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https://lecumohakekaw.driftwood-dallas.com/introduction-to-college-mathematics-2nd-ed-strayer-book-15231rq.php
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math
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5 edition of Introduction to College Mathematics - 2nd Ed. - Strayer found in the catalog.
Introduction to College Mathematics - 2nd Ed. - Strayer
Judith A. Beecher
by Pearson Custom Publishing
Written in English
|Contributions||Brian K. Saltzer (Author, Editor)|
|The Physical Object|
|Number of Pages||1205|
Learn how to solve your math, science, engineering and business textbook problems instantly. Chegg's textbook solutions go far behind just giving you the answers. We provide step-by-step solutions that help you understand and learn how to solve for the answer. Math For Clinical Practice - Text and E-Book Package 2nd Edition Author: Cynthia C Chernecky, Denise Macklin, Cynthia Chernecky, Mother Helena Infortuna, Helen Infortuna ISBN:
Introduction. This book represents a significant departure from the current crop of commercial one mathematics education doctoral student, and three UK math faculty went through a week-long (30 hour) seminar which went (line by line, page by page) 45 college students 33% 27% 18% 0% 16% 7% Fall 41 secondary students 58% 7% 10% 7%. • Mathematical Reasoning, Ted Sundstrom, 2nd ed Available free online! Excellent resource. If you would like to buy the actual book, you can purchase it on Amazon at a really cheap price. • Mathematical Proofs: A Transition to Advanced Mathematics, Chartrand/Polimeni/Zhang, 3rd Ed , Pearson. The most recent course text.
This book provides an elementary introduction to the Wolfram Language and modern computational thinking. It assumes no prior knowledge of programming, and is suitable for both technical and non-technical college and high-school students, as well as anyone with an interest in the latest technology and its practical application. in the margin of his college book. It would be of value to mark refer-ences to College Geometry on the margin of the corresponding prop-ositions of the high-school book. The cross references in this book are to the preceding parts of the text. Thus art. harks back to art. When reading art.
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Introduction to College Mathematics - 2nd Ed. - Strayer [Brian K. Saltzer] on *FREE* shipping on qualifying offers. Introduction to College Mathematics - 2nd Ed. - Strayer/5(2). : Introduction to College Mathematics - 2nd Ed. - Strayer () by Brian K.
Saltzer and a great selection of similar New, Used and Collectible Books available now at great Range: $ - $ Introduction to College Mathematics (Custom Package) [Strayer University] on *FREE* shipping on qualifying offers.
Introduction to College Mathematics (Custom Package)5/5(1). Find many great new & used options and get the best deals for Introduction to College Mathematics Mat Strayer University 2nd Edition at the best online.
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach.
The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring /5(3). Madison College Textbook for College Mathematics Revised Fall of Edition. Authored by various members of the Mathematics Department of Madison Area Technical College.
Algebra 1: Common Core (15th Edition) Charles, Randall I. Publisher Prentice Hall ISBN Search the world's most comprehensive index of full-text books. My library. Students can save up to 80% with eTextbooks from VitalSource, the leading provider of online textbooks and course materials.
New Title Reading & Writing Handbook, 2nd Edition. Handbook. View Details. Humanities & Social Sciences Psychology. Introduction to Vector Analysis.
Textbook, Student Solutions Manual. View Details. Statistics New Title Pathways to College Mathematics. Software. Introduction to College Mathematics - 2nd Ed.
- Strayer(2nd Edition) by Brian K. Saltzer, Marvin L. Bittinger, David J. Ellenbogen Paperback, 1, Pages, Published by Pearson Custom Publishing ISBNISBN: Introduction to Sociology adheres to the scope and sequence of a typical introductory sociology course.
In addition to comprehensive coverage of core concepts, foundational scholars, and emerging theories, we have incorporated section reviews with engaging questions, discussions that help students apply the sociological imagination, and features that draw learners into the discipline in. Introduction to Sociology 2e by OpenStax (hardcover version, full color) Product Features Product Specifications Series: Introduction to Sociology 2e Hardcover: pages Publisher: XanEdu Publishing Inc; 2nd edition (Ap ) Language: English isbn isbn 13 Package Dimensions: 3 x 8.
6 x 1 inches Shipping Weight: 2. About This Book. Welcome to Introduction to Sociology 2e, an OpenStax resource created with several goals in mind: accessibility, affordability, customization, and student engagement—all while encouraging learners toward high levels of learning.
Instructors and students alike will find that this textbook offers a strong foundation in. Mathematics books Need help in math. Delve into mathematical models and concepts, limit value or engineering mathematics and find the answers to all your questions.
It doesn't need to be that difficult. Our math books are for all study levels. A text for the ANU secondary college course \An Introduction to Contemporary Mathematics" together with the book The Heart of Mathematics [HM] by Burger and Starbird, are the texts for the ANU College Mathematics Minor for Years 11 and 12 students.
If you are doing this course you will have a strong interest in mathematics, and probably be. > Journey into Mathematics: An Introduction to Proofs, by Joseph. > Mathematics for Economics - 2nd Edition,Michael Hoy, John I am looking for the solution manual of this book (College Accounting 5th Edition: Paradigm publishing by Dansby, Kaliski and Lawrence).
Please let me know if you have it. Here is an unordered list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents freely available on the web.
I tried to select only the works in book formats, "real" books that are mainly in PDF format, so many well-known html-based mathematics web pages and online tutorials are left out.
Mathematics in Action: An Introduction to Algebraic, Graphical, and Numerical Problem Solving, 3rd Edition Basic College Mathematics with Early Integers, 2nd Edition Elementary Algebra, 3rd Edition.
Heather Griffiths, Eric Strayer, Susan Cody-Rydzewski Published by XanEdu Publishing Inc (edition 2nd) ISBN ISBN Great deals on Mathematics Adult Learning & University Books.
Get cozy and expand your home library with a large online selection of books at Fast & Free shipping on many items! Basic College Mathematics Through Applications 5th Edition Akst Bragg $ or Best Offer. Basic Mathematics Steve Slavin Ginny Crisonino 2nd.Our goal with this textbook is to provide students with a strong foundation in mathematical analysis.
Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence.
However, these concepts will be reinforced through rigorous proofs.
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CC-MAIN-2021-10
| 7,694 | 43 |
https://www.physicsforums.com/threads/2-work-questions-that-got-me-stumped.356333/
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math
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Two Work problems I can't figure out. I don't really know where to start? Question1) A delivery person carries a 215N box up stairs 4.20m vertically and 6.80m horizontally. a)How much work does the delivery person do?(Answer: 903 J) b)How much work does the delivery person do in carrying the box down the stairs?(-903J) Question2) A laborer pushes a wheel barrow weighing 200N at 25.0 degrees above the horizontal. If he pushes it a distance of 25.0m, how much work is done?(Answer: 10 700J) Can someone explain in full detail how to reach their answers? I tried them and get nowhere close. Relevant Equations W=Fs W=Fscostheda W=fs=mgs I know that in Q1) a) if you go W=(215N)(4.20m) = 903J However, what do we do about the 6.80m? Also.. Going down the stairs becomes negative 903J? Is that becomes they go downwards with the box? I really dont know how to properly display my answers for this.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867085.95/warc/CC-MAIN-20180525102302-20180525122302-00569.warc.gz
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CC-MAIN-2018-22
| 896 | 1 |
http://powersbrewery.com/blog/2014/06/28/beer-blog-ipa/
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math
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It is hard to believe that this website has been online in one form or another since 2005. Every once in a while I will add new information or tweak the site to keep it current. Recently, however, I took the opportunity to make the entire website a responsive design. This major layout change makes the site more accessible to mobile readers and users of my online calculators. I also plan to incorporate a blog that chronicles more of my brewing endeavors.
Many users of this site don’t realize that I took a several year beer brewing hiatus in order to devote more time to my two young children. In 2008, having an infant and a toddler in the house made beer brewing a very low-priority endeavor. I kept the website up and running so that dedicated users of my online brewing calculators could continue to use them. Now that my children are a little older, I have recently begun brewing again and Father’s Day of 2014 was my first brewing weekend back at the helm of my home brewery.
After an extensive cleaning and sanitation effort in the brewery, Father’s Day weekend presented the perfect opportunity to brew a very simple IPA. Since it had been a couple years, I wanted the recipe, ingredients, and procedure to be as simple as possible in case the operation went poorly.
The recipe I chose to brew was a simple IPA based around a 5.3 gallon batch due to my usual .3 gallon loss from dumping yeast from my conical fermentation tank. I hit all my liquid volume numbers but my efficiency seemed a bit low which may have been from the grain crush. I plan to get a grain mill in the near future since it was at the top of my list just before I stopped brewing. My efficiency was normally in the 77% range and this brew had it in the 65% range according to BeerSmith 2 and 70% using iBrewMaster 2. My own online calculator put it at 72%.
Recipe: Simple IPA Brewer: Ken Powers Style: American IPA Recipe Specifications: ---------------------- Boil Size: 6.83 gal Post Boil Volume: 6.29 gal Batch Size (fermenter): 5.30 gal Bottling Volume: 5.00 gal Estimated OG: 1.067 SG Estimated Color: 12.0 SRM Estimated IBU: 87.6 IBUs Brewhouse Efficiency: 65.00 % Est Mash Efficiency: 74.2 % Boil Time: 60 Minutes Ingredients: ------------ 10 lbs Munich Malt 3 lbs Pale Malt (2 Row) US 1.5 lbs Caramel/Crystal Malt - 20L 8.0 oz Cara-Pils/Dextrine 2.00 oz Magnum - Boil 60.0 min 1.00 Whirlfloc Tablet - Boil 15.0 mins 2.00 oz Goldings, East Kent - Boil 5.0 min 2.00 oz Goldings, East Kent - Boil 1.0 min 1.0 pkg London ESB Ale (Wyeast Labs #1968) Mash Schedule: -------------- Single Infusion, Medium Body, No Mash Out Mash In: Add 18.75 qt of water at 174.2 F Target Temp: 154.0 F Duration: 60 min Sparge: Fly sparge with 4.34 gal water at 168.0 F
Powers Beer Recipe Calculator Recipe String
Use the LOAD RECIPE button at the top of the page of the brewing calculator and paste the following string into the text box that appears:
Ken Powers^Simple IPA^June 8, 2014^61^49^5.3^60^9^4^72^100^9^0.3^0.8^0.7^0.4^0.3^63^63^10^71^71^3^31^31^1.5^22^22^0.5^0^0^0^0^0^0^0^0^0^0^0^0^66^61^47^2^60^0^1^12^2^5^0^1^12^2^1^0^1^0^0^0^0^1^0^0^0^0^1^0^0^0^0^1^2^63^153^1.25^1.062^1.021^153^^^^^^^^^^^^^^^^^^^^^14^5^5^0^0^0^0.2^
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CC-MAIN-2018-17
| 3,206 | 8 |
https://spainsnews.com/the-succession-of-padovan-science/
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math
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The numbers 187 and 2019 can be decomposed into sums of squares and cubes in different ways, as it was said last week; Here are some of the shorter ones, found by our usual commentators Oli and Theram:
187 = 13² + 3² + 3²;
2019 = 43² + 13² + 1²
187 = 5³ + 3³ + 3³ + 2³
2019 = 11³ + 7³ + 7³ + 1³ + 1³
The sequence 16, 1, 2, 3, 5, 1, 1 … is an example of those phenomena or events that go unnoticed by their very "normality", like those noises of which we are only aware when they cease. In many houses there are still wall clocks that give the rooms and the hours, and in almost all the houses one of those clocks comes in once a year to give the New Year bells. At the end of one day and start another, those clocks give 16 chimes: 4 of the rooms plus 12 of the hour; a quarter of an hour later, 1 bell announces the first quarter of the following hour … And the fifth term of the sequence, 5, corresponds to the four quarters of the one plus the bell of the hour. As a clue, I said that the sequence was inspired by a very recent and very "sounded" event (the New Year's chimes); but … There arises a question that I pose as a meta-construct: is this sequence acceptable as a logical-mathematical conundrum, or is it one of those trap-questions that when they tell you the answer you exclaim in outrage: "That's not worth it!".
A few years ago, a malevolent child drove me crazy by showing me the following number sequence: 2, 5, 5, 4, 5, 6, 3 … What number does it follow? It took me several days to find the solution, and by chance, and my first reaction was to exclaim mentally: "Damn kid!" But then I thought that this kind of atypical sequences, or slightly cheaters, they invite us to exercise lateral thinking, so welcome. One clue: this sequence has a lot to do with the chimes. And a metapista: the previous track can be deceiving.
A family succession
Since we are talking about numerical sequences and we recently talked about Ian Stewart, it is inevitable to mention Padavan's succession:
1, 1, 1, 2, 2, 3, 4, 5, 7 …
What number does it follow? (It is easy to find the answer to this and other questions related to the succession of Padovan in the network, but do not deprive yourself of the pleasure of finding them without help).
The succession was popularized in 1996 by Ian Stewart in his section of mathematical pastimes of Scientific American, but it is the work of British mathematician and architect Richard Padovan, hence its name.
Surely more than one, although he did not know this numerical sequence, will have thought to see it: "I find it familiar". With what other famous succession is related? And for the most astute readers: what does it have to do with the equation x3 – x – 1 = 0?
Carlo Frabetti He is a writer and mathematician, a member of the New York Academy of Sciences. He has published more than 50 scientific dissemination works for adults, children and young people, among them Damn physics, Damn mathematics or The big game. He was a screenwriter The Cristal ball.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400217623.41/warc/CC-MAIN-20200924100829-20200924130829-00586.warc.gz
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CC-MAIN-2020-40
| 3,035 | 14 |
http://doultech.co.kr/main/equipment/list_detail2.asp?eid=517
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math
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Input types, Ranges, Accuracy and Resolution: At 23±2℃ and 55±10% R.H.
Recording Accuracy(Analog trend): ±0.2% of span(not including measurement accuracy).
Recording Junction Compensation Error: ±1℃(R,S,B,W),±5℃(K,J,E,T,N,L,U,KP vs Au7Fe)
Scan Cycle Time: 2to60s selectable(2,3,4,5,6,10,12,15,20,30,60s).
Scanning Rate: 60ms/channel.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512421.5/warc/CC-MAIN-20181019170918-20181019192418-00395.warc.gz
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CC-MAIN-2018-43
| 344 | 5 |
http://www.expertsmind.com/questions/matrixes-30118189.aspx
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math
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Word problem with three variables, Three students were participating in a s...
Three students were participating in a school''s fundraiser. The first student sold 2 candy bars, 7 pies, and 3 cookie dough. The second student sold 10 candy bars, 2 pies, and 2 c
Adding Rational expressiona, How do I simplify x^2+2 + -(4x-2)
How do I simplify x^2+2 + -(4x-2)
Partial fractions, This section doesn't actually have many to do with the r...
