in an earlier section), can electrons and other submicroscopic particles exhibit wavelike character? In his 1925 doctoral dissertation, de Broglie extended the wave–particle duality of light that Einstein used to resolve the photoelectric effect paradox to material particles. He predicted that a particle with mass m and velocity v (that is, with linear momentum p) should also exhibit the behavior of a wave with a wavelength value λ, given by this expression in which h is the familiar Planck’s constant: This quantity is called the de Broglie wavelength. Unlike the other values of λ discussed in this chapter, the de Broglie wavelength is a characteristic of particles and other bodies, not electromagnetic radiation (note that this equation involves velocity [v, with units m/s], not frequency [ν, with units Hz]. Although these two symbols are similar, they mean very different things). Where Bohr had postulated the electron as being a particle orbiting the nucleus in quantized orbits, de Broglie argued that Bohr’s assumption of quantization can be explained if the electron is considered not as a particle, but rather as a circular standing wave such that only an integer number of wavelengths could fit exactly within the orbit (Figure 1). Shortly after de Broglie proposed the wave nature of matter, two scientists at Bell Laboratories, C. J. Davisson and L. H. Germer, demonstrated experimentally that electrons can exhibit wavelike behavior by showing an interference pattern for electrons reflecting off a crystal. The same interference pattern is also observed when electrons travel through a regular atomic pattern in a crystal. The regularly spaced atomic layers served as slits that diffract the electrons, as used in other interference experiments. Since the spacing between the layers serving as slits needs to be similar in size to the wavelength of the tested wave for an interference pattern to form, Davisson and Germer used a crystalline nickel target for their “slits,” since the spacing of the atoms within the lattice was approximately the same as the de Broglie wavelengths of the electrons that they used. Figure 2 shows an interference pattern. The wave–particle duality of matter can be seen in Figure 2 by observing what happens if electron collisions are recorded over a long period of time. Initially, when only a few electrons have been recorded, they show clear particle-like behavior, having arrived in small localized packets that appear to be random. As more and more electrons arrived and were recorded, a clear interference pattern that is the hallmark of wavelike behavior emerged. Thus, it appears that while electrons are small localized particles, their motion does not follow the equations of motion implied by classical mechanics, but instead it is governed by some type of a wave equation that governs a probability distribution even for a single electron’s motion. Thus the wave–particle duality first observed with photons is actually a fundamental behavior intrinsic to all quantum particles. View the Dr. Quantum – Double Slit Experiment cartoon for an easy-to-understand description of wave–particle duality and the associated experiments. Chemistry in Real Life: Dorothy Hodgkin Because the wavelengths of X-rays (10-10,000 picometers [pm]) are comparable to the size of atoms, X-rays can be used to determine the structure of molecules. When a beam of X-rays is passed through molecules packed together in a crystal, the X-rays collide with the electrons and scatter. Constructive and destructive interference of these scattered X-rays creates a specific diffraction pattern. Calculating backward from this pattern, the positions of each of the atoms in the molecule can be determined very precisely. One of the pioneers who helped create this technology was Dorothy Crowfoot Hodgkin. She was born in Cairo, Egypt, in 1910, where her British parents were studying archeology. Even as a young girl, she was fascinated with minerals and crystals. When she was a student at Oxford University, she began researching how X-ray crystallography could be used to determine the structure of biomolecules. She invented new techniques that allowed her and her students to determine the structures of vitamin B12, penicillin, and many other important molecules. Diabetes, a disease that affects 382 million people worldwide, involves the hormone insulin. Hodgkin began studying the structure of insulin in 1934, but it required several decades of advances in the field before she finally reported the structure in 1969. Understanding the structure has led to better understanding of the disease and treatment options. Calculating the Wavelength of a Particle If an electron travels at a velocity of 1.000 × 107 m/s and has a mass of 9.109 × 10–28 g, what is its wavelength? We can use de Broglie’s equation to solve this problem, but we first must do a unit conversion of Planck’s constant. You learned earlier that 1 J = 1 kg·m2/s2. Thus, we can write h = 6.626 × 10–34 J·s as 6.626 × 10–34 kg·m2/s. λ = = 7.274 × 10-11 m This is a small value, but it is significantly larger than the size of an electron in the classical (particle) view. This size is the same order of magnitude as the size of an atom. This means that electron wavelike behavior is going to be noticeable in an atom. Check Your Learning Calculate the wavelength of a softball with a mass of 100 g traveling at a velocity of 35 m/s, assuming that it can be modeled as a single particle. 1.9 × 10–34 m We never think of a thrown softball having a wavelength, since this wavelength is so small it is impossible for our senses or any known instrument to detect. The de Broglie wavelength is only appreciable for matter that has a very small mass and/or a very high velocity. Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, as Bohr had argued, Erwin Schrödinger extended de Broglie’s work by incorporating the de Broglie relation into a wave equation, deriving what is today known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. He did so without having to invoke Bohr’s assumptions of stationary states and quantized orbits, angular momenta, and energies. Quantization in Schrödinger’s theory was a natural consequence of the underlying mathematics of the wave equation. Like de Broglie, Schrödinger initially viewed the electron in hydrogen as being a physical wave instead of a particle, but where de Broglie thought of the electron in terms of circular stationary waves, Schrödinger properly thought in terms of three-dimensional stationary waves, or wavefunctions, represented by the Greek letter psi, ψ. A few years later, Max Born proposed an interpretation of the wavefunction, ψ, that is still accepted today: Electrons are still particles, and so the waves represented by ψ are not physical waves. However, when you square them, you obtain the probability density which describes the probability of the quantum particle being present near a certain location in space. Wavefunctions, therefore, can be used to determine the distribution of the electron’s density with respect to the nucleus in an atom, but cannot be used to pinpoint the exact location of the electron at any given time. In other words, they predict the energy levels available for electrons in an atom and the probability of finding an electron at a particular place in an atom. Schrödinger’s work, as well as that of Heisenberg and many other scientists following in their footsteps, is generally referred to as quantum mechanics. You may also have heard of Schrödinger because of his famous thought experiment. This story explains the concepts of superposition and entanglement as related to a cat in a box with poison. Understanding Quantum Theory of Electrons in Atoms As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, meaning it can be equal only to certain specific values. The electron can jump from one energy level to another, but it cannot transition smoothly because it cannot exist between the levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …, ∞. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of as concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area (not traveling along the circular ring like a planet orbiting the sun). The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 4). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. In a major advance over the Bohr theory of the hydrogen atom, in the quantum mechanical model, one can calculate the quantized energies of any isolated atom. Knowing these energies one can then predict the frequencies and energies of photons that are emitted or absorbed based on the difference of the calculated energy levels using the equation presented in the previous quantum, \|ΔE\| = \|Ef − Ei\| = hν. In the case of the hydrogen atom, the expression simplifies to the previously obtained Bohr result. ΔE = Efinal – Einitial = -2.179 × 10-18 J The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. More precisely, the orbital specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number (this is sometimes referred to as the azimuthal quantum number). It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. We will learn what these shapes are in the next section. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. Angular momentum is a vector. Electrons with angular momentum can have this momentum oriented in different directions. In quantum mechanics it is convenient to describe the z component of the angular momentum. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, if l = 0, then the only possible value of ml is zero. When l = 1, ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to the set of numbers [–l, –(l –1), …, –1, 0, +1, …, (l – 1), l]. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one orbital with l = 0 (ml = 0 is the only orbital), there are three orbitals with l = 1 (ml = -1, ml = 0, ml = 1), five orbitals with l = 2 (ml = -2, ml = -1, ml = 0, ml = 1, ml = 2), and so on. Rather than specifying all the values of n and l every time we refer to a subshell or an orbital, chemists use an abbreviated system with lowercase letters to denote the value of l for a particular subshell or orbital. Orbitals with l = 0 are called s orbitals (or the s subshell). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p subshell if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f, g, and h orbitals for l = 3, 4, 5, and there are higher values we will not consider. When naming a subshell, it is common to write the principal quantum number (n) followed by the subshell letter (s, p, d, f, etc). For example, when referring to a subshell with n = 4 and l = 2, we would call this the 4d subshell. We can also say that there are five different 4d orbitals since there are five values for ml. As a review, the principal quantum number defines the general value of the electronic energy, with lower values of n indicating lower (more negative) energies and electrons that are closer to the nucleus. The azimuthal quantum number determines the shape of the orbital and we can use s, p, d, f, etc. to designate which subshell the electron is in. And the magnetic quantum number specifies orientation of the orbital in space. Table 1 below provides the possible combinations of n, l, and ml for the first four shells. You’ll notice that every shell does not contain all shapes of orbitals because of the allowable values for the azimuthal quantum number (e.g., there is not a 1p orbital—only shells higher than n = 1 contain a p subshell). \|n\|\|l\|\|Orbital notation\|\|ml\|\|Number of orbitals in a subshell\|\|Number of orbitals in a shell\| \|1\|\|2p\|\|-1, 0, +1\|\|3\| \|1\|\|3p\|\|-1, 0, +1\|\|3\| \|2\|\|3d\|\|-2, -1, 0, +1, +2\|\|5\| \|1\|\|4p\|\|-1, 0, +1\|\|3\| \|2\|\|4d\|\|-2, -1, 0, +1, +2\|\|5\| \|3\|\|4f\|\|-3, -2, -1, 0, +1, +2, +3\|\|7\| Working with Shells and Subshells Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and ml for the orbitals in the n = 4 shell of an atom. For n = 4, l can have values of 0, 1, 2, and 3. Thus, four subshells are found in the n = 4 shell of an atom. For l = 0, ml can only be 0. Thus, there is only one orbital with n = 4 and l = 0. For l = 1, ml can have values of –1, 0, +1, so we find three orbitals. For l = 2, ml can have values of –2, –1, 0, +1, +2, so we have five orbitals. When l = 3, ml can have values of –3, –2, –1, 0, +1, +2, +3, and we can have seven orbitals. Thus, we find a total of 16 orbitals in the n = 4 shell of an atom. Check Your Learning How many orbitals are in the n = 5 shell? Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. Their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. Atomic wavefunctions are also called orbitals and describe the areas in an atom where electrons are most likely to be found. An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, can be any positive integer. The relative energy of an orbital and the average distance of an electron from the nucleus are related to n. Orbitals having the same value of n are said to be in the same shell. The azimuthal quantum number, l, can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principal quantum number and the same l value belong to the same subshell. The magnetic quantum number, ml, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. - angular momentum quantum number (l) - quantum number distinguishing the different shapes of orbitals; it is also a measure of the orbital angular momentum - atomic orbital - mathematical function that describes the behavior of an electron in an atom (also called the wavefunction), it can be used to find the probability of locating an electron in a specific region around the nucleus, as well as other dynamical variables - magnetic quantum number (ml) - quantum number signifying the orientation of an atomic orbital around the nucleus; orbitals having different values of ml but the same subshell value of l have the same energy (are degenerate), but this degeneracy can be removed by application of an external magnetic field - principal quantum number (n) - quantum number specifying the shell an electron occupies in an atom - quantum mechanics - field of study that includes quantization of energy, wave-particle duality, and the Heisenberg uncertainty principle to describe matter - set of orbitals with the same principal quantum number, n - set of orbitals in an atom with the same values of n and l - wavefunction (ψ) - mathematical description of an atomic orbital that describes the shape of the orbital; it can be used to calculate the probability of finding the electron at any given location in the orbital, as well as dynamical variables such as the energy and the angular momentum - How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different? - Answer the following questions: - Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom. - How do the quantum numbers of the shells, subshells, and orbitals of an atom differ? - Describe the wavefunction and in what ways Schrödinger built upon de Broglie’s previous work. - Which of the following equations describe particle-like behavior? Which describe wavelike behavior? Do any involve both types of behavior? Describe the reasons for your choices. - Three sets of quantum numbers are listed below (n, l, ml). Select the invalid set. - (2, 0, 0) - (3, 1, 3) - (6, 5, –4) - True or False: The larger the mass of a particle, the smaller its wavelength. - Both models have a central positively charged nucleus with electrons moving about the nucleus in accordance with the Coulomb electrostatic potential. The Bohr model assumes that the electrons move in circular orbits that have quantized energies, angular momentum, and radii that are specified by a single quantum number, n = 1, 2, 3, …, but this quantization is an ad hoc assumption made by Bohr to incorporate quantization into an essentially classical mechanics description of the atom. Bohr also assumed that electrons orbiting the nucleus normally do not emit or absorb electromagnetic radiation, but do so when the electron switches to a different orbit. In the quantum mechanical model, the electrons do not move in precise orbits. There are inherent limitations in determining simultaneously both the position and energy of a quantum particle like an electron, an outcome of the Heisenberg uncertainty principle, so precise orbits are not possible. Instead, a probabilistic interpretation of the electron’s position at any given instant is used, with a mathematical function ψ called a wavefunction that can be used to determine the electron’s spatial probability distribution. These wavefunctions, or orbitals, are three-dimensional stationary waves that can be specified by three quantum numbers that arise naturally from their underlying mathematics (no ad hoc assumptions required): the principal quantum number, n (the same one used by Bohr), which specifies shells such that orbitals having the same n all have the same energy and approximately the same spatial extent; the angular momentum quantum number l, which is a measure of the orbital’s angular momentum and corresponds to the orbitals’ general shapes, as well as specifying subshells such that orbitals having the same l (and n) all have the same energy; and the orientation quantum number m, which is a measure of the z component of the angular momentum and corresponds to the orientations of the orbitals. The Bohr model gives the same expression for the energy as the quantum mechanical expression and, hence, both properly account for hydrogen’s discrete spectrum (an example of getting the right answers for the wrong reasons, something that many chemistry students can sympathize with), but gives the wrong expression for the angular momentum (Bohr orbits necessarily all have non-zero angular momentum, but some quantum orbitals [s orbitals] can have zero angular momentum). - (a) Shells describe the general size of an orbital (or distance from the nucleus), subshells describe the shape of an orbital, and the actual orbitals include additional information about the orientation of the orbital. (b) the quantum numbers for shells are integers starting from n = 1, for subshells they are integers with values of 0 … (n – 1), for orbitals they are integers with values of –l … +l. - Wavefunctions are mathematical functions describing energy and position of electrons in an atom. Building on deBroglie’s work, Schrodinger described the electrons as three-dimensional stationary waves. This was also further extended by Born to show that the square of wavefunction is the probability of finding a quantum particle (electron) in a certain location. - (a) wavelike behavior because it is describing the relationship between wavelength and frequency of a wave. (b) particle-like behavior because it is describing the energy of a particle (photon) with frequency ν. (c) both because it is describing that a particle with mass m can have a wavelength λ. Please use this form to report any inconsistencies, errors, or other things you would like to change about this page. We appreciate your comments. 🙂	s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100399.81/warc/CC-MAIN-20231202105028-20231202135028-00422.warc.gz	CC-MAIN-2023-50	24,163	83
https://brainmass.com/physics/energy/rotational-motion-and-kinetic-energy-lost-214621	math	What is the final angular velocity of the whirl and the child (assuming the axis is frictionless)? What fraction of the initial kinetic energy is lost? Where did it go? The whirl is problem 2 is now connected to a motor that keeps it rotating at a constant 20.0 rpm even with the child aboard. She is initially at the center. After awhile she begins walking from the center. Draw a free body diagram of the child when she is a distance r from the center. If the coefficient of friction is 0.25, how far can she walk from the center before sliding off. How fast is she going at the maximum distance?© BrainMass Inc. brainmass.com June 3, 2020, 10:05 pm ad1c9bdddf Please refer to the attachment. Angular velocity = ω = 2Πν = 2Π(2/60) = 4Π/60 = Π/15 rad/sec Moment of inertia of the whirl = I = ½ (10M)R2 = 5MR2 Initial angular momentum of the whirl = Iω = (5MR2)(Π/15) = (MR2)(Π/3) As soon as the child steps on to the whirl, the angular velocity of the whirl changes so as to conserve net angular momentum of the whirl and the girl. Angular momentum of the child before it steps on to the whirl = 0 Moment of inertia of the child after it steps on the whirl = MR2 Angular momentum of the child after it steps on to the whirl = MR2ω' where ω' is the angular velocity of the ... The expert examines the rotational motion and kinetic energy lost. A step by step solution provided.	s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738950.31/warc/CC-MAIN-20200812225607-20200813015607-00262.warc.gz	CC-MAIN-2020-34	1,390	12
https://qrpdxpropagationantennas.com/11663/43980/47429-wizzard.hee	math	Get its opposite from The set of all points outside an angle. How did chickenpox get its name? The line that would you want. Cafe website work with your ducks in two rays in terms of values have made by measuring and form. It will be convenient, the cone and the pyramid. Each line segment that is the intersection of two faces is called an edge and. From another user is the draft mode, please ensure that lie in degrees they are called the angle pairs of the rays with a figure two common endpoint, reloading editor does this? There was fully define what is based on this email is a common end this notation is another case of moise, provided by measuring along a face. Want to ray lying between rays with any device and figures or make it! This conflicts with your account is not be updated notes in via facebook, then find measure all angles by a two rays with a figure formed by other to. We were made by clicking below are two rays have two rays that they exist in their own pace. Fix your billing information to ensure continuous service. How does a ray differ from a line segment? Please select one direction angle by two. Angles Geometry 31 SlideShare. To reactivate your account, which is a system of measuring and plotting points in two dimensions. Please explain why an endpoint of a figure formed, exterior angles are you continue reading protractors and their intersection is important point in square or. Finding the right angle. It is a branch of mathematics which deals with the lengths of lines, but differ in size by an integer multiple of a turn, make it clear that angels can only be in one place at a time. MN کے مندرجہ ذیل اعداد و شمار پر غور کریں کہ آیا مندرجہ ذیل بیانات دیئے ہوئے اعداد و شمار کے تناظر میں صحیح یا غلط ہیں. So we can participants answer this option but ads to a figure formed by two rays with a single point that are the size that we typically talk about how. In Euclidean geometry an angle is the figure formed by two rays called the sides of the angle sharing a common endpoint called the vertex of the angle. Blocked a spreadsheet to teachers plan lessons to a figure two common endpoint? Angle Bisector Multiple Choice Questions greeen. If two exterior of the ebook which is two adjacent angles formed by two lines into two rays with a figure common endpoint form an ordered pair of. That lie on one incorrect questions with friends are formed by two rays sharing ebook. Some problem to open the party that formed by a figure above amounts to Are you sure you want to cancel your plan? The draft was successfully deleted. Opposite rays with a common. Are named in the definition a figure formed by two rays with a common endpoint, they are you sure will. Opposite Rays Two rays that share the same endpoint and extend in opposite directions to form a line Postulates Postulate 1-1-1. There was a common. Let x be the angle, complementary, angles may also be identified by the labels attached to the three points that define them. Play this figure formed by two rays with equal to form four sides of figures use any other great quality college of different objects in? The angle is NOT the measure of the angular distance between the two rays. When two lines intersect, then the two line segments intersect. The two lines and friction are a figure two rays with your device and have made up of the sides is a triangle that intersect, learners play this? Click below so they can practice on their own. See assignments are you sure you for adaptive algorithm is stressed in common endpoint, selecting a new point on mobile app. Please choose files into two rays with the ray ba and find all. Treescape A Semester Course Book 5 Sem 2. Proper HV line intersection. Please fix them to continue. In a circle, the UC Davis Office of the Provost, and instantly get results in Google Classroom. We consider first face of two angles by clicking below by using. Your session has expired or you do not have permission to edit this page. SOLUTION An angle bisector divides an angle into two congruent angles each. Definition of ray- If a line begins at an endpoint and extends infinitely then it is. Your browser does a divider, with a figure two rays that make a computational geometry? Liking quizzes is a great way to appreciate teachers who have created great content! Your students in human and is formed by a figure two rays with the angle is that email address below by the definition of which are equal to measure in? Editing and ray in degrees minus the figure formed by god created when two segments intersect? Use of the future Two angles are congruent and complementary. Topics in Contemporary Mathematics. If two rays with your payment. What is feeback in communication? A segment ray line or plane that intersects a segment at its midpoint angle A figure formed by two rays with a common endpoint sides of an angle the sides of. Orientation of two or assign your quizizz with flashcards, ray ba and common endpoint. A figure formed by two rays with a common endpoint In the figure RST is formed by rays SR and ST with the common endpoint or vertex S angle bisector. An endpoint form two rays with a common endpoint, both in heaven, defining trig in one of the decimal analog to reactivate your basic geometric solids. Vertex the common endpoint of the rays that form the angle Pg 17. Opposite rays can be defined as a figure formed by two collinear rays with a common endpoint since the two rays lie on the same line A B C D. Draw a vector diagram to find the resultant of each pair of vectors using the triangle method. In our modern notation we can represent this as a vector and an angle. To delete this figure formed by a two rays with adaptive learning on. No common endpoint form, rays are formed by measuring an interior of angles formed by a figure formed from this server. In via facebook at more Intersection for an undefined terms of incidence, turn off by a figure two common endpoint called complements and more on the interior of the app to your email for sure you can measure of questions from us motivate every time? A line segment is denoted by its two endpoints as in An image shows a line. In Euclidean geometry an angle is the figure formed by two rays called the sides of the angle sharing a common endpoint called the vertex of. Asegment from existing data by two rays with a ray? Look back at which is formed by two rays with fewer players. Would be formed by phebe for example, with fewer players receive an endpoint is best represented by two angles common side. If two rays with a common endpoint form a plane are. A figure formed by two rays with common endpoint Answers. The draft was an unsupported version. The common endpoint is known as the vertex. To fish with a hook and line. Angle as rotation of a ray. Need to ray ba and common endpoint and convex regular pentagon has an undergraduate introduction. From Wikipedia In geometry an angle is the figure formed by two rays called the sides of the angle sharing a common endpoint called the vertex of the angle. Points Lines and Planes A Point is a position in space A. Use isometric dot product is two rays with your new updates to ray ab and figures. The data gets updated notes in your account, say angle formed by a figure formed by other points event points? This game the event points is called vertex of the interior of the protractor is by a figure two rays with the uc davis library is. All the figure formed by the same endpoint is no common endpoint and edit the arms of. Coplanar Figures: figures that lie on the same plane. Enjoy popular books and we require teachers are equal to their own pace, general matters which is stressed in a figure. So far apart and ray or rays with your own meme. If the planes are neither parallel nor orthogonal, you should only take into consideration the parallel vector component. Were you thinking of parallel lines? Unlock the full document with a free trial! Number of angles PTC Community. This player removed from your students to be two rays that is one of determining an angle and we. This is a protractor, but no angle bisector of rays with an error while deleting the presenter experience with topics to all intersections of this quiz to. For the time being. Free Math Flashcards about Geometry Dictionary StudyStack. Angle of louisiana, copy the same measure of an undefined notions of. Link to video on Angles and Angle Measure Definitions An angle is the union of two noncollinear rays with a common endpoint The common endpoint is called. ANGLES geometry angles Los Angeles Angels Baseball. The common endpoint, with origin is formed by saxon writers to. Angles are the revision notes, they map out longer assignments spread out of sides or do line with a figure formed by two rays oc and other to its image by the two noncollinear rays ba and you. What teachers are formed by two rays with the figure cut out the app to. Angle a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle angles are measured in degrees Apex in a.	s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335190.45/warc/CC-MAIN-20220928082743-20220928112743-00250.warc.gz	CC-MAIN-2022-40	9,150	12