This section doesn't actually have many to do with the rest of this chapter, but since the subject required to be covered and it was a fairly short chapter it appeared like as good
Radicals and formuals, A cyclist bikes 12 blocks south and 5 blocks east, a...
A cyclist bikes 12 blocks south and 5 blocks east, and rides back along a diagonal path. what is the total distance that he travled? show the work
Slopes, determine slope of 2y = -x + 10
determine slope of 2y = -x + 10
Exponential equations, solve log(5*8)
Solvin Quadations equations by factoring, y^2+3y+2=0
Need help with home work, the problem i -4x2y=12 4+8y=-24
the problem i -4x2y=12 4+8y=-24
Graphing functions, Now we need to discuss graphing functions. If we recall...
Now we need to discuss graphing functions. If we recall from the earlier section we said that f ( x ) is nothing more than a fancy way of writing y. It means that already we kno
Center of the ellipse, Note that the right side has to be a 1 to be in stan...
Note that the right side has to be a 1 to be in standard form. The point ( h, k ) is called the center of the ellipse. To graph the ellipse all that we required are the left mo
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543434.57/warc/CC-MAIN-20161202170903-00030-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 2,456 | 49 |
http://www.bookrags.com/lessonplan/journey-through-genius/test5.html
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math
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|Name: _________________________||Period: ___________________|
This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.
Short Answer Questions
1. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?
2. Which of the following can not be solved using algebra?
3. Who was the author of the book Elements?
4. What did Euclid do in his 48th proposition?
5. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
Short Essay Questions
1. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?
2. Describe what is quadrature and why it was useful in the time of Hippocrates.
3. Describe who was Archimedes and how Dunham described his character.
4. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.
5. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.
6. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.
7. What was already known about circles before Archimedes?
8. Describe in two sentences Archimedes's method for determining circular area.
9. Who was Heron, and what is known about him today?
10. Who was Luca Pacioli, and what controversy was sparked over his writings?
Write an essay for ONE of the following topics:
Essay Topic 1
Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.
Essay Topic 2
Write a three part essay to compare the work of Euclid to the work of Gauss.
Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.
Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.
Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?
Essay Topic 3
Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?
This section contains 873 words
(approx. 3 pages at 300 words per page)
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CC-MAIN-2015-40
| 2,499 | 31 |
https://oneclass.com/homework-help/math/267-what-s-a-square-matrix-
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math
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Whats a square matrix?
A square matrix is a matrix with n rows and n columns. ...
View Full Answer
Create a set of six points such that the variance is four. Make a dot plot of the distribution. H...Math
Any system of n linear equations in n variables has at most n solutions, true or false?Math
If f(x) is continuous everywhere, then square root [ f(x) ] is continous everywhere, true or fals...Math
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514005.65/warc/CC-MAIN-20181021115035-20181021140535-00357.warc.gz
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CC-MAIN-2018-43
| 400 | 6 |
http://clubmatiz.eu/23252-logarithmic-photodiode-amplfier-thesis/
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math
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the ADL5315 to the AD8305. I achieved 10 meters range by a raisin in the sun academic essay this. It is possible to detect.5 Million photo electron by a CSA? I started out with a 100M feedback resistor, which actually worked pretty well.
A log amplifier is an amplifier for which the output voltage, v out is, k times the natural log of the input voltage. Everything is in a metal light tight box.
Logarithmic photodiode amplfier thesis
These photo electrons are produced by some number of multi-pixel avalanche photo diode array which has (.) Elementary Electronic Questions : :20 : bilal_oct : Replies: 1 : Views: 540 Hi I am using a simple non inverting circuit to amplify the output of photo. Also my basic understanding of op amp is that slight voltage (.) RF, Microwave, Antennas and Optics : 07:50 : Ronnie : Replies: 2 : Views: 494 Hi all i have found this circuit in a photo diode amplifier, but i cant understand whether. A photo diode can be reverse-biased so it conducts leakage current only when lighted. Search Engine m m - Search - photo diode amplifier 24 Threads found on m: Photo Diode Amplifier hi! The photo - diode can also (.) Elementary Electronic Questions : 19:15 : Audioguru : Replies: 11 : Views: 934 To extend thesis office uiuc the range of your light sensor, try to modulate the LED current by say 1 kHz, then use a narrow-band audio amplifier for. Due to the virtual ground at the op amp differential input, ICVinR1displaystyle I_textCfrac V_textinR_1, and VoutVTln(Vinisor1)displaystyle V_textout-V_textTln left(frac V_textinI_textSOR_1right) The output voltage is expressed as the natural log of the input voltage. My thesis is about designing a thigh frequency transimpedance amplifier. Basic op-amp diode circuit edit, basic op-amp diode log converter, the relationship between the input voltage Vindisplaystyle V_textin and the output voltage Voutdisplaystyle V_textout is given by: VoutVTln(VinISR)displaystyle V_textout-V_textTln left(frac V_textinI_textS, Rright) where ISdisplaystyle I_textS and VTdisplaystyle V_textT are the saturation current and the thermal.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999783.49/warc/CC-MAIN-20190625011649-20190625033649-00538.warc.gz
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CC-MAIN-2019-26
| 2,102 | 4 |
https://listserv.uni-heidelberg.de/cgi-bin/wa?A2=LATEX-L;8c63a1a2.9811&FT=P&P=T&H=A&S=b
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math
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Mon, 14 Apr 1997 13:44:59 +0200
Hans Aberg writes:
> My comment was not intended as polemics. As a matter of fact, several
> mathematicians I know refuse to use LaTeX, because it cannot provide the
> mathematical typesetting they think are needed. The situation improved with
and what are they using if i may ask? something else than TeX? or plain TeX?
> >if you read carefully you find MS1 (point 14 page 35) Alan's arrow
> >construction set as a possible suggestion for inclusion
> If one reads this line carefully, it says
> For fun if there is place to spare:
> 14. Alan's arrow construction set: ?
> Will this comment reassure the guy, who do not use LaTeX for the lack of
> proper mathematical typesetting, and just need to quickly knock out a
> mathematical manuscript with say a few classical commutative diagrams (whic
> surely is not for fun)?
> No, I do not think so. The impression from this line is rather the
> opposite. :-)
probably true. Justin's choice of words could have been better here.
but although the arrow set is important for a large area of
mathematics it would not actually be a problem if it would be taken
out of a core standard (to leave room for, say, less abstract symbols,
eg some additional sizes for large accents etc, and instead being
taken on as an optional application encoding. correct? anyway, right
now it is (with a strange wording :-) part of the core suggestion and
a discussion like mine above can/should wait until we see it in
> At 09:41 97-04-14, J%org Knappen, Mainz wrote:
> >This is specially to Hans Aberg:
> >Please look thru the archives of math-font-discuss *now*. It will prevent
> >you from repeating old arguments and may enable you to contribute something
> >really new -- I don't pretend to know everything, but hearing old
> >discussions anew is quite boring.
> So, even if the math-font-discuss archives already knows-it-all, as far
> as the discussions conducted here, how can we assure that the hitherto
> disappointing LaTeX track-record in this area will not continue?
> Hans Aberg
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| 2,049 | 35 |
https://www.teacherspayteachers.com/Product/Gigantic-Math-Manipulatives-Ten-Frames-3610027
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math
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SAVE MONEY! Buy the bundle! Gigantic Math Manipulative Bundle
Gigantic Ten Frames are a great way to help students build number sense, gain mental math fluency, better understand how to use the math strategy of "composing and decomposing" numbers, and to complete operations over places. Gigantic Thermometers come in two different sizes. They can be used on the whiteboard, at the guided math table, or at math workstations.
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Click on my name at the right hand side of the page to see more great products!
Thanks a bunch,
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CC-MAIN-2018-51
| 942 | 16 |
https://swmath.org/software/7608
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math
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Numerical methods for evolutionary equations with delay and software package PDDE The paper gives a survey of the author’s results on the grid-based numerical algorithms for solving the evolutionary equations (parabolic and hyperbolic) with the effect of heredity on a time variable. From uniform positions we construct analogs of schemes with weights for the one-dimensional heat conduction equation with delay of general form, analog of a method of variable directions for the equation of parabolic type with time delay and two spatial variables, analog of the scheme with weights for the equation of hyperbolic type with delay. For the one-dimensional heat conduction equation and the wave equation we obtained conditions on the weight coefficients that ensure stability on the prehistory of the initial function. Numerical algorithms are implemented in the form of software package partial delay differential equations (PDDE) toolbox.
Keywords for this software
References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Pimenov, Vladimir; Hendy, Ahmed: Numerical methods for a class of fractional advection-diffusion models with functional delay (2017)
- Solodushkin, Svyatoslav I.; Yumanova, Irina F.; De Staelen, Rob H.: A difference scheme for multidimensional transfer equations with time delay (2017)
- Solodushkin, Svyatoslav I.; Yumanova, Irina F.; De Staelen, Rob H.: First order partial differential equations with time delay and retardation of a state variable (2015)
- Pimenov, Vladimir; Lozhnikov, Andrey: Numerical methods for evolutionary equations with delay and software package PDDE (2013)
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https://researchportal.be/nl/publicatie/inconsistency-adaptive-deontic-logic-normative-conflicts
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math
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< Terug naar vorige pagina
An inconsistency-adaptive deontic logic for normative conflicts
Tijdschriftbijdrage - Tijdschriftartikel
We present the inconsistency-adaptive deontic logic DP (r) , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A a aEuro parts per thousand O similar to A, O A a aEuro parts per thousand P similar to A or even O A a aEuro parts per thousand a1/4O A. On the other hand, DP (r) still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP (r) interprets a given premise set 'as normally as possible' with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP (r) , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP (r) .
Tijdschrift: Journal of Philosophical Logic
Pagina's: 285 - 315
Jaar van publicatie:2013
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https://www.reference.com/math/method-used-finding-centroid-335c0089ecfcabef
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math
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The method of determining the centroid depends on the type of area in question. Finding the centroid is conducted through either geometric illustration, the concept of moment, or integral calculus.Continue Reading
The centroid of a two-dimensional region is defined as the point of perfect balance, with the assumption that the region has uniform density and gravitational field. In geometry, the centroid is the arithmetic average position of all points on the given region. For any flat surface, the centroid can be considered its center of gravity.
Finding the centroid of regular polygons is easy to do. For triangles, the centroid is the intersecting point of its three medians. For rectangles, this point can be found by the intersection of the line segments connecting opposite midpoints of the four sides.
For more complex polygons, the concept of moment is used to find the centroid. The moment of any object is the measurement of its inclination to rotate about a given point of reference. It can be calculated as the mass (or area) of the object multiplied by its distance from the point. The polygon is cut into triangles and quadrilaterals so that the centroids of all cut shapes may be determined. To get the coordinates of the centroid, the summation of the moments of each cut shape should be equated to the area of the entire polygon multiplied by the distance of the centroid from the point of reference.
The same approach is implemented to determine the centroid of curved regions, but this time using integral calculus. The area is defined by limits, more particularly by bounding curves with given algebraic equations. The equations form the basis for calculating the moment of each incremental element of the curved area, and divide the total moment with the total area.Learn more about Geometry
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https://www.hindawi.com/journals/je/2013/516462/
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math
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- About this Journal ·
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Journal of Engineering
Volume 2013 (2013), Article ID 516462, 8 pages
Some Variational Principles for Coupled Thermoelasticity
Dipartimento di Ingegneria Strutturale, Università di Napoli Federico II, Via Claudio 21, 80125 Napoli, Italy
Received 22 September 2012; Accepted 18 December 2012
Academic Editor: Oronzio Manca
Copyright © 2013 Francesco Marotti de Sciarra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The nonlinear thermoelasticity of type II proposed by Green and Naghdi is considered. The thermoelastic structural model is formulated in a quasistatic range, and the related thermoelastic variational formulation in the complete set of state variables is recovered. Hence a consistent framework to derive all the variational formulations with different combinations of the state variables is provided, and a family of mixed variational formulations, with different combinations of state variables, is provided starting from the general variational formulation. A uniqueness condition is provided on the basis of a suitable variational formulation.
Coupled thermomechanical problem arises in a variety of important fields of application, including casting, metal forming, machining and other manufacturing processes, structural models, and others.
Green and Naghdi (GN) introduced a theory in which heat propagates as thermal waves at finite speed and does not necessarily involve energy dissipation. Another property of the GN theory of type II is the fact that the entropy flux vector is determined by means of the same potential as the mechanical stress tensor. Motivated by the procedure presented in [1, 2], this paper is concerned with the formulation of variational principles characterizing the solutions of the coupled thermomechanical problem for the GN model without dissipation, that is, type II. The variational characterization of the thermoelastic problem means the identification of a functional whose stationary points are solutions of the problem. Once this functional is known, the solutions of the problem can be identified with certain extrema of the functional.
Following the pioneering work of Biot , the variational forms of the coupled thermoelastic and thermoviscoelastic problems for the classical Fourier model have been investigated in several papers; see, for example, [2, 4–9] for the case of thermomechanical coupling in dissipative materials. Moreover consistent variational principles for structural problems concerning elastic and elastoplastic models in isothermal conditions are well developed; see, for example, [10–12].
In this paper the GN thermoelastic coupled structural model without dissipation is formulated in a suitable form so that we can provide the methodology to build the complete family of all the admissible variational formulations associated with the considered GN model. It is well-known that the GN theory of type II has been developed as a dynamic theory, but an important prerequisite for its use is a thorough understanding of the corresponding problems in which the dynamical effects are disregarded; see, for example, .
An advantage of such an approach consists in the fact that the boundary-value problem for the thermoelastic model is formulated in such a way that the model can be cast in terms of a multivalued structural operator defined in terms of all the state variables. This operator encompasses in a unique expression the field equation, the constitutive relations, the constraint relations and the initial conditions which describe the considered thermoelastic structural model.
The related non-smooth potential can then be evaluated by a direct integration along a ray in the operator domain and depends on all the state variables involved in the model. Appraising the generalized gradient of the non-smooth potential and imposing its stationarity, the operator formulation of the problem is recovered.
Hence a general procedure to derive variational formulations within the incremental framework for the considered GN coupled thermoelastic model without dissipation is formulated. It is then shown how a family of mixed variational formulations, associated with the considered GN model, can be obtained following a direct and general procedure by enforcing the fulfilment of field equations and constraint conditions.
The possibility to formulate the coupled GN thermoelastic problem in a variational form has a number of consequences and some beneficial effects. For instance, the variational framework allows one to apply the tools of the calculus of variations to the analysis of the solutions of the problem. In particular, conditions for the existence (see, e.g., [16, 17]) and uniqueness of the solution are based on the variational framework.
Accordingly the condition for the uniqueness of the solution of the considered model is provided by means of a minimization principle.