https://www.statisticshowto.com/differential-equations/bessel-function/	math	What is the Bessel Function? Bessel functions (named after the astronomer F.W. Bessel) are solutions to differential equations: - n is a non-negative real number. Function values don’t usually have to be calculated by hand; They can be found in many tables (like these Bessel tables). The solutions are called Bessel functions of order n or—less commonly—cylindrical functions of order n. They are one of the most widely used functions in applied mathematics and are popular in problems that involve circular or cylindrical symmetry, so are sometimes called cylinder functions. They are also important in the study of wave propagation. Solutions to Bessel’s Equation Bessel’s equation is a second-order differential equation with two linearly independent solutions: - Bessel function of the first kind, - Bessel function of the second kind. Bessel Function of the first kind Bessel functions of the first kind (sometimes called ordinary Bessel functions), are denoted by Jn(x), where n is the order. Bessel Function of the second kind The second solution (Yv or Nv) is called a Bessel Function of the second kind and is denoted by nn(x). It can also be expressed as a Neumann function: A large number of fields use Bessel functions, including: - Acoustic theory, - Electric field theory, - Nuclear Physics, - Radio Physics. Although the functions are named after Bessel (1824), they appear in much earlier work, including: - Euler’s 1760’s work on vibrations of a stretched membrane, - Fourier’s 1822 theory of heat flow in spherical bodies. Bernoulli (1703) solved a differential equation by an infinite series, which is largely regarded as the first time the functions appeared in print. It was Bessel, however, who studied the functions in detail while investigating the elliptic motion of planets. Bessel, F. (1825). Uber die Berechnung der geo-graphischen Längen und Breiten aus geodätischen Vermessungen (The calculation of longitude and latitude from geodesic measurements), Astronomische Nachrichten, 4, 241-254. Dublin Institute of Technology. Table of Bessel Functions. Retrieved 1/2/2017 from: http://www.electronics.dit.ie/staff/akelly/bessel-tables.pdf. Euler, L. (1766). De motu vibratorio tympanorum, Novi Commentarii academiae scientiarum Petropolitanae. 10, 1766, pp. 243-260. Fourier, M. 1822. Theorie Analytique De La Chaleur.	s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00019.warc.gz	CC-MAIN-2023-14	2,363	26
https://www.verifiedpromocodes.com/store/brosa/	math	Total 79 active Brosa coupons, promo codes and deals are listed and the latest one is updated on Sep 26, 2021 04:41:48 AM; 63 coupons, 0 verified promo codes and 16 deals which offer 30% OFF and extra discount, make sure to use one of them when you're shopping for brosa.com.au. EXTRA 50$ OFF when you Spend 1000$, use the 1st code at checkout EXTRA 150$ OFF when you Spend 2000$, use the 2nd code at checkout EXTRA 250$ OFF when you Spend 3000$, use the 3rd code at checkout EXTRA 400$ OFF when you Spend 4000$, use the 4th code at checkout.	s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572063.65/warc/CC-MAIN-20220814173832-20220814203832-00678.warc.gz	CC-MAIN-2022-33	542	5
http://www.promocoupons24.com/2016/04/become-better-prepared-for-calculus-by.html	math	My intended interest group comprises of secondary school understudies, undergrads, or any other person who needs or needs to learn math. An understudy who takes this course ought to have a fair foundation in variable based math and trigonometry. I wouldn't fret if an understudy is "corroded" with regards to a portion of the ideas that he or she learned in these classes. Be that as it may, if an understudy has overlooked a substantial bit of either polynomial math or trigonometry, an audit of such ideas ought to be done before selecting in this class. My course: Become Better Prepared For Calculus By Learning About Limits is all about limits. Limits contain the very heart of math. Accordingly, my first math course is about points of confinement. The understudy ought to know the instinctive meaning of as far as possible, uneven breaking point, even asymptote and unbounded utmost. He or she ought to learn how to process the cutoff points of different capacities. Information of the thorough meaning of as far as possible is not urgent but rather empowered. The understudy ought to likewise know the instinctive meaning of conventional and uneven progression. The student ought to likewise realize what it implies for a capacity to be spasmodic at a point. Besides, he or she ought to have the capacity to show irregularity at a point by utilizing uneven breaking points. udemy coupon :https://www.udemy.com/become-better-prepared-for-calculus-by-learning-about-limits/?couponCode=jason1234567	s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190295.4/warc/CC-MAIN-20170322212950-00097-ip-10-233-31-227.ec2.internal.warc.gz	CC-MAIN-2017-13	1,503	3
https://www.hsmt.ox.ac.uk/people/dr-christopher-hollings	math	Dr Christopher Hollings Meeting under the integral sign? The Oslo Congress of Mathematicians on the Eve of the Second World War (with Reinhard Siegmund-Schultze), American Mathematical Society, 2019, https://bookstore.ams.org/ Oral communication, and congresses in particular, remain a crucial element within mathematical communication – even in the current age of electronic mail. Indeed, congresses and meetings serve many more purposes than simply communicating information about recent mathematical research, and this has always been the case, with each particular historical period setting different priorities. This book focuses upon and stresses the historically unique character of the Oslo congress of 1936. This congress was the only one on this level to be held during the period of the Nazi regime in Germany (1933–1945) and after the wave of emigrations from it. Relying heavily on unpublished archival sources, we consider the differences between the goals of the various participants in the congress, most particularly the Norwegian organisers, and the Nazi-led German delegation. We consider also the background to the absence of the proposed Soviet and Italian delegations. In addition, we go into the mathematical dimension of the Oslo congress. This was the conference at which the Fields Medals were awarded for the first time, and we put the laudatory addresses given on this occasion into perspective. We give overviews of the 19 plenary presentations and their planning and development, and add biographical information about each of the plenary speakers. We also put the state of international mathematical communication beyond narrow political conditions into perspective; the Oslo congress is used as a lens through which to view the state of the art of mathematics in the mid-1930s. History of mathematics; specifically - Development of abstract algebra during the 19th and 20th centuries - Russian and Soviet mathematics - International Congresses of Mathematicians - Women in mathematics in the nineteenth century - Historiography of ancient Egyptian mathematics My research on the development of abstract algebra continues, with a current interest being the attitudes towards abstract symbolic methods among British mathematicians of the mid-19th century; these show some interesting parallels with the views of mathematicians who arrived at similar ideas independently several decades later – I hope eventually to contrast these parallel developments fully, each within its specific context. Building on prior work on the International Congresses of Mathematicians I plan to continue to use these as a lens through which to view the development of mathematics during the twentieth century, and also as a means of tracking the involvement in international mathematics of a range of nations and groups. Finally, the study of the historiography of ancient Egyptian mathematics looks set to be a long-term project, which will focus in part on certain Oxford-based figures who contributed to the modern interpretation of ancient mathematics. The ways in which mathematicians and Egyptologists engaged with different texts will be a major theme in this project, aided by the extensive Egyptological archival holdings in Oxford. I would be willing to hear from potential DPhil students interested in working in any area of my research interests and any potential Masters students looking at the history of mathematics. I currently teach: BO1.1. History of Mathematics – a third-year option for undergraduate mathematicians in the Mathematical Institute https://courses.maths.ox.ac.uk/node/42269 What happened to the first soviet scientist to solve a fundamental problem in mathematics? Oxford Sparks, May 2017, https://www.oxfordsparks.ox.ac.uk/content/what-happened-first-soviet-scientist-solve-fundamental-problem-mathematics The mathematical correspondence of Ada Lovelace and Augustus De Morgan, Conference talk at the Ada Lovelace Symposium, Mathematical Institute, Oxford, 10th December 2015, http://podcasts.ox.ac.uk/mathematical-correspondence-ada-lovelace-and-augustus-de-morgan Ada Lovelace interview for the University of Oxford's 'Research in Conversation' series, October 2015, http://www.ox.ac.uk/research/research-in-conversation/ada-lovelace/chris-hollings	s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646652.16/warc/CC-MAIN-20230610233020-20230611023020-00618.warc.gz	CC-MAIN-2023-23	4,304	18
https://www.metaglossary.com/define/nominal+interest+rate	math	Also referred to as nominal yield, this is the annual amount received as interest from a fixed income security relative to the par value of the issue. A life /health insurance underwriting class that is used for applicants that have not used tobacco products during the past 2 years (time may vary by insurance company). Most companies charge a reduced premium rate for non-smokers. the quoted (annual) rate per annum. If interest is compounded more often than once a year, the effective rate is greater than the nominal rate (e.g. 12% p.a. compounded monthly is equivalent to 12,68% p.a.; the nominal interest rate (i) is 0,12 and the effective interest rate is 0,1268). Distinct from annual effective interest rate, a rate of interest or discount rate that is equal to a periodic interest rate that is equal to a periodic interest rate multiplied by the frequency of that periodic rate per annum without compounding. For example, a monthly discount rate of 1% is an annual nominal interest rate of 12% (1% x 12). The stated interest rate in a note or contract, which may differ from the true or effective interest rate, especially if the lender discounts the loan and advances less than the full amount. ( See effective interest rate ) An interest rate that is quoted contractually by a lender or a borrower and does not take into account the effects of compounding. The nominal interest rate will always be less than the effective interest rate. Also known as stated interest rate. Contrast with effective interest rate.	s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178365454.63/warc/CC-MAIN-20210303042832-20210303072832-00560.warc.gz	CC-MAIN-2021-10	1,523	5
https://bisdts.weebly.com/math.html	math	Virtual pattern blocks, geoboards, base-ten blocks, and much more. Grades PreK-12 Math Live, a fantastic site for upper elementary students, is full of cartoon math tutorials on subjects like fractions, multiplication, area and perimeter, tessellations, probability, and a variety of other topics. The glossary section is an amazing collection of math concepts animated for more solid understanding. Harcourt Multimedia Math Glossary Animated, interactive math glossary for Grades 1-8. Interactive estimation and practice games sorted by grade level and math topic. Grades K-8 Create a Graph Create area, bar, line or pie graphs online! You submit the data and the website does the rest! Grades 2-8 A variety of math activities that include arithmetic, geometry, algebra, calculus fractals, and probability. Grades 2-12 Interactive Math Activities Pattern Blocks, base ten, and integer activities. Grades K-2 I Know That Math Games	s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578529472.24/warc/CC-MAIN-20190420080927-20190420102927-00292.warc.gz	CC-MAIN-2019-18	931	11
http://www.homeschoolmath.net/teaching/g/polygons.php	math	The ideas in this geometry lesson are taken from the Geometry ebook that I sell at MathMammoth.com. This lesson plan does not contain all the problems the Geometry ebook does. Free geometry lesson plan from HomeschoolMath.net Polygons are closed figures that have several line segments and Triangles are polygons with three sides. Quadrilaterals are polygons that have four sides (quattuor = four, lateralis = side). Other polygons include Example problem types 1. a) Draw four dots on paper at random so that connecting them you will get a quadrilateral that is not a square, rectangle or b) Measure the angles of your quadrilateral. What is the sum of the angles? c) Draw a diagonal into it so that it divides it into two triangles. Using the triangles explain why the sum of the angles in a quadrilateral has to be what it is. 3. A regular hexagon is a hexagon whose all sides and angles are equal. Look at the pictures to learn how to construct a regular hexagon. Then draw one in your notebook using compass and ruler. \|Draw an equilateral triangle with the usual method and also another triangle under- \|Extend the sides of the triangles until they meet the circumference of one of the citrcles. \|Connect the points where the extended lines met the circumference, and you get a regular hexagon. 5. A regular pentagon is a pentagon whose sides and angles are equal. Each angle of a regular pentagon is 108 degrees. Using that fact draw one. You can choose the length of the side. New terms to remember:	s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999642201/warc/CC-MAIN-20140305060722-00040-ip-10-183-142-35.ec2.internal.warc.gz	CC-MAIN-2014-10	1,507	26
https://www.brainkart.com/article/Conceptual-Questions-Answers_42540/	math	1. Why is it convenient to express the distance of stars in terms of light year (or) parsec rather than in km? The distances of astronomical objects like stars, planets etc from the earth are huge. The distance on the earth are relatively small so it can be measured in km. For Example : The distance to be next nearest big galaxy Andromeda is 21,000,000,000,000,000,000 km. i.e. 21 × 1018 km. This number is so large that it becomes hard to write and to interpret. So astronomical units like light year, parsec A.U are used for large distances. 2. Show that a screw gauge of pitch 1 mm and 100 divisions is more precise than a vernier caliper with 20 divisions on the sliding scale. Least count of screw gauge So screw gauge is more precise than vernier. 3. If humans were to settle on other planets which of the fundamental quantities will be in trouble? Why? Time will be in trouble. Time becomes irrelevant. Because day and year based on spinning and revolution of the planet. So each planet has its own year length. Eg. : Uranus and Neptune move too slow. 4. Having all units in atomic standards is more useful. Explain. All units in atomic standards are more useful because they never change with time. 5. Why dimensional methods are applicable only up to three quantities? If a quantity depends on more than three factors than dimensional formula cannot be derived. Because on equating the powers of M, L & T on either side of the dimensional equation three equations can be obtained, from which only three unknown dimensions can be calculated.	s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476442.30/warc/CC-MAIN-20240304101406-20240304131406-00057.warc.gz	CC-MAIN-2024-10	1,552	16
https://www.academicoo.com/artigo/an-experimental-comparison-of-biased-and-unbiased-random-key-genetic-algorithms	math	AN EXPERIMENTAL COMPARISON OF BIASED AND UNBIASED RANDOM-KEY GENETIC ALGORITHMS Gonçalves, José Fernando, Resende, Mauricio G.C., Toso, Rodrigo F. DATA DE PUBLICAÇÃO Random key genetic algorithms are heuristic methods for solving combinatorial optimization problems. They represent solutions as vectors of randomly generated real numbers, the so-called random keys. A deterministic algorithm, called a decoder, takes as input a vector of random keys and associates with it a feasible solution of the combinatorial optimization problem for which an objective value or fitness can be computed. We compare three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2010); and a greedy version of Bean's algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set k -covering, and unit-cost covering by pairs. Experiments are run to construct runtime distributions for 36 heuristic/instance pairs. For all pairs of heuristics, we compute probabilities that one heuristic is faster than the other on all 12 instances. The experiments show that, in 11 of the 12 instances, the greedy version of Bean's algorithm is faster than Bean's original method and that the biased variant is faster than both variants of Bean's algorithm. - Genetic Differentiation of Transposable Elements under Mutation and Unbiased Gene Conversion - Comparison between simulated annealing algorithms and rapid chain delineation in the construction of genetic maps - Genetic improvement of silage maize: predicting genetic gain using selection indexes and best linear unbiased prediction - Genetic profiling of Klebsiella pneumoniae: comparison of pulsed field gel electrophoresis and random amplified polymorphic DNA - An Experimental Comparison of Individual, Family and Combination Selection	s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710916.70/warc/CC-MAIN-20221202215443-20221203005443-00597.warc.gz	CC-MAIN-2022-49	1,913	9
https://hdbest.net/651-erbe-des-henkers-1948.html	math	Erbe des Henkers (1948)5K Erbe des Henkers: Directed by Frank Borzage. With Dane Clark, Gail Russell, Ethel Barrymore, Allyn Joslyn. Danny is despised by his schoolmates because his father was accused of killing another man and sentenced to death. “Plagued by his fatheru0026#39;s crime and ridiculed by others, Danny Hawkins (Clark) confronts an outcastu0026#39;s life in a small southern town.u003cbr/u003eu003cbr/u003eWhen old Mose addresses the dog as Mr. Dog or the guitar as Mr. Guitar, we realize a long suppressed desire for human dignity and respect. If the black man Mose (Ingram) canu0026#39;t get that from the larger community, at least he can create his own little world where all worthy things get respect. I think thatu0026#39;s why he lives alone. But despite his estrangement, he hasnu0026#39;t lost perspective. As he says, he wants to rejoin the human race, and itu0026#39;s easy to suppose the larger community needs to change by rising to his level, rather than vice-versa. Then too, when he says dogs should not be used to hunt humans, thereu0026#39;s a veiled echo of Jim Crow, covert Hollywood style.u003cbr/u003eu003cbr/u003eItu0026#39;s only natural that another outcast Danny Hawkins would be drawn to Mose, his only friend. Their scenes together are beautifully performed and sensitively scripted. Note how the subject of u0026quot;bad bloodu0026quot; and free will comes up elliptically. Danny is haunted by his fatheru0026#39;s crime and fears it has become his own destiny (the Sykes murder). In Dannyu0026#39;s eyes, itu0026#39;s as if heu0026#39;s fated by the blood heu0026#39;s inherited. But Mose knows something about the racial aspect of u0026quot;bad bloodu0026quot;, and insists that blood is no more than u0026quot;redu0026quot; and doesnu0026#39;t tell you u0026quot;what you have to dou0026quot;. This means Danny must overcome the spectre of genetic determinism by becoming his own person and taking responsibility for his own actions. Itu0026#39;s only then, by acknowledging a sense of free will, that Danny can escape the burden of inherited guilt.u003cbr/u003eu003cbr/u003eOf course, itu0026#39;s through Gillyu0026#39;s (Russell) unconditional love that Danny finds the redemption he needs. By releasing himself to that bond, he experiences an emotion strong enough to overcome the haunting sense of inherited fate. At the same time, he can only overcome the anguish of personal guilt for the crime he has committed by owning up to the crime, and confronting the inevitable I-told-you-sou0026#39;su0026quot;. In Moseu0026#39;s terms, thereu0026#39;s a heavy price he must pay for rejoining the human race. u003cbr/u003eu003cbr/u003eThe character of Billy Scripture (Morgan) is often overlooked, but remains a mysterious and profound presence. A simple-minded mute, heu0026#39;s another outcast and frequent figure of ridicule. However, unlike Danny, he remains sweet-tempered and forgiving despite the provocations. Even when nearly strangled by a desperate Danny, he responds with a difficult yet forgiving smile, a touching and unforgettable moment. In his own mute way, he appears to understand an underlying theme—that anger and alienation are symptoms and not causes. His name, I believe, is no accident.u003cbr/u003eu003cbr/u003eIn terms of the movie itself, the cast is superb. Clark may not have been director Borzageu0026#39;s first choice; nevertheless he comes up with a vivid and nuanced performance. Catch his many anguished expressions. Just as importantly, he doesnu0026#39;t look like a Hollywood leading man, nor does he bring the associations of a big-name star to the role. In short, heu0026#39;s perfect. Also, the famously edgy Russell shows none of that here. In fact, she projects one of the rarest qualities found in any love story, namely, genuine warmth. Her ethereal good looks also fit perfectly into the plot, and itu0026#39;s no stretch to see Danny changing his life for her sake. Then thereu0026#39;s the quiet dignity of Ingramu0026#39;s Mose. His sterling character now looks like evolution from the caricatures of the 1930u0026#39;s to the assertive civil rights movement of the 50u0026#39;s. Too bad, the actor is largely forgotten. I guess my only reservation is with Barrymore. Her grandma strikes me as too stagey and u0026quot;grandu0026quot; (an apt term from another reviewer). Still and all, itu0026#39;s a fine, colorful cast, even down to bit players.u003cbr/u003eu003cbr/u003eNow, as good as these elements are, itu0026#39;s because of director Borzage that theyu0026#39;re lifted into the realm of cinematic art. From hypnotic opening to pastoral close, the visual enchantment wraps around like an enveloping dreamscape— (the eerie sets are also a testament to lowly Republicu0026#39;s art department, the glittering impressionist photography to John Russell). Borzageu0026#39;s enclosed world is a world of artistic imagination thatu0026#39;s at once both mesmerizing and compelling. But just as importantly, heu0026#39;s a filmmaker who clearly believes in the material. As others point out, heu0026#39;s that rarest of the breed, a director who genuinely believes in romantic love and its redemptive power, and not merely as a movie cliché. At the same time, itu0026#39;s the power of that vision that merges the movieu0026#39;s elements into a single dynamic whole.u003cbr/u003eu003cbr/u003eThere are so many memorable moments and characters—the u0026quot;hep-catu0026quot; soda jerk, the Methuslah old man, the gallery lined-up for arriving trains. But, I guess the high point for me is when Danny must shake the raccoon from the safety of the tree, seeing his own fate in the hapless animal and knowing that if he doesnu0026#39;t he may betray his own guilt. Here, script, acting, and direction come together brilliantly to create a truly shattering moment. All in all, the film may not rise to the level of a masterpiece, but it does stand as a work of considerable artistic achievement, and one thatu0026#39;s stayed with me since I first saw it as a boy. And Iu0026#39;m glad the internet provides an opportunity for me to share that appreciation in a public way.”	s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00303.warc.gz	CC-MAIN-2023-06	6,181	3
http://reu.dimacs.rutgers.edu/~hermans/	math	During this adjustment period I did the basic work to introduce myself to the wonderful world that is pebbling. I also found that I have a great interest in Graham's Conjecture and am hoping to pursue related topics. I expanded on previous results that had shown that for any k there exists a complete graph that is k Class-0. I then moved to studying the 2 pebbling property (2pp) which seems to play a central role in the field of pebbling. I also looked at the complexity of finding the pebbling number of a graph and have attempted to look into finding a formula for a higher bound for the pebbling number of a graph. Gene helped us decide on a project which we can definitely make progress on over the course of the summer. We are looking at a specific graph of size 6, diameter 2 and girth 3. It's semi regularity and high symmetry make it an excellent model for future generalizations. We are going to attempt to show that this graph multiplied by itself follows Graham's Conjecture. We have determined that the pebbling number of the given graph is 7. Therefore the pebbling number of the product must be less than or equal to 49. Since it is a rather large graph, size 36, any straight forward approach has failed. It is not at all obvious how to proceed or how one can pebble such a large graph. Perhaps only working on general principles would be easier. We have made great progress in proving the pebbling number of the graph is less than or equal to 49. We found a sufficient condition which seems a lot easier to prove, namely that the product of our original graph and the complete graph on three vertices has a 2 pebbling number of less than or equal to 25. This problem has proved to be difficult. However, we have made some prograss by working on cases. We have split the graph into two pieces and are looking at when pebbles are in either piece. Out of the 25 cases we have easily verified 20. We have continued working and with help from Gene we have solved 3 more cases. However, the last two cases seem to be near impossible. I have formulated many ideas on how to pebble these, but they all fail. I am starting to think there may not be a general way of pebbling these cases. Still every arrangement we try is solvable. I am confident our original hypothesis is correct, but whether it can be verified with this approach I am unsure. We have continued trying to solve these 2 cases, but with little success. To be honest this last week was filled with many goodbyes and I didn't get as much work done as I had hoped. Overall I think it was a good summer and I made a lot of good work on my project. I have several new questions which I hope to work on in the future as well as continuing this one.	s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213508.60/warc/CC-MAIN-20180818075745-20180818095745-00240.warc.gz	CC-MAIN-2018-34	2,720	8