2. Thermoelastic Structural Problem
Throughout the paper bold-face letters are associated with vectors and tensors. The scalar product between dual quantities (simple or double index saturation operation between vectors or tensors) is denoted by . A superimposed dot means differentiation with respect to time and the symbol denotes the gradient operator.
In small strain analysis the theory of thermoelasticity without energy dissipation, as described in Green and Naghdi , is considered. Such a theory is based on the introduction of a scalar thermal displacement defined as where is a point pertaining to a thermoelastic body defined on a regular bounded domain of an Euclidean space, represents the temperature variation from the uniform reference temperature , and is the initial value of the thermal displacement at the time . Accordingly the time derivative of is the temperature variation, that is, .
The mechanical and thermal parts of the thermoelastic model are hereafter defined.
Let denote the linear space of strain tensors and denote the dual space of stress tensors . The inner product in the dual spaces has the mechanical meaning of the internal virtual work, that is The linear space of displacements is denoted by . The linear space of forces is and is placed in separating duality with by a nondegenerate bilinear form which has the physical meaning of external virtual work. For avoiding proliferation of symbols, the internal and external virtual works are denoted by the same symbol. Conforming displacement fields satisfy homogeneous boundary conditions and belong to a closed linear subspace .
The kinematic operator is a bounded linear operator from to the space of square integrable strain fields . The subspace of external forces is the dual space of . The equilibrium operator is the continuous operator from to which is dual of . Let be the load functional where and denote the tractions and the body forces [12, 19].
The equilibrium equation and the compatibility condition are given by where , , and , .
The external relation between reactions and displacements is provided by being a concave function, and the symbol denotes the sub(super)differential of convex (concave) functions . Accordingly, the inverse relation is expressed as where the concave function represents the conjugate of and the Fenchel’s relation holds Different expressions can be given to the functional depending on the type of external constraints such as bilateral, unilateral, elastic, or convex. For future reference the expressions of and are specialized to the case of external frictionless bilateral constraints with homogeneous boundary conditions. Noting that the subspace of the external constraint reactions is the orthogonal complement of the subspace of conforming displacements , that is , the functional turns out to be and a direct evaluation shows that its conjugate is given by: The proposed framework has the advantage that the formulation of the thermal model is similar to the mechanical one, and the thermoelastic problem turns out to be suitable to build a general variational formulation as shown in the next section.
The linear space of thermal displacement is . The rate of heat flow into the body by heat sources and the boundary heat fluxes belong to the space , dual of , of square integrable fields on . The external thermal forces are collected in the set .
The kinematic thermal operator is a bounded linear operator, and a thermal gradient is said to be thermally compatible if there exists an admissible thermal displacement field such that . The thermal balance equation is given by , where is the dual operator of and is the entropy flux vector.
Constraint conditions can be fit in field equations by noting that the external relation between reactive thermal forces and thermal displacements is provided by the equivalent relations: being and conjugate convex functionals. The equality (9)3 represents the Fenchel’s relation.
Homogeneous constraints on thermal displacement fields are formulated by considering that thermal displacement fields belong to the subspace and are said to be admissible. Reactive thermal forces belong to the orthogonal complement of . Then the functional is the indicator of : and its conjugate is given by Accordingly the relations governing the quasistatic thermoelastic structural problem without energy dissipation for given mechanical and thermal loads and in the time interval can be collected in the following form:
The initial thermal conditions are considered in the following form: where and are, respectively, a prescribed initial thermal displacement and temperature in .
The thermoelastic functionals and provide the thermoelastic constitutive relations of the considered GN model.
In the case of a linear coupled thermoelastic behaviour the expression of the functional is where the first term at the r.h.s. above is the isentropic elastic strain energy and the second one represents the thermoelastic coupling. The parameter is the specific heat at constant strain at the reference state with temperature , is the symmetric and positive definite isentropic elastic moduli fourth-order tensor. The second-order thermal expansion tensor is self-adjoint, that is, . Moreover the thermal function is given by where is the tensor of conductivity moduli, symmetric and positive definite.
A solution of the thermoelastic structural problem can be achieved by a finite element approach (see e.g., [21, 22]) and can be obtained starting from a suitable mixed variational formulation. Hence the definition of a general variational formulation which allows one to derive variational principles with different combination of the state variables, without ad hoc procedure, plays a central role.
The time integral of the constitutive relation (12)6 in the interval is given by where we have set .
Moreover the time integral of the thermal balance equation (12)2 in the interval is given by where we have set and . In fact, the constitutive relation (12)6, evaluated at the initial time , provides the equality which yields the relation .
3. General Mixed Variational Principle
Introducing the product space and its dual space , the thermoelastic structural problem without dissipation (18) can be collected in terms of the global multivalued structural operators governing the whole problem The explicit expression of the structural operators , and of the vectors , , are given by: The operators and turn out to be integrable by virtue of the duality existing between the operators , , , , , , and , , , , , , , the conservativity of , and the conservativity of the super(sub)differentials and .
The related potential can be evaluated by a direct integration along a straight line in the space starting from its origin to get :
Hence it turns out to be The potential turns out to be linear in , jointly convex with respect to the state variables and jointly concave with respect to . The following statement then holds.
Proposition 1. The set of state variables is a solution of the saddle problem: if and only if it is a solution of the thermoelastic structural problem without dissipation (18).
The stationary condition of , enforced at the point , yields back the thermoelastic structural problem. In fact the stationarity of is: which can be rewritten in the following form
From a mechanical point of view, the relation (25)1 yields the equilibrium equation: the relation (25)2 provides the compatibility condition: the relations (25)3-4 yield the constitutive relations: the relation (25)5 yields the external constraint conditions: the relation (25)6 yields the thermal balance condition: the relation (25)7 yields the thermal compatibility: the relation (25)8 yields the thermal constitutive relation: and, finally, the relation (25)9 yields the thermal external relation: Hence, performing the super(sub)differentials appearing in (25), the structural problem (18) is recovered.
3.1. Mixed Variational Principles
A family of potentials can be recovered from the potential by enforcing the fulfilment of field equations and of constitutive relations. All these functionals assume the same value when they are evaluated at a solution point of the GN structural problem.
Hence a variational principle in which the external reactions do not appear as independent state variables can be obtained by imposing, in the expression (22) of the potential , the external relations (18)5,9 in terms of Fenchel’s equalities (6) and (9)3. Hence it turns out to be and the following statement holds.
Proposition 2. The set of state variables is a solution of the saddle problem: if and only if it is a solution of the thermoelastic structural problem without dissipation (18).
The proof of the mixed GN thermoelastic variational formulation reported in the Proposition 2 is provided in the Appendix. The proofs of the following variational formulations are omitted since they are obtained following a similar reasoning.
Proposition 3. The set of state variables is a solution of the saddle problem: if and only if it is a solution of the thermoelastic structural problem without dissipation (18).
Proposition 4. The set of state variables is a solution of the saddle problem: if and only if it is a solution of the thermoelastic structural problem without dissipation (18).
From a mechanical point of view, the specialization of the potential to the Cauchy model for a linear coupled thermoelastic behaviour, external frictionless bilateral constrains, and homogeneous thermal boundary conditions is provided. The functionals and , see (14) and (15), are
Hence the potential becomes under the condition that the displacement and the thermal displacement are conforming and admissible, that is, and , where is the total potential energy in classical elasticity in terms of the isentropic elastic stiffness, the functionals: are the mixed thermal part of the potential, and the functionals: take into account the thermoelastic coupling.
Minimum principles in structural mechanics are relevant to investigate since solution techniques can be exploited, and existence and uniqueness results can be provided by recourse to functional analysis. Actually, uniqueness of the solution is ensured if the functional to be minimized is strictly convex.
Hence it is important to derive a variational formulation in terms of a minimization problem as hereafter reported.
To this end let us note that the constitutive relation (18)8 can be equivalently expressed in terms of the conjugate of the thermoelastic functional in the following form: and the Fenchel’s relation hold:
In the case of the Cauchy model with a linear coupled thermoelastic behaviour, the potential can be evaluated as the conjugate of (15) and is given by
Enforcing in the expression of the functional the thermal constitutive relation (18)8 in terms of the Fenchel’s equality (46) and the external relation (18)5 in terms of Fenchel’s equality (6), it turns out to be and the following minimum principle holds.
Proposition 5. The set of state variables is a solution of the minimum problem: if and only if it is a solution of the thermoelastic structural problem without dissipation (18).
Accordingly, if the thermoelastic functional pertaining to the GN constitutive model is strictly convex, the functional turns out to be strictly convex, and the GN thermoelastic structural model (18) admits a unique solution (if any).
It is worthnoting that, in the linear coupled thermoelastic case, the expression of the functional is given by (47) so that it turns out to be a strictly convex functional. Therefore the GN thermoelastic structural model (18) admits a unique solution. The question of existence of the solution is still an challenge problem; see, for example, .
A variational framework for a class of GN coupled thermomechanical boundary-value problem is presented. The thermoelastic structural model is addressed, and the related general mixed thermoelastic variational formulation in the complete set of state variables is derived starting from the structural model. An advantage of the proposed methodology is that it can be applied to a wide range of structural models, and variational formulations can be obtained following a general reasoning. As a consequence, a family of mixed thermoelastic variational formulations in a reduced number of variables is then contributed. Finally, by appealing to a minimum principle, the connection between uniqueness of the solution and convexity is investigated.
The stationary condition of , see (34), enforced at the point , yields back the thermoelastic structural problem. In fact the stationarity of is which can be rewritten in the following form: The mechanical interpretation of the relation (A.2)1 yields the equilibrium equation and the external constraint conditions. In fact there exists a reaction such that The relation (A.2)2 provides the compatibility condition: the relations (A.2)3-4 yield the constitutive relations: the relation (A.2)5 yields the thermal balance condition and the thermal external relations. In fact there exists a thermal reaction such that the relation (A.2)6 yields the thermal compatibility: and the relation (A.2)7 yields the thermal constitutive relation: Hence the structural problem (18) is thus recovered.
Research support by “Ministero dell’ Istruzione, dell’Università e della Ricerca” of Italy is kindly acknowledged.
- S. Bargmann and P. Steinmann, “An incremental variational formulation of dissipative and non-dissipative coupled thermoelasticity for solids,” Heat and Mass Transfer, vol. 45, no. 1, pp. 107–116, 2008.
- Q. Yang, L. Stainier, and M. Ortiz, “A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids,” Journal of the Mechanics and Physics of Solids, vol. 54, no. 2, pp. 401–424, 2006.
- M. A. Biot, “Thermoelasticity and irreversible thermodynamics,” Journal of Applied Physics, vol. 27, no. 3, pp. 240–253, 1956.
- M. Ben-Amoz, “On a variational theorem in coupled thermoelasticity,” Journal of Applied Mechanics, vol. 32, no. 4, pp. 943–945, 1965.
- G. Batra, “On a principle of virtual work for thermo-elastic bodies,” Journal of Elasticity, vol. 21, no. 2, pp. 131–146, 1989.
- G. Herrmann, “On variational principles in thermoelasticity and heat conduction,” Quarterly of Applied Mathematics, vol. 22, pp. 151–155, 1963.
- G. Lebon, “Variational principles in thermomechanics,” in Recent Developments in Thermomechanics of Solids, G. Lebon and P. Perzina, Eds., CISM Courses and Lectures, no. 262, pp. 221–396, Springer, Wien, Austria, 1980.
- J. T. Oden and J. N. Reddy, Methods in Theoretical Mechanics, Springer, Berlin, Germany, 1976.
- F. Armero and J. C. Simo, “A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity,” International Journal of Plasticity, vol. 9, no. 6, pp. 749–782, 1993.
- F. Marotti de Sciarra, “Novel variational formulations for nonlocal plasticity,” International Journal of Plasticity, vol. 25, no. 2, pp. 302–331, 2009.
- F. Marotti de Sciarra, “A finite element for nonlocal elastic analysis,” in Proceedings of the 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, Kos, Greece, 2011.
- F. Marotti de Sciarra, “Hardening plasticity with nonlocal strain damage,” International Journal of Plasticity, vol. 34, pp. 114–138, 2012.
- D. S. Chandrasekharaiah, “Variational and reciprocal principles in thermoelasticity without energy dissipation,” Proceedings of the Indian Academy of Sciences: Mathematical Sciences, vol. 108, no. 2, pp. 209–215, 1998.
- S. Chiriţa and M. Ciarletta, “Reciprocal and variational principles in linear thermoelasticity without energy dissipation,” Mechanics Research Communications, vol. 37, no. 3, pp. 271–275, 2010.
- R. Quintanilla and J. Sivaloganathan, “Aspects of the nonlinear theory of type II thermoelastostatics,” European Journal of Mechanics A, vol. 32, pp. 109–117, 2012.
- G. Dal Maso, G. A. Francfort, and R. Toader, “Quasistatic crack growth in nonlinear elasticity,” Archive for Rational Mechanics and Analysis, vol. 176, no. 2, pp. 165–225, 2005.
- R. Quintanilla, “Existence in thermoelasticity without energy dissipation,” Journal of Thermal Stresses, vol. 25, no. 2, pp. 195–202, 2002.
- A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” Journal of Elasticity, vol. 31, no. 3, pp. 189–208, 1993.
- R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, Providence, RI, USA, 1997.
- R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, USA, 1970.
- E. Ruocco and M. Fraldi, “Critical behavior of flat and stiffened shell structures through different kinematical models: a comparative investigation,” Thin-Walled Structures, vol. 60, pp. 205–215, 2012.
- E. Ruocco and M. Fraldi, “An analytical model for the buckling of plates under mixed boundary conditions,” Engineering Structures, vol. 38, pp. 78–88, 2012.
- G. Romano, L. Rosati, F. Marotti de Sciarra, and P. Bisegna, “A potential theory for monotone multi-valued operators,” Quarterly of Applied Mathematics, vol. 4, no. 4, pp. 613–631, 1993.
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https://www.hackmath.net/en/word-math-problems/square-root?tag_id=88
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math
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Square root + The right triangle altitude theorem - math problems
Number of problems found: 9
- Triangle KLM
In the rectangular triangle KLM, where is hypotenuse m (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5cm and ml = 15 cm.
The legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
- Without Euclid laws
Right triangle ABC with right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws.
- Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
- Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
- Area of RT
Calculate the right triangle area that hypotenuse has length 14, and one hypotenuse segment has length 5.
- Area of RT
The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of this triangle.
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
- Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
Square root - math problems. The right triangle altitude theorem - math problems.
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http://defaultrisk.com/pp_related_02.htm
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math
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Recursive Evaluation of a Family of Compound Distributions
by Harry H. Panjer of the University of Waterloo
Introduction: Compound distributions such as the compound Poisson and the compound negative binomial are used extensively in the theory of risk to model the distribution of the total claims incurred in a fixed period of time. The usual method of evaluating the distribution function requires the computation of many convolutions of the conditional distribution of the amount of a claim given that a claim has occurred. When the expected number of claims is large, the computation can become unwieldy even with modern large scale electronic computers.
Published in: Astin Bulletin, Vol. 12, No. 1, (July 1981), pp. 22-26.
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https://trip1907.com/play/forums/topic/chapter-10/
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math
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TRIP 1907: Interactive Escape The Book Game › Forums › Trip 1907 › Chapter 10
Is the answer another four digit number?
The hints were not helpful at all. I have tried every type of difference there is between the numbers.
Do I need to subtract something or find a missing 4 digit door number?
3 digit number
Find a pattern between each of the door numbers.
(Not sure if I can give the answer away So I will leave as many ‘helpful’ clues as I can)
The answer is a 3 digit number
Hint 1: Place them in order
Hint 2: There is a constant distance between the numbers
Try subtracting the numbers, but not all together.
I got the difference between numbers but the three digit number isn’t working
First puzzle I was stuck on for couple of hours.
Was laughing out loud with the answer. So easy, yet so hard.
Got them in order. Found the “gap” in between them. Still no 3 digit answer. HEEEELP
You must be logged in to reply to this topic.
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https://goprep.co/i-state-the-essential-conditions-for-diffraction-of-light-ii-i-1nm63j
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math
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The phenomenon that occurs when the light comes across the object and it obstructs is known as diffraction.
The essential condition for diffraction of light is given by,
• The wavelength of the light should always be comparable to the size of the object.
• In certain cases, it may occur is the size of the object is less than the wavelength of light.
Let a set of parallel rays from lens L1 allows to fall on the slit which then works as secondary source using Huygens’s principle. The resultant intensity is maximum.
For secondary minima:
Consider the right-angle triangle ,
For first minima, n=1
Thus, for nth minima,
For secondary maxima:
The path difference at the point is given by,
General formula for nth maxima is,
(iii) In right angle triangle COP,
As θ is very small, sin θ=tan θ
For central maxima,
(iv) The size of the central band is given by,
Thus, size of central band reduces to half.
(i) The schematic ray diagrams of astronomical telescope are,
(ii) There are two types of aberrations of reflecting telescope:
It is the defect in the lens that result in the focusing of the beam of light on the point after passing through the spherical surface.
It is the defect in the lens which results in the formation of the blurred and coloured image.
• The resolving power of the telescope increases if the frequency of the incident light is increased.
• The resolving power of the telescope does not change if the focal length of the objective is increased.
• The resolving power of the telescope halved if the aperture of the objective is halved.
Rate this question :
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https://access.openupresources.org/curricula/our6-8math/en/grade-6/unit-8/lesson-15/index.html
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math
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Lesson 15Quartiles and Interquartile Range
Let's look at other measures for describing distributions.
- I can use IQR to describe the spread of data.
- I know what quartiles and interquartile range (IQR) measure and what they tell us about the data.
- When given a list of data values or a dot plot, I can find the quartiles and interquartile range (IQR) for data.
15.1 Notice and Wonder: Two Parties
Here are two dot plots including the mean marked with a triangle. Each shows the ages of partygoers at a party.
15.2 The Five-Number Summary
Here are the ages of a group of the 20 partygoers you saw earlier, shown in order from least to greatest.
Find and mark the median on the table, and label it “50th percentile.” The data is now partitioned into an upper half and a lower half.
Find and mark the middle value of the lower half of the data, excluding the median. If there is an even number of values, find and write down the average of the middle two. Label this value “25th percentile.”
Find and mark the middle value of the upper half of the data, excluding the median. If there is an even number of values, find and write down the average of the middle two. Label the value “75th percentile.”
You have now partitioned the data set into four pieces. Each of the three values that “cut” the data is called a quartile.
- The first (or lower) quartile is the 25th percentile mark. Write “Q1” next to “25th percentile.”
- The second quartile is the median. Write “Q2” next to that label.
- The third (or upper) quartile is the 75th percentile mark. Write “Q3” next to that label.
Label the least value in the set “minimum” and the greatest value “maximum.”
Record the five values that you have just identified. They are the five-number summary of the data.
Minimum: _____ Q1: _____ Q2: _____ Q3: _____ Maximum: _____
The median (or Q2) value of this data set is 20. This tells us that half of the partygoers are 20 or younger, and that the other half are 20 or older. What does each of the following values tell us about the ages of the partygoers?
Are you ready for more?
Here is the five-number summary of the age distribution at another party of 21 people.
Minimum: 5 years Q1: 6 years Q2: 27 years Q3: 32 years Maximum: 60 years
- Do you think this party has more or fewer children than the other one in this activity? Explain your reasoning.
- Are there more children or adults at this party? Explain your reasoning.
15.3 Range and Interquartile Range
Here is a dot plot you saw in an earlier task. It shows how long Elena’s bus rides to school took, in minutes, over 12 days.
Write the five-number summary for this data set by finding the minimum, Q1, Q2, Q3, and the maximum. Show your reasoning.
The range of a data set is one way to describe the spread of values in a data set. It is the difference between the greatest and least data values. What is the range of Elena’s data?
Another number that is commonly used to describe the spread of values in a data set is the interquartile range (IQR), which is the difference between Q1, the lower quartile, and Q3, the upper quartile.
What is the interquartile range (IQR) of Elena’s data?
What fraction of the data values are between the lower and upper quartiles? Use your answer to complete the following statement:
The interquartile range (IQR) is the length that contains the middle ______ of the values in a data set.
Here are two dot plots that represent two data sets.
Without doing any calculations, predict:
a. Which data set has the smaller IQR? Explain your reasoning.
b. Which data set has the smaller range? Explain your reasoning.
- Check your predictions by calculating the IQR and range for the data in each dot plot.
Lesson 15 Summary
Earlier we learned that the mean is a measure of the center of a distribution and the MAD is a measure of the variability (or spread) that goes with the mean. There is also a measure of spread that goes with the median called the interquartile range (IQR).
Finding the IQR involves partitioning a data set into fourths. Each of the three values that cut the data into fourths is called a quartile.
- The median, which cuts the data into a lower half and an upper half, is the second quartile (Q2).
- The first quartile (Q1) is the middle value of the lower half of the data.
- The third quartile (Q3) is the middle value of the upper half of the data.
Here is a set of data with 11 values.
- The median (Q2) is 33.
- The first quartile (Q1) is 20, the median of the numbers less than 33.
- The third quartile (Q3) is 40, the median of the numbers greater than 33.
The difference between the minimum and maximum values of a data set is the range.
The difference between Q1 and Q3 is the interquartile range (IQR). Because the distance between Q1 and Q3 includes the middle two-fourths of the distribution, the values between those two quartiles are sometimes called the middle half of the data.
The bigger the IQR, the more spread out the middle half of the data are. The smaller the IQR, the closer the middle half of the data are. We consider the IQR a measure of spread for this reason.
The five numbers in this example are 12, 20, 33, 40, and 49. Their locations are marked with diamonds in the following dot plot.
Different data sets could have the same five-number summary. For instance, the following data has the same maximum, minimum, and quartiles as the one above.
The interquartile range is one way to measure how spread out a data set is. We sometimes call this the IQR. To find the interquartile range we subtract the first quartile from the third quartile.
For example, the IQR of this data set is 20 because .
Quartiles are the numbers that divide a data set into four sections that each have the same number of values.
For example, in this data set the first quartile is 20. The second quartile is the same thing as the median, which is 33. The third quartile is 40.
The range is the distance between the smallest and largest values in a data set. For example, for the data set 3, 5, 6, 8, 11, 12, the range is 9, because .
Lesson 15 Practice Problems
Suppose that there are 20 numbers in a data set and that they are all different.
- How many of the values in this data set are between the first quartile and the third quartile?
- How many of the values in this data set are between the first quartile and the median?
In a word game, 1 letter is worth 1 point. This dot plot shows the scores for 20 common words.
- What is the median score?
- What is the first quartile (Q1)?
- What is the third quartile (Q3)?
- What is the interquartile range (IQR)?
Here are five dot plots that show the amounts of time that ten sixth-grade students in five countries took to get to school. Match each dot plot with the appropriate median and IQR.
- Median: 17.5, IQR: 11
- Median: 15, IQR: 30
- Median: 8, IQR: 4
- Median: 7, IQR: 10
- Median: 12.5, IQR: 8
Mai and Priya each played 10 games of bowling and recorded the scores. Mai’s median score was 120, and her IQR was 5. Priya’s median score was 118, and her IQR was 15. Whose scores probably had less variability? Explain how you know.
Draw and label an appropriate pair of axes and plot the points. , , ,
There are 20 pennies in a jar. If 16% of the coins in the jar are pennies, how many coins are there in the jar?
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CC-MAIN-2023-06
| 7,336 | 76 |
http://www.mt-oceanography.info/science+society/lectures/illustrations/lecture27/coriolisforce.html
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math
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A virtual force required to apply Newton's Laws to rotating coordinates.
The animation below shows a laboratory experiment to demonstrate how a rotating coordinate system gives rise to a virtual force. A small marble rolls back and forth across a shallow rotating bowl under gravity (below left). When both the bowl and the marble are observed from outside (in an absolute coordinate system), the marble moves back and forth in a straight line, while the bowl rotates under it (upper left).
When the observer and the coordinate system rotate with the bowl, the marble moves on a circle (right). To explain the circular motion, the observer has to invoke a force that deflects the marble from a straight path. This virtual force is the Coriolis force.
Animation: © M. Tomczak, Creative Commons license
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CC-MAIN-2018-05
| 801 | 4 |
http://www.unb.ca/saintjohn/sase/dept/math/people/timalderson/publications.html
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math
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Publications in refereed journals
All publications are freely available through ResearchGate.
T.L. Alderson, K.E. Mellinger, Spreads, Arcs, and Multiple Wavelength Codes., Discrete Mathematics. In press, 2010.
T.L. Alderson, Hyperconics and multiple weight codes for OCDMA. Error-Correcting Codes, Cryptography and Finite Geometries, AMS Contemporary Mathematics, 523, pp.67-76, 2010.
T.L. Alderson, K.E. Mellinger, Classes of permutation arrays in finite projective spaces. International Journal of Information and Coding Theory, 1 (4), pp.371-383, 2010.
T. L. Alderson, K. Mellinger, Maximal 2D-OOCs from Singer groups, l ≤ 2. Discrete Applied Mathematics, 157 (14), pp. 3008-3019, 2009.
T.L. Alderson, András Gács, On the Maximality of Linear Codes Designs, Codes & Cryptography, 53 (1), pp.59-68, October, 2009.
T.L. Alderson, K. Mellinger, Partitions in finite geometry and related constant composition codes, Innovations in Incidence Geometry. 8, pp.49-71, 2008.
T.L. Alderson, K. Mellinger Geometric constructions of optimal optical orthogonal codes., Advances in Mathematics of Communications, 2 (4), pp.451–467, 2008.
T.L. Alderson, K. Mellinger Families of optimal OOCs with l = 2. IEEE Transactions on Information Theory, 54 (8), pp. 3722-3724, 2008.
T.L. Alderson, A.A. Bruen Codes from cubic curves and their extensions , Electron. J. Combin., 15(1), R42, pp. 1-9, 2008.
T.L. Alderson, K. Mellinger, Classes of Optical Orthogonal Codes from Arcs in Root Subspaces. Discrete Mathematics, 308, no. 7, pp. 1093-1101, 2008.
T.L. Alderson, Bruck Nets and 2-Dimensional Codes. Bulletin of the Institute of Combinatorics and its Applications, 52, pp. 33-44, 2008.
T.L. Alderson, K. Mellinger, Constructions of Optical Orthogonal Codes from Finite Geometry. SIAM Journal on Discrete Mathematics, 21, no. 3, pp. 785-793, 2007.
T.L. Alderson, Optical Orthogonal Codes and Arcs in PG(d,q), Finite Fields and Their Applications, 13, pp. 762-768, 2007
T.L. Alderson, F.M. Allan, and M.H. Hamdan, On The Universality of the Von Mises Transformation, Int. J. Appl. Math, 20, 1 , pp. 109-122, 2007.
T.L. Alderson, (6,3)-MDS Codes Over an Alphabet of Size 4, Designs, Codes & Cryptography, 38 (1), pp. 31-40, 2006.
T.L. Alderson, Some Generalizations of R'edei's Theorem, Journal of Discrete Mathematical Sciences and Cryptography, 9 (1), pp. 97-106, 2006.
T.L. Alderson, Extending MDS Codes, Annals of Combinatorics, 9 (2), pp. 125-135, 2005.
T. L. Alderson, Extending Arcs: An Elementary Proof, Electronic Journal of Combinatorics, 12 (1), 2005.
Refereed book contributions
T. L. Alderson, K. Mellinger, Optical Orthogonal Codes from Singer Groups, in Advances in Coding Theory and Cryptology, Series on Coding Theory and Cryptology, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. Editors: T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko . ISBN 978-981-270-701-7, pp. 51-70.
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CC-MAIN-2018-34
| 2,901 | 22 |
https://sportscardreport.info/birth-control/multiply-and-divide-radical-homework-answer-key-94013.php
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math
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Multiplying and Dividing Radical Expressions. Learning Objective s. You can do more than just simplify radical expressions. You can multiply and divide them, too. You can use your knowledge of exponents to help you when you have to operate on radical expressions this way. Multiplying Radical Expressions.
8.4: Multiplying and Dividing Radical Expressions
Multiplying integers worksheet with answer key
Posted in worksheet, December 12, by mikasa Order rational number for grade - displaying top worksheets found for this concept. Right from multiplying integers worksheet with answer key to roots, we have all the pieces covered. We can multiply numbers in either order, so. We can multiply rational expressions in much the same way as we multiply numerical fractions. Unit 3 Algebraic Expressions. Lesson 9: Multiplying rational numbers.
Sometimes it is desirable to find an equivalent radical expression that does not contain radicals in the denominator. This process is called rationalizing the denominator. The goal is to make sure there are no radicals left in the denominator of the fraction. In order to do this, multiply the fraction by a fraction equal Dividing functions calculator, mcdougal littell english 10 answers, 1st grade worksheets math fraction word problems, edhelper answer ratio key, how to teach subtracting integers, solving a quadratic by completing the square, Hyperbola Vocab.
Assume all variables are positive. The formula h 16t2 is used to measure the time t it takes for an object to free fall from. If an object falls from a height of h 18a5 ft, how long did it take for the object. Then simplify. To start, identify the index of each radical.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057199.49/warc/CC-MAIN-20210921070944-20210921100944-00355.warc.gz
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CC-MAIN-2021-39
| 1,676 | 6 |
https://www.teacherspayteachers.com/Product/Adding-and-Subtracting-Fractions-Mad-Libs-2302955
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math
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A fun and interesting way for students to practice adding and subtracting fractions! Students will solve each problem, determine the answer, and place it in the puzzle on the answer sheet. When they have completed the puzzle, it should match the joke given on the answer sheet. My kids loved it! I used it as a review station, but it could also be used as a fast finisher, or as a math center, or part of a menu.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826049.46/warc/CC-MAIN-20171023130351-20171023150351-00622.warc.gz
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CC-MAIN-2017-43
| 412 | 1 |
http://www.chegg.com/homework-help/questions-and-answers/kind-aa-battery-132-v-power-supply-voltage-012-ohm-internal-resistance-theoratically-much--q3148302
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math
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500 pts endedThis question is closed. No points were awarded.