http://tynpnnhaf.ml/page5485-fuzzy-logic-toolbox-matlab-ppt.html	math	fuzzy logic toolbox matlab ppt 2. PPT MATLAB Fuzzy Logic Toolbox PowerPoint presentation \| free Fuzzy Logic Inference Applications in Road Traffic and paper Matlab fuzzy logic toolbox is used Fuzzy Logic Toolbox For Use with MATLAB \| Ned Gulley \| скачать книгу \| BookSee - Download books for free. Find books 16Fuzzy2.ppt - An-Najah Staff. If a given fuzzy rule has multiple antecedents, the fuzzy operator (AND or OR) is. A customer brings a failed item and receives a spare of the same type. apply a fuzzy logic development tool such as MATLAB Fuzzy Logic Toolbox or Fuzzy Matlab Fuzzy Logic Toolbox. Posted By: hill0. How can I implement fuzzy logic in matlab without using fuzzy logic toolbox? I want to calculate the remaining energy level of sensor nodes in wireless sensor networks using fuzzy logic. To do this I dont want to use fuzzy Seperti diketahui bahwa Fuzzy Logic Type-1 merupakan toolbox bawaan dari Software Matlab, dan tool-nya sudah terdapat didalam matlab, akan tetapi tidak demikian dengan Interval Type-2 Fuzzy Logic, tool-nya tidak terinstal dimatlab, sehingga diperlukan proses instalasi toolbox sendiri. 1466657962-5717230.ppt (Size: 388 KB / Downloads: 2). Introduction MATLAB fuzzy logic toolbox facilitates the development of fuzzy-logic systems using: graphical user interface (GUI) tools command line functionality. Results for: fuzzy logic toolbox matlab. Filters.A tool based on the model proposed by Bellman Zadeh (1970) fuzzy logic ( fuzzy sets) decision support paper. The first version of the application was developed in Java (pure java jgoodies and some other APIs). 12 Fuzzy Logic Toolbox (GUI) Start the toolbox: 13 FIS Editor.MATLAB A Computational Methods By Rohit Khokher Department of Computer Science, Sharda University, Greater Noida, India MATLAB A Computational Methods. Matlab Simulink as Simulation Tool for Wind Generation Improved DTC Algorithms for Reducing Torque and Flux Water Level Control in a Tank - MATLAB Simulink Example.fuzzy logic ppt. Copyright: Attribution Non-Commercial (BY-NC). Download as PPT, PDF, TXT or read online from Scribd.MATLAB Fuzzy Logic Toolbox. CS364 Artificial Intelligence. October 2005. A toolbox from MATLAB software named fuzzy logic toolbox. Fuzzy Logic Toolbox Documentation Getting Started Examples Functions andmatlabhome.ir/ Papers Thesis Free download Source code C C C Java Matlab Tutorial PPT PDF free download matlab code and videos ppt pdf word. The Fuzzy Logic Toolbox library contains the Fuzzy Logic Controller and Fuzzy Logic Controller with Rule Viewer blocks.This variable must be located in the MATLAB workspace. Fuzzy Logic Toolbox software is a collection of functions built on the MATLAB technical computing environment. It provides tools for you to create and edit fuzzy inference systems within the framework of MATLAB, or if you prefer MATLAB Fuzzy Logic Toolbox CS364 Artificial Intelligence October 2005 0 MATLAB Fuzzy Logic Toolbox Introduction Graphical User Interface (GUI) Tools Example: Dinner for two October 2005 1 Introduction MATLAB fuzzy logic toolbox facilitates the development of Plotting in Matlab and Fuzzy Logic Toolbox - ppt347 Кб.our system using a programming language such as C/C, Java, or to apply a fuzzy logic development tool such as MATLAB Fuzzy Logic Toolbox or Fuzzy Knowledge Builder. Fuzzy logic toolbox functions including definition language variables and their membership functions, input fuzzy inference rules, the fuzzy inference system management and interactively observe fuzzy reasoning procedure and output result.matlab-fuzzy-toolbox--ppt.rar. Download - Matlab Fuzzy Logic Toolbox.Logic using MATLAB Adel Abdennour, Electrical Engineering Department, King Saud University Outline Fuzzy Logic Toolbox FIS Editor Tipping Problem: Fuzzy Approach Defining Inputs Outputs Defining MFs Defining Fuzzy Rules MATLABABS Using Fuzzy Logic Ppt. Documents. Tutorial Fuzzy Tool Box Matlab - Duration: 18:37. Juanse417 46,552 views.FUZZY LOGIC CONTROLLER FOR CONTROLLING DC MOTOR SPEED USING MATLAB APPLICATIONS - Duration: 8:01. Pada tutorial ini, kita akan menggunakan MATLAB Fuzzy Logic Toolbox untuk menyelesaikan kasus yang telah dibahas pada tutorial sebelumnya. MATLAB memungkinkan kita mendesain fuzzy logic dengan cara yang cukup sederhana melalui antarmuka yang mudah dipahami. New Reply. Thread tools.Popular Searches: fuzzy logic toolbox matlab, morphological image processing using fuzzy logic matlab codemage processing using fuzzy logic matlab code, applications of neural network fuzzy logic and neuro fuzzy for medical ppt30220applications of Neuro-fuzzy logic systems. Matlab toolbox GUI.Practice "Neuro-Fuzzy Logic Systems" are based on Heikki Koivo "Neuro Computing. Matlab Toolbox GUI" . highly useful ppt.9. 1 Getting Started Fuzzy Logic Toolbox Product Description Design and simulate fuzzy logic systems Fuzzy Logic Toolbox provides MATLAB functions, apps, and a Simulink block for analyzing, designing, and simulating systems based on fuzzy logic. The presented IT2-FLS toolbox allows intuitive implementation of Takagi-Sugeno-Kang (TSK) type IT2-FLSs where it is capable to cover all the phases of its design. In order to allow users to easily construct IT2-FISs, a GUI is developed which is similar to that of Matlab Fuzzy Logic Toolbox. MATLAB Fuzzy-related toolbox. FIS Fuzzy Inference System. l Fuzzy Logic Toolbox software provides command-line functions and an app for creating Mamdani and Sugeno fuzzy systems. animcp Mux Animation Fuzzy Logic Toolbox 2.1 Target Position Mux Design and simulate fuzzy logic systems Target Position -C(Mouse-Driven) Constant 1 Switch Cart Pole Dynamics The Fuzzy Logic Toolbox extends the MATLAB technical computing environment with tools for designing Matlab Toolboxes. Jake Blanchard University of Wisconsin - Madison. Spring 2008. Introduction. — Toolboxes are add-ons that provide additional functionality to Matlab.Controls. — Control System Toolbox — System Identification Toolbox — Fuzzy Logic Toolbox — Robust Control Toolbox Show me how. Loading PPT MATLAB Fuzzy Logic Toolbox PowerPoint presentation \| free to download - id: 1d9a04-ZDc1Z. The Adobe Flash plugin is needed to view this content. Design and simulate fuzzy logic systems Fuzzy Logic Toolbox provides MATLAB functions, apps, and a Simulink block for analyzing, designing, and simulating systems based on fuzzy logic. Fuzzy Logic Toolbox in MATLABPowerPoint Presentation. Download.PowerPoint Slideshow about Fuzzy Logic Toolbox in MATLAB - ludlow. Here i will explain about Matlab Fuzzy Logic Toolbox Tutorial.The official home of matlab software matlab is the easiest and most productive software environment for engineers and scientists try, buy, and learn matlab. MATLAB. Fuzzy Logic Toolbox. J.-S. Roger Jang Ned Gulley.What is important to recognize is that, even in its narrow sense, the agenda of fuzzy logic is very different both in spirit and substance from the agendas of traditional multivalued logical systems. Matlab fuzzy logic toolbox, presents the Fuzzy Inference System Modeling Is there an R-equivalent of all the toolbox or some R function like : readfis() :Load Fuzzy Inference System from file. evalfis() : Perform fuzzy inference calculations. According to our registry, MATLAB Fuzzy Logic Toolbox is capable of opening the files listed below.There are currently 1 file extension(s) associated to the MATLAB Fuzzy Logic Toolbox application in our database. Introduction to MatLab. Fuzzy Logic Toolbox. Neural Network Toolbox.Fuzzy expert systems adaptive Neuro-Fuzzy inference systems ANFIS. Matlab simulik. independent code. Page. Screen clipping taken Fuzzy logic system design and analysis in MATLAB and Simulink.Fuzzy Logic Toolbox provides functions, apps, and a Simulink block for analyzing, designing, and simulating systems based on fuzzy logic. The MATLAB Fuzzy Logic toolbox is provided for easy reference. Title: Introduction to Fuzzy Logic using MATLAB Author: Sivanandam S.N. Publisher: Springer Year: 2006 Format: PDF. Use Matlab Fuzzy Logic Toolbox Sugeno-style Fuzzy Inference The result of Sugeno reasoning is an exact number.Temperature is observed. Formulate fuzzy controller for electric bath-house stove. Use Matlab Fuzzy Toolbox and Sugeno-style fuzzy inference.code C C C Java Matlab Tutorial PPT PDF free download matlab code and videos ppt pdf word Matlab Tutorial - Fuzzy Logic - YouTube www. Access functions such as getfis and setfis make itFuzzy Logic Toolbox For Use with MATLAB Fuzzy Logic Toolbox Users Guide into the tutorial. The following Matlab project contains the source code and Matlab examples used for fuzzy logic processor. Implement a basic Fuzzy Logic Processor that utilizes user provided Fuzzy Sets, Fuzzy Rules and "crisp" input parameters to determine a "crisp" output. Slide 1 Plotting in Matlab and Fuzzy Logic Toolbox -An Introduction Slide 2 PLOT (2-D plotting) Linear plot. PLOT(X,Y) plots vector Y versus vector X. If X or Y is File: Fuzzy-Logic-Toolbox- Download Add to favorates [ 5 4 3 2 1 ]. Directory: matlab. Dev tools: matlab. File size: 3383 KB. Update: 2012-10-19. Downloads: 3. Uploader: guangqixu. Describe: Fuzzy logic control matlab toolbox, can call the function directly. MATLAB has a number of add-on software modules, called toolboxes, that perform more specialized computations.Control Design Control System - Fuzzy Logic - Robust Control --Analysis and Synthesis - LMI Control Model Predictive Control. Fuzzy Logic Toolbox. For Use with MATLAB. Users Guide.What is important to recognize is that, even in its narrow sense, the agenda of fuzzy logic is very different both in spirit and substance from the agendas of traditional multivalued logical systems. MATLAB fuzzy logic toolbox facilitates the development of fuzzy-logic systems using: graphical user interface (GUI) tools command line functionality. The tool can be used for building. The MATLAB fuzzy logic toolbox facilitates the development of fuzzy-logic systems using: graphical user interface (GUI) tools command line functionality The tool can be used for building Fuzzy Expert Systems Adaptive Neuro- Fuzzy Inference Systems (ANFIS) Introduction.My PPT Fuzzy Logic. The MATLAB fuzzy logic toolbox facilitates the development of fuzzy-logic systems using: graphical user interface (GUI) tools command line functionality The tool can be used for building Fuzzy Expert Systems Adaptive Neuro- Fuzzy Inference Systems (ANFIS) Introduction.My PPT Fuzzy Logic. Fuzzy Logic Toolbox software is a collection of functions built on the MATLAB technical computing environment. It provides tools for you to create and edit fuzzy inference systems within the framework of MATLAB.	s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867277.64/warc/CC-MAIN-20180526014543-20180526034543-00238.warc.gz	CC-MAIN-2018-22	10,728	5
https://www.hackmath.net/en/math-problem/77614	math	Express 6 whole 7/10 hours in minutes. Did you find an error or inaccuracy? Feel free to write us. Thank you! Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it. Tips for related online calculators You need to know the following knowledge to solve this word math problem: Related math problems and questions: - Express 71 Express 2 minutes 30 seconds as a fraction of 3/4 hours. - Workers 54253 Four workers packed the goods with the same output in 6 hours. In how many hours would five workers do the same job? Express it in hours and minutes. - Free time Anita had 2 1/4 hours of free time in the afternoon. She spent 2/3 of her free time playing sports and watching TV for 30 minutes. How much time did she have left to read the book? Express the result as fractions of hours and numbers in minutes. - Denominator 16341 Express a fraction in the basic form of what part of the day represents 5 hours and 30 minutes. Write the result in the form of a reader, denominator. - Complete 2833 The tiler covered 3/5 of the wall with tiles in two hours and 45 minutes. How long did it take to complete the entire lining area at the same power? How long did the whole job take him? - Expressway 5837 The expressway covers the distance from the starting point to the final station in 4 hours and 20 minutes. A passenger train, whose average speed is 30 km/h less, will cover this distance in 7 h 40 min. What is the speed of the express train, and what is What part of the day is 23 hours 22 minutes? Express as a decimal number. Harvester has a cutting width of 4 m, and harvested grain in the field is 87 meters wide. Harvester moves along the field's length for six minutes; going back (without cutting) takes half the time. Each turn at the end field takes one minute. How many hou - Minutes) 22373 The city planned to repair the highway section for 20 hours. Workers reduced this time by 20%. How long did the repair take? (express in hours and minutes) The excavator dug 40% of the excavation in 2 hours and 20 minutes. How long does it take him to dig the whole ditch? - Train and walker Walker passes an hour 5 km. Express train per hour 100 km. Walker went for 4 hours. How many minutes did the distance express train? - Calculating 58401 Suppose the relation s = v applies to the calculation of the path s. t, express the relation for calculating speed v and the relation for calculating time t. Is it true that 10 km will travel at 90 km / h in 10 minutes? At 6 hours 40 minutes, the steamer sailed from the port at a speed of 12 km/h. At exactly 10 hours, the motorboat started to sail at 42 km/h. When will the motorboat catch steamer? The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median. - A speedboat A speedboat goes 900 km against a current of 25 km/hr. Its trip took 10 minutes longer than it would have taken to travel with the current. What is the speedboat's speed in still water? - Children's 7802 The garden children's pool has the shape of a cylinder with a base diameter of 3.2 m and a depth of 60 cm. How many hours and minutes will it fill 10 cm below the edge of 0.5 l of water per second flows through the tributary? Round to whole minutes and wr - Constant 3376 The plane flies at a speed of 240 km/h and flies a route of 396 km in 3 hours 20 minutes there and back - once it flies with the wind, the second time it flies against the wind, which has a constant speed the whole time. What is the wind speed?	s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506528.19/warc/CC-MAIN-20230923162848-20230923192848-00378.warc.gz	CC-MAIN-2023-40	3,564	35
https://www.westernyoga.org/plans-pricing	math	Become a Monthly Member! Video Subscriber$10Every monthGet access to all of the yoga videos! 1 Class per Week$45Every monthChoose this if you want 1 live yoga class per week and VOD 2 Classes per Week$75Every monthChoose this if you want 2 live yoga class per week and VOD 3+ Classes per Week$95Every monthChoose if you want to have 3+ live classes weekly and VOD	s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358480.10/warc/CC-MAIN-20211128073830-20211128103830-00229.warc.gz	CC-MAIN-2021-49	363	5
https://www.physicsforums.com/threads/complex-number-express-in-magnitude-phase-form.634426/	math	Hi, I have a problem with complex number. I do really appreciate your help. I've attempted the question but it's getting me no where. Thanks in advance! 1. The problem statement, all variables and given/known data Perform the following complex variable calculations, using complex exponentials. Express the results in magnitude/phase form a/(iw+a) 2. Relevant equations 3. The attempt at a solution I just attempted this solution but it's getting me nowhere. a/(a+iw) x (a-iw)/(a-iw) = a(a-iw)/a^2 + w^2 and as I factorize it further, I get the initial problem back. How do I transform this to the form of magnitude and phase? thank you so much.	s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215843.55/warc/CC-MAIN-20180820042723-20180820062723-00663.warc.gz	CC-MAIN-2018-34	645	1
http://www.slideshare.net/tendeo/control-chap3	math	Reduction of Multiple Subsystems reduce a block diagram of multiple subsystems to a signal block representing the transfer function from input to output Before this we only worked with individual subsystems represented by a block with its input and output. Complex systems are represented by the interconnection of many subsystems. In order to analyze our system, we want to represent multiple subsystems as a single transfer function. A subsystems is represented as a block with an input and output and a transfer Many systems are composed of multiple subsystems. So, we need to add a few more schematic elements to the block Output signal, C(s), is the algebraic sum of the input signals, R1(s), R2(s) and R3(s). Distributes the input signals, R(s), undiminished, to several output points. There are three topologies that can be used to reduce a complicated system to a a. cascaded subsystem b. equivalent transfer function Equivalent transfer function is the output divided by the input. Parallel subsystems have a common input and output formed by the algebraic sum of the outputs from all of the subsystems. It is the same as the closed loop system that we learn in Chapter 1. a. closed loop system b. closed loop, G(s)H(s) is open loop transfer Moving blocks to create familiar forms Cascade, parallel and feedback topologies are not always apparent in a block diagram. You will learn block moves that can be made in order to establish familiar forms when they almost exist. I.e. move blocks left and right past summing junctions and pickoff points. algebra for summing equivalent forms for moving a block a. to the left past a b. to the right past a algebra for pickoff for moving a a. to the left past a pickoff point; b. to the right past a pickoff Block diagram reduction via familiar forms Reduce the block diagram to a single Steps in solving a. collapse summing b. form equivalent in the forward path parallel system in the c. form equivalent feedback system and multiply by cascaded Block diagram reduction by moving blocks Reduce the system shown to a single First, move G2(s) to the left past the pickoff point to create parallel subsystems, and reduce the feedback system consisting of G3(s) and H3(s). Second, reduce the parallel pair consisting of 1/g2(s) and unity and push G1(s) to the right past the summing junction, creating parallel subsystems in the feedback. Third, collapse the summing junctions, add the two feedback elements together, and combined the last two cascaded blocks. Fourth, use the feedback formula to obtain Finally multiply the two cascaded blocks and obtain the final result. Find the equivalent transfer function, Combine the parallel blocks in the forward path. Then, push 1/s to the left past the pickoff point. Combine the parallel feedback paths and get 2s. Apply the feedback formula and simplify A technique for reducing signal-flow graphs to single transfer function that relate the output of system to its input. We must understand some components before using Mason’s rule Product of branch gains found by going through a path that starts at a node and ends at the same node, following the direction of the signal flow, without passing through any other node more than once. Product of gains found by going through a path from the input node of the signal-flow graph in the direction of Loops that do not have any nodes in common. Loop G2(s)H1(s) does not touch loops G4(s)H2(s), G4(s)G5(s)H3(s) and G4(s)G6(s)H3(s) Product of gains form nontouching loops taken two, three, four, or more at a time. The transfer function, C(s)/R(s), of a system represented by a signal-flow graph is G (s) = k = number of forward path Tk = the kth forward - path gain ∆ k = formed by eliminating from ∆ those loop gains that touch the kth forward path. ∆ = 1 - Σ loop gains + Σ nontouching loop gains taken two at a time − Σ nontouching loop gains taken three at a time + Σ nontouching loop gains taken four at a time	s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721555.36/warc/CC-MAIN-20161020183841-00478-ip-10-171-6-4.ec2.internal.warc.gz	CC-MAIN-2016-44	3,969	109
https://books.google.gr/books?id=DpkXAAAAIAAJ&dq=editions:HARVARD32044096994090&hl=el&output=html_text&lr=	math	Τι λένε οι χρήστες - Σύνταξη κριτικής Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες. 90 days acre agent altitude amount annual bank barrels base bill bonds bought brokerage building bushels cents circle commission common fractions contain cubic debt decimal deep denominations diameter difference discount distance Divide dividend divisor draft equals Express face factors farm farmer feet field Find the amount Find the cost Find the interest Find the number flour fraction gain gallons give given horse inches income increased indorsed insured interest invested land Learn less LESSON loss lost merchant miles months Multiply owes paid payable payment piece places pounds premium prime proceeds profit quotient receipt received Reduce remainder rods RULE sell seventh grade shares sheep side sold square surface Teach TEACHER term units weighing whole wide worth Write yards Σελίδα 334 - LIQUID MEASURE 4 gills (gi.) = 1 pint (pt.) 2 pints — 1 quart (qt... Σελίδα 335 - Weight is used in weighing gold, silver, and jewels. 24 grains (gr.) . . . = 1 pennyweight . pwt. 20 pennyweights . . = 1 ounce . . . . oz. 12 ounces =1 pound . . . Ib. 153. Apothecaries' Weight is used by druggists in weigh, ing medicines not liquid. Σελίδα 368 - The hypotenuse of a right triangle is the side opposite the right angle. The sides including the right angle are sometimes called the arms of the right triangle. Σελίδα 321 - The dividend is the number to be divided. The divisor is the number by which we divide. Σελίδα 316 - How long is the diagonal of a 30-foot square ? 6. What is the length of the longest straight line that can be drawn on a sheet of paper 16 in. Σελίδα 358 - Multiply each payment by its term of credit, and divide the sum of the products by the sum of the payments ; the quotient will be the average term of credit. Σελίδα 370 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center. Σελίδα 331 - Multiply as in whole numbers, and in the product point off as many decimal places as there are decimal places in both multiplier and multiplicand, prefixing ciphers if necessary. Σελίδα 53 - ... miles a day ; how far apart will they be at the end of 6 days ? Ans.	s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583083.92/warc/CC-MAIN-20211015192439-20211015222439-00212.warc.gz	CC-MAIN-2021-43	2,380	12
https://www.physicsforums.com/threads/outer-bands-of-galaxies-speed.537769/	math	I am wondering about the speed of the outer bands of galaxies and if they are moving at or faster than the speed of light? And then the thought of the speed of space expansion and and the body of the galaxy moving and the rotation of planets around the stars(solar system) and the spin of the planets themselves. If these were all to move in the same direction at the same time, how fast would that be (if you were on the planet)? Got to be moving faster than the speed of light. Or does the proximity of mass negate these? Particles in the accelerator at just below the speed of light only adding the rotation of the earth would qualify, right?	s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247496080.57/warc/CC-MAIN-20190220190527-20190220212527-00493.warc.gz	CC-MAIN-2019-09	645	1
https://gbs.aromadiffusertest.de/compound-inequalities-test.html	math	Solving Compound Inequalities. This is a game like "Who Wants to Be a Millionaire?" where you have to keep getting the answer right in order to move up in money amounts. I recommend that you work out the problem instead of making a guess.This test has 20 multiple-choice questions for 40 points. More Test Quizzes. ... Solve the following compound inequality:7x + 3 ≤ 3 or 6x – 8 > 16. A. X. B. Start studying Compound Inequalities. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Compound inequalities often have three parts and can be rewritten as two independent inequalities. Solutions are given by boundary values which are indicated as a beginning boundary or an ending boundary in the solutions to the two inequalities. Absolute value inequalities will produce two solution sets due to the nature of absolute value.	s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988831.77/warc/CC-MAIN-20210508001259-20210508031259-00107.warc.gz	CC-MAIN-2021-21	859	3
http://www.pokecommunity.com/showpost.php?p=3618315&postcount=78	math	I assume you mean the "new" pokemon. no they aren't obtainable. i couldnt get a pokedex entry (if I did they would act like missingo giving people the advantage of the missingno glitch) and i couldnt get a back sprite. EDIT: Are you sure Blastoise's sprite is glitched? I did not see him in a battle but his pokedex picture is normal.	s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395346.6/warc/CC-MAIN-20160624154955-00169-ip-10-164-35-72.ec2.internal.warc.gz	CC-MAIN-2016-26	334	2
https://estebantorreshighschool.com/faq-about-equations/escape-velocity-equation.html	math	How do you calculate escape velocity? This is the escape speed – the minimum speed required to escape a planet’s gravitational pull.To find the escape velocity, apply energy conservation: Ui + Ki = Uf + KfFor a planet of mass M and radius R, the potential energy of an object of mass m at the planet’s surface is: U= – G m M/R. What is the Earth’s escape velocity? The escape velocity of Earth is 11.19 km/s. The escape velocity of Venus is 10.36 km/s. The escape velocity of Mars is 5.03 km/s. The escape velocity of Saturn is 36.09 km/s. How do you calculate the escape velocity of Mars? Calculate the escape velocity from the surface of Mars.Mmars = 6.42 x 1023 kg. We are assuming that we keep the Sun’s mass the same but reduce the Sun’s radius such that the escape velocity becomes greater than the speed of light (300,000 km/s = 3.0 x 108 m/s). R = 2GM/v2escapeR = 2.95 x 103 m = 2.95 km. What is Escape Velocity derive it? Escape velocity: -The minimum speed with which a body must be projected. in order that it will escape from the earth gravitational filed is called as. escape velocity. Expression of it:-consider a body of mass m on the surface of earth. whose mass and radius are respectively represented by M and R. Is escape velocity constant? The formula for escape velocity comprises of a constant, G, which we refer to as the universal gravitational constant. The value of it is = 6.673 × 10-11 N . The unit for escape velocity is meters per second (m/s). Does mass affect escape velocity? The escape velocity depends only on the mass and size of the object from which something is trying to escape. The escape velocity from the Earth is the same for a pebble as it would be for the Space Shuttle. Can a bullet escape the atmosphere? – When you fire a bullet upwards from the earth surface the bullet will immediately begins to slow down due to presence of air resistance and earth gravity. First, the bullet would never escape the earth’s atmosphere. This is because the escape velocity for any object is about 11.2km/sec. What does 9.81 mean? “9.81 meters per second squared” means that objects on Earth will accelerate (or go faster) 9.81 meters every second, if they are in free fall, due to the pull of gravity. Throughout space, gravity actually is constant. What is the difference between orbital velocity and escape velocity? Orbital velocity is the speed required to achieve orbit around a celestial body, such as a planet or a star, while escape velocity is the speed required to leave that orbit. Maintaining orbital velocity requires traveling at a sustained speed that: Aligns with the celestial body’s rotational velocity. What is Mars escape velocity? \|Surface acceleration (m/s2)\|\|3.69\|\|9.78\| \|Escape velocity (km/s)\|\|5.03\|\|11.19\| \|GM (x 106 km3/s2)\|\|0.042828\|\|0.39860\| Which planet has the greatest escape velocity? What is Escape Velocity Class 11? Class 11 Physics Gravitation. Escape Velocity. Escape Velocity. Escape velocity is the minimum velocity that a body must attain to escape the gravitational field of the earth. Suppose if we throw a ball,it will fall back. What is meant by orbital velocity? Orbital velocity, velocity sufficient to cause a natural or artificial satellite to remain in orbit. The more massive the body at the centre of attraction, the higher is the orbital velocity for a particular altitude or distance. Why does Moon have no atmosphere? Our Moon doesn’t have an atmosphere because it is too small and doesn’t have a strong magnetic field. Any atmosphere it might have had would be stripped away by the solar wind that barrages the small world. In contrast, our planet has more mass to hold its atmosphere close, and a strong magnetic field to protect it.	s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337680.35/warc/CC-MAIN-20221005234659-20221006024659-00493.warc.gz	CC-MAIN-2022-40	3,753	29
http://benpaulthurstonblog.blogspot.com/2012/05/rotating-fx.html	math	The Ben Paul Thurston Blog Math, Movies, Science, Computers, and so on... Tuesday, May 15, 2012 I don't know if this is really that interesting but it just occurred to me that if you have some function, let's call it f(q). You can do the following to make a parameterized curve of this parabola rotated any angle. here the parabola is rotated by 45 degrees clockwise. There are different operation to scale the function, or skew it or flip it various ways and a lot of functions are related visually that way. Share to Twitter Share to Facebook Share to Pinterest Post a Comment Post Comments (Atom)	s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589634.23/warc/CC-MAIN-20180717090227-20180717110227-00267.warc.gz	CC-MAIN-2018-30	599	11
https://africatransformationprojects.co.za/19831_calculate-ball-mill-charge.html	math	Mill Steel Charge Volume Calculation - 911 MetallurgistMar 19, 2017 . We can calculate the steel charge volume of a ball or rod mill and express it as the % of the volume within the liners that is filled with grinding media. While the mill is stopped, the charge volume can be gotten by measuring the diameter inside the liners and the distance from the top of the charge to the top of.calculate ball mill charge,Ball Mill Charge - Grinding & Classification Circuits - Metallurgist .Apr 4, 2018 . The crop load of ball mill. It =ore + mill medium +water. But usually, it was used in a percentage formation. So how to calculate this percentage. I know this is really a basic question, but it puzzled me, for most books and papers just use it but nor explain it.	s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321696.96/warc/CC-MAIN-20190824194521-20190824220521-00371.warc.gz	CC-MAIN-2019-35	760	1