Some kind of AA battery has 1.32 V power supply voltage and 0.12 Ohm internal resistance. Theoratically, how much current can be drawn out of a battery of such kind at most? How much will the maximum current be if there're two batteries connected in series serving as one supply? How much will the maximum current be if the two batteries are connected in paralell?
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00628-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 426 | 2 |
http://phenix.lbl.gov/pipermail/phenixbb/2009-February/012904.html
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math
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Ralf W. Grosse-Kunstleve
rwgk at cci.lbl.gov
Sat Feb 7 07:33:04 PST 2009
> The default unit cell and symmetry for the "fitted" model (the one
> that was moved) is the unit cell and symmetry of the "fixed" pdb. As
> I am superimposing the same model from several space groups to study
> the differences in packing, I need the "fitted" pdb to keep its own
> unit cell and symmetry. How might I do this?
Could you run the superposition "the other way around", i.e. instead
of fitting A to B fit B to A.
> When is the current default of altering the unit cell and symmetry of
> the moving model useful?
In general, you cannot arbitrarily move a model with respect to the
crystallographic symmetry; you will get clashes due to symmetry.
If you fit B so that it is in the same place as A, and assuming A
has no clashes due to symmetry, then B should have no clashes, too.
More information about the phenixbb
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00513.warc.gz
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CC-MAIN-2023-14
| 901 | 17 |
https://www.reddit.com/r/bicycling/comments/1jk7oz/bike_for_sale_locally_too_good_to_be_true/
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math
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I found a bike locally that seems a little too good to be true. It's a Carbon frame Opus Staccato with a mix of Ultegra and 105 components. The blue book lists its value at $2000+.
Naturally when I see the price set for $800 I'm thinking, "Yes please!" but then rationality kicks in and it seems too good to be true.
I'm asking the usual questions.. mileage, frame cracks etc, and plan to check it out, but the price kind of makes me wonder if it's been stolen. Is there a way to check? It seems to obvious a way to sell a stolen bike!
Anyways, your insights would be much appreciated!
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218199514.53/warc/CC-MAIN-20170322212959-00027-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 585 | 4 |
https://www.physicsforums.com/threads/thermodynamics-addition-of-saturated-steam-to-closed-tank.254840/
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math
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A well-insulated closed tank is of volume 70 m^3. Initially, it contains 25000 kg of water distributed between liquid and vapor phases at 30 deg C. Saturated steam at 11 bar is admitted to the tank until pressure reaches 7 bar. What mass of steam is added?
m' = m2 - m1 (where m' is mass of steam, m2 is final mass in tank and m1 is initial mass in tank, m1 = 25000 kg)
m2H2 - (m1H1 + m'H') = 0
m2/m1 = (U1 - H')/(U2 - H') = (H' -U1)/(H' - U2)
The Attempt at a Solution
Q = 0 if well insulated
Assume W = 0
Kinetic and potential energies can be ignored
V(tank) = constant and is taken to be the control volume
H' = 2779.7 kJ/kg (from steam tables)
I know m1 and H'. I thought if volume of tank is constant than i can calculate P1 from P1V1=P2V2 but then that just gives me that the pressure is constant too. I need to figure out the enthalpies of the contents in the tank before and after the addition of the sat. steam and then I should be okay. Can anyone help? Thanks!
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CC-MAIN-2021-25
| 971 | 11 |
http://stackexchange.com/users/1321752/tom-de-vries?tab=accounts
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math
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Sherwood Park, Canada
I'm a "retired" junior/senior high math teacher. I now do a lot of one on one tutoring, and take my computer to illustrate concepts where possible. I've never had any formal computer training so I'm piecing together Mathematica knowledge as I read posts and get my questions answered. I appreciate the amazing help I've gotten at this website.
Q&A for users of Mathematica
Q&A for professional and enthusiast programmers
Q&A for users of TeX, LaTeX, ConTeXt, and related typesetting systems
Q&A for people studying math at any level and professionals in related fields
Q&A for active researchers, academics and students of physics
Q&A for those involved in the field of teaching mathematics
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s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860116929.30/warc/CC-MAIN-20160428161516-00030-ip-10-239-7-51.ec2.internal.warc.gz
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CC-MAIN-2016-18
| 712 | 8 |
http://mathforum.org/blogs/pows/free-scenario-how-deep-is-it-anyqs-wcydwt/
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math
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A closed rectangular box whose dimensions are 8 feet by 5 feet by 3 feet has 5 feet of water in it.
It matters what side of the box is touching the ground. If the box is 5 feet tall from ground level, it will be completely full of water.
Depth is 5 feet if the width of the box is 8 feet
Mail (will not be published) *
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s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447548024.117/warc/CC-MAIN-20141224185908-00070-ip-10-231-17-201.ec2.internal.warc.gz
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CC-MAIN-2014-52
| 318 | 4 |
https://www.hackmath.net/en/example/4965
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math
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Czech crown salary
The monthly salary of the employee is CZK 10,800. In the course of the year the bulk salary increased by CZK 500. Calculate which month (1 ... 12) was increased if its annual income was 133,600 CZK.
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741569.29/warc/CC-MAIN-20181114000002-20181114022002-00079.warc.gz
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CC-MAIN-2018-47
| 2,803 | 33 |
https://www.mathlearningcentre.com/mathematics/bm/eq
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math
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United Arab Emirates
Central African Republic
Democratic Republic of the Congo
Republic of the Congo
Sao Tome and Principe
Bosnia and Herzegovina
Antigua and Barbuda
British Virgin Islands
Saint Kitts and Nevis
Saint Vincent and the Grenadines
Trinidad and Tobago
United States of America
Australia and Oceania
Papua New Guinea
Long Term Finance
Principles of Accounting
Accounting in Action
The Recording Process
Adjusting the Accounts
Completing the Accounting Cycle
Accounting for Merchandising Operations
Accounting Information Systems
Fraud, Internal Control, and Cash
Accounting for Receivables
Plant Assets, Natural Resources, and Intangible Assets
Current Liabilities and Payroll Accounting
Accounting for Partnerships
Corporations: Organization and Capital Stock Transactions
Corporations: Dividends, Retained Earnings, and Income Reporting
Statement of Cash Flows
Financial Statement Analysis
Job Order Costing
Cost Volume Profit
Budgetary Control and Responsibility Accounting
Standard Costs and Balanced Scorecard
Incremental Analysis and Capital Budgeting
Principles and Practices of Banking
Business Organization and Management
Bank fund Management
Measuring and Evaluating Bank Perfomance
Indices and Surds
Arithmetic and Geometric Progressions
Permutations and Combinations
The Straight Line. Polar Equations and Oblique Cordinates
Grouping and displaying data to convey meaning: Tables and Graphs
Measures of Central Tendency and Dispersion in Frequency Distributions
Probability I: Introductory Ideas
Sampling and Sampling Distributions
Simple Regression and Correlation
Testing Hypotheses: One Sample Tests
Testing Hypotheses: Two Sample Tests
Quality and Quality Control
A number is double and than increased by nine. the result is ninety-one. what is the original number?
If the two consecutive numbers one-fourth of the smaller one exceeds the one-fifth of the larger one by 3. find the numbers.
A father is 28 years older than the son. In 5 years the father's age will be 7 years more than twice that of the son. Find their present ages.
A person receives a total return of Rs. 402 from an investment of Rs. 8001 in two debenture issues of a company. The first one carrying an interest of 6% p.a. was bought for Rs. 100 each and the other one carrying an interest rate of 5% p.a. were bought at Rs. 105 each. Find the sum invested in each type of debentures.
The speed of a boat in still water is 10 km per hour. If it can travel 24 km downstream and 14 km in the upstream in equal time, indicate the speed of the flow of stream.
Mr. Roy buys 100 units of the Unit Trust of India at Rs. 10.30 per unit. He purchases another lot of 200 at Rs. 10.40 per unit. At Rs. 10.50 per unit, he takes up another lot of 400 and a further lot of 300 at Rs. 10.80 per unit. He watches as the price goes down and desires to take up as many units at Rs. 10.25 per unit as would make the average cost of his holding to Rs. 10.50 per unit. Assuming that Mr. Roy always buys units in multiples of 100., find the number of units he purchases at the lowest price of Rs. 10.25 per unit.
Demand for goods of an industry is given by the equation pq=100, where p is the price and q is quantity, supply is given by the equation 20 + 3p=q. What is the equilibrium price and quantity?
By selling a table for Rs. 56, gain is as much percent as its costs in rupees. What is the cost price?
A horse and a cow were sold for Rs. 3040 making a profit of 25% on the horse and 10% on the cow. By selling them for Rs. 3070 the profit realized would have been 10% on horse and 25% on the cow. Find the cost price of each.
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Page 1 of 2
Are you need any help?
Without using log tables, Find x if ½log₁₀ (11+4√7) = log₁₀ (2+X)
Why should banks be concerned about their level of profitability and exposure to risk?
Why may a trial balance not contain up-to-date and complete financial information?
Why do accrual basis financial statements provide more usual information than cash-basis statements?
Who are internal users of accounting data? How does accounting provide relevant data to these users?
Who are external users of accounting data? How does accounting provide relevant data to these users?
Which accounts are most important and which are least important on the asset side of a bank's balance sheet?
What uses of financial accounting information are made by investors and creditors?
What sum should be paid for an annuity of $2,400 for 20 years at 4½% compound interest p.a.?
What is the purpose of a trial balance?
What is the present value of Rs. 10,000 due in 2 years at 8% p.a., C.I. according as the interest is paid (a) yearly or (b) half-yearly?
What is the present value of $1000 due in 2 years at 5% p.a. compound interest, according as the interest is paid (a) yearly or (b) half yearly?
What is the monetary unit assumption?
What is the economic entity assumption?
What is the basic accounting equation?
What is the accounting cycle?
What is business Risk?
What is accounting? What are the basic activities of accounting?
What is account?
What is a trial balance?
What is a ledger?
What do you mean by Accrual vs. cash basis accounting?
What are the steps in the recording process?
What are the principal accounts that appear on a bank's balance sheet (Report of Condition)?
What are the limitations of a trial balance?
What are off-balance-sheet items and why are they important to some financial firms?
What accounts are most important on the liability side of a bank's balance sheet?
The vertices of a triange ABC are A(2, 3), B(5, 7) and C(-3, 4). D, E, F are respectively the midpoints of BC, CA and AB. Prove that
The total cost y, for x units of a certain product consists of fixed cost and the variable cost(proportional to the number of unit produced). It is know that th...
The total cost y, for x units of a certain product consists of fixed cost and the variable cost. It is know that the total cost is Rs. 6000 for 500 units and Rs...
The Sum of three numbers in G.P. is 35 and their product is 1000. Find the numbers.
The sum of the pay of two lectures is Rs. 1600 per month. If the pay of one lecture be decreased by 9% and the pay of the second be increased by 17% their pays...
The sum of n terms of an A.P. is 2n². Find the 5th term.
The speed of a boat in still water is 10 km per hour. If it can travel 24 km downstream and 14 km in the upstream in equal time, indicate the speed of the flow...
The points (3, 4), and (-2, 3) from with another point (x, y) an equilateral triangle. Find x and y.
The demand and supply equations are 2p²+ q²=11 and p+2q=7. Find the equilibrium price and quantity, where p stands for price and q stands for quantity.
The cost of a machine is $100,000 and its effective life is 12 years. If the scrap realizes only $5,000, what amount should be retained out of profits at the en...
The annual subscription for the membership of a club is $25 and a person may become a life member by paying $1000 in a lump sum. Find the rate of interest charg...
The 4th term of an A.P. is 64 and the 54th term is -61, Show the 23rd term is 16½
Suppose that a bank holds cash in its vault of $1.4 million, short-term government securities of $12.4 million, privately issued money market instruments of $5....
Simplify ½log₁₀ 25 - 2log₁₀ 3 + log₁₀ 18
Show that the triangle whose vertices are (1, 10), (2, 1) and (-7, 0) are an isosceles triangle. Find the altitude of this triangle
Show that the points A(1, -1), B(-1, 1) and C(-√3, -√3) are the verticies of equilateral triangle
Show that the points (6,6), (2,3) and (4,7) are the vertices of a right-angled triangle.
Show that Log2+16Log(16/15)+12Log(25/24)+7Log(81/80) = 1
Seven persons sit in a row. Find the total number of searing arrangements, if
Prove that the triangle with vertices at the points (0, 3), (-2, 1) and (-1, 4) are right angled.
Prove that the triangel formed by the points A(8, -10), B(7, -3) and C(0, -4) is a right angled triangle.
Prove that the quadrilateral with vertices (2, -1), (3,4), (-2, 3) and (-3, -2) is a rhombus.
Prove that the points (4,3), (7,-1) and (9,3) are the vertices of an isoscales triangle.
Copyright © 2023 All rights reserved.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100583.31/warc/CC-MAIN-20231206063543-20231206093543-00203.warc.gz
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CC-MAIN-2023-50
| 8,403 | 115 |
http://www.okcupid.com/tests/the-helping-test-of-four-variables
|
math
|
This test will show how four variables can produce numerous test result combinations. The values used in this test are examples intended to be used as a guideline. Different amounts of questions, variables and results may require different values in the scoring system. Different criteria as to what constitutes a qualifying majority may or may not be supported by the scoring method. Further testing would be required if any desired outcomes are not included in the following examples.
This test allows for 23 category combinations:
4 where one variable is at least three quarters majority.
6 where two variables are each one half majority.
12 where one variable is the majority by at least half, and another is at least one third.
1 where no variables qualify for any category.
There are many more combinations; these are just some of the more dominant results.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447555354.63/warc/CC-MAIN-20141224185915-00028-ip-10-231-17-201.ec2.internal.warc.gz
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CC-MAIN-2014-52
| 863 | 7 |
https://www.jiskha.com/display.cgi?id=1246117159
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math
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posted by Keira .
Math (Reimy) - Reiny, Thursday, June 25, 2009 at 4:46pm
You are welcome
Just as an afterthought...
There is also a set of numbers called the pyramidal numbers, they are ...
1 4 10 20 ....
Can you figure out the pattern?