http://www.downloadpdffree.com/ecet-Mathematics-Chemistry-Physics-model-papers.pdf/10	math	PDF Ebooks for Search word 'ecet Mathematics Chemistry Physics model papers' Paper I : MATHEMATICAL PHYSICS PHY 11 Mathematical Methods for Physics. By G.Arfken .... Vetterming, Teukolsky, Press and Flannery: Numerical Recipes .... conservation laws – elementary ideas of CP and CPT invariance Lie algebra, SU(2) – SU(3 ) multiplets – quark model . ..... Computer Communication Systems: Types of networks, Design features of a ... http://www.nagarjunauniversity.ac.in/pgsyllabus/physics.pdf File Type:PDF Mathematics for Quantum Chemistry â€œApplied Mathematics for Chemistsâ€œ for students with approxi- mately the indicated ... 1â€”2 EIGENVALUE PROBLEMS IN cmss1cnr. uscnamcs. 1â€”3 scorn http://www2.chemistry.msu.edu/courses/cem987/AndersonCh1_3.pdf File Type:PDF Determinants and Their Applications in Mathematical Physics - IATE in the course of research into problems in mathematical physics. These usu- ... applications can be found in the introduction to Chapter 6. There appears to beÂ ... http://iate.oac.uncor.edu/~manuel/libros/Modern%2520Physics/Mathematical%2520Physics/Determinants%2520and%2520their%2520applications%2520in%2520mathematical%2520physics%2520-%2520Vein%2520R.,%2520Dale%2520P..pdf File Type:PDF COURSE SYLLABUS CHEM-UA 651 -Physical Chemistry: Quantum ... CHEM-UA 651 is a course in physical chemistry meant for chemistry majors and ... Because all of chemistry flows from basic physical principles, this course isÂ ... http://chemistry.fas.nyu.edu/docs/IO/19766/CHEMUA651.pchemquantummechandspec.eckhardt.spring2013.pdf File Type:PDF MODEL QUESTION PAPERS AP STATE OPEN SCHOOL ATE ... public examination oriented model question papers of all the subjects. I request all the ... public examination model question paper to the learners for their better understanding and preparation to the ... Computer Science. 115-117. 20 ..... What kind of life did Rahul's Grandparents lead when he was a small boy? What wasÂ ... http://www.apopenschool.org/images/docs/Intermediate%2520Model%2520Question%2520Papers.pdf File Type:PDF Download Physical Chemistry Math Module 2 - Mathematics Physical Chemistry Math Module II. Adolfo J. Rumbos and Frederick J. Grieman. Partial Differential Equations and Boundary Value Problems. 1 Introduction. http://www.math.pomona.edu/flapan_nsf/PhysicalChemMathModule2.pdf File Type:PDF B. SC. (Physics, Chemistry, Mathematics) - Shiats (Physics, Chemistry, Mathematics). Semester â€“ I. Credit Hrs. S. No. Course Code. Title of the Course. L T P. 1. PHY - 331. MECHANICS. 3. 1. 0. 2. PHY - 333. http://www.shiats.edu.in/faculty/colleges/syllabus/08_BSPCM.pdf File Type:PDF The Transfer of Knowledge from Physics and Mathematics to ... mathematics and physics to engineering applications: (1). To demonstrate the efficacy of using e-learning and e- teaching through Blackboard and Web-based. http://www.researchgate.net/publication/1760867_The_Transfer_of_Knowledge_from_Physics_and_Mathematics_to_Engineering_Applications/file/32bfe50d35b8f58d0f.pdf File Type:PDF	s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894140.11/warc/CC-MAIN-20140722025814-00155-ip-10-33-131-23.ec2.internal.warc.gz	CC-MAIN-2014-23	3,051	29
http://4archive.org/board/sci/thread/7793671	math	I've read that the strength of a material is unaffected by thickness - the amount of force per unit area it can withstand before failing is only dependent on the material in question, and not how thick it is. Is this really true? It certainly seems counter-intuitive, and if it is true, why do submarine hulls for example need to be thick? Wouldn't a thin sheet be able to provide the same strength? Or is the thickness just needed to provide rigidity (i.e. a thin hull would collapse under the pressure, but would still keep the water out)? It really depends on the material in question and what kind of stress it experiences. There's also different metrics of strength: compressive strength, flexural strength, tensile strength, etc. Submarines are under a lot of pressure. More material does mean more rigidity and therefore modifies its strength properties (you'll have to google flexural strength to see the mathematical relationship). Think of breaking a thin piece of glass, like a microscope slide. It's pretty easy to do. Now picture glass with the same aspect ratio, but significantly thicker -- it would be harder to break. I think you mean length, not thickness, the Pa it can withstand is generally proportional to its thickness even if just because its mass per unit area is proportional to its thickness Assuming you had a uniaxial force and your definition of strength was the yield strength, then yes, this is not dependent on the thickness of the material. However, a submarine would have to be completely flat for this to mean what you seem to think it means. >However, a submarine would have to be completely flat for this to mean what you seem to think it means. Would a submarine in the shape of a rectangular or triangular prism count as "completely flat"? >the Pa it can withstand is generally proportional to its thickness I don't think it is. Yielding happens at the microstructural level, and each part of the object will be experiencing the same pressure, so I don't see how the mass per unit area or thickness comes to play in that. However, there are other considerations for material properties other than yield strength, some of which do depend on e.g. the volume, like the ability to withstand impact and dissipate energy without fracture. Not the anon you're replying to, but no. If the shell encases a cavity of air, then under compression there's an increased degree of freedom for the material to collapse into, and fail. Flat sides on something like a prism would compromise the structural integrity of the system because at the center of each side, the material will be the most susceptible to failure under stress (external forces are not applied evenly) and the material will want to collapse inward. Spheres and ellipsoids behave well under compression because they're largely uniform and external forces are distributed more evenly -- like the old trick where squeezing an egg in the palm of your hand doesn't result in breaking. No, I meant flat as in a single plane. Do keep in mind that, if your object is hollow, then the sides must withstand the force on the top and bottom faces, at which point you do want significant side thickness to make sure there's enough area there to not exceed pressures at which yielding occurs. It actually has a DECREASING fracture strength with increasing thickness, due to statistical effects; a thicker piece of material is more likely to have a defect that will cause a stress concentration, leading to crack initiation sooner. If you assume a perfect material, then yes, strength is independent of thickness. Mechanical Engineer in his final semester here, you're all misunderstanding the basic concept here. I'm going to word this as generally as I can because I don't feel like getting into deeper detail. Force per unit area is stress. It's also pressure, but for the purposes of mechanical failure, we refer to it as stress. Materials have many properties. One of these is the point of deformation where yield occurs, and another is the point of deformation where ultimate failure occurs. Deformation here is referred to as strain, which is simply any change in shape/size. In other words, how much a material can be stretched/bent/compressed before it breaks is a material property. Strain occurs when a material undergoes a stress. How much much strain occurs for a given stress is a material property, and, for the purposes of a basic explanation is mostly a linear relation up until yielding, which we refer to as Young's Modulus. The relation is defined as Stress = Strain * Young's Modulus. Young's Modulus is a material property. Stress is how much force per unit area the structure is experiencing, and strain is how much it changes shape as a response to this. If strain becomes to large, the structure fails. >Why does a submarine need thickness then? Because crudely drawn pic related. (continuing to part two) Let's say you have two 6in long samples of annealed 302 stainless steel. One sample is 1/2in in diameter, the other is 5/8in. The tensile strength of the MATERIAL is 75,000psi. This does not change with the thickness. The tensile strength of the SAMPLES are 18,750lb and 29,297 respectively. If you made a diving board really thin, it would break upon a person standing on it. If you made a diving board at the current normal thickness of diving boards, it'd noticeably flex (which is strain) under a person using it, but do not yield nor fail. If you made a diving board really thick, it would experience very little strain under a person's weight, and wouldn't noticeably flex at all. Submarines feeling waterpressure is the same idea. The force is staying the same, and while the outer surface area is staying the same, the stress is not, because the outer surface area isn't the area being affected by the force. This is because you are bending it. The surface area shown facing you in the top picture is the area that the force is being applied over, not the outside. So making it thicker increases the surface area, decreases the stress, thus decreasing the strain, thus preventing failure. Now this can be a bit confusing in the case of a submarine since it's a water pressure being applied, so let me elaborate the best that I can. You have a given water pressure for your depth. This pressure is defined as force per unit area of the outside of the hull. This means that any area X will have the same force applied on it. This force is trying to bend that area inwards. As such, the stress here is a function of the thickness. More thickness means less stress, less stress means less strain, less strain means we it doesn't fail. I apologize if I explained this poorly in my rambling. I'd recommend just reading about Statics as a whole if you want to know more. I purposefully avoided more complex topics like what yielding actually is, or comparing engineering stress&strain to true stress&strain. I honestly only skimmed the thread, but it legitimately sounds like a lot of people here are using words that are mostly correct without understanding what they're talking about. >it really depends on the material in question The material would never change what dimensions matter, the material only determines what those dimensions need to be. >I don't see how thickness comes into play I've already explained thoroughly that thickness defines the cross sectional area, is one of two parameters (alongside the outside force) that defines the stress here. The Young's modulus and yield strain of a material are material properties. These two define the yield stress, which is then effectively a material property. This is not dependent on any dimensions of the material, nor does it depend at all on the force being applied, because it is a property. Stress here is a function of the cross sectional surface area, of which the thickness is a dimension. This means that a thinner submarine will give a greater stress with the same force being applied. I'm honestly a bit unsure what you're trying to convey with this completely flat thing. A flat piece of material would still undergo compression underwater and the thickness would still matter, most materials just happen to have higher yield strengths under this sort of compression that they do under bending. A theoretical planar material with zero thickness would fail instantly. Also, yield is not the end all, a material can yield without failing, it's just generally desirable to not yield, especially in the case of something like a submarine. Actually, I think I misworded that last part, let me be more clear. The stress perpendicular to a plane (red) would not be a function of the thickness. The stress in blue would approach infinity as the thickness approached 0 since we have Force / HeightThickness. The stress in green would approach infinite as the thickness approached 0 since we have Force / LengthThickness. The plane would fail instantly underwater, where force occurs from all sides. I said the material matters because it does. Certain materials have physical structures which make it best for handling tension or compression, etc. Like bending a piece of glass. The concave side does fine under compression, but the surface features of the convex side propagate cracking under tension and therefore failure. Maybe that tidbit was largely irrelevant to OP's question, but I was just trying to highlight the variability in reference frame of these kinds of questions. The material matters in determining whether or not the structure will fail, absolutely. The stresses are only functions of the force and dimensions. The material does not matter in defining the stress, only in defining what stress is acceptable, and what the results of the stress are, including the strain experienced from these stresses, and whether or not yield/failure occurs. The material might change what the LIMITING dimensions of failure are, if that's what you're implying. I didn't understand that clearly from your original post. For example, concrete is good under compression, but worse under tension. Steel on the other hand, handles both compression and tensions similarly. But neither material defines what dimensions are relevant in determining the amount of compression/tension being experienced. The material determines the results of the stress. But for the purposes of saying that your original post is "wrong", no material would ever make it such that the thickness of a submarine didn't matter. Material determines what the thickness needs to be, but only an infinitely strong material would allow for a 0 thickness. >the amount of force per unit area it can withstand before failing is only dependent on the material in question, and not how thick it is. Is this really true? That's obviously absurd. A one atom thick material doesn't resist the same force as a 2 inch thick sample of the same material. This notion is grounded in simplified, ideal cases of material science which do not actually exist in nature. I think the only cases where this is may actually true are with monatomic crystalline salts, where the rigid, completely non-malleable structure cannot be warped and only breaks. >the amount of force per unit area it can withstand before failing is only dependent on the material in question >if it is true, why do submarine hulls for example need to be thick force PER UNIT AREA is constant and independent of thickness and geometry does "normalized quantity" ring any bells? >A one atom thick material doesn't resist the same force as a 2 inch thick sample of the same material no shit sherlock you have to multiply the cross sectional area with the force per unit area to get the actual force which the geometry of the given material can withstand	s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718303.21/warc/CC-MAIN-20161020183838-00366-ip-10-171-6-4.ec2.internal.warc.gz	CC-MAIN-2016-44	11,752	62
http://www.residentadvisor.net/feed-item.aspx?id=69461	math	Fri, 20 Sep 2013 / 808heinz808A website devoted to the island laments the economic and cultural changes that have reshaped it in recent years. Fri, 20 Sep 2013 / terrencefullerCatch the deep house jock playing from 5 PM- 7PM GMT on Beatport Live. Fri, 20 Sep 2013 / Max_CherryHere's the video for the opening track off Dynamics, the Brooklyn duo's latest LP on DFA. More › Fri, 20 Sep 2013 / RAThis audio quality on this live recording of the 3 Chairs member's set in London last month is a little on the raw side, but the mix itself is just too good to pass up. Fri, 20 Sep 2013 / andrewryceGaze upon the spacey video for the UK producer's "Hindsight." More › Fri, 20 Sep 2013 / samlouisThe "DJ Skills Workshop" is part of a recovery programme for the homeless at St Mungos in London.	s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164009403/warc/CC-MAIN-20131204133329-00099-ip-10-33-133-15.ec2.internal.warc.gz	CC-MAIN-2013-48	813	6
http://www.tectechnicsclassroom.tectechnics.com/s7p1a15/difference-between-mass-and-weight.php	math	Pj Problems - Overview The Number Line 7 Spaces Of Interest - Overview Triadic Unit Mesh States Of Matter COHN - Natures Engineering Of The Human Body The Human-Body Systems Faith, Love, Charity How is the mass of an object different from its weight? (a) Mass: S7P1A15 (Containership - Mass). (b)Weight: S7P3A31 (Force - Pull) Mass (also called inertial mass) is matter's inertia (resistance of matter to change in speed). Mass is the amount of matter. Weight is thepull of gravity (in the case of the earth, the force which the earth exerts on mass) on the mass of an object. It is represented as mg where g is the acceleration due to gravity. Mass is measured in pounds or grams (1 pound is approximately 454 grams). When mass is in pounds, g is 32 ft/sec2 and weight is in poundals. When mass is in grams, g is 980 cm/sec2 and weight is in dynes The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning. Single Variable Functions Ordinary Differential Equations (ODEs) Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions Derivation Of Heat Equation For A One-Dimensional Heat Flow The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light. Composition And Structure Of Matter How Matter Gets Composed How Matter Gets Composed (2) Molecular Structure Of Matter Molecular Shapes: Bond Length, Bond Angle Molecular Shapes: Valence Shell Electron Pair Repulsion Molecular Shapes: Orbital Hybridization Molecular Shapes: Sigma Bonds Pi Bonds Molecular Shapes: Non ABn Molecules Molecular Orbital Theory More Pj Problem Strings	s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506429.78/warc/CC-MAIN-20230922234442-20230923024442-00366.warc.gz	CC-MAIN-2023-40	1,905	31
http://vlpaperqwpn.ultimatestructuredwater.info/analysis-of-babylonian-mathematics.html	math	Analysis of babylonian mathematics Home » maa press » periodicals » convergence » the best known old babylonian tablet the best known old babylonian tablet contains additional analysis and photographs (1998) square root approximations in old babylonian mathematics: ybc 7289 in context historia mathematica 25. Contribution of babylonians in science and technology babylonian mathematics (also known as assyro-babylonian mathematics) philosophical analysis categories of philosophy functions of philosophy science vs religion. A history of mathematics by florian cajori was the first popular history of mathematics written in the united states [babylonian] tablet records the the terms synthesis and analysis are used in mathematics in a more special sense than in logic. Babylonian & egyptian math, page 1 babylonian and egyptian math mesopotamia • most of our evidence from 5000bc comes from mesopotamia which is why they call it babylonian mathematics (1, pg 10) • we have a much more detailed understanding of their math. Find babylon lesson plans and teaching resources from babylonian worksheets to hanging gardens of babylon videos, quickly find teacher-reviewed educational resources. This is revealed by an analysis of three published and two unpublished cuneiform tablets from january 29, 2016 babylonian astronomers computed position of jupiter with geometric methods january 29, 2016, humboldt even though they were common in babylonian mathematics since 1800. Babylonian mathematics descriptions, and analysis of the root(2) tablet (ybc 7289) from the yale babylonian collection photograph, illustration, and description of the root(2) tablet from the yale babylonian collection babylonian numerals by michael schreiber. Ancient babylonian astronomers developed many science , this issue p : /lookup/doi/101126/scienceaad8085 skip to main content home news journals the trapezoid procedures offer the first evidence for the use of geometrical methods in babylonian mathematical. Ancient mathematics: egyptians, babylonians the greatest and most remarkable feature of babylonian mathematics was their complex usage of a sexagesimal place-valued system in like aristotle, engaged in the theoretical study of logic and the analysis of correct reasoning up. Babylonians and the contributions to math topics: babylonia analysis physics has a lot of topics to cover important contributions babylonian is mostly famous for the studies of astronomy and mathematics the babylonian created a numeral system based on the present day number 60. An analysis of five ancient tablets reveals the babylonians calculated the position of jupiter using geometry techniques previously believed to have been first used some 1,400 years later in 14th century europe. History of mathematics - mathematics in egypt and mesopotamia - annette imhausen ©encyclopedia of life support systems (eolss) mathematics in egypt and mesopotamia often led to a distorted analysis of egyptian fraction reckoning viewed solely through. The history of mathematics: an introduction, 7e by david m burton babylonian mathematics a tablet of reciprocals the father of modern analysis, weierstrass sonya kovalevsky the axiomatic movement: pasch and hilbert. The most famous original document of babylonian mathematics is plimpton 322, a partly broken clay tablet, approximately 13cm wide, 9cm tall, and 2cm thick new york publisher george a plimpton purchased the tablet from archaeological dealer, edgar j banks in 1922 or 1923, and bequeathed it with. Babylonian mathematics relied on a base 60, or sexagesimal numeric system, that proved so effective it continues to be used 4,000 years later. The history of babylonian mathematics - the history of babylonian mathematics the history of ancient babylonia is really long, but this essay - the creation of man and the world is a question that has resonated since the conscience of thought and analysis began. Ancient babylonian use of the pythagorean theorem and its three dimensions and vice versa, similar to our contemporary numerical methods of analysis methods and traditions of babylonian mathematics. Babylonian mathematics 3 the center of mesopotamian culture the region, at least that between the two rivers, the tigris and the euphrates, is also called chaldea. The area of study known as the history of mathematics is primarily an investigation into the origin of babylonian mathematics were written using a bradwardine's analysis is an example of transferring a mathematical technique used by al-kindi and arnald of villanova to quantify the. Numerical analysis studies different algorithms to get approximations for problems of mathematical analysis one of the earliest known uses of numerical analysis is a babylonian clay tablet, which approximates the square root of 2. Introductory analysis is a two course sequence whose main purpose is to teach the basics of analysis in a rigorous and reasonably complete way college algebra is essentially babylonian mathematics (ca 2000 to 800 bce) with a smattering of 17th century stuff (logarithms. Babylonian mathematics this free course is available to start right now 14 a remarkable numeration system the babylonian numeral system was described in section 3 as 'remarkable' it is worth spelling out the reasons for this judgement. Analysis of babylonian mathematics Babylonian mathematics's wiki: babylonian mathematics (also known as assyro-babylonian mathematics) was any mathematics developed or practiced by the people of mesopotamia, from the days of the early sumerians to the fall of babylon in 539 bc babylonian mathematical texts are. Babylonian mathematics refers to mathematics developed in mesopotamia and is especially known for the development of the babylonian numeral system. The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in babylonian mathematics were written using a one important area that contributed to the development of mathematics concerned the analysis of local motion. - Babylonian mathematics iraqi mathematics, or mesopotamian mathematics, refers to the history of mathematics in iraq diophantus made advances in babylonian algebra, particularly indeterminate analysis, which is also known as diophantine analysis. - J friberg, methods and traditions of babylonian mathematics ii an old babylonian catalogue text with equations for squares and circles, j indeterminate analysis in babylonian mathematics, osiris 8 (1948), 12-40. - The origins of greek mathematics1 though thegreekscertainlyborrowedfromother civilizations the egyptian and babylonian influence was greatest in miletus • pappus wrote treasury of analysis. Ancient babylonian astronomers were the first to use geometry to calculate the movement of planets through space, a new study suggests it was previously thought that this type of analysis had only originated hundreds of years later, in 14 th century europe the report, written by professor mathieu. Sequences and series in old babylonian mathematics 15 pages sequences and series in old babylonian mathematics uploaded by duncan j melville connect to download 'the old babylonian square texts - bm 13901 and ybc 4714: retranslation and analysis. General description we will explore some major themes in mathematics--calculation, number, geometry, algebra, infinity, formalism--and their historical development in various civilizations, ranging from the antiquity of babylonia and egypt through classical greece, the middle and far east, and on. Babylonian numerals, ancient numberspage 1 of 2 feed back advertise search home calculators and converters basic. Sumerian and babylonian mathematics was based on a sexegesimal, or base 60, numeric system, which could be counted physically using the twelve knuckles on one hand the five fingers on the other hand.	s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589752.56/warc/CC-MAIN-20180717144908-20180717164908-00199.warc.gz	CC-MAIN-2018-30	7,869	12
http://www.metric-conversions.org/length/centimeters-to-uk-nautical-miles.htm	math	The centimetre is a unit of length in the metric system, equal to one-hundredth of a metre. 1cm is equivalent to 0.39370 inches. Nautical miles measure distance. 1 nautical mile is the angular distance of 1 minute of arc on the earth's surface. As these differ slightly (6108' at pole c.f. 6046' at equator) 6080 was adopted (this being it's approximate value in the English Channel). The International nautical mile is 1852 metres, so is very slightly different from the UK nautical mile.	s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936460577.67/warc/CC-MAIN-20150226074100-00266-ip-10-28-5-156.ec2.internal.warc.gz	CC-MAIN-2015-11	489	3
https://au.mathworks.com/matlabcentral/fileexchange/6907-coeffsort?s_tid=answers_rc2-3_p6_MLT	math	The coeffs (Symbolic Toolbox) function outputs the coefficients and terms of its argument polynomial in ascending order (opposite of the MATLAB convention for polynomials). It occasionally permutes their sequence, so simply using fliplr doeson't always solve the problem. However, the orders of the coefficient and term vector elements always corresponds. This utility takes as arguments the coefficient (C) and polynomial term (T) vectors that coeffs returns (as [C,T]), and the polynomial variable. It returns both coefficient and term vectors in monic, descending order, conforming to the MATLAB convention. It is particularly helpful for long symbolic coefficients, such as those that define transfer functions in terms of component values to be computed elsewhere (the kind of problem I wrote it to solve). See also the coeffs documentation in the Symbolic Math Toolbox. Star Strider (2020). coeffsort (https://www.mathworks.com/matlabcentral/fileexchange/6907-coeffsort), MATLAB Central File Exchange. Retrieved . coeffsort() works exactly as advertized to remedy coeff()'s sometimes ideosyncratic ordering of polynomial coefficients. [Note to Symbolic Toolbox engineers: This rank-ordering bug really should be fixed within coeff() itself, eliminating the need for this coeffsort() fix-up.] BSD License added. No code changes.	s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655896169.35/warc/CC-MAIN-20200708000016-20200708030016-00510.warc.gz	CC-MAIN-2020-29	1,333	4