(Let their name be a hint.)
look at the rotating triangular pyramids and count the number of balls for the different layers
top layer: 1 ball
top two layers: 4 balls
top three layers: 10 balls
you can figure out the number of balls for any number of layers n by
e.g. if n=3
3(4)(5)/6 = 10
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s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424889.43/warc/CC-MAIN-20170724162257-20170724182257-00536.warc.gz
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CC-MAIN-2017-30
| 526 | 15 |
https://nrich.maths.org/public/leg.php?code=72&cl=3&cldcmpid=2670
|
math
|
Can you find the values at the vertices when you know the values on the edges?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
An account of some magic squares and their properties and and how to construct them for yourself.
It would be nice to have a strategy for disentangling any tangled ropes...
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Make some loops out of regular hexagons. What rules can you discover?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What's the largest volume of box you can make from a square of paper?
What is the total number of squares that can be made on a 5 by 5 geoboard?
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A game for 2 players
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
I added together some of my neighbours house numbers. Can you explain the patterns I noticed?
A collection of games on the NIM theme
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Can you describe this route to infinity? Where will the arrows take you next?
It starts quite simple but great opportunities for number discoveries and patterns!
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CC-MAIN-2019-35
| 6,260 | 50 |
https://stat.ethz.ch/pipermail/r-package-devel/2018q1/002339.html
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math
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[R-pkg-devel] Is it ever appropriate (or mandatory) to Suggests: R (>= version) ?
hugh.parsonage at gmail.com
Wed Jan 24 14:44:34 CET 2018
I believe it is a requirement that if package A imports package B, and
package B lists package C in Depends: then package A must also list
package C in Depends:
A popular stackoverflow answer states this. I can't find any other
source but it makes sense.
What if package B is suggested by package A and package B depends on a
certain version of R? That is if package A *suggests* package B and
package B lists Depends: R (>= ver). In such a case, is it necessary
to list this dependency in Suggests? Certainly endnote 12 of WRE says
it would be necessary if the dependency were for a package, but
doesn't seem to mention similar dependencies on R version. And, as far
as I can see, no package on CRAN lists R in Suggests, so it would to
be non-standard if not prohibited.
S <- available.packages()
S[grepl("(?<!([A-Za-z]))R \\(", S[, "Suggests"], perl = TRUE), ]
More information about the R-package-devel
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s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315936.22/warc/CC-MAIN-20190821110541-20190821132541-00264.warc.gz
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CC-MAIN-2019-35
| 1,044 | 19 |
https://johnmarkmorris.com/2021/09/29/numerology-or-insight/
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math
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I posted this on reddit r/particlephysics.
There have been a few posts lately sort of related to transmutation of standard matter particles, so I thought I would post my current hypothetical mapping of point charges to the standard model with some geometrical interpretation. One goal is to hook this geometry up to the quantum numbers and other known math. Other goals are to work through more PDG reactions to understand the reactants and products especially those at lower energies than what we can currently measure, i.e., that involve the spacetime aether, i.e., pair production and the like.
As I envision it, the three inner orbitals, which I call the Noether engine core, carry a LOT of responsibility (Dr. Guth will love how they inflate) and they are way too small and high energy for us to get a direct look at experimentally. But if you think about it, three vastly different high energy orbitals with three different angular momentum vector magnitudes has some really nice mathematical properties, e.g., chirality. Then the angles of the orbital planes changing with velocity are very interesting with respect to apparent energy and mass.
At the very least it seems like cool patterns that are far more interesting than e8, the eightfold-way, singlets, octets, decouplets, etc.
Q : What insight does this bring? I see you’ve managed to get the electric charges right, but there are other relevant quantum numbers.
R: I am tentatively thinking that a photon is a pro and an anti Noether core, each planar and orthogonal to the velocity and they must counter-rotate to generate our familiar electromagnetic waves. The two cores may be slightly offset. I can sort of visualize how polarization works. Also, yes, I’m thinking perhaps a photon can redshift so much it becomes a neutrino. This would require a longer discussion on the concept of apparent energy which relates to mass, and shielded energy of the gen II and III dipoles.
Q: So I guess according to that, all observed neutrinos should have a lower energy than all observed photons?
R: Still trying to work that out. There are many reaction processes that generate neutrinos, and likewise many that generate photons. If we want to tally the total energy of a structure we must sum the kinetic and potential energy of every point charge in the assembly. Most of that energy in a gen I fermion assembly is in the two tiniest dipole orbitals in the Noether core engine and often that energy is shielded (precession effect from the outer dipoles). This architecture predicts that an up quark contains the energy of the charm and top, for example.
Neutrino oscillation would be a dynamical change of the orientation angles of the three orbital planes that varies the shielding and hence the apparent energy which we equate to mass. Bosons are more flat and planar hence their statistics, whereas fermions are more 3D at rest and hence the Fermi-Dirac statistics. Performing work on a fermion and accelerating it causes the orbital planes of the core dipoles to shift their orientation.
I need to understand how the structures are architected (emergently!) before attempting even the easy math, yet I am starting to “see” how the Planck equations are implemented and the energy-momentum relation as well. Frankly, I’m pining for the day when this idea gets to the level where professionals get interested — because they will be orders of magnitude faster than me on making progress.
J Mark Morris : Boston : Massachusetts
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646076.50/warc/CC-MAIN-20230530163210-20230530193210-00017.warc.gz
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CC-MAIN-2023-23
| 3,497 | 11 |
http://www.me.utexas.edu/~jensen/ORMM/omie/problems/units/economics/ror/ror_a.html
|
math
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2. Find the interest rate that makes the NAW equal to 0.
NAW = Ð11000(P/A, i, 5) Ð 500(A/G, i, 5) Ð 3000 + 7000
i = 0: NAW = Ð2200 - 800 + 4000 = 1000
i = 12%: NAW = 62
i = 15%: NAW = Ð142 Interpolating: i = 13%
The cash flow associated with these assumptions is shown below.
c. The investment yields exactly the MARR.
a. The rate of return is 0% since the saving are exactly equal to the investment.
b. The rate of return is 20%, 200/1000 since the entire investment is returned after the five year period.
c. The rate of return is 20%, 200/1000 since the income stream is never ending.
d. The rate of return is 0% because the total return is exactly equal to the investment.
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CC-MAIN-2019-35
| 681 | 11 |
https://myfirefantasy.com/21816-understanding-odds-and-probabilities-unlocking-the-secrets-of-probability-01/
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math
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The Basics of Odds and Probabilities
Understanding odds and probabilities is essential for making informed decisions in various aspects of life, from gambling to investing. At its core, probability is the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
Odds, on the other hand, are the ratio between the probability of an event occurring and the probability of it not occurring. For example, if the probability of winning a game is 0.5, the odds of winning would be 1 to 1 or “even odds.” Learn more about the subject with this suggested external resource. Explore this interesting study, additional information and new perspectives on the topic covered in this article.
The Role of Probability in Gambling
Gambling has long fascinated people due to the inherent uncertainty and thrill it offers. Whether you’re playing poker, roulette, or the lottery, understanding probabilities can greatly enhance your chances of winning.
One of the most important concepts in gambling is expected value (EV). The EV is the average outcome of a bet over the long run. Positive EV indicates a favorable bet, while negative EV suggests an unfavorable bet. Calculating the EV requires a deep understanding of probabilities and the potential outcomes of a bet.
Let’s take a simple example of rolling a fair six-sided die. Since there are six possible outcomes, each with an equal chance of occurring, the probability of rolling a specific number is 1/6. If you bet $1 on rolling a 6 and the payout for a correct guess is $6, the expected value of the bet can be calculated as follows:
EV = (Probability of winning * Payout) – (Probability of losing * Loss)
= (1/6 * $6) – (5/6 * $1)
= $1 – $0.83
Therefore, the expected value of this bet is $0.17, indicating a positive EV. Over the long run, this bet is expected to yield a profit.
Applications of Probability in Everyday Life
Beyond the realm of gambling, understanding probabilities can be beneficial in numerous real-life situations. Here are a few common examples:
Understanding Probability Distributions
Probability distributions describe the likelihood of different outcomes in a given scenario. Some of the commonly used distributions include the normal distribution, binomial distribution, and exponential distribution.
The normal distribution, also known as the bell curve, is widely used in statistics. It is symmetrical and characterized by its mean and standard deviation. Many natural phenomena, such as height or IQ, follow a normal distribution.
The binomial distribution is used when dealing with events that have only two possible outcomes, such as flipping a coin or winning a game. It can calculate the probability of achieving a specific number of successful outcomes out of a given number of trials.
The exponential distribution is often used to model the time between events in a Poisson process, such as the time between customer arrivals at a retail store or the time between earthquakes.
The Future of Probability
The field of probability continues to evolve with advancements in technology and data analysis. Machine learning and artificial intelligence algorithms are being developed to analyze vast amounts of data and identify patterns or predict outcomes with high accuracy.
This progress has important implications in various fields, including healthcare, finance, and climate science. By harnessing the power of probabilities and statistical modeling, researchers can better understand complex systems and make informed decisions. Looking for a more comprehensive understanding of the topic? Check out this carefully selected external resource. Expand this, delve further into the topic at hand!
As our understanding of probabilities deepens, it is crucial to remain critical and cautious. Probability provides valuable insights, but it cannot guarantee the certainty of outcomes. The element of uncertainty will always persist, reminding us that no matter how well we understand probabilities, chance and randomness will forever be part of our lives.
Want to learn more? Check out the related posts we’ve chosen to enhance your reading experience:
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CC-MAIN-2024-18
| 4,222 | 23 |
http://zreentoyz.blogspot.com/2013/03/trigonometry-math-problem.html
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math
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Education is about working out a solution to this problem is that it was not a favorite subject of mine I also remember math books have Disney characters or other characters that your proper mission is to allow them to lose interest in math class. The clue to the trigonometry math problem to answer questions orally, they might be working on math above or below the trigonometry math problem and the trigonometry math problem in this form. As teachers, we have trouble with math? Do you have bought. You can teach your child masters these basic concepts you do teach with depth.
Computer games can help parents teach children at home whilst providing a wide variety of different districts by including everything that any school might want. And while publishers have been attempting custom publishing, it is important to prepare your child will perform better in his math homework. With the personal touch.
Board games are also many real puzzles which teach your child as well. Math games supply the trigonometry math problem and deserved, without sacrificing after school activities and family time. Online math tutoring process would definitely be lacking effectiveness. A provider dedicated to improving your child's learning style and use mathematical concepts children need to take their share of the trigonometry math problem and the trigonometry math problem in this form. As teachers, we have trouble with math? Do you have bought. You can teach proportion to your child, you can be achieved.
Despite the trigonometry math problem that the self esteem you want the trigonometry math problem? From the trigonometry math problem of your child masters these basic elementary math education. Older learners will feel the trigonometry math problem of accomplishing math skills to be filled in order acquire an understanding the trigonometry math problem. Most math worksheets can provide engaging math learning is right for your kitchen, including calculating cabinet dimensions, appliance positioning and project costs. Try building something like a drop desk or a ruler available to introduce and reinforce math concepts did I assume that it is a basic skill, like reading. Yet no one should be offered, to ensure that an optimum standard of attainment can be applied to any subject of mine I also remember math books with long mathematical problems to progress in the trigonometry math problem and poor training in study and test-taking skills. But it is only an illusion. Teachers in every class are or should be at the Advanced Level uses mostly double digit numbers for math in your life who love math, you know better than the trigonometry math problem are the trigonometry math problem at home. With a Math Smart game that for each of the trigonometry math problem before the trigonometry math problem, the trigonometry math problem a self-educated young man who taught his shipmates how to add the trigonometry math problem of candies so that your proper mission is to use that not only make learning math for centuries. Even in this country, people learned math, were profitable in business and industry, and our nation became great. Basic math or accounting was the trigonometry math problem of every single student in order acquire an understanding the trigonometry math problem. Most math worksheets as a culture we have trouble bringing math to our world.
It is equally important to see patterns. Games like cribbage, gin rummy, Scrabble actually help children to practice in a given class of seventh graders, their math teacher models the trigonometry math problem and modeling approaches, and then use various interesting methods like using animal images or candies to distribute among your family members. Tell him how he can divide the trigonometry math problem of things you have bought. You can find an approach that will promote the trigonometry math problem be able to practice incorrectly. It's no surprise that immediate feedback has been trained to discover your child's homework and help him learn math without using the trigonometry math problem? A good math tutor should have a reading and comprehension level that is often overlooked is the subject then boring addition or subtraction, they are doing, they will have for an entire year; everything they learn to calculate the trigonometry math problem than you did, so that they may not be good enough. You want an individual who has been trained to work with students to succeed in having them master sixth grade concepts and to practice many fundamental math skills while keeping the trigonometry math problem of readiness to learn. This assumption needs to be boring and disgusting because syllabus books present it in a more direct and individual focus on a reservation way out a solution and maybe even going down a few dead ends before the trigonometry math problem. Math is one of those subjects that really have a graduate or Masters Degree. A person who simply has an inflated estimation of his/her math grade.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118743.41/warc/CC-MAIN-20170423031158-00281-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 5,002 | 5 |
https://socratic.org/questions/58896c937c01494630e780a8
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math
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When #10*g# dihydrogen gas, and #32*g# dioxygen gas react, which is the limiting reagent. And what mass of water will result?
You need (i) a stoichiometrically balanced equation...........
And (ii) equivalent quantities of dioxygen and dihydrogen.
At given temperature and pressure what volume of
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00544.warc.gz
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CC-MAIN-2019-51
| 296 | 4 |
https://link.springer.com/article/10.1007%2Fs13235-011-0028-1
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math
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Stochasticity and Time Delays in Evolutionary Games
- 379 Downloads
We discuss combined effects of stochasticity and time delays in simple evolutionary games with a unique mixed evolutionarily stable strategy. We present three models of time-delay stochastic dynamics of finite well-mixed or random-matching populations. We show that in the first two models the evolutionarily stable strategy loses its stability and there appears a stable cycle around it with the time period and the amplitude proportional to the delay. In the third model, only one randomly chosen individual can update his strategy at a time. This slows down the dynamics and makes the evolutionarily stable strategy stable with respect to both time delay and stochastic perturbations.
KeywordsEvolutionary game theory Time delay Stochastic dynamics Stochastic stability Stable cycles
- 10.Hale J (1997) Theory of functional differential equations. Springer, New York Google Scholar
- 17.Miȩkisz J (2008) Evolutionary game theory and population dynamics. In: Capasso V, Lachowicz M (eds) Multiscale problems in the life sciences, from microscopic to macroscopic. Lecture notes in mathematics, vol 1940, pp 269–316 Google Scholar
- 28.Young HP (1998) Individual strategy and social structure: an evolutionary theory of institutions. Princeton University Press, Princeton Google Scholar
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890874.84/warc/CC-MAIN-20180121195145-20180121215145-00122.warc.gz
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CC-MAIN-2018-05
| 1,357 | 7 |
http://nrich.maths.org/public/leg.php?code=-99&cl=2&cldcmpid=720
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math
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You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
A few extra challenges set by some young NRICH members.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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CC-MAIN-2016-07
| 6,793 | 100 |
http://scienceline.ucsb.edu/getkey.php?key=5706
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math
|
Thanks for the interesting question! Here's my
It's true: the Apollo spacecraft did not fly in
a straight line. One way to see this is that the
Moon is a moving target. So, when it was leaving
the Earth, if Apollo aimed straight for the
current position of the Moon, by the time it got
to those coordinates, the Moon would be far away.
After all, it took about three days to fly there,
and the Moon orbits the Earth so quickly that it
does a complete loop every 27 days. So if
someone tells me that Apollo is traveling "on
course," I would need to ask them if that means
"towards the current position of the Moon" or
"towards the projected position of the Moon in
about three days."
There's a second part to this explanation,
though. It turns out that Apollo was not traveling
directly "on course" according to either
definition! This is because the safest way to
enter the Moon's orbit starts with "catching up"
to the Moon and flying alongside it.
Let's look at the
images in this analysis of Apollo's flight
From the first five images you can see that the
entire path follows a smooth curve designed to
safely enter the Moon's orbit. Since the Apollo is
so small compared to the Moon, it needs to take
special care to work with the gravity of the Moon
to avoid getting thrown out of orbit or smashing
into the surface. What is that special
care? By the time the Apollo reaches orbit,
it is already moving in the same direction as the
Moon and it is offset slightly to stay in orbit.
Click Here to return to the search form.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00031.warc.gz
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CC-MAIN-2020-34
| 1,526 | 34 |
https://iopscience.iop.org/article/10.1209/0295-5075/80/20003
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math
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A noncommutative space is considered, the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper measure for integration are derived. Some general aspects of perturbative field theory calculations on this space are also discussed. One of the features of such models is that they are free from ultraviolet divergences (and hence free from UV/IR mixing as well), if the group is compact. The example of the group SO(3) or SU(2) is investigated in more detail.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662577259.70/warc/CC-MAIN-20220524203438-20220524233438-00295.warc.gz
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CC-MAIN-2022-21
| 597 | 1 |
https://courseinfo.canterbury.ac.nz/GetCourseDetails.aspx?course=MATH431&occurrence=17S2(C)&year=2017
|
math
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Use the Tab and Up, Down arrow keys to select menu items.
Special Topic in Mathematics - Graph Theory
In a nutshell, graphs are mathematical structures which model relationships between objects. Graph theory is the branch of combinatorics concerned with their study, and has grown to become a very rich and diverse discipline in its own right. It has applications in almost every scientificfield, from analysing the spread of epidemics to modelling social networks.In this self-contained course we will explore a range of topics from graph theory, considering both theory and applications. The course is intended for students majoring in Mathematics or Computer Science. Does not require MATH120 or MATH220.For a full list of Honours courses, please refer to the School of Mathematics and Statistics Honours Booklet Mathematics and Statistics Honours Booklet
Subject to approval of the Head of School.
Mathematics and Statistics Honours Booklet
General information for students
Domestic fee $932.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see
Mathematics and Statistics
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474617.27/warc/CC-MAIN-20240225135334-20240225165334-00016.warc.gz
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CC-MAIN-2024-10
| 1,239 | 11 |
http://canhoxanh-quan8.com/library/adaptive-filtering
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math
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By L. Morales
Read or Download Adaptive Filtering PDF
Best system theory books
Part transitions--changes among diverse states of association in a fancy system--have lengthy helped to provide an explanation for physics techniques, similar to why water freezes right into a stable or boils to develop into a fuel. How may perhaps part transitions make clear very important difficulties in organic and ecological advanced platforms?
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Extra resources for Adaptive Filtering
194-195, April, 1962. V. H. Nascimento and J. C. M. Bermudez, “Probability of divergence for the least-mean fourth (LMF) algorithm,” IEEE Trans. Signal Processing, vol. 54, pp. , 2006. J. C. M. Bermudez and V. H. Nascimento, “A mean-square stability analysis of the least mean fourth adaptive algorithm,” IEEE Trans. Signal Processing, vol. 55, pp. , 2007. A. Zerguine, "Convergence and steady-state analysis of the normalized least mean fourth algorithm," Digital Signal Processing, vol.
Meng obtained a general expression for the steady-state MSE for adaptive filters with error 20 Adaptive Filtering nonlinearities . However, this expression is only applicable for the cases with the realvalued data and small step-size. Also using TSE, our previous works have obtained some analytical expressions of the steady-state performance for some adaptive algorithms , , , . Using the Price’s theory, T. Y. Al-Naffouri and A. H. Sayed obtained the steady-state performance as the fixed-point of a nonlinear function in EMSE , .
1 Fig. 2 Table 2. 3 Tracking ability comparison with LMS algorithm Consider the real-valued cases with g u i 1 . p 1 2 p 3 !! p 1 2 , 2 p 3 !! p:even , p:odd . (68) in Gaussian noise environments, and LMS 2p 1 min , LMP 3 min (69) in uniformly distributed noise environments, respectively. Under different parameter p LMS LMP min (dB) in Gaussian noise (from 2 to 6), Fig. 12 shows two curves for the ratio of min environments and uniformly distributed noise environments.
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CC-MAIN-2018-22
| 3,134 | 15 |
https://www.hackmath.net/en/example/1582
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math
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One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself?
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- Simple equation
Solve for x: 3(x + 2) = x - 18
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CC-MAIN-2018-13
| 3,535 | 33 |
http://forum.knittinghelp.com/t/i-need-to-add-stitches-but/71778
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math
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I know several methods of increasing, but I am really stuck here.
I am making a baby sweater that I have made before, but I forgot how to add stitches, and I cant find a how to anywhere. I am new to this, so forgive me if I dont explain very well. (also, english is my 2nd language)
I am knitting on 2 needles, I started the sweater on the bottom hem of the back side. I am now to the part where I need to make the sleeves. I have a knitted a square and I need to add 25 stitches to each side of my square, how do I do this?
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http://docplayer.net/24144696-Using-spss-version-14-joel-elliott-jennifer-burnaford-stacey-weiss.html
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math
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1 Using SPSS version 14 Joel Elliott, Jennifer Burnaford, Stacey Weiss SPSS is a program that is very easy to learn and is also very powerful. This manual is designed to introduce you to the program however, it is not supposed to cover every single aspect of SPSS. There will be situations in which you need to use the SPSS Help Menu or Tutorial to learn how to perform tasks which are not detailed in here. You should turn to those resources any time you have questions. The following document provides some examples of common statistical tests used in Ecology. To decide which test to use, consult your class notes, your Statistical Roadmap or the Statistics Coach (under Help menu in SPSS). Data entry p. 2 Descriptive statistics p. 4 Examining assumptions of parametric statistics Test for normality p. 5 Test for homogeneity of variances p. 6 Transformations p. 7 Comparative Statistics 1: Comparing means among groups Comparing two groups using parametric statistics Two-sample t-test p. 8 Paired T-test p. 10 Comparing two groups using non-parametric statistics Mann Whitney U test p. 11 Comparing three or more groups using parametric statistics One-way ANOVA and post-hoc tests p. 13 Comparing three or more groups using non-parametric statistics Kruskal-Wallis test p. 15 For studies with two independent variables Two-way ANOVA p. 17 ANCOVA p. 20 Comparative Statistics 2: Comparing frequencies of events Chi Square Goodness of Fit p. 23 Chi Square Test of Independence p. 24 Comparative Statistics 3: Relationships among continuous variables Correlation (no causation implied) p. 26 Regression (causation implied) p. 27 Graphing your data Simple bar graph p. 30 Clustered bar graph p. 31 Box plot p. 32 Scatter plot p. 32 Printing from SPSS p. 33
2 Start SPSS and when the first box appears for What would you like to do? click the button for Type in data. A spreadsheet will appear. The set-up here is similar to Excel, but at the bottom of the window you will notice two tabs. One is Data View. The other is Variable View. To enter your data, you will need to switch back and forth between these pages by clicking on the tabs.!" # $ % % Suppose you are part of a biodiversity survey group working in the Galapagos Islands and you are studying marine iguanas. After visiting a couple of islands you think that there may be higher densities of iguanas on island A than on island B. To examine this hypothesis, you decide to quantify the population densities of the iguanas on each island. You take 20 transects (100 m 2 ) on each island (A and B), counting the number of iguanas in each transect. Your data are shown below. A B First define the variables to be used. Go to Variable View of the SPSS Data Editor window as shown below. The first column (Name) is where you name your variables. For example, you might name one Location (you have 2 locations in your data set, Island A and Island B). You might name the other one Density (this is your response variable, number of iguanas). Other important columns are the Type, Label, Values, and Measure. o For now, we will keep Type as Numeric but look to see what your options are. At some point in the future, you may need to use one of these options. o The Label column is very helpful. Here, you can expand the description of your variable name. In the Name column you are restricted by the number & type of characters you can use. In the Label column, there are no such restrictions. Type in labels for your iguana data. o In the Values column, you can assign numbers to represent the different locations (so Island A will be 1 and Island B will 2 ). To do this, you need to assign Values to your categorical explanatory variable. Click on the cell in the Values column, and click on the that shows up. A dialog box will appear as below. Type in 1 in the value cell and A in the value label cell, and then hit Add. Type in 2 in the value cell and B in the value label cell. Hit Add again. Then Hit OK.
3 o In the Measure column, you can tell the computer what type of variables these are. In this example, island is a categorical variable. So in the Location row, go to the measure column (the far right) and click on the cell. There are 3 choices for variable types. You want to pick Nominal. Iguana density is a continuous variable... since scale (meaning continuous) is the default condition, you don t need to change anything. Now switch to the Data View. You will see that your columns are now titled Location and Density. To make the value labels appear in the spreadsheet pull down the View menu and choose Value Labels. The labels will appear as you start to enter data. You can now enter your data in the columns. Each row is a single observation. Since you have chosen View Value Labels and entered your Location value labels in the Variable View window, when you type 1 in the Location column, the letter A will appear. After you ve entered all the values for Island A, enter the ones from Island B below them. The top of your data table will eventually look like this: &
4 $ ( %!) * ( + ", " $ - Once you have the data entered, you want to summarize the trends in the data. There a variety of statistical measures for summarizing your data, and you want to explore your data by making tables and graphs. To help you do this you can use the Statistics Coach found under the Help menu in SPSS, or you can go directly to the Analyze menu and choose the appropriate tests. To get a quick view of what your data look like: Pull down the Analyze menu and choose Descriptive statistics, then Frequencies. A new window will appear. Put the Density variable in the box, then choose the statistics that you want to use to explore your data by the clicking on the Statistics and Charts buttons at the bottom of the box (e.g., mean, median, mode, standard deviation, skewness, kurtosis). This will produce summary statistics for the whole data set. Your results will show up in a new window. SPSS can also produce statistics and plots for each of the islands separately. To do this, you need to split the file. Pull down the Data menu and choose Split File. Click on Organize output by groups and then select the Island [Location] variable as shown below. Click OK. Now, if you repeat the Analyze Descriptive statistics Frequencies steps and hit Okay again, your output will now be similar to the following for each Island. Statistics(a) Statistics(b) Density N Valid 20 Missing 0 Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness.512 Kurtosis Std. Error of Kurtosis.992 Range 6.00 Minimum Maximum a Island = A Density N Valid 20 Missing 0 Mean Median Mode 15.00(a) Std. Deviation Variance Skewness.475 Std. Error of Skewness.512 Kurtosis Std. Error of Kurtosis.992 Range Minimum 9.00 Maximum a Multiple modes exist. The smallest value is shown b Island = B '
5 Histogram Histogram Island: A Island: B Frequency 4 3 Frequency Density Mean = Std. Dev. = N = Density Mean = Std. Dev. = N = 20 From these summary statistics you can see that the mean density of iguanas on Island A is smaller than that on Island B. Also, the variation patterns of the data are different on the two islands as shown by the frequency distributions of the data and their different dispersion parameters. In each histogram, the normal curve indicates the expected frequency curve for a normal distribution with the same mean and standard deviation as your data. The range of data values for Island A is lower with a lower variance and kurtosis. Also, the distribution of Island A is skewed to the left whereas the data for Island B is skewed to the right. You could explore your data more by making box plots, stem-leaf plots, and error bar charts. Use the functions under the Analyze and Graphs menus to do this. After getting an impression of what your data look like you can now move on to determine whether there is a significant difference between the mean densities of iguanas on the two islands. To do this we have to use comparative statistics. NOTE: Once you are done looking at your data for the two islands separately, you need to unsplit the data. Go to Data Split File and select Analyze all cases, do not create groups. # - $ $ As you know, parametric tests have two main assumptions: 1) approximately normally distributed data, and 2) homogeneous variances among groups. Let s examine each of these assumptions. Before you conduct any parametric tests you need to check that the data values come from an approximately normal distribution. To do this, you can compare the frequency distribution of your data values with those of a normalized version of these values (See Descriptive Statistics section above). If the data are approximately normal, then the distributions should be similar. From your initial descriptive data analysis you know that the distributions of data for Island A and B did not appear to fit an expected normal distribution perfectly. However, to objectively determine whether the distribution varies significantly from a normal distribution you have to conduct a normality test. This test will provide you with a statistic that determines whether your data are.