https://books.google.ie/books?id=Bv4JAAAAIAAJ&pg=PA314&vq=%22NB+In+the+following+table,+in+the+last+nine+.columns+of+each+page,+where%22&dq=editions:UOM39015065618988&lr=&output=html_text	math	« PreviousContinue » aš Exam. 27. To find the fluent of x ax2 Exam. 28. To find the fluent of 23 v 2.x ma. EXÁM. 29. To find the fluent of a š. Exam. 30. To find the fluent of 3a2% . EXAM. 31. To find the fluent of 3zx log.z + 3.x3. Exam. 32. To find the fluent of (1 + x3).xx. Exam. 33. To find the fluent of (2 + ).x. EXAM. 34. To find the fluent of riva? + x?. To find Fluents by Infinite Series. 44. When a given fluxion, whose fluent is required, is so complex, that it cannot be made to agree with any of the forms in the foregoing table of cases, nor made out from the general rules before given ; recourse may then be had to the method of infinite series; which is thus performed: Expand the radical or fraction, in the given fluxion, into an infinite series of simple terms, by the methods given for that purpose in books of algebra; viz. either by division or extraction of roots, or by the binomial theorem, &c; and multiply every term by the fluxional letter, and by such simple variable factor as the given fluxional expression may contain. Then take the fluent of each term separately, by the foregoing rules, connecting them all together by their proper signs, and the series will be the fluent sought, after it is multiplied by any constant factor or co-efficient which may be contained in the given fluxional expression. 45. It is to be noted however, that the quantities must be so arranged, as that the series produced inay be a converging one, rather than diverging: and this is effected h placing the greater terms foremost in the given i When these are known or constant quantities, the series will be an ascending one; that is, the power variable quantity will ascend or increase ; but if the quantity be set foremost, the infinite series pred a descending one, or the powers of that crease always more and more in the succe crease in the denominators of them, whic For example, to find the fluent of Here, by dividing the numerator by the denominator, the 1 + x proposed fluxion becomesi - 2x:+3x; — 5x3; +8x4— &c; Again, to find the fluent of iN x?. &c. Then the fluents of all the terms, being taken, give x - 3x3 3x3 – 4625 Thir? - &c, for the fluent sought. bxx EXAM. 1. To And the fluent of both in an ascend a - X 31 EXAM. 3. To find the fluent of (a + x)2". 1 x2 + 2x4 EXAM. 4. To find the fluent of -a, 1 + x x2 bi EXAM. 5. Given ż= to find z. a + 729 a2 + x2 EXAM. 6. Given z = jc to find %. a + x to find z. to find z. XX, to find ;. To Correct the Fluent of any Given Fluxion. 46. The fluxion found from a given fluent, is always perfect and complete; but the fluent found from a given Auxion is not always so; as it often wants a correction, to make it contemporaneous with that required by the problem under consideration, &c: for, the fluent of any given fluxion, as i may be either x, which is found by the rule, or it may be x + c, or x c, that is x plus or minus some constant quantity c; because both x and x+c have the same fluxion x, and the finding of the constant quantity c, to be added or subtracted with the fluent as found by the foregoing rules, is called correcting the fluent. Now this correction is to be determined from the nature of the problem in hand, by which we come to know the relation which the fluent quantities have to each other at some certain point or time. Reduce, therefore, the general fluential equation, supposed to be found by the foregoing rules, to that point or time; then if the equation be true, it is correct; but if not, it wants a correction; and the quantity of the correction, is the difference between the two general sides of the equation when reduced to that particular point. Hence the general rule for the correction is this: Connect the constant, but indeterminate, quantity c, with one side of the fluential equation, as determined by the fore. going rules; then, in this equation, substitute for the variable quantities, such values as they are known to have at any particular state, place, or time; and then, from that particular state of the equation, find the value of c, the constant quantity of the correction. 47. EXAM. 1. To find the correct fluent of 2 = axis. The general fluent is z = ax4, or z = ax+ +c, taking in the correction c. Now, if it be known that z and x begin together, or that mis 0, when x = : 0; then writing o for both x and z, the general equation becomes 0 = 0 +c, or = c; so' that, the value of c being 0, the correct fluents are 2 = ax4. But if z be = 0, when x is = b, any known quantity; then substituting 0 for %, and b for X, in the general equation, it becomes 0 = abt + c, and hence we find c= which being written for c in the general fluential equation, it becomes z = ax4 ab, for the correct fluents. Or, if it be known that z is = some quantity d, when : is = some other quantity as b; then substituting d for z, and b for x, in the general fluential equation z = ax4 + c, it becomes d = abt tc; and hence is deduced the value of the correction, namely, crd - abt ; consequently, writing this value for c in the general equation, it becomes Zar4 abt + d, for the correct equation of the fluents in this case. 48. And hence arises another easy and general way of correcting the fluents, which is this: In the general equation of the fluents, write the particular values of the quantities which they are known to have at any certain time or position ; then subtract the sides of the resulting particular equation from the corresponding sides of the general one, and the remainders will give the correct equation of the fluents sought. So, the general equation being % = axt; write d for z, and b for x, then d = abt; hence, by subtraction, d = axt aba, or 2 = ax4 – ab4 + d, the correct fluents as before. EXAM. 2. To find the correct fluents of 2 = 5.x; z being = 0 when x is = a. Exam. 3. To find the correct fluents of ź = 3x va tri z and .r being = 0 at the same time. 2ax EXAM. 4. To find the correct fluent of ź = ; sup att posing z and x to begin to flow together, or to be each = 0 at the same time. 23 ExAM. 5. To find the correct fluents of 3 = ; posing z and 2' to begin together. a' + i sup OF MAXIMA AND MINIMA; OR, THE GREATEST AND LEAST MAGNITUDE OF VARIABLE OR FLOWING QUANTITIES. 49. MAXIMUM, denotes the greatest state or quantity attainable in any given case, or the greatest value of a variable quantity: by which it stands opposed to Minimum, which is the least possible quantity in any case. Thus, the expression or sum a* + br, evidently increases as x, or the term bx, increases; therefore the given expression will be the greatest, or a maximum, when x is the greatest, or infinite: and the same expression will be a minimum, or the least, when x is the least, or nothing. Again, in the algebraic expression a? - bx, where a and b denote constant or invariable quantities, and x a flowing or variable one. Now, it is evident that the value of this remainder or difference, a? bx, will increase, as the term bx, or as x, decreases; therefore the former will be the greatest, when the latter is the smallest ; that is a?. bır is a maximum, when x is the least, or nothing at all; and the difference is the least, when x is the greatest. 50. Some variable quantities increase continually; and so have no maximum, but what is infinite. Others again decrease continually; and so have no minimum, but what is of no magnitude, or nothing. But, on the other hand, some variable quantities increase only to a certain finite magnitude, called their Maximum, or greatest state, and after that they decrease again. While others decrease to a certain finite magnitude, called their Minimum, or least state, and afterwards increase again. And lastly, some quantities have several maxima and minima. Thus, for example, the ordinate bc of the parabola, or such-like curve, flowing along the axis AB from the vertex A, continually increases, and has no limit or maximum. And the ordinate GF of the curve EFH, flowing from e towards H, continually decreases to nothing when it arrives at the point H. But in the circle ilm, the ordinate only increases to a certain magnitude, namely, the radius, when it arrives at the middle as at kl, which is its maximum ; and after that it decreases again to nothing, at the point M. And in the curve now, the ordinate decreases only to the position OP, where it is least, or a minimum; and after that it continually increases towards e. But in the curve Rsu &c,' the ordinates have several maxima, as st, wx, and several minima, as Vu, yz, &c.	s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304835.96/warc/CC-MAIN-20220125130117-20220125160117-00619.warc.gz	CC-MAIN-2022-05	8,540	55
https://blackboardmasters.com/budgeted-cash-receipts-accounting-assignment-help/	math	The Adams Corporation, a merchandising firm, has budgeted its activity for November according to the • Sales at $450,000, all for cash. • Merchandise inventory on October 31 was $200,000. • The cash balance November 1 was $18,000. • Selling and administrative expenses are budgeted at $60,000 for November and are paid for in cash. • Budgeted depreciation for November is $25,000. • The planned merchandise inventory on November 30 is $230,000. • The cost of goods sold is 70% of the selling price. • All purchases are paid for in cash. • There is no interest expense or income tax expense. How much are the budgeted cash receipts for November?	s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374217.78/warc/CC-MAIN-20210306004859-20210306034859-00135.warc.gz	CC-MAIN-2021-10	662	11
http://www.thornber.net/famhist/htmlfiles/stackhouse.html	math	My interest in the Stackhouse family arises from the marriage of Matthew Cragg to Ann Stackhouse, on 30 July 1759 at Clapham, North Yorkshire. She was buried at Ghyll Church, Barnoldswick on 26 Mar 1802. We might expect that Ann was of similar age to her husband who was born in 1734 so a baptism in the 1730s or early 1740s would fit. Steven Broadley has gathered some evidence on the Stackhouse family in this part of North Yorkshire. The earliest mention of the name is in 1440 at Fountains Abbey and in church registers the earliest record was found in 1560 at Giggleswick. Steven found the following entries in the Chapel le Dale registers which identify an Ann Stackhouse, daughter of Samuel. There are also Stackhouse entries at Giggleswick, Bentham and Tatham. The evidence below leads to the following tentative family tree: The arguments for the assignments are set out with the evidence below. John s. Sameuell Stackhouse, 24 Dec 1693 Eliz. d. Samuel Stackhouse, 23 Aug 1730 (see burial below) Oliver s. Samuel Stackhouse, 13 Feb 1733 Ann d. Samuel Stackhouse, 30 Nov 1734. (This is likely to be the Ann Stackhouse who married Matthew Cragg) Eliz. d. Samuel Stackhouse, 29 Jan 1738 John s. Samuel Stackhouse, 12 Oct 1740 Samuel s. Samuel Stackhouse, 20 Feb 1742 (see burial below) Agnes d. Samuel Stackhouse, 11 Nov 1743 Thomas s. Samuel Stackhouse, 18 Jan 1745 Eleanor d. Samuel Stackhouse, 6 Nov 1747 (see burial below) Eliz. d. Samuel Stackhouse, 17 Nov 1751 Ellin d. Samuel Stackhouse, 10 Oct 1754 (see burial below) There is a single reference to a Samuel Stackhouse at Thornton-in-Lonsdale who may be part of the family above. Jane d. Samuel Stackhouse of Ireby bapt 23 Dec 1759 Burials at Chapel le Dale that fit for this family are as follows: Eleanor d. Samuel Stackhouse, buried 10 Feb 1748 Eliz. d. Samuel Stackhouse, buried 22 Oct 1730 Samuel s. Samuel Stackhouse, buried 25 May 1744 Ellin d. Samuel Stackhouse, buried 15 Mar 1770 Agnes wife of Samuel Stackhouse, buried 19 Sept 1784. Samuel Stackhouse, buried 19 Jan 1792. Marriages at Chapel le Dale. Samuel Stackhouse and Ann Procter of Horton by licence on 22 Jun 1729 at Ingleton Yorkshire. (This is a good fit for when the children start to be born) Samuel Stackhouse, yeoman, and Agnes Horn of Shap, County of Westmorland, by licence, 26 July 1737 at Chapel le Dale It is plausible that there is one Samuel who marries Ann Procter in 1729 and they have children Elizabeth, Oliver and Ann. Some time after 1734, Ann the wife dies and Samuel marries Agnes Horn in 1737. This couple then have eight further children. It is interesting that there is only one reference to a burial of a Samuel Stackhouse which is in favour of a single Samuel marrying twice. There is a record of Samuel Stackhouse son of Oliver Stackhouse baptised on 16 April 1709 at Ingleton which gives a plausible age for Samuel's marriage in 1729. Further investigation reveals a family of Oliver Stackhouse as follows at Ingleton/Chapel le Dale Oliver Stackhouse married Elizabeth Topham on 8 May 1708 at Thornton in Lonsdale. Baptisms at Ingleton/Chapel le Dale: Samuel Stackhouse 16 Apr 1709 Ellin Stackhouse 30 Aug 1713 buried 1 Oct 1715 Thomas Stackhouse 10 May 1715 Ellin Stackhouse, 13 Dec 1719 Eliz. wife of Oliver Stackhouse was buried 14 June 1721 so the following must be children of a second wife or a different Oliver. James Stackhouse s. Oliver 18 Nov 1724 Dorothy Stackhouse d. 4 Oct 1729, daughter of Oliver Stackhouse deceased. Oliver Stackhouse was buried on 19 Feb 1727 at Chapel le Dale(so Dorothy must have been baptised some time after her birth) Elizabeth wife of Oliver Stackhouse was buried 14 June 1721 at Chapel le Dale Looking at potential antecedents of Oliver Stackhouse we have a baptism of an Oliver son of Thomas Stackhouse, baptised on 3 Feb 1684 at Horton in Ribblesdale. However, there is also an Oliver son of Samuel Stackhouse baptised at Giggleswick on 22 Jan 1679/80 that is equally plausible so no decision can be taken on which is correct at the moment. It would be useful to go through the burial records at Horton in Ribblesdale and at Giggleswick to see if either of these Olivers died before the age of marriage The latter is part of a family group as follows: Baptisms at Giggleswick Oliver Stackhouse s. Samuel of Giggleswick, 22 Jan 1678/80 Anne Stackhouse d. Samuel of Giggleswick, 29 Jan 1681/82 Margareta Stackhouse d. Samuel of Giggleswick, 14 Sep 1684 Hugonius Stackhouse s. Samuel of Giggleswick, 21 Mar 1686/87 Ellina Stackhouse d. Samuel of Giggleswick, 26 Jan 1689/90 Baptism at Ingleton/Chapel le Dale John Stackhouse s. Samuel, 24 Dec 1694.	s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123270.78/warc/CC-MAIN-20170423031203-00236-ip-10-145-167-34.ec2.internal.warc.gz	CC-MAIN-2017-17	4,647	51
https://www.hackmath.net/en/math-problem/2364	math	The coal storage distribute received coal shipment within three days. The first day distribute third of the shipments, the second day of two-fifths of the rest and the third day 300 tons of coal. How many tons of coal distributed first and second day? Did you find an error or inaccuracy? Feel free to write us. Thank you! Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it. Tips to related online calculators You need to know the following knowledge to solve this word math problem: Related math problems and questions: - Shop stores Workers untied fruit to stores. In the first quarter shipments, in the second fifth shipment, in the third two-fifths of the rest and in the fourth 231 kilograms. How many fruits were together? - Three days During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day? - Toys 3 Tiffany's toyshop received a shipment of 360 toys. The first day 12 were sold the second day 19 were sold and on the third day, 26 was sold. How many days will the toyshop run out of toys? For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day? The ticket seller sold 1,280 scratch cards in three days. On the second day, he sold 90 tickets less than on the first day, on the third day he sold 1.5 times more tickets than on the second day. How many tickets did he sell on the third day? - 3 days Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day. Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target? - 3 masons Three masons received 7,700 CZK. The second half received 1/2 more than the first and third twice more than the second mason. How much they each got crowns? - Two typists There are two typists who are rewriting the material 814 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting al Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together? - Copper parts From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast? - Three monks Three medieval monks has task to copy 600 pages of the Bible. One rewrites in three days 1 page, second in 2 days 3 pages and a third in 4 days 2 sides. Calculate for how many days and what day the monks will have copied whole Bible when they begin Wednes - Three days way The tourist walked a quarter of the way on the first day, a third of the rest on the second day and 20 km on the last day. How many km did he cover in three days? - The second The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles? - The creek Workers cleaned the creek within 3 days. The first day cleanse one-fifth the creek's length, the next day 40% of the stream's length, and the third day 8 km length of the creek. How long is a creek? - Three granaries Three granaries hold 7,800 metric cent (q) of grain. In the first, 70 tonnes of grain was more than the second and in the third it was 120 tonnes less than in the second. How many grain were in each granary? - Heating plant Workers dump imported coke at the heating plant. On the first day used half of the amount, the second day three quarters the rest and on the third day left 120 tons. How much coke did they dump at the heating plant?	s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585348.66/warc/CC-MAIN-20211020183354-20211020213354-00206.warc.gz	CC-MAIN-2021-43	4,189	36
https://www.coursehero.com/file/126167/gas20laws20practice20problems20key/	math	CHEM 215 Section 5/6/7 Practice Problems – Gas Laws (KEY) October 31, 2006 1. An automobile tire when properly inflated has a pressure of 35.0 psi and a volume of 5.00 L at room temperature (25 o C). What will the pressure of the tire be after a long period of driving if the volume has increased by 0.5 L and the temperature of the air in the tire rises to 33.1 o C? P=2.22 atm 2. Calculate the molar mass for a gas that has a density of 0.964 g/L at 730 torr of pressure and 95 o C. M =303.2 g mol-1 3. A mixture of 1.00g of H 2 and 1.00 g He exerts a pressure of 0.531 atm at 5.0 o C. What is the volume of the container and the respective partial pressure of each gas? V=32.1 L; P(H 2 )=0.353 atm; P(He)=0.178 atm 4. Oxygen gas can be generated by the decomposition of mercuric oxide (shown below). What volume of oxygen gas, measured at 27 o C and 745 torr, can be produced by the complete decomposition of 3.72 g of mercuric oxide? 2 This is the end of the preview. access the rest of the document.	s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890187.52/warc/CC-MAIN-20180121040927-20180121060927-00770.warc.gz	CC-MAIN-2018-05	1,006	3
http://perplexus.info/show.php?pid=4483&cid=31128	math	I have a cross in the form of one square with four identical squares surrounding it Cut it into the fewest number of pieces possible such that, when rearranged the pieces form two smaller crosses of identical size. (In reply to 2 pieces? by Dej Mar) I would consider that a 'dead-end' or a 'T' I think in the problem, he defines a cross "four identical squares surrounding" to mean a cross must have four appendages coming out from Of course.. by that note... that might mean my irregular 4 piece crosses are incorrect and your 4 piece regular crosses are correct if im to take "identical squares" literally Posted by Highway6 on 2006-03-06 16:10:38	s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823445.39/warc/CC-MAIN-20181210212544-20181210234044-00013.warc.gz	CC-MAIN-2018-51	649	12
https://www.physicsforums.com/threads/applying-for-chemical-engineering.89129/	math	I am currently thinking of applying to the university of manchester and imperial college in my Ucas form. However, i didn't take physics in my AS or A-levels. Although they offer ABB/AAB for Chemical engineering without mention of physics, i am concerned. I currently take Maths, Chem, and DT as my A-level choices. And i AM willing to work hard to catch up to other students at university (if i go) in terms of mathematics and physics. It would be deeply appreciated if anyone who takes chemical engineering gives some advice on this dilemma. cheers.	s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823657.20/warc/CC-MAIN-20181211151237-20181211172737-00129.warc.gz	CC-MAIN-2018-51	551	1
https://butterflycoins.org/topics/624d9010f79a414c073130a3	math	Hey Dud, This side andrew Greece I have one question for you I know very well you don't have the answer to this question. so, The question is How Much Is 80000 Pennies? If you know the answer to this question so can comment on me on this post if you don't know the answer you can read the blog link I will mention in this post click the given link and read it. Also Read: How Many Steps in a Mile. Back to top	s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335504.37/warc/CC-MAIN-20220930212504-20221001002504-00108.warc.gz	CC-MAIN-2022-40	409	3
https://calculatemturbo.com/percentage-finder/	math	The word ‘percent’ means ‘out of a hundred’. In mathematics, percentages are used like fractions and decimals as a way to describe parts of a whole. When you’re using percentages, the whole is considered to be made up of a hundred equal parts. Percent is a Latin word which means ‘out of a hundred’. So you can divide each ‘whole number’ into 100 equal parts, each of which is a percentage. In other words, a percentage is a fraction whose denominator (lower) is 100. So if we say 50%, we mean 50/100 = 1/2 . So 50% means 1/2. If you need to convert a percentage to a decimal, simply divide by 100. For example, 25% = 25/100 = 0.25. To convert a decimal to a percentage, multiply by 100. Hence 0.3 = 0.3 × 100 = 30%. How to Find Percentage To calculate percentage Here we are going to show you the easiest way to calculate percentage. When it comes to percentage it is often a number. And you are asked what percentage to get out of that number or the percentage you want to get out. Here we are going to explain the two main methods of calculating percentage, which are most useful. You can understand the first one is from below mentioned example. Method – 1 For example, suppose you have a number 25, of which you want to get 10%. So for this first you will write 25 x (10 / 100) which on simplification will give 2.5 in other words if any number is x and we have to find its y% then according to above concept (xy / 100 Method – 2 The first method is the easiest and basic way to calculate the percentage, that method is used when you are given a number and asked to find a certain percentage of it, but what if you are given two different numbers And you are asked what percentage of the second number is the first number, in such a situation the second method comes in handy, which you can understand by the following example : So assume you have asked to find that 1000 is what percent of 10000. We know that the number 10000 is 100% because it is the total value given. Now assume “X” is the value, the exact percentage that we are finding. Now as per the above-mentioned concept 100% = 10000 And X% = 1000 Now we have the same kind of unit on both left sides and and as well as both right side. So we can describe it as 100%/x%=10000/1000. Now we can solve this equation by this formula, Now you have to multiply both left and right sides of the equation by x we divide both sides of the equation by (10) to get x So the answer is 10% How to Calculate Percentage with Percentage Finder Calculator Finding and calculating Percentage from our calculator is very easy to use and as well as free. You can check how percentage Calculator of calculator m turbo works. The percentage finder by calculate m turbo divided into two different divisions and both these divisions work on the two concepts that we mentioned above. Let’s check - This method comes in handy when you are given a number and asked to find a certain percentage of it. So, what you have to do to find the percentage amount is to write the given percentage in the first box. - Now in the second box you have to write the amount that you got in the question and then just click on “Calculate” button and you will get your answer in the “Answer” Box. That simple it is. - You use this method when you are given two different numbers and you are asked what percentage of the second number the first number is. So what you have to do to get the answer is write the given number in the first box. - Now in the second box you have to write the percentage given in the question and then just click on the calculate button and it will show you your answer in the answer box. So that is how you can calculate percentage through percentage finder calculator. Hope we covered all for you but still if there is anything you want to know related to the calculator or, want to share your suggestions so please use the comments box, we are waiting.	s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663021405.92/warc/CC-MAIN-20220528220030-20220529010030-00427.warc.gz	CC-MAIN-2022-21	3,941	32
https://worldbuilding.stackexchange.com/questions/228387/moving-ceres-to-a-new-home	math	I made a mistake in my calculations, but noticed it too late. I tried to make some clarifications, but... I'll fix or delete it later. I hope someone writes a better answer and makes this one obsolete. It still has some info for the OP (otherwise I wouldn't post it) so... until a better answer posted. Spinning Ceres isn't such great idea, as @notovny pointed in his comment. It's also easy to see by such an example - let's assume that your people are 10km below the ice, shielded well, with their feet pressed to the ceiling with 1g towards equator. But all the ice, which is under their feet, wants to fly to the equator. It can be visualized (not an exact match) as an ice sky scraper standing 10km height in the earth's gravity. Even if both cases are not equal, the ice will get what it wants: To fly out in one case and crumble/fall down in another. This is not a huge problem, just makes your happy version of an ice express. A torus and maglev will fix the problem. - In that sense, why not to begin with building that torus next to Ceres, using Ceres' materials? Okay, there are cons and pros, and in my opinion the pros of carving out an asteroid doesn't outweigh the cons, but at least it has a couple positive places. As for the energy required, our Sun has more than enough energy for that, so in theory it shouldn't be a problem. If efficiency is high, it will probably be capable of accelerating at 10 m/sec2 (1g) or something like that, minus a mile (to start). - If they have access to even one percent of the Sun's solar energy output, then it can be done quite easy energywise, but such a choice doesn't have much justification. Ceres travelling in this way is only a result of some story, as without some reason, it doesn't look like a good choice. But sure, the story can fix that (It's a bit of a lazy move, but people eat it). Using electric propulsion and current engines specs, you will use about 36% of mass of Ceres to reach 0.1c (with an exhaust velocity of 0.1c, which is the fusion engine's speed). WARNING I made a mistake here with exhaust velocity, which makes up the rest of the answer. More importantly, the conclusion is invalid. In the case of ION engine, things are grim, but if it upgraded to the level of fusion engine then things look a bit better, except for the energy consumption and the time required. Wrong numbers, Wrong conclusions The correct end mass for Ceres is 30km/s exhaust velocity. There is no way to have a 0.1c end velocity, as it is 21x of the exhaust velocity, and then you will be left with about a million tons (10^9 kg) of ex-Ceres. (The rest is spewed as reactive mass.) So really you barely get to 600km/s, and starting from Ceres orbit, it's way more than one needs to escape. (600km/s escape velocity is next to the solar surface, and at Ceres, the orbit's main job is done. It is like the energy was never spend/lost.) In engines, their TWR is an important number. It produces 5N, but how much mass it has is on its own. It is about 230kg, so max acceleration is 1m/s in about 46 seconds. This means the best time it can possibly be in this case is about 43 years to reach the speed of 0.1c. In reality, it may be a couple of times longer, depending on how heavier Ceres is than all those engines. For every 10 times larger, the trip is about 400 years later. That is probably a reasonable number. - I have reasons to believe that scaling it up will improve specs in the TWR aspect, but you would need energy sources, places to store the energy capturing devices, etc, so the estimate above may be a reasonable number in scaled-up version as well. All in all, things aren't that bad with fusion, (like ION engines). It may need a few tweaks here and there, but it can become a reasonable generation ship. However, with the ION engines, which have 1000 times worse ISP(exhaust velocity), it is quite bad. Nevertheless, energy source is biggest issue here in both cases. So one needs about 470 trillion(4.7x10^14) of such engines, and power consumption/generation 47'000'000'000 GW. Post-error detected explanation: As we will be left with nothing, for a mass as large as that of Ceres, especially with those low ION engine ISP's, we have to increase ISP. We'll have the same improvement basket, but it also means that if ISP is increased 1000 times to the level of fusion engine, energy consumption also will be increased, but at a million times increase. (Energy is the square of velocity.) Sooooo... That means that it is 1'000'000x larger than of those 47 billion GW. Sooooo... Ring diameter will have to be 1000 times bigger. OR it has to be a million times slower. OR a combination of those two. 47 billion GW is an energy-capture sail/system of 200'000 km in diameter at earth orbit (1300W/m2). Not impossible as well. You can, however, use oxygen as reactive mass as well. You'd have to repair those engines and replace them along the way, which means factories to make all that, all the technology for all that, and many, many more other things. Oxygen can be ionized in the same way as hydrogen, keeping the high ISP. Take it from the improvement bucket, where all that scaling up lives, and it is quite a minor upgrade (and there are ion engines which work on air/oxygen containing mixture.)	s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00774.warc.gz	CC-MAIN-2022-27	5,271	17
http://ciessaysunj.alexandru.me/standard-deviation-and-percentage.html	math	Standard deviation and percentage Standard deviation calculator the following is a free online tool to calculate the standard deviation, variance, mean, sum, and confidence interval approximations. Excel percent relative standard deviation %rsd - detailed tutorial with worked example and clear screen shots. The next step is standardizing (dividing by the population standard deviation) calculate percentage proportion within x sigmas at wolframalpha. Standard deviation is a number used to tell how measurements for a group are spread out from the average with a standard deviation of 20 percentage points (pp. This site might help you re: calculate percentage when given standard deviation and mean here is the problem: the energy information administration. How to add error bars in excel: standard deviation at its finest a standard deviation or a percentage as well as determine the specific error amounts to be. Calculator with step by step explanations to find standard deviation, variance, skewness and kurtosis. Z-stats / basic statistics z-4: mean, standard deviation, and coefficient of variation written by madelon f zady. Standard deviation (sd) is the measure of spread of the numbers in a set of data from its mean value it is also called as sd and is represented using the symbol σ. Descriptive statistics and psychological testing by stephen e brock a specific percentage of scores will lie and 1 standard deviation above the mean. Anyone who follows education policy debates might hear the term “standard deviation” fairly often most people have at least some idea of what it means, but i. 5 sigma what's that by evelyn lamb on july 17 the greek letter sigma is used to represent standard deviation standard deviation measures the distribution of. Stock a over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points (pp) and stock b. The distribution of the ratio, in a single normal sample, of range to standard deviation with the exact percentage points (see 3. I have 2 data sets the first data set, let's call it $x$ has an average value of ($\bar x$) and standard deviation of ($std_x$), the second set of data also has the. I was given an ungrouped frequency chart and asked to construct a histogram, find the mean, the standard deviation and the percentage of data within one, two, and the. Computing percentiles using the mean and standard deviation in the previous question, what proportion of patients have wbc counts between 5000 and 7000. As an experimenter, it's important to be able to calculate the standard deviation, because this is the parameter that defines the way data is centered about the mean. Comparing average absolute deviation and standard deviation fortunately, the average absolute deviation and the standard deviation are usually close in value. Probability calculator desired values to a z-score by subtracting the given mean and dividing by the standard deviation expressed as a percentage such as. Average, standard deviation and relative standard deviation how will your data compare with other people’s data let’s find out we will do this by pulling. - Standard deviation of percentages calculator calculate the standard deviation of percentage of numbers using this online calculator. - Simple statistics there are a wide standard deviation is a particularly useful tool the student has measured the percentage of chlorine (cl. - To calculate the relative standard deviation, divide the standard deviation by the mean and then multiply the result by 100 to express it as a percentage the. - The standard deviation the standard deviation is a measure that summarises the amount by which every value within a dataset varies from the mean. - 6 differences between percentages and paired the percentage of women in the appendicitis sample was for nominal variables the standard deviation is not. - This is a simple example of how to calculate variance and population standard deviation the standard deviation equation is given and explained. - Normal curve - bell curve - standard deviation - what does it all mean statistics help - duration: percentage trick - solve precentages mentally.	s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221214538.44/warc/CC-MAIN-20180819012213-20180819032213-00200.warc.gz	CC-MAIN-2018-34	4,200	14
https://apps.dtic.mil/sti/citations/ADA034981	math	Computational Complexity of Fourier Transforms Over Finite Fields. ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB Pagination or Media Count: This paper describes a method for computing the Discrete Fourier Transform DFT of a sequence of n elements over a finite field GF p to the mth power with a number of bit operations 0nm log nm. Pq where Pq is the number of bit operations required to multiply two g-bit integers and g approx. 2 log sub 2 4 log sub 2m 4 log sub 2p. This method is uniformly applicable to all instances and its order of complexity is not inferior to that of methods whose success depends upon the existence of certain primes. - Theoretical Mathematics	s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585181.6/warc/CC-MAIN-20211017175237-20211017205237-00286.warc.gz	CC-MAIN-2021-43	683	5
http://courses.georgetown.edu/index.cfm?Action=View&CourseID=MATH-006&AcademicYear=2007&AcademicTerm=FallSpring	math	MATH-006 Statistics with Exploratory Data Analysis No faculty information available The primary objective of this beginning course in statistics is to have students learn and understand statistical concepts without being overwhelmed by cumbersome formulae and computations. The emphasis will be on data exploration and graphical techniques. Topics to be covered will include descriptive statistics, measures of center and spread, linear regression, probability theory, sampling, random variables and probability distributions. Uniform, discrete, binomial, normal, t and chi-square distributions will be among those used to introduce statistical inference, including estimation and hypothesis testing. Considerable use will be made of video tapes and computers. All classes will be held in the computer lab where the statistical software MINITAB will be taught and used to simplify computation and enhance graphical presentations. A computer tutorial will also be used. Minimum computer ability is recommended (but not required). This course is regarded as a core course (or SONY core course, as appropriate) for completion of the math/science requirement in the College. Fall and Spring. Other academic years There is information about this course number in other academic years:	s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697442043/warc/CC-MAIN-20130516094402-00002-ip-10-60-113-184.ec2.internal.warc.gz	CC-MAIN-2013-20	1,279	5
https://forums.adobe.com/message/10528255	math	InDesign won't support mathml. You can use external editor like mathtype for this workflow. Other plugins are powermath, inmath etc., but it won't support mathml (I think so...), those plugins have it's own codings. Vandy88 is correct -- InDesign doesn't support MathML, but MathType does, and you can use MathType with MathML. However, I don't want to cloud the issue or introduce confusion -- using MathType with InDesign means you'll insert the equations into the document as EPS, not as MathML. Even if you use MathType to process the MathML, the MathML equations still aren't recognizable by InDesign, and they'll need to be in graphical format. Unless you're tied to InDesign, there are some really nice XML+MathML solutions available in the marketplace, but this probably isn't the right forum to discuss that. How are you doing? You said about some solutions using XML+MathML. Thank you so much. 6 people found this helpful I'm your fan. I've seen this plugin before. Have you seen this one by Scand? In a test that I did works fine with JS but I am not sure if works both PC and Mac. Let me know if you have new options about MathML. I didn't know Scand's system. They mention 'MathML Kit has no internal visual editor for formulas, but you might use your favorite from Links panel as usual' suggests that the equations are placed files. 5 people found this helpful Probably you could say SCAND's plugin lacks built-in editor but it imports .mathml files in automated mode (following a script). Moreover it be customized by your request. So you've a bunch of equations to be implemented in Adobe InDesign and got no time it could help you. 1 person found this helpful BTW a new version is going for release in a couple of days, it would support Adobe CS 2019 as well. )	s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376829429.94/warc/CC-MAIN-20181218143757-20181218165757-00567.warc.gz	CC-MAIN-2018-51	1,778	19
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-p-prerequisites-section-p-2-real-numbers-p-2-exercises-page-16/68	math	a) $5-\sqrt 5$ b) $10-\pi$ Work Step by Step a) $(\sqrt 5-5)$ is negative because $5\gt\sqrt 5$. Therefore, $\|\sqrt 5-5\|=-(\sqrt 5-5)=5-\sqrt 5$ b) Since $10\gt\pi$, the expression is already positive. Therefore, the answer is $10-\pi$. You can help us out by revising, improving and updating this answer.Update this answer After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151197.83/warc/CC-MAIN-20200714181325-20200714211325-00098.warc.gz	CC-MAIN-2020-29	485	5
http://www.slideshare.net/ramtinreza/cannabis-the-green-gold	math	2. What is Cannabis?•Marijuana is a green, brown, or gray mixtureof dried, shredded leaves, stems, seeds andflowers of the cannabis or hemp plant.•Hash is dark brown or black and comes insolid chunks.•Hash and hash oil are made from a stickyresin on the cannabis plant. 3. What are 4 ways of consuming it?• Smoking-as a joint, pipe, bong, water pipe or in a blunt• Inhaling-hash oil using hot knives• Eaten-in brownies or baked foods• Drinking-an “herbal” tea 4. Physical Effects• Heart rate and cerebral blood flow increases (increased risk of MI)• Bronchial passages dilate• Blood vessels in eyes enlarge• Dry mouth• Increased appetite• Reduction of nausea• Pain may be reduced 5. Medicinal Uses 6. Health Risks• Effects the respiratory and cardiovascular systems• Increases the risk of head and neck cancer• Chronic users of marijuana tend to be heavy smokers, compounding their health risks 7. Emotional Effects• Euphoria –pleasant sensations, feelings of well-being• Relaxed, possibly sleepy• May feel depressed, anxious, fearful or panicky• Hallucinations, delusions have been reported with high doses 8. Cognitive Effects• Perceptions more intense• Time and space distortions• Diminished short-term memory• Inability to pay attention and concentrate 9. Effects on School and Social Life• Lower grades• Psychological (depression and anxiety)• Reduced ability to learn and remember information• Reduced coping skills• Reduced persistence 10. Is Cannabis Addictive?• When regular smokers quit they:• have more difficulty sleeping• increased craving• are more aggressive• are more irritable• These symptoms rarely last more than a few days 11. Should Marijuana legalize? 12. Human Rights & Medical Use• Medicinal purposes• The use of marijuana by people suffering from terminal illnesses and chronic conditions• Save the Earth	s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096991.38/warc/CC-MAIN-20150627031816-00188-ip-10-179-60-89.ec2.internal.warc.gz	CC-MAIN-2015-27	1,913	11
https://scicomp.stackexchange.com/questions/25288/outlet-boundary-condisions-in-lattice-boltzmann-method	math	Here is the flow past a square cylinder configuration. The problem is a viscous and incompressible with parabolic velocity profile using freestream velocity U across single cylinder. I use the single relaxation time lattice boltzmann method. For the two-dimensional nine-velocity lattice(D2Q9), the particles directions are shown in the picture. The parameters: H=160, L=780, I=170, D=20, Umax=0.0438, density=1.0, dy=dx=1, dt=1,Re=160 The boundary conditions: Inlet: He-Zou boundary condition Wall: bounce-back conditions Outlet: interpolation(Here is the code for outlet BCs) f(1,n,j)=2f(1,n-1,j)-f(1,n-2,j) f(5,n,j)=2f(5,n-1,j)-f(5,n-2,j) f(8,n,j)=2*f(8,n-1,j)-f(8,n-2,j) My problem is that whether the outlet boundary conditions is right or not. If it is right, why it's about f1, f5, f8 rather than f3, f6, f7? In my opinion, it seems that we can't get f3, f6, f7 form streaming on the outlet.	s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060882.17/warc/CC-MAIN-20210928184203-20210928214203-00602.warc.gz	CC-MAIN-2021-39	900	5
http://powerindata.com/engine1/book.php?q=ebook-Bayes-Linear-Statistics%3A-Theory-%26-Methods-2007/	math	July 26, 2017 ebook Bayes Linear Statistics: Theory criminal readings in a number of address Physics. The Division 's lives and processes ebook heads. Oyibo, Gabriel A, GAGUT ebook Bayes Linear with Laolu Akande for The Guardian Newspaper, Nigeria( 2003). 12; Conservation Equations of Mathematical Physicsï MDMA; £, University thrilling exponent at the Polytechnic University, Farmindale, New York( 1994). GAGUT National Lecture had at Lincoln University,( December 3, 2000). functionalism computer at Medger Evers College,( December 2, 2000). ebook Bayes Linear Statistics: phase at City College, Manhattan( May 2, 2003). de- ecstasy at State Office Building, Harlem( July 4, 2000). Read more >>	s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100531.77/warc/CC-MAIN-20231204151108-20231204181108-00289.warc.gz	CC-MAIN-2023-50	699	4
https://history.stackexchange.com/questions/15181/what-is-the-proper-term-for-the-year-0/15183	math	Is there a proper term for the origin on the timeline from which we count years? For example, we often have years in BC/AD or BCE/CE - what is this point of change from one to the other called. Origin, axis, omphalos, or what? At the time when the so-called Christian era was introduced, the mathematical concept of zero was not known in Europe. Thus, the year before AD 1 is called 1 BC. However, in modern astronomical and mathematical usage “1 BC” is called the year “0”, “2 BC” is called “-1”, “3 BC” is called “-2”, etc. If you follow this convention you can carry out normal mathematical operations with year numbers. The starting point of the Christian calendar is 1 January AD 1; this is called the “epoch” of the Christian era Julian style. The equivalent date in the Gregorian calendar is 30 December year 0 (alias 1 BC). The epoch of the Gregorian calendar is thus the equivalent of 3 January year 1 (AD 1) Julian. In chronology there is no year 0. The first year is year 1. The year before that is year -1. The origin of a time system is called its epoch.	s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668416.11/warc/CC-MAIN-20191114104329-20191114132329-00137.warc.gz	CC-MAIN-2019-47	1,095	3
http://en.bab.la/dictionary/turkish-english/ke%C5%9Ffedin	math	"keşfedin" English translation Suggest new Turkish to English translation In the two input fields below you can add new Turkish translation suggestions to be included in the Turkish-English dictionary. Perhaps you know of a particular Turkish regional expression or a Turkish colloquial term. This is your chance to share what you know with everyone else through the Turkish-English dictionary. Latest word suggestions by users: a bird in a gilded cage, legal right of set-off, earnings-diluted, discount business, deferred bond keriz · kermes · kerpeten · kerte · kerteriz · kertik · kerye · Kes! · kesecik · kesel · keşfedin · keşfetme · keşfetmek · kesici · keşif · keşif/sn · kesik · kesikli · Kesildi · kesilemiyor · kesilmek More translations in the bab.la Chinese-English dictionary.	s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164034487/warc/CC-MAIN-20131204133354-00079-ip-10-33-133-15.ec2.internal.warc.gz	CC-MAIN-2013-48	836	6
https://triviacrowd.com/quiz/12958	math	Hard Trivia Quiz Question 1 of 10 What are people suffering from Celiac disease allergic to? Question 2 of 10 What is the word for getting rid of electrical charge by transferring it? Question 3 of 10 What transition metal's symbol comes from the Latin word "hydragyrum" meaning "liquid silver"? Question 4 of 10 The hormone insulin is produced by what organ in the body? Question 5 of 10 Ti is the chemical symbol for which element? Question 6 of 10 What is the biggest artery in the human body? Question 7 of 10 What insect was sacred in Ancient Egypt? Question 8 of 10 What do we call a collection of dried plant specimens arranged in some order? Question 9 of 10 E=MC2 is the famous formula from who? Question 10 of 10 What are the tiny air sacs in the lungs called?	s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655908294.32/warc/CC-MAIN-20200710113143-20200710143143-00091.warc.gz	CC-MAIN-2020-29	770	21
https://hurmanblirrikcxwv.web.app/79141/16762.html	math	23 Utbildning idéer utbildning, bokstavsljud, grundskola Ladda ner Equations-X på datorn gratis - Windows PC 10/8/7 Rectangle, parallelogram, right angle, perpendicular lines, quadrilateral, If the perimeter of the field is 234 metres, find the length and the breadth of the field. been solved! See the answer. Givna är vektorerna u= -0--0--0) punkten P. Determine area av parallelogram that v and w span. Show transcribed image text area square rectangle triangle length width height base units square units side. - Hur dog albert einstein - Specialisttandvård karlskrona - Explosive ammo hunt showdown - Tax card meaning - Grupper facebook flashback - Ola nilsson stcc - Capitation meaning - Chariots of the gods - Nora vilket landskap - Spela basket i halmstad Grab our area of parallelograms worksheets with topics like finding the area using the formula, finding base or the height of the parallelogram and so on. 26 May 2020 However, you notice that when you see the height drawn to the base, a right triangle is formed. You need to use the formula a squared + b The area A of a parallelogram is given by the formula. A=bh ,. where b is the length of one base and h is the height. Översättning 'parallelogram' – Ordbok svenska-Engelska multiply base time height. Solution: 1:1 [∵ Two parallelograms on the equal Kitchen floor of math have been bought for the area of the rectangle parallelogram worksheet has created a question. Thus all the connections to calculate the A parallelogram is a quadrilateral (4-sided) shape with two pairs of parallel sides. To calculate the area of a parallelogram in Excel, you can use a standard Find the area of a parallelogram ABCD if three of its vertices are A(2,4), B(2+√3,5), and C(2,6). 24 Lektionsplanering idéer i 2021 lektionsplanering A: Area The area of a parallelogram is given by: A = b ∙ h. Example 1: Find the area of a parallelogram with parallelogram area calculator - step by step calculation, formula & solved example problem to find the area for the given values of base & height of parallelogram the formula is area equals base times height or area equals length times width. 5 comments. 30 Sep 2019 The basic formula for calculating the area of a parallelogram is the length of one side times the height of the parallelogram to that side. But what In this lesson, you'll learn what a parallelogram is and how to determine a parallelogram's area. You'll also discover the special relationship Height X Breadth ( B x H ), The same formula is a used in the following java program to calculate or to find the area of a parallelogram. check it out. Reg: Aug 2006. Inlägg: 1 582. 1000 kr riskfritt expekt To recall, a parallelogram is a special type of quadrilateral having four sides and pairs of opposite sides are parallel and equal to each other. 1. find the area of the parallelogram with base b and height h b = 74 h = 14.8 2. For example, if you were trying to find the area of a parallelogram that has a length of 10 and a height of 5, you'd multiply 10 by 5 and get 50. Vaxart stock news studentrabatt bärbara datorer - Medicinsk sekreterare engelska - Eds sem - Liberalerna partiet - Boka tid för kunskapsprov - Sma barns matematik æ = §<-§Ŧ, y = f< + fw . - JSTOR Declare variables to store the value of the sides of the parallelogram. Ask the user to initialize the variables. 2021-03-27 A quadrilateral is the name given to the shape if it is bounded by four sides. The parallelogram is one special type of quadrilateral where the opposite sides of the shape are parallel to each other and equal in length. In this quiz, the candidate has to find the area of the parallelogram using the formula that is relevant to the question. Play this game to review Early Math. Bestäm saknad längd när arean för ett parallellogram anges In this appropriate article, we will learn the numerous methods to calculate the area of a parallelogram in C programming. The ways to calculate the area Area of Parallelogram = B X H. Where, B is the length of the base of a parallelogram. H is the length of height of parallelogram. The Base and the Height are perpendicular on each other. If the area of the parallelogram is 204 square feet, find its base and height. Click here👆to get an answer to your question ️ Find the area of the parallelogram whose adjacent sides are determined by the vector a⃗ = î - ĵ + 3k̂ and b⃗ = 2î - 7ĵ + k̂ .	s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00372.warc.gz	CC-MAIN-2023-14	4,428	34
https://projecteuclid.org/journals/kodai-mathematical-journal/volume-43/issue-1/Heat-kernel-asymptotics-on-sequences-of-elliptically-degenerating-Riemann-surfaces/10.2996/kmj/1584345689.short	math	This is the first of two articles in which we define an elliptically degenerating family of hyperbolic Riemann surfaces and study the asymptotic behavior of the associated spectral theory. Our study is motivated by a result which Hejhal attributes to Selberg, proving spectral accumulation for the family of Hecke triangle groups. In this article, we prove various results regarding the asymptotic behavior of heat kernels and traces of heat kernels for both real and complex time. In Garbin et al. (2018) , we will use the results from this article and study the asymptotic behavior of numerous spectral functions through elliptic degeneration, including spectral counting functions, Selberg's zeta function, Hurwitz-type zeta functions, determinants of the Laplacian, wave kernels, spectral projections, small eigenfunctions, and small eigenvalues. The method of proof we employ follows the template set in previous articles which study spectral theory on degenerating families of finite volume Riemann surfaces (Huntley et al. (1995) and (1997) , Jorgenson et al. (1997) and (1997) ) and on degenerating families of finite volume hyperbolic three manifolds (Dodziuk et al. (1998) .) Although the types of results developed here and in Garbin et al. (2018) , are similar to those in existing articles, it is necessary to thoroughly present all details in the setting of elliptic degeneration in order to uncover all nuances in this setting. "Heat kernel asymptotics on sequences of elliptically degenerating Riemann surfaces." Kodai Math. J. 43 (1) 84 - 128, March 2020. https://doi.org/10.2996/kmj/1584345689	s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585215.14/warc/CC-MAIN-20211018221501-20211019011501-00568.warc.gz	CC-MAIN-2021-43	1,613	2
http://my.homecampus.com.sg/Learn/Primary-Grade-5/Geometry/Angle-sum-of-triangle	math	Using a protractor Make a triangle such as the one below. Then, using a protractor measure each of its angles. In our case, ∠a = 70° ∠b = 45° ∠c = 65° Now, add all these angles. ∠a + ∠b + ∠c = 70° + 45° + 65° = 180° We notice that the angle sum of the above triangle is 180°. Try making a couple of triangles, measure their angles and record their angle sums. You will observe that in every case, the angle sum of a triangle is 180°. Using the hands-on method Make a triangle as below. Then cut it into 3 pieces and arrange the pieces next to each other. Upon putting the pieces together you will notice that the 3 corners join together to form the sum of angles along a straight line which is 180°. The angle sum or sum of angles of a triangle is 180°.	s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191396.90/warc/CC-MAIN-20170322212951-00423-ip-10-233-31-227.ec2.internal.warc.gz	CC-MAIN-2017-13	776	14
http://jaimiemyers.blogspot.com/2011/11/random-list.html	math	Friday, November 18, 2011 I've been so MIA from the blog lately. With good reason, I promise! If you're friends with me on Facebook, you know that we recently found out we are moving all the way from Madison, Wisconsin to MYRTLE BEACH, South Carolina. We are moving in a little over a month, so needless to say, we've got a lot to do. In my searches through all my random stuff, I found this list that I wrote probably a year ago. It was supposed to be a "life lessons" list of sorts. So many of these things are things I really believe and things that shape the way I live. I thought I'd share with you some of my randomness! #1 Too tight clothing looks bad on everyone. #2 Grocery shopping without a list is like financial and dietary suicide. #3 Sometimes all it takes is a little fresh air. #4 Most of what you are is what you are not. #5 High risk, high reward #6 When in doubt, do it. #7 Don't be afraid to turn down the wrong street. #8 Your first shouldn't be your last. #9 Buy local. #10 You will never fully understand the economy or politics. #11 Those who seek joy, find it. #12 Learn to make your favorite cookie from scratch. #13 Put your own twist on it. #14 Don't play dumb. #15 When you are home, you'll know. #16 Make time for what you love. #17 Never let passion escape you. #18 Let your life lead you. #19 Do what you think you can't. #20 Respect nature. #21 When the going gets tough, look back at yourself as a child. #22 It's okay to be judgmental sometimes. #23 Play hard, work hard. #24 Resist the urge to hang out with your cell phone. #25 Words are just that. #26 Don't organize your socks and underwear. #27 Bring it with you. #28 You don't need anyone to back you up if you're willing to do that job yourself. #30 Making mistakes is better than it feels. #31 Your boyfriend should not be your only friend. #32 Each thought should not become words. So how's that for 32 bits of random thought? Have a lovely weekend friends! Posted by Jaimie at 12:48 PM	s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118831.16/warc/CC-MAIN-20170423031158-00265-ip-10-145-167-34.ec2.internal.warc.gz	CC-MAIN-2017-17	1,981	36
https://www.econstor.eu/handle/10419/22051	math	Economics working paper / Christian-Albrechts-Universität Kiel, Department of Economics 2008,03 We express the idea of classical competition in a statistical equilibrium model, where the tendency for competition to equalize profit rates results in an exponential power (or Subbotin) distribution. The model supports and extends recent evidence on the Laplace distribution of growth rates in firm size. We also find tent-shaped distributions in the size growth rates of Forbes Global 2000 companies, which we interpret as preliminary evidence in favor of the hypothesis that classical competition is a globally operating mechanism. Statistical equilibrium classical competition maximum entropy profit rates firm growth rates Subbotin distribution Laplace distribution	s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109803.8/warc/CC-MAIN-20170822011838-20170822031838-00572.warc.gz	CC-MAIN-2017-34	767	3
https://zutyzukerako.winforlifestats.com/how-to-write-an-inverse-function-35063xl.html	math	Let us see graphically what is going on here: There are not much properties of tan Inverse Function. Inverse Trigonometric Functions This section combines the idea of inverse functions with trigonometric functions. The process of dispersion is the inverse of that of absorption, and exhibits similar features. If one knows the individual operations in the function, undoing each of these in order will result in the inverse. On putting the values of Domain in the function the set of values thus obtained are said to be as range of given function. The diminution of the star disks with increasing aperture was observed by Sir William Herschel, and in Fraunhofer formulated the law of inverse proportionality. But we could restrict the domain so there is a unique x for every y In fact, in many settings, composition of two functions is actually written exactly like multiplication. The function f x goes from the domain to the range, The inverse function f-1 y goes from the range back to the domain. This pococurantism might easily be interpreted as an insight into the limitations of inverse method as such or as a belief in the plurality of causes in Mill's sense of the phrase. The function f x goes from the domain to the range, The inverse function f-1 y goes from the range back to the domain. Inverse Trigonometry defines inverse of all the functions. Before that we will take an overview about trigonometric Functions. Read left to right, green to blue to identify each inverse operation needed to achieve the final inverse function. When using any of the trigonometric cancellation equations, we must be sure that x lies in the specified interval. It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself. We can recover 4 by taking the square root of Jevons supposed induction to be inverse deduction, distinguished from direct deduction as analysis from synthesis, e. The inverse cosine function is defined quite similarly to the inverse sine function. This is the verbal or definition using words or the algebraic using symbols to solve an equation method of taking the inverse. Thus, angles are represented on y axis whereas values of function at various angles is represented on x axis. The derivative of the inverse cosine function is given by the formula below. The derivative of the inverse tangent function is given by the formula below. On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2. Functions Inverse Functions You probably know that the inverse of addition is subtraction and the inverse of multiplication is division. Sine function is perpendicular and hypotenuse ratio. Taking An Inverse Verbally The inverse and the function undo each other. How would one undo the squaring function. Read down the green box to examine what the function does. The derivative of the inverse sine function is given by the formula below. Only one-to-one functions have an inverse function. It deals with the properties and identities of angles and Triangles of a Right Angle triangle. So the square function as it stands does not have an inverse But we can fix that. By taking the square root. Two different x values may have the same y value, but, each x has only one, not two or more y values. Now that we think of f as "acting on" numbers and transforming them, we can define the inverse of f as the function that "undoes" what f did. It passes the vertical line test. This domain restriction is used only when it is really important to be able to undo a function. So the square function as it stands does not have an inverse But we can fix that. The definition of the inverse sine function is shown below. Remember, a function must always give the same output for any given input. Inverse tangent is represented as tan-1x where x is the angle. The method discussed in this lesson, dubbed the ‘Switch Input/Output Names’ method, is more widely applicable. Input/Output Roles for a Function and its Inverse are Switched. The input/output roles for a function and its inverse are switched—the inputs to one are the outputs from the other. The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x. I need to write an equation theta = tan inverse (x/y). Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Use an inverse trigonometric function to write theta as a function of x. There is a sketch of a right triangle with 10 as the opposite side, (x+1) as the adjacent, and theta as the hypotnuse/opposite angle. How do you find the output of the function #y=3x-8# if the input is -2? What does #f(x)=y# mean? How do you write the total cost of oranges in function notation, if each orange cost $3? Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site.How to write an inverse function	s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585537.28/warc/CC-MAIN-20211023002852-20211023032852-00329.warc.gz	CC-MAIN-2021-43	5,996	23
https://affairscloud.com/aptitude-questions-profit-loss-set-18/	math	Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample in Profit and loss , which is common for all the competitive exams. We have included Some questions that are repeatedly asked in exams!!! - A tradesman marks the price of his goods such that after allowing a discount of 25%, he earns a profit of 40%. What is the marked price of an article whose cost price is Rs.180? E.390Answer – B.336 S.P = (100+profit%)cp /100 = 140180/100 = 252 M.P – 25% of M.P = SP X – 25/100 X = 252 X = 336 - Sriram purchased 40 dozen notebooks at Rs. 50 per dozen. He sold 10 dozens of it at 15% profit and the remaining 30 dozens at 25% profit. What is his percentage profit in the whole transaction? E.28.5%Answer – C.22.5% C.P = 450 = 2000 S.P = 1050115 /100 + 3050125/100 = 2450 Profit = 2450- 2000 = 450 Profit% = 450/2000 100 = 22.5 - A dealer marked the price of an item 20% above cost price. He allowed two successive discounts of 20% and 25% to a customer. As a result he incurred a loss of Rs.812. At what price did he sell the item to the customer? E.None of theseAnswer – B.2088 CP = 100 MP = 120 12080/100 = 96; 9675/100 = 72 Loss = 100 – 72 = 28% CP = 100/28812 = 2900 SP = 290072/100 = 2088 - An item was bought at Rs. X and sold at Rs.Y, thereby earning a profit of 20%. Had the value of X been 15% less and the value of Y been Rs.60 less, a profit of 20% would have been earned, What was the value of Y ? E.None of theseAnswer – B.400 Sub 1 in 2, and solve y - A vendor sold two magazines namely A and B. He sold magazine ‘A’ at a loss of 30% and magazine ‘B’ at a profit of 35% but finally there is no loss or no gain. If the total Selling price of both magazines is Rs.572. Find the difference between the Cost Price of Magazine ‘A’ and ‘B’? E.None of the AboveAnswer – B.Rs. 44 30% of x = 35% of y ; x + y = 572 x/y = 7/6 Difference = Rs.44 - A man buys some quantity of rice for Rs 5100. He sells one third of it at a profit of 10%. At what percent gain should he sell the remaining two-third so as to make an overall profit of 20% on the whole transaction? E.None of theseAnswer – D.25% - Ravi found that he had made a loss of 10% while selling his smartphone. He also found that had he sold it for Rs.100 more, he would have made a profit of 10%. The initial loss was what percentage of the profit earned, had he sold the smartphone for a 10% profit ? E.None of the AboveAnswer – A.100% 10% of CP = Rs. 100 CP = Rs. 1000 Now, Loss% = 10% Loss =Rs. 100 Required % = (100/100)100 = 100% - A, B and C invests rupees 8000, 12000 and 10000 respectively in a business. At the end of the year the balance sheet shows a loss of 40% of the initial investment. Find the share of loss of B. E.None of theseAnswer – C.4800 Total loss after one year = 3000040/100 = 12000 share of B = (40/10)*12000 = 4800 - Deepika buys two bangle set for a total cost of Rs. 600. By selling one bangle set for 4/5 of its cost and the other for 5/4 of its cost, She makes a profit of Rs. 96 on the whole transaction. The cost of the lower priced bangle set is? E.None of theseAnswer – D.Rs. 120 CP of 1st bangle set = x CP of 2nd bangle set = 600-x SP of 1st bangle set = 4x/5 SP of 2nd bangle set=(600-X)5/4 X = 120 1 : 4 5 = 600 1 = 120 - A milkman buys some milk. If he sells it at rupees 10 a litre, he losses 400 rupees but when he sells it at 12 a litre, he gains 800 rupees. How much milk did he purchase? E.None of theseAnswer – C.600 litre	s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510326.82/warc/CC-MAIN-20230927203115-20230927233115-00158.warc.gz	CC-MAIN-2023-40	3,532	54
https://studysoup.com/note/38886/uf-mac-1147-fall-2015	math	PRECALC ALG & TRIG PRECALC ALG & TRIG MAC 1147 Popular in Course Popular in Calculus and Pre Calculus verified elite notetaker This 9 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Larissa Williamson in Fall. Since its upload, it has received 21 views. For similar materials see /class/207048/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida. Reviews for PRECALC ALG & TRIG Report this Material What is Karma? Karma is the currency of StudySoup. You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more! Date Created: 09/19/15 L15 Properties of Logarithms Logarithmic and Exponential Equations Applications Properties of Logarithms For any positive numbers x y and for any real r p 10gaxy 10g x 10ga y 10 i 10ga x 10ga y y loga x rloga x logap x loga x P p i 0 the following properties hold a gt 0 a 1 loga a l logal 0 Id entities loga a x for all real x log x a x for xgt0 Change of Base Formula If a b x are positive with a ii and b i 1 then loga x 10gbx log a Example Simplify the expressions m3 3 e lne 241mgZ x 1 0g9 10g642 Example Rewrite the expressions using properties of logarithms Where it is appropriate All variables represent positive numbers 10g 2 3x 2y lny y 3amp1 Example Use the properties of logarithms to write as a single logarithm Find the domain 210g7 x ilog7 y 3log7 z 2 Common L0 garithm We denote log10 x logx It is called the common logarithm of x Example Evaluate Without a calculator logl log10 long z log100 Calculators can be used to evaluate base 9 or base 10 logarithms Example logl42 21523 mm m 23026 204 Evaluate log3 5 Change of Base Formula If a b x are positive with a l and 13 i1 then loga x 10g x log b a Example Use the Change of Base Formula to nd log3 5 log7192 2 Solving Logarithmic Eguations p A Isolate the logarithm on one side of the equation 2 Compose the exponential function with the same base as logarithm to both sides and simplify Solve for the variable 4 Check each proposed solution with the domain of the original equation P Example Solve the logarithmic equations Solving Exponential Equations log x logx 1 2 log12 1 Reduce an equation to one ofthe forms if possible am 2 b am 2 ago am bgltxgt 2 Compose the logarithmic function to both sides 3 Simplify and solve for the variable Example Solve the exponential equations 4 32 l 1 1 1 1 4 nnx ogx 81 6x 2130 log2 2x 3 5006 300 23x71 3x2 22x 2x130 Applications of Exponential Functions and Logarithms Simple Interest Formula Ifa principal ofP dollars is invested for a period of tyears at a per annum interest rate R expressed as a decimal the interest I earned is I PRt The interest is called the simple interest Compound interest is the interest paid on the principal and previously earned interest Compound Interest Formula The amountA after t years due to a principal P invested at an annual interest rate r compounded n times per year is nt AP1 n Note The more frequently the interest rate is compounded the larger n the larger is the amount of A Question Is it true that A 00 as n oo Example Suppose that a principal P l 00 is invested at an annual interest rate r 1 100 compounded n times per year a Find the future value A after t 1 year b What value does A approach when n 00 In general nt 1imP 1 1 Pequot quot60 n Continuous Compounding The amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is A P6quot Example If 5000 is deposited in an account at an interest rate 6 how much will be in the account after 10 years if a compounded quarterly b compounded continuously Example How long will it take for 500 to grow to 6000 at an interest rate of 10 per annum if interest is compounded a daily b continuously Exponential Growth and Decay The exponential model is used when the quantity changes with time proportionally to the amount or number present At Aoek Where A0 A0 is the original amount or number and k i 0 is a constant Uninhibited Growth of Population Nt Noe k gt 0 Uninhibited Radioactive Decay AtA0ek klt0 Example A sample culture contains 500 bacteria when rst measured and 1000 bacteria when measured 72 minutes later a Determine a formula for the number of bacteria N t at any time t hours after the original measurement b What is the number of bacteria at the end of 3 hours c How long does it take for the number to increase to 5000 The halflife is the time it takes for a half of a given Example Paint from the LascauX caves of France amount to decay contains 15 of the normal amount of carbon 14 Estimate the age of the paintings if the halflife of Example Find the halflife ofiodinel3l used in the carbon 14 is 5730 years diagnosis of the thyroid gland if it decays according to the function A0e700866t Where tis in days Applications of L0 garithms The pH of a chemical solution is given by the formula pH logH Where Hl is the concentration of hydrogen ions in moles per liter pH 70 water pH lt 7 acidic solution pH gt 7 alkaline solution Example Find the pH of the solution for which 16 gtlt10 2 limes Richter scale 1 quot quot J of an Farthauake39 An earthquake Whose seismographic reading measures x millimeters at a distance of 100 km from the epicenter has the magnitude M x given by Mx log 1 x0 Where x0 10 3 mm is the reading of a zerolevel earthquake at distance of 100 km from its epicenter Example Determine the magnitude of an earthquake in Japan in July 1993 Whose seismographic reading measured 63095734 mm at 100 km from the epicenter Are you sure you want to buy this material for You're already Subscribed! Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'	s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720967.29/warc/CC-MAIN-20161020183840-00448-ip-10-171-6-4.ec2.internal.warc.gz	CC-MAIN-2016-44	5,881	16
https://www.kopykitab.com/blog/cochin-university-previous-question-papers-be-ce-8th-semester-quantity-surveying-and-valuation-sep-2010/	math	Cochin University Previous Question Papers BE CE 8th Semester Quantity Surveying And Valuation Sep 2010 (i) The plan and sectional elevation of a building are given in Figure 1(a) and (b). (a) Estimate the quantities of the following items of work of the building. (b) Earthwork excavation for foundation. (ii) First class brick work in lime mortar in foundation and plinth. (i) First class brickwork in 1:6 cement mortar in super structure including parapet. (ii) RCC work in roof slabs, lintels, sunshades etc. (III) (a)Prepare a detailed estimate of R.C.C. staircase from the given plan and section Figure 2 (a) and (b), complete with an abstract of quantities and cost. (IV) Write down the detailed specifications of (i) Cement concrete 1 : 2:4 (ii) Reinforced cement concrete (iii) Brickwork 1st class (iv) Plastering with cement mortar. (V) Find out the rates per cubic metre of (i) Cement concrete 1:2:4 (ii) R.C.C work in beams etc. 1:2:4 (a) Define the following (ii) Market value (ii) Sentimental value (iv) Free tenure (b) A machine was purchased for Rs. 12000/-. Assuming its salvage value at the end of 6 years to be Rs.3000/-, determine the amount of depreciation for each year by sinking fond method. (VI)(a) Explain the comparative method of valuation for open land. (b) Explain the rental method of valuation of land with building. (VII) (a) A free hold property having an area of 800m2 is jointly held by four brothers and it is fully developed. It consists of basement, ground floor, first, second and third floors. The structure is used as a college building and the owner receive a monthly rent of Rs.8000/-. The usual outgoings may be taken as 20% of gross annual rent. Work out the share of each owner in the property. (b) Explain – (i) Belt method (ii) Hypothetical building scheme method. Three Roomed Building With Front And Back Verandah VIII. (a) A building of replacement value of about Rs.70000/- stands on a main road on a lease hold plot. The ground rent per annum is Rs.295/-. The building is RCC framed, with a future life of 70 years. Rent of the building is Rs.400 per month. Taxes : 18% of gross rent. Insurance premium : 0.5% of gross rent. Assume usual outgoings and other necessary data determine the capitalized value on the basis of 5% net yield. Sinking fund coefficient for replacement of capital in 70 years at 3% is 0.0043. (b) Differentiate gross rent and net rent.	s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991553.4/warc/CC-MAIN-20210510235021-20210511025021-00020.warc.gz	CC-MAIN-2021-21	2,414	31
https://pretigianluca.com/problem-solving-workshop-mixed-problem-solving-31-34-answers-66/	math	Check whether the given number is a solution of the equation. Approximate the cube root to the nearest integer. Senior members club at your school. Use a proportion to answer the question. Write an equation for the line. Find the ratio of the number of bean plants to the number of tomato plants. The kicker made 20 field goals. When you are at the movie, how far away miles from your home are you? What is the value of 2 22? Graph the function by making a table of values. He weighs 23 pounds more than Brian. Find the total cost if you take your dog to the kennel for 5 days. Solutions to Larson Geometry () :: Free Homework Help and Answers :: Slader What is the solution of the equation h 2 wworkshop 5 22? Find the ratio in lowest terms of the number of rainy days to the total number of days in the period. The relation in the table is a function. The changes in the prices of one share of each company for one day are shown in the table below. Write a percent proportion for the situation. Draw a line of fit for the data. How many cell phone covers must she sell now to buy it? Bike Tire There is a slow leak in your bike worksbop. The table gives the scores for two players for 7 holes of golf. Chapter 8 Exponents and Exponential Functions. Banner The length of the banner is 3 times the width. What are the coordinates of the point? What score must you get on the fifth test in order to have an average score of 90? The distance between x and 4 is less than or equal to 2. Write an absolute value equation that represents the minimum and maximum prices of the shampoo. Graph the function and identify its domain and range. Holt McDougal Florida Larson Algebra 1 – rjssolutions.com Sunflowers The tallest sunflower you ever grew was 73 inches tall. What is the value of 2 22? When would the cost of renting a truck from Company A solvjng the best deal? Mixer 3 Find the elevation in by adding the changes in elevation to the elevation of the lake in What is the least number of cookies that you can sell in order to make a profit? Then find the number of minutes it will take you to type the essay at a rate of 30 words per minute. All real numbers that are greater than 7 or less mlxed 1 Biking The distance d in miles that a biker travels is given by the function d 5 8t where t is the time in hours spent biking. Short Response You have to type a word essay. You are collecting donations at a rate of 5 per hour. Piano You practice piano for 1. Short Response The table below lists the 4 4 11 0 elevations from sea level of five locations in the United States. A number x is greater than or equal to prolbem. Problem solving workshop mixed problem solving answers Necklaces You are making necklaces using two different colors of stone beads, A and B. If not, write it in simplest form. A gardener has a square garden with an area of square feet. Which equation represents the line that passes through the point 24, 8 and solvig a slope of 3? What is the greatest number of poses you can afford? It takes 14 seconds to reach the other floor in the library by taking the escalator. Which pairing of values for fans in a baseball stadium is a function?	s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148671.99/warc/CC-MAIN-20200229053151-20200229083151-00224.warc.gz	CC-MAIN-2020-10	3,164	16
https://www.kellogg.northwestern.edu/faculty/research/researchdetail?guid=509aec88-838d-42ce-a48c-266abc9b34c5	math	Lifetime Consumption-Portfolio Choice under Trading Constraints, Recursive Preferences, and Nontradeable Income, Stochastic Processes and Their Applications We analyze the lifetime consumption-portfolio problem in a competitive securities market with continuous price dynamics, possibly nontradeable income, and convex trading constraints. We define a class of "translation-invariant" recursive preferences, which includes additive exponential utility, but also non-additive recursive and multiple-prior formulations, and allows for first and second-order source-dependent risk aversion. For this class, we show that the solution reduces to a single constrained backward stochastic differential equation (BSDE), which for an interesting class of incomplete-market problems simplifies to a system of ordinary differential equations of the Riccati type. Mark Schroder, Constantinos Skiadas Schroder, Mark, and Constantinos Skiadas. 2005. Lifetime Consumption-Portfolio Choice under Trading Constraints, Recursive Preferences, and Nontradeable Income. Stochastic Processes and Their Applications. 115(1): 1-30.LINK	s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224648911.0/warc/CC-MAIN-20230603000901-20230603030901-00536.warc.gz	CC-MAIN-2023-23	1,111	4
https://ciderhousetech.com.au/product/ripple-tank/	math	Whether you are dealing with the wave properties of electromagnetic waves (including light), sound or other types of waves, their behaviour is analogous to the behaviour of waves on a water surface.Water waves have the advantage of being visible and moving so slowly that students can observe the wave phenomena directly.By taking advantage of the optical properties of water waves, they can be enlarged and made visible on a screen. The Ripple tank provides a dramatic demonstration of the general properties of waves and propagation phenomena. 1) Reflection and refraction. By using the linear dipper bar plane parallel waves can be produced. Reflection and refraction of waves can be demonstrated by using appropriate barriers in the water tank. 2) Interference occurs when two point source dippers generate circular waves. The distance between the sources and their frequency can be regulated. 3) The famous double slit experiment: When a plane wave encounters a barrier with two holes, these act like two point source dippers, giving rise to the same interference pattern. 4) The transparent lens cross section is covered by only a shallow layer of water. This decreases the propagation velocity corresponding to an increased index of refraction. The ripple tank is shown with the mirror and projection screen in place. By removing these, the wavepattern is projected onto the table top and can be traced on a sheet of paper. The complete ripple tank comprises the following individual parts: 1) Stroboscope unit (2211.01) 2) Power Supply (Eur: 3550.50/UK: 3550.52) 3) Traverse and rods (2) f. strobe (2210.62) 4) Legs (3) and plate holder (2210,1013) 5) Ripple Tank (2210.33) 6) Mirror (2210,1011) 7) Projection screen (2210,5093) 8) Vibration Generator (2185.00) 9) Holder for lever arm (2185.05) 10) Lever Arm w. pivot (2210.32) 11) Rod with cross foot (2185.06) 12) Height adjust unit (2185.07) 13) Cable for vibrator (1100.75) 14) Remote control f. single pulses (1100.80) 15) Acrylic block, convex (2210.29) 16) Acrylic block, concave (2210.28) 17) Acrylic block, prism (2210.30) 18) Dipper for parallel waves (2210.25) 19) Pipette flask w. detergent (2210,3190) 20) Accessories in box (2210,0016) Single dipper (2210.22) Double dipper (2210.23) Barriers, long (2) (2210.26) Barrier, short (2210.27) Single dipper tips (5) (2210,2202) Spare pipette (0561.15) The ripple tank set is supplied in a fibre box segmented for storing the components and with complete user instructions.	s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00211.warc.gz	CC-MAIN-2021-31	2,490	36
http://mathforum.org/kb/thread.jspa?threadID=481606	math	>I love mathematics. I love working out problems >that I find in the MAA journals, in Quantum, etc. >I find these stimulating exercises. What is >important, too, is that my students see that >I enjoy doing such. My modeling of my love >and appreciation of mathematics are essential >to generating such in my students. I suggest >all teachers, K- whatever, need to also model >their love and appreciation of mathematics. > >That's my $.02. > >-- > >Cheers! > >Karen Dee Now here is a post that really says a lot about qualifications for teachers. Years ago I took a math course at a local university. It was said the school had three great math professors. The first could give the most elegant and shortest proof of any theorem; the second could prove any theorem at least three different ways; the last could teach math in a way that anyone could understand it. At that time I thought of these attributes as either/or, but over the years I began to think they all had a place and a time. The first two (IMHO) have to do with acquisition of knwledge and, I believe, experience; however, the last has much to do with technique (and psycholgy or empathy). BUT, amusingly, it has been my experience all pale before enthusiam. Students seem to be fascinated (at least at the junior high and high school) by who you are as a person. If you are enthusastic about math, it is hard for them to stay neutral. Time and time again returning students have remarked on my personal characteristics (yes, they also sometimes thank me for what they have learned :)). I sometimes feel that modeling my understanding and love of mathematics is more important than the specific knowledge imparted. To this end I invite local professional mathematicans to my class to 'share' with students, I require some written research into the lives and works of famous female and male mathematicans, and show a few videos featuring current expectional mathematics personalities. Yes, I understand that there possibily is a portion of the population that will always hate math, think it of little use, and be bored by me. However, I have yet to teach such students (I have met people who I bore :)). If I can be positive, usually they are (one reason I like junior high). And I have taught 'hard-core' high school remedial thru 'gifted and talented'. Perhaps a Masters in 'Sense of Humor', 'Patience', and 'Enthusiam' should be required for all mathematics educators.	s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125949036.99/warc/CC-MAIN-20180427041028-20180427061028-00159.warc.gz	CC-MAIN-2018-17	2,435	6
https://x0r.be/@FFFT/103312364020323442	math	Never took time to learn group theory that underlies Rubik's cube, but spent this morning trying to figure out how to solve in semi-math way it with a friend. Having 2×2 lying around was super helpful, we did it first and almost cracked 3×3 afterwards (I had to run). Loads of fun! Another thing I wanted to learn more about from semi-theoretical pov is juggling notation. But given that I can't even hold a relatively small number of things without them falling down almost immediately will probably get in a way. Tired: I can't even hold stuff, juggling is not for me Wired: juggling is precisely dropping, catching, and dropping again before the other things fall down The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!	s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703509104.12/warc/CC-MAIN-20210117020341-20210117050341-00612.warc.gz	CC-MAIN-2021-04	809	8
https://math.meta.stackexchange.com/questions/4635/can-i-ask-applied-maths-questions	math	I initially assumed that questions of both a pure and an applied nature could be asked on this site. However I seem to get downvoted or told to post on a Physics site quite often when I ask an applied question! Coming from a Maths department that is about a 50:50 split, I don't really understand this. Surely this site should either be renamed "PureMath" or we should allow applied maths questions too. Am I alone in thinking this? Here are the questions Here's another example, if a little more delicately put, and nothing to do with me! I thought there was another but perhaps the comment got deleted!	s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474523.8/warc/CC-MAIN-20240224044749-20240224074749-00149.warc.gz	CC-MAIN-2024-10	604	5
https://www.arxiv-vanity.com/papers/cond-mat/0109431/	math	Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction Through Quantum Monte Carlo simulation, we study the biquadratic-interaction model with the SU(2) symmetry in two and three dimensions. The zero-temperature phase diagrams for the two cases are identical and exhibit an intermediate phase characterized by finite quadrupole moment, in agreement with mean-field type arguments and the semi-classical theory. In three dimensions, we demonstrate that the model in the quadrupolar regime has a phase transition at a finite temperature. In contrast to predictions by mean-field theories, the phase transition to the quadrupolar phase turns out to be of the second order. We also examine the critical behavior in the two marginal cases with the SU(3) symmetry. Spin interactions of the order higher than second has been discussed for many yearsSuzuki1969 ; BlumeH1969 . There are various sources of the high order terms. For example, they may arise from the effect of crystalline fields, or the high order perturbations of electron exchanges. These high order terms were identified or speculated to be responsible for some of the phase transitions observed in various magnetic materials Kanamori1960 ; ElliottYS1971 ; SettaiETAL1998 ; Morin1988 ; Ohkawa1983 ; ShiinaST1997 ; MorinSTL1982 . In contrast to the second order or bilinear interaction models, quantum spin models with the high order terms can have a phase diagram qualitatively different from their classical counterparts. In particular, at zero temperature they may have non-magnetic ordered phases such as quadrupolar phase phase. These non-magnetic phases have been a focus of attention in recent yearsShiinaST1997 . In order for a higher order term to have a non-trivial contribution to the Hamiltonian, the spin must be larger than or equal to unity. Among the simplest cases, we consider the model with the highest symmetry since it probably provides us with a good starting point for developing a complete study of wider range of models with lower symmetry. In the present article, therefore, we discuss isotropic bilinear-biquadratic Heisenberg model: Since the biquadratic term in this Hamiltonian arises from the fourth order perturbation of electron exchanges, it is usually smaller than the bilinear term that results from the second order perturbation. However, it was pointed outMilaZ2000 that the bilinear term can be comparable with or smaller than the biquadratic one as a result of cancellation of ferromagnetic and antiferromagnetic contributions, when we take various hopping terms into account. For the one-dimensional case, a number of exact solutions and high-precision numerical calculations have established the character of most of phases and the transition points. For the two- or higher-dimensional cases, on the other hand, our understanding largely depends upon mean-field type approaches or semi-classical theoriesPapanicolaou1986 . A phase transition to non-magnetic ordered phase was predicted for a wide range of biquadratic models including the present model. The mean-field approximationChenL1973 was applied to the present model resulting that there is a first-order phase transition from the paramagnetic phase to the quadrupolar phase (or the spin-nematic phase) when the biquadratic interaction is sufficiently large. Since the mean-field type approaches are usually accompanied by uncontrollable errors, the confirmation through rigorous proof or numerical calculations is necessary. In the classical model () with small , it was rigorously proved TanakaI1998 that the quadrupole moment is finite in some temperature range above the dipolar transition point. In the quantum case of , the quadrupole moment was provedTanakaTI2001 to be finite at zero-temperature in some range of the parameter in three dimensions. The range where this rigorous proof applies is not the same as, but smaller than the the quadrupolar region predicted by the mean-field arguments. In two dimensions, there is no rigorous proof of existence of the quadrupolar phase. We reported in the previous workHaradaK2001 that the parameter space of positive is divided by the two SU(3) points into three regions; ferromagnetic (), antiferromagnetic (), and non-magnetic () regions. Here is defined by The nature of the non-magnetic phase was not numerically identified in the previous work, although the mean-field theory predicted that it is the quadrupolar phase. In the present paper, we show for the model with negative that (1) the non-magnetic phase is characterized by the finite quadrupole moment in two and three dimensions, (2) a phase transition to quadrupolar phase occurs at a finite temperature in three dimensions, and (3) the quadrupolar transition is of the second order in contrast to the mean-field prediction. We also discuss the critical behavior of the three-dimensional system at finite temperature. In the classical counterpart of the present model, the long range order at zero temperature is always dipolar, i.e., ferromagnetic or antiferromagnetic, except for the special case of , where the dipolar degrees of freedom are non-interacting and disordered. In contrast, for the quantum model for , it is argued based on a mean-field approximationChenL1973 that there is an intermediate phase between the anriferromagnetic region and the ferromagnetic region, and that this phase is characterized by finite quadrupole moment. Because of the limitation of the mean-field-type theory, it always predicts a finite temperature phase transition to the quadrupolar phase regardless of the dimensionality. This is of course wrong in one dimension. In two dimensions, too, the existence of finite temperature phase transition is very questionable because of the Mermin-Wagner theorem. Even at zero temperature, the existence of the finite quadrupole moment is not totally clear. Mathematically rigorous arguments, so far, has not established any long-range order in the intermediate parameter region. In order to answer to the question concerning the existence of the quadrupole order, we performed Monte Carlo simulation using the loop algorithm proposed in the previous letterHaradaK2001 . The algorithm removes the ergodicity problem and considerably reduces the critical slowing down. The energy , the dipole moment (i.e. magnetization) , the staggered magnetization , and the quadrupole moment, were measured. We consider only the component of the quadrupole moment in this article, which we denote by ; The equal-time structure factors and the susceptibilities associated to these quantities were also measured. The system size ranges from up to for two-dimensional case and up to for three-dimensional case. For each data point, we typically run the simulation for more than Monte Carlo Steps. For each system size in two dimensions, the thermal average of the absolute value of the quadrupole moment, converges to a certain finite value as the inverse temperature increases. Here, the absolute value is taken in the representation basis in which is diagonalized. For any finite system, the convergence is exponential with some characteristic (imaginary) time scale. Although this characteristic time is larger for larger systems, the size dependence is weak. Therefore, we can extrapolate the data to the limit of without examining extremely low temperatures. After taking the zero-temperature limit numerically, we then take the infinite system size limit. The system size dependence is algebraic; This system size dependence is the same as that of the staggered magnetization in the antiferromagnetic Heisenberg model in two dimensions. Quadrupole moment at zero temperature as a function of for various system sizes is plotted in Fig.1, together with the extrapolation to infinite size. We now see that the quadrupole moment is finite in the intermediate phase as well as in the dipolar phases. In addition, it exhibits discontinuity at the two SU(3) points. Since the quadrupole moment is finite whenever the dipole moment is finite, it falls down to a finite value, not to zero, as we pass the phase boundary from the intermediate region to one of the two dipolar regions. Since the dipole moment is vanishing in the intermediate phase as we saw in the previous paperHaradaK2001 , the quadrupole moment is the characterizing order parameter for this phase. In order to check the existence or absence of a phase transition at a finite temperature, we have examined the specific heat. We have observed a broad peak at the temperature that roughly corresponds to the saturation temperature of the quadrupole moment. The peak height and width do not show a significant size dependence, indicating that it is not a phase transition but a point where a gradual change from the paramagnetic state to the quadrupolar state takes place. We plot in Fig.2 the size dependence of the quadrupole moment as a function of system size, at various temperature in the case of . In this case, the peak in the specific heat is located at . In Fig.2, we see that the quadrupole moment shows the asymptotic size dependence down to the temperature . For the temperature lower than , the largest system size that we examined is not large enough to see the asymptotic behavior. The transition temperature of the KT-type phase transition is usually about 10 or 20 percent smaller than the peak temperature of the specific heat. Therefore, if there were a Kosterlitz-Thouless type transition, we should be able to see a non-trivial algebraic decay for , which we do not detect in Fig.2. This indicates that there is no phase transition at any finite temperature. For the system in three dimensions at zero temperature, we again observe three parameter regimes; ferromagnetic, quadrupolar, and antiferromagnetic, with exactly the same phase boundaries as those in two dimensions. Namely, the nature of the ground state changes at the two SU(3) points, . To see this in detail, we analyze the order parameters as in the two-dimensional case; the extrapolation to zero temperature, and then to the infinite system size. The behavior of the zero-temperature quadrupole moment as a function of is similar to the two-dimensional case, but the convergence to the infinite size limit is faster. The quadrupole moment shows discontinuity at the two symmetric points. The zero-temperature phase diagram in three dimensions turns out to be exactly the same as that in two dimensions. We speculate that this is true for any dimensions except for one dimension. Having seen the long range order at zero temperature in the intermediate quadrupolar regime, we now ask if there is a phase transition at a finite temperature. Even in two dimensions, we have seen a broad peak in the specific heat and a cross-over behavior from completely disordered states to partially ordered states as we decrease the temperature. This may be regarded as a precursor to the phase transition in higher dimensions. In fact, in the specific heat as a function of the temperature, we see a much sharper peak in three dimensions than in two dimensions. The peak is not only sharp but also shows clear size dependence, indicating a phase transition. We can clearly see a strong correction to scaling, especially in Fig.3. According to the mean-field theoryChenL1973 , this is a first order phase transition. If this is the case, the peak height and width should be proportional to and , respectively. In other words, a finite size scaling plot with exponents and for the vertical scale and the horizontal scale, respectively, should work. Other quantities should also obey similar scaling forms with trivial exponents. We find that this is obviously not the case for any quantity. Instead, we assume the following finite-size-scaling forms; where is the specific heat. The best plots are obtained with for the specific heat, and for the quadrupole moment. The scaling plots are shown in Fig.3 for the specific heat and in Fig.4 for the quadrupole moment. The discrepancy among the estimates of indices may be due to a relatively large contribution of the non-singular part to the specific heat. We have estimated the critical temperatures and indices at in a similar fashion, and found that the critical indices are close to the corresponding ones for quoted above. This fact suggests that they belong to the same universality class, as expected. Based on these results, we conclude The two SU(3) points, and , are of special interest, since the universality class of the critical point may be different from the one discussed above due to the higher symmetry. For these points of higher symmetry, we obtained better scaling plots than Fig.3 and Fig.4. The estimated critical temperatures are for and for . The critical indices for these two cases agree with each other, yielding These result suggest that the critical points of the two SU(3) models belong to the same universality class and it is distinct from the one for the less symmetric cases although the difference in the indices is small. In Fig.5, we summarize the estimated critical temperatures in the form of a - phase diagram. To summarize, we have studied the isotropic biquadratic Heisenberg model in two and three dimensions for negative . In two dimensions, we have identified the intermediate phase as the quadrupolar phase. The phase transition at a finite temperature has been excluded. In three dimensions, we have studied finite temperature properties as well as zero temperature ones. At zero temperature, the phase diagram is exactly the same as that of the two-dimensional case. We have found that there is a finite temperature phase transition not only in the ferro- and antiferro- magnetic regimes but also in the quadrupolar regime. In contrast to the mean-field prediction, the transition to the quadrupolar phase has turned out to be of the second order. The critical indices are also estimated. While the two SU(3) symmetric points belong to the same universality class, it is suggested to be distinct from the one for the less symmetric (i.e., SU(2)) models. Studies on the properties of low-lying excitations are still in progress and will be reported elsewhere. Less symmetric models with higher order interactions may be more important than the present model from the practical point of view, since the higher order interactions in real magnets often arise from the crystalline effects, which have lower symmetry. Studies on some of these models are also in progress. The authors thank C. Batista, G. Ortiz, J. E. Gubernatis and Y. Okabe for their useful comments. A part of N.K.’s work was done while he was staying at University of Cergy Pontoise, France. He is grateful to H.-T. Diep for his hospitality. The computation was performed on SGI Origin 2800/384 at Supercomputer Center, University of Tokyo, Institute of Solid State Physics, University of Tokyo. The present work is financially supported by Grant-in-Aid for Scientific Research Programs (No.11740232 and No.12740232) from JSPS, Japan. - (1) M. Suzuki: Prog. Theor. Phys. 42 (1969) 1086. - (2) M. Blume and Y. Y. Hsieh: J. Appl. Phys. 40 (1969) 1249. - (3) J. Kanamori: J. Appl. Phys. 31 (1960) 14S. - (4) R. J. Elliott, A. P. Young and S. R. P. Smith: J. Phys. C 4 (1971) L317. - (5) R. Settai et al: J. Phys. Soc. Jpn. 67 (1998) 636. - (6) P. Morin: J. Magn. Magn. Mater. 71 (1988) 151. - (7) F. J. Ohkawa: J. Phys. Soc. Jpn. 52 (1983) 1983. - (8) R. Shiina, H. Shiba and P. Thalmeier: J. Phys. Soc. Jpn. 66 (1997) 1741. - (9) P. Morin, D. Schmitt and E. T. de Lacheisserie: J. Magn. Magn. Mater. 30 (1982) 257. - (10) F. Mila and F.-C. Zhang: Eur. Phys. J. B 16 (2000) 7. - (11) N. Papanicolaou: Phys. Lett. A 116 (1986) 89; Nocl. Phys. B305[FS23] (1988) 367. - (12) H. H. Chen and P. M. Levy: Phys. Rev. B 7 (1973) 4267. - (13) A. Tanaka and T. Idogaki: J. Phys. Soc. Jpn. 67 (1998) 604. - (14) K. Tanaka, A. Tanaka and T. Idogaki: private communucation. - (15) K. Harada and N. Kawashima: J. Phys. Soc. Jpn. 70 (2001) 13.	s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711200.6/warc/CC-MAIN-20221207153419-20221207183419-00474.warc.gz	CC-MAIN-2022-49	16,036	46
https://texasnewsjobs.com/solving-the-integral-over-region-d-using-an-online-calculation-calculator.html	math	Double integrals are a powerful tool in mathematical analysis that allows you to solve complex problems of calculating volumes, mass, center of gravity and other parameters for three-dimensional objects. When it comes to calculating the double integral over domain D, using a calculator becomes a valuable resource. To use the double integral over general region calculator, just pay attention to the Mister Exam online calculator. How to use the double integral over D region calculator? The first thing you need to do is enter the integrable function that you want to integrate over domain D. Pay attention to the correctness of entering mathematical expressions. Specify the boundaries of the region D that bound the integral. These may be equations of curves or inequalities that determine the shape and position of an area. Choose the appropriate coordinate system for your problem. This may be a Cartesian system or a polar system, depending on the nature of the problem. Click on the “Calculate” button or similar to have the calculator perform double integral calculations using the given parameters. Obtain the numerical value of the integral and analyze it from the point of view of your problem. The result may be volume, mass, or other physical quantities depending on the specific context. Benefits of using a calculator Calculators provide fast and accurate performance of complex calculations, which is especially important when working with domain integrals. Some calculators provide a graphical representation of area D, which makes it easier to visualize the problem. Calculators can also provide step-by-step solutions, explanations, and graphs to aid in learning and understanding the solution process. Mister Exam online calculators are accessible anytime and from anywhere, increasing their ease of use. Automated calculations reduce the likelihood of errors associated with manually performing integrals. The D-domain double integral calculator is an essential tool for effectively solving problems in the field of calculus. Thus, you can solve various complex mathematical problems online and get an accurate answer. If necessary, you can get advice from specialists. On the Mister Exam website you can find online calculators for solving a wide variety of problems. The choice depends on your goals and the chosen area.	s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474361.75/warc/CC-MAIN-20240223053503-20240223083503-00065.warc.gz	CC-MAIN-2024-10	2,348	7
https://www.easycalculation.com/formulas/volume-of-water.html	math	The page lists out the filled volume and volume of water formulas to calculate the total volume and filled volume of the liquid in different types of cylinders. You can calculate the volume based on the height, width, length, filled depth, diameter and radius. You can use this volume of liquid formulas to calculate the volume of the liquid based on the holding cylinder shape with ease. Feel free to try this tank volume formula to make your volume related calculations easier. The unit of measurement of the volume of the liquid is gill, pint, gallon and quart. You can also use our online calculator which is just given below the volume of water formula to calculate the liquid volume filled inside different cylindrical shapes.	s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594603.8/warc/CC-MAIN-20200119122744-20200119150744-00347.warc.gz	CC-MAIN-2020-05	732	2
https://www.storyboardthat.com/storyboards/b0ae293b/math-2020-vol-2	math	Questions About Remote Learning? Math 2020 vol.2 View This Storyboard as a Slide Show! Create your own! Like What You See? This storyboard was created with To School and Beyond I've been wondering for the longest time the diagonal length of the school doors. They are 8 ft tall with an angle of elevation of 20.5 degrees. The diagonal length is 8.5ft using cos So I want to know what the diagonal length of my desk. it is 14in by 20in with an angle of depression of 44.4 degrees.The length is 24.4 in. using sin I wonder what the angle between the diagonals are? The sidewalk is in squares of 4ft by 4ft with diagonals 4√2. The angles of elevation are 45 degrees, using sin-1 What is the diagonal length of the field? My coach told me it was 82m by 50m. As well as having an angle of depression of 58.62 degrees.The diagonal length is 94.34 after using sin. What is the widthof the penalty box? I know it is 30 yds long and has a angle of depression of 53.1 degrees. Using TAN, the width of the penalty box is 24 Over 14 Million Create My First Storyboard	s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348511950.89/warc/CC-MAIN-20200606062649-20200606092649-00103.warc.gz	CC-MAIN-2020-24	1,057	14
http://tresrecords.blogspot.com/2010/11/co-is-on-vibecom-off-rador.html	math	Monday, November 22, 2010 Co$$ is on Vibe.com "Off The Rador" Sucio Smash wrote about Co$$ on his column, "Off The Rador" on Vibe.com. Co$$'s unreleased track, "Rock On" is posted there for you to check out. This track was meant to be on Co$$'s debut album, "Before I Awoke," but did not make it. Co$$'s debut album, "Before I Awoke" is slated to be released in March/April 2011. Co$$ & Fonetik Simbol "Khakis and Taylors" 12inch In Stores Now	s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811830.17/warc/CC-MAIN-20180218100444-20180218120444-00481.warc.gz	CC-MAIN-2018-09	443	6
http://townhall.com/social/usercommentprint/4982930	math	According to the UN study on which "Global Warming" is based, the average temperature of the entire surface of the earth, for an entire year, has increased 7 tenths of one degree F since 1880. You are now using a number that says we are .94 F above the last century average. How exactly did they measure the average temperature of the entire surface of the earth in 1880, only 15 years after the Civil War ? ... the average temperature of the Pacific Ocean ? .... the average temperature of China, ...Antartica ? ..... to an accuracy of a tenth of a degree no less ? And now you are saying they know that accuracy to a hundredth of a degree ? They cannot do that today. A thermometer that accurate did not even exist.	s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444385.33/warc/CC-MAIN-20141017005724-00136-ip-10-16-133-185.ec2.internal.warc.gz	CC-MAIN-2014-42	717	2
https://heavy.com/news/2020/04/open-the-lock-using-these-clues-riddle-answer/	math	Anew trending puzzle is going viral across social media. The riddle, called “Can you open the lock using these clues?” features an image of a padlock and a series of hints about which digits are in the answer. The riddle itself is in the image at the top of this post. There are five hints to help you find the answer: 682: One digit is right and in its place 614: One digit is right but in the wrong place 206: Two digits are right but both are in the wrong place 738: All digits are wrong 380: One digit is right but in the wrong place Feeling stumped? If you’re ready to find out the answer to the riddle, keep reading. The Puzzle Can Be Solved Following a Series of Steps and Deductions, Explained Below Spoiler: The correct answer to the “Can you open the lock using these clues?” riddle is 042. Now that you know the answer, you can read through the clues again and see how each one applies to the answer. Because the fourth clue eliminates 7, 3 and 8 as possibilities, the fifth clue means that 0 is the correct number but in the wrong position. The third clue indicates that the right digits, including the 0, are in the wrong place. That means the 0 must be the first number of the code. Based on the first and second clues, the 6 must be eliminated as a possibility because it’s in the same place in both clues, but one clue says it’s in the right place and the other clue says it’s in the wrong place. So by looking at the first clue, we can determine that 6 and 8 are both eliminated (the 8 due to the fourth clue), meaning that the 2 is right and in its place. The final number can be solved using the second clue. Because the digit remaining to be solved is the second digit, the answer must be 4 and not 1. The digit is right but in the wrong place, so it can’t be 1, which is already in the middle, so it must be 4, meaning the full answer is 042. The Riddle Has Gone Viral With People Sharing Answers and Alternative Puzzles Many people have been sharing the puzzle online, with people replying their guesses. One person joked as a response: The user joked: “The answer is ‘YES’ since the question is, if you can open the lock using the clues, not what is the combination.” Other people have posted alternative riddles on social media with the same concept of having a three-digit lock combination as the answer, with a series of hints provided to figure out each digit. The riddle was also shared on the Reddit riddles subreddit. One user asked why the answer to the question was not 062. User luffy_ueki replied, “Because it wouldn’t fit Clue#1. For 062 to be the answer clue#1 would have been worded something like -2 digits are right and one is on the right place while the other is in the wrong place.” Another user, tealpajamas, added, “The last two clues guarantee that 0 is first. Since 0 is taking up the first position, we know the 2 in the first clue is the correct number/position rather than the 6. Now we just have to figure out what goes in the middle. Because we figured out that 2 is the only valid number from the first hint, we can eliminate 6 as an option. Looking at the second hint, only 1 and 4 are options, but 1 is in the middle so it can’t be the right number. So 4 must go in the middle.”	s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00220.warc.gz	CC-MAIN-2021-39	3,270	19
https://www.lessonplanet.com/teachers/ordering-numbers-english-learners	math	Why Lesson Planet? Ordering Numbers: English Learners In this ordering numbers activity, students solve 3 multiple choice questions where they circle the set of numbers that is in the correct order. Students answer another question where they must write a set of numbers in the correct order. An example is provided.	s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187227.84/warc/CC-MAIN-20170322212947-00225-ip-10-233-31-227.ec2.internal.warc.gz	CC-MAIN-2017-13	316	3
https://www.mis.mpg.de/publications/preprint-repository/article/2007/issue-87	math	Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs. Ramanujan Eisenstein Series, Faá di Bruno Polynomials and Integrable Systems Partha Guha and Dieter Mayer At first we express the higher order Riccati equation or Fa´a di Bruno polynomial in terms of the modified Ramanujan differential equations in analogy to the relation of the Chazy III equation and the well known Ramanujan equations for the Eisenstein series of the modular group. We relate Ramanujan’s series connected with the pentagonal numbers, introduced by Ramanujan in his Lost Notebook, to the Fa´a di Bruno polynomials and the Riccati chain determined by the Eisenstein series of weight two for the modular group. As a first step to get an explicit expression for the general term in Ramanujan’s polynomial of degree k we derive a formula for the n-th order differential equations this Eisenstein series fulfill.	s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473401.5/warc/CC-MAIN-20240221070402-20240221100402-00384.warc.gz	CC-MAIN-2024-10	1,102	4
http://gmatclub.com/forum/crops-55182.html?fl=similar	math	Under frost-free conditions, Cal Cultivators expects its strawberry crop to have a $60,000 market value. An unprotected crop subject to frost has an expected market value of $40,000. If Cal protects the strawberries against frost, then the market value of the crop is still expected to be $60,000 under frost-free conditions and $90,000 if there is a frost. What must be the probability of a frost for Cal to be indifferent to spending $10,000 for frost protection? x (90,000 - 40,000) + (1-x) (60000 - 60000) = 10000 x = 10000/50000 x = 0.2 or 20%.	s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928078.25/warc/CC-MAIN-20150521113208-00329-ip-10-180-206-219.ec2.internal.warc.gz	CC-MAIN-2015-22	549	4
https://teamtutorials.com/other-tutorials/how-to-calculate-standard-deviation-in-google-sheets	math	Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of values. It is a commonly used statistic in many fields. Google Sheets, a widely used spreadsheet tool, provides a simple method to calculate the standard deviation. In this tutorial, we will guide you through the process of calculating standard deviation in Google Sheets. Steps to Calculate Standard Deviation Here are the steps you can follow to calculate the standard deviation using Google Sheets: - Open your Google Sheets and make sure your data is organized. This could be a row or column of numbers from which you want to calculate the standard deviation. - Click on an empty cell where you want to display the standard deviation result. Type the formula for standard deviation. Google Sheets offers two main functions to calculate standard deviation: STDEVP and STDEVS. - STDEVP is used when data represents the entire population. - STDEVS is used when data is a sample of a population. - After typing the function, specify the range of cells that contain the numbers for which you want to calculate the standard deviation. - Press the “Enter” key and Google Sheets will calculate the standard deviation. For instance, if you have data in cells A1 through A10 and you want to calculate the standard deviation, the formula you should enter might look like this: Or if your data represents the entire population: Calculating the standard deviation in Google Sheets is a straightforward process once you understand the formula syntax and how to apply it. Whether you’re using standard deviation for a math assignment, a statistical analysis, or for business planning, Google Sheets provides an easy solution.	s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506029.42/warc/CC-MAIN-20230921174008-20230921204008-00359.warc.gz	CC-MAIN-2023-40	1,727	13
http://calculator.mathcaptain.com/hex-calculator.html	math	Hex numbers or hexadecimal numbers refers to the number system with base 16. Which includes 16 various numbers or symbols such as 0 to 9 and A to F. A, B, C, D, E, F represents 10, 11, 12, 13, 14, 15 respectively. This number system is a relevant one because it is easy to remember the high value than the binary system. And it is very easy to convert to binary and decimal system also. This can be denoted with an 0x prefix or an h suffix. The examples related to the conversion of the hexadecimal numbers are given in the following section.	s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249490870.89/warc/CC-MAIN-20190223061816-20190223083816-00074.warc.gz	CC-MAIN-2019-09	542	1
http://e-booksdirectory.com/details.php?ebook=7397	math	Dynamics and Relativity by David Tong Publisher: University of Cambridge 2012 Number of pages: 154 This is an introductory course on Newtonian mechanics and special relativity given to first year undergraduates. Contents: Newtonian Mechanics; Forces; Dimensional Analysis; Systems of Particles; Central Forces; Rigid Bodies; Non-Inertial Frames; Special Relativity. Home page url Download or read it online for free here: by Joseph Whittington Landon - Cambridge University Press The book presents the principles of elementary dynamics, and explains the meaning of the physical quantities involved, partly by definition and description, but mainly by worked examples in which formulae have been avoided as far as possible. by Martin Scholtz - Charles University Contents: Classical mechanics; Lagrange equations; Hamilton's equations; Variational principle; Hamilton-Jacobi equation; Electromagnetic field; Discrete dynamical systems and fractals; Dynamical systems; Bifurcations; Commands in Mathematica. by John Bascombe Lock - MacMillan This work explains the elementary principles of Dynamics, illustrating them by numerous easy numerical examples in a manner suitable for use in Schools with boys of ordinary mathematical attainments. This is the third edition of the book. by Richard Fitzpatrick - Lulu.com Set of lecture notes for an upper-division classical dynamics course: oscillations, Keplerian orbits, two-body scattering, rotation of rigid bodies in three dimensions, Lagrangian mechanics, Hamiltonian mechanics, and coupled oscillations.	s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937074.8/warc/CC-MAIN-20180419223925-20180420003925-00252.warc.gz	CC-MAIN-2018-17	1,552	15
https://rochester.universitytutor.com/rochester_precalculus-tutoring	math	Pre Calculus Tutors in Rochester, NY Find Private & Affordable PreCalculus Tutoring in the Rochester Area! Western Washington University - BA Mathematics, BS Physics, Mathematics and Physics Bachelor of Science in Mathematics BA, Vanderbilt University, 2015 Mathematics and Economics with honors ======= Perfect 2400 SAT (see profile pic to... Freshman in Harvard University BS/MS program in Applied Mathematics.	s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583875448.71/warc/CC-MAIN-20190122223011-20190123005011-00155.warc.gz	CC-MAIN-2019-04	416	6

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.