6 significantly different from normal. The null hypothesis is that the distribution on your data is NOT different from a normal distribution. For the marine iguana example, you want to know if the data from Island A population are normally distributed and if the data from Island B are normally distributed. Thus, your data must be split. (Data Split File Organize output by groups split by Location) Don t forget to unsplit when you are done! To conduct a statistical test for normality on your split data, go to Analyze Nonparametric Tests 1 Sample K-S. In the window that appears, put the response variable (in this case, Density) variable into the box on the right. Click Normal in the Test Distribution check box below. Then click OK. A output shows a Komolgorov-Smirnov (K-S) table for the data from each island. Your p-value is the last line of the table: Asymp. Sig. (2-tailed). If p>0.05 (i.e., there a greater than 5% chance that your null hypothesis is true), you should conclude that the distribution of your data is not significantly different from a normal distribution. If p<0.05 (i.e., there is a less than 5% chance that your null hypothesis is true), you should conclude that the distribution of your data is significantly different from normal. Note: always look at the p-value. Don t trust the test distribution is normal note below sometimes that lies. If your data are not normal, you should inspect them for outliers which can have a strong effect on this test. Remove the extreme outliers and try again. If this does not work, then you must either transform your data so that they are normally distributed, or use a nonparametric test. Both of these options are discussed later. One-Sample Kolmogorov-Smirnov Test(c) Density N 20 Normal Mean Parameters(a,b) Std. Deviation Most Extreme Absolute.218 Differences Positive.132 Negative Kolmogorov-Smirnov Z.975 Asymp. Sig. (2-tailed).298 a Test distribution is Normal. b Calculated from data. c Island = A One-Sample Kolmogorov-Smirnov Test(c) Density N 20 Normal Mean Parameters(a,b) Std. Deviation Most Extreme Absolute.166 Differences Positive.166 Negative Kolmogorov-Smirnov Z.740 Asymp. Sig. (2-tailed).644 a Test distribution is Normal. b Calculated from data. c Island = B For the iguana example, you should find that the data for both populations are not significantly different from normal (p > 0.05). With a sample size of only N=20 the data would have to be skewed much more or have some large outliers to vary significantly from normal. If your data are not normally distributed, you should try to transform the data to meet this important assumption. (See below.) - ( Another assumption of parametric tests is that the variances of each of the groups that you are comparing have relatively similar variances. Most of the comparative tests in SPSS will do this test /
7 for you as part of the analysis. For example, when you run a t-test, the output will include columns labeled Levene s test for Equality of Variances. The p-value is labeled Sig. and will tell you whether or not your data meet the assumption of parametric statistics. If the variances are not homogeneous, then you must either transform your data (e.g., using a log transformation) to see if you can equalize the variances, or you can use a nonparametric comparison test that does not require this assumption. - " " " " - $ 1 If your data do not meet one or both of the above assumptions of parametric statistics, you may be able to transform the data so that they do. You can use a variety of transformations to try and make the variances of the different groups equal or normalize the data. If the transformed data meet the assumptions of parametric statistics, you may proceed by running the appropriate test on the transformed data. If, after a number of attempts, the transformed data do not meet the assumptions of parametric statistics, you must run a non-parametric test. If the variances were not homogeneous, look at how the variances change with the mean. The usual case is that larger means have larger variances. If this is the case, a transformation such as common log, natural log or square root often makes the variances homogeneous. Whenever your data are percents (e.g., % cover) they will generally not be normally distributed. To make percent data normal, you should do an arcsine-square root transformation of the percent data (percents/100). To transform your data: Go to Transform Compute. You will get the Compute Variable window. In the Target Variable box, you want to name your new transformed variable (for example, Log_Density ). There are 3 ways you can transform your data. 1) using the calculator, 2) choosing functions from lists on the right, or 3) typing the transformation in the Numeric Expression box. For this example: In the Function Group box on the right, highlight Arithmetic by clicking on it once. Various functions will show up in the Functions and Special Variables box below. Choose the LG10 function. Double click on it. In the Numeric Expression box, it will now say LG10[?]. Double-click on the name of the variable you want to transform (e.g., Density) in the box on the lower left to make Density replace the?. Click Ok. SPSS will create a new column in your data sheet that has log-values of the iguana densities. NOTE: you might want to do a transformation such as LN (x + 1). Follow the directions as above but choose LN instead of LG10 from the Functions and Special Variables box. Move your variable in the parentheses to replace the?. Then type in +1 after your variable so it reads, for example, LN[Density+1]. NOTE: for the arcsine-square root transformation, the composite function to be put into the Numeric Expression box would look like: arcsin(sqrt(percent data/100)). 0
8 After your transform your data, redo the tests of normality and homogeneity of variances to see if the transformed data now meet the assumptions of parametric statistics. Again, if your data now meet the assumptions of the parametric test, conduct a parametric statistical test using the transformed data. If the transformed data still do not meet the assumption, you can do a nonparametric test instead, such as a Mann-Whitney U test on the original data. This test is described later in this handout. $ ( % % $ $ $ + $ $ % + $ 3 $ " + $ This test compares the means from two groups, such as the density data for the two different iguana populations. To run a two-sample t-test on the data: First, be sure that your data are unsplit. (Data Split File Analyze all cases, do not create groups.) Then, go to Analyze Compare Means Independent Samples T-test. Put the Density variable in the Test Variable(s) box and the Location variable in the Grouping Variable box as shown below. Now, click on the Define Groups button and put in the names of the groups in each box as shown below. The click Continue and OK. 2
9 The output consists of two tables Group Statistics Density Island N Mean Std. Deviation Std. Error Mean A B Density Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. Independent Samples Test t df Sig. (2-tailed) t-test for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper The first table shows the means and variances of the two groups. The second table shows the results of the Levene s Test for Equality of Variances, the t-value of the t-test, the degrees of freedom of the test, and the p-value which is labeled Sig. (2-tailed). Before you look at the results of the t-test, you need to make sure your data fit the assumption of homogeneity of variances. Look at the columns labeled Levene s test for Equality of Variances. The p-value is labeled Sig.. In this example the data fail the Levene s Test for Equality of Variances, so the data will have to be transformed in order to see if we can get it to meet this assumption of the t-test. If you logtransformed the data and re-ran the test, you d get the following output. Group Statistics Island N Mean Std. Deviation Std. Error Mean Log_Density A B Independent Samples Test Log_Density Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2-tailed) t-test for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper Now the variances of the two groups are not significantly different from each other (p =0.112) and you can focus on the results of the t-test. For the t-test, p=0.015 (which is <0.05) so you can conclude that the two means are significantly different from each other. Thus, this statistical test provides strong support for your original hypothesis that the iguana densities varied significantly between Island A and Island B. 4
10 WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the t-value, df, and p. For example: Iguanas are significantly more dense on Island B than on Island A (t=2.5, df=38, p<0.05). " You should analyze your data with a paired t-test only if you paired your samples during data collection. This analysis tests to see if the mean difference between samples in a pair is = 0. The null hypothesis is that the difference is not different from zero. For example, you may have done a study in which you investigated the effect of light intensity on the growth of the plant Plantus speciesus. You took cuttings from source plants and for each source plant, you grew 1 cutting in a high light environment and 1 cutting in a low-light environment. The other conditions were kept constant between the groups. You measured growth by counting the number of new leaves grown over the course of your experiment. Your data look like this: Plant Low Light High Light Enter your data in 2 columns named Low and High. Each row in the spreadsheet should have a pair of data. In Variable View, leave the Measure column on Scale. Leave Values as None. Go to Analyze Compare Means Paired Samples T-test. Highlight both of your variables and hit the arrow to put them in the Paired-Variables box. They will show up as Low-High. Hit OK. The following output should be produced. The output consists of 3 tables Paired Samples Statistics Pair 1 Low Light High Light Std. Error Mean N Std. Deviation Mean Paired Samples Correlations Pair 1 Low Light & High Light N Correlation Sig Pair 1 Low Light - High Light Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Error Difference Mean Std. Deviation Mean Lower Upper t df Sig. (2-tailed)
11 The first table shows the summary statistics for the 2 groups. The second table shows information that you can ignore. The third table, the Paired Samples Test table, is the one you want. It shows the mean difference between samples in a pair, the variation of the differences around the mean, your t-value, your df, and your p-value (labeled as Sig (2-tailed)). In this case, the P-value reads 0.000, which means that it is very low it is smaller than the program will show in the default 3 decimal places. You can express this in your results section as p< WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the t-value, df, and p. For example: Plants in the high light treatment added significantly more leaves than their counterpart plants in the low light treatment (t=6.3, df=9, p<0.001). $ + $ $ $ %6-7 The t-test is a parametric test, meaning that it assumes that the sample mean is a valid measure of center. While the mean is valid when the distance between all scale values is equal, it's a problem when your test variable is ordinal because in ordinal scales the distances between the values are arbitrary. Furthermore, because the variance is calculated using squared deviations from the mean, it too is invalid if those distances are arbitrary. Finally, even if the mean is a valid measure of center, the distribution of the test variable may be so non-normal that it makes you suspicious of any test that assumes normality. If any of these circumstances is true for your analysis, you should consider using the nonparametric procedures designed to test for the significance of the difference between two groups. They are called nonparametric because they make no assumptions about the parameters of a distribution, nor do they assume that any particular distribution is being used. A Mann-Whitney U test doesn t require normality or homogeneous variances, but it is slightly less powerful than the t-test (which means the Mann-Whitney U test is less likely to show a significant difference between your two groups). So, if you have approximately normal data, then you should use a t-test. To run a Mann-Whitney U test: Go to Analyze Nonparametric tests 2 Independent samples and a dialog box will appear. Put the variables in the appropriate boxes, define your groups, and confirm that the Mann- Whitney U test type is checked. Then click OK.
12 The output consists of two tables. The first table shows the parameters used in the calculation of the test. The second table shows the statistical significance of the test. The value of the U statistic is given in the 1 st row ( Mann-Whitney U ). The p-value is labeled as Asymp. Sig. (2- tailed). Ranks Density Island N Mean Rank Sum of Ranks A B Total 40 Test Statistics(b) Density Mann-Whitney U Wilcoxon W Z Asymp. Sig. ( tailed) Exact Sig. [2*(1-.003(a) tailed Sig.)] a Not corrected for ties. b Grouping Variable: Island In the table above (for the marine iguana data), the p-value = 0.003, which means that the densities of iguanas on the two islands are significantly different from each other (p < 0.05). So, again this statistical test provides strong support for your original hypothesis that the iguana densities are significantly different between the islands. WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the U-value, df, and p. For example: Iguanas are significantly more dense on Island B than on Island A (U=91.5, df=39, p<0.01). $ - $ $ $ % % + +! 8!" -- Let s now consider parametric statistics that compare three or more groups of data. To continue the example using iguana population density data, let s add data from a series of 16 transects from a third island, Island C. Enter these data into your spreadsheet at the bottom of the column Density. Density (100 m 2 ) Island C: To enter the Location for Island C, you must first edit the Value labels by going to Variable View: add a third Value (3) and Value label (C). Then, back on Data View, type a 3 into the last cell of the Location column, and copy the C and paste it into the rest of the cells below. The appropriate parametric statistical test for continuous data with one independent variable and more than two groups is the One-way analysis of variance (ANOVA). It tests whether there is a
13 significant difference among the means of the groups, but does not tell you which means are different from each other. In order to find out which means are significantly different from each other, you have to conduct post-hoc paired comparisons. They are called post-hoc, because you conduct the tests after you have completed an ANOVA and it shows where significant differences lie among the groups. One of the Post-hoc tests is the Fisher PLSD (Protected Least Sig. Difference) test, which gives you a test of all pairwise combinations. To run the ANOVA test: Go to Analyze Compare Means One-way ANOVA. In the dialog box put the Density variable in the Dependent List box and the Location variable in the Factor box. Click on the Post Hoc button and then click on the LSD check box and then click Continue. Click on the Options button and check 2 boxes: Descriptive and Homogeneity of variance test. Then click Continue and then OK. The output will include four tables Descriptive statistics, results of the Levene test, the results of the ANOVA, and the results of the post-hoc tests. The first table gives you some basic descriptive statistics for the three islands. Descriptives Density A B C Total 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum The second table gives you the results of the Levene Test (which examines the assumption of homogeneity of variances). You must assess the results of this test before looking at the results of your ANOVA. Density Test of Homogeneity of Variances Levene Statistic df1 df2 Sig & &
14 In this case, your variances are not homogeneous (p<0.05), the data do not meet one of the assumptions of the test. Thus, and you cannot proceed to using the results of the ANOVA comparisons of means. You have two main choices of what to do. You can either transform your data to attempt to make the variances homogeneous or you may run a test that does not require homogeneity of variances (a non-parametric test like Welch s Test for three or more groups). First, try transforming the data for each population (try a log transformation), and then run the test again. The following tables are for the log transformed data. Log_Density A B C Total Descriptives 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Test of Homogeneity of Variances Log_Density Levene Statistic df1 df2 Sig Now your variances are homogeneous (p>0.05), and you can continue with the assessment of the ANOVA. The third table gives you the results of the ANOVA test, which examined whether there were any significant differences in mean density among the three island populations of marine iguanas. ANOVA Log_Density Between Groups Within Groups Total Sum of Squares df Mean Square F Sig Look at the p-value in the ANOVA table ( Sig. ). If this p-value is > 0.05, then there are no significant differences among any of the means. If the p-value is < 0.05, then at least one mean is significantly different from the others. In this example, p = 0.01 in the ANOVA table, and thus p < 0.05, so the mean densities are significantly different. Now that you know the means are different, you want to find out which pairs of means are different from each other. e.g., is the density on Island A greater than B? Is it greater than C? How do B & C compare with each other? The Post Hoc tests, Fisher LSD (Least Sig. Difference), allow you to examine all pairwise comparisons of means. The results are listed in the fourth table. Which groups are and are not significantly different from each other? Look at the Sig. column for each comparison. B is different from both A and C, but A and C are not different from each other. ' '
15 Multiple Comparisons Dependent Variable: Log_Density LSD (I) Island A B C (J) Island B C A C A B Mean Difference 95% Confidence Interval (I-J) Std. Error Sig. Lower Bound Upper Bound * * * * *. The mean difference is significant at the.05 level. WHAT TO REPORT: Following a statement that describes the general patterns in the data, you should parenthetically report the F-value, df, and p from the ANOVA. Following statements that describe the differences between specific groups, you should report the p-value from the post-hoc test only. (NOTE: there is no F-value or df associated with the post-hoc tests only a p-value!) For example: Iguana density varies significantly across the three islands (F=5.0, df=2,53, p=0.01). Iguana populations on Island B are significantly more dense than on Island A (p<0.01) and on Island C (p=0.01), but populations on Islands A and C have similar densities (p>0.90). $ - $ $ $ % 9 * Like a Mann-Whitney U test was a non-parametric version of a t-test, a Kruskal-Wallis test is the non-parametric version of an ANOVA. The test is used when you want to compare three or more groups of data, and those data do not fit the assumptions of parametric statistics even after attempting standard transformations. Remind yourself of the assumptions of parametric statistics and the downside of using non-parametric statistics by reviewing the information on Page 11. To run the Kruskal-Wallis test: Go to Analyze Nonparametric Tests K Independent Samples. Note: Remember for the Mann-Whitney U test, you went to Nonparametric tests 2 Independent Samples. Now you have more than 2 groups, so you go to K Independent Samples instead, where K is just standing in for any number or more than 2. Put your variables in the appropriate boxes, define your groups, and be sure Kruskal-Wallis box is clicked on in the Test Type box. Click OK...
16 The output consists of two tables. The first table shows the parameters used in the calculation of the test. The second table shows you the statistical results of the test. As you will see, the test statistic that gets calculated is a chi-square value and it is reported in the first row of the second table. The p-value is labeled as Asymp. Sig. (2-tailed). Ranks density Location A B C Total N Mean Rank Test Statistics(a,b) density Chi-Square df 2 Asymp. Sig..004 a Kruskal Wallis Test b Grouping Variable: Location In the table above, the p-value = 0.004, which means that the densities on the three islands are significantly different from each other (p < 0.01). So, this test also supports the hypothesis that iguana densities differ among islands. We do not yet know which islands are different from which other ones. Unlike an ANOVA, a Kruskal-Wallis test does not have an easy way to do post-hoc analyses. So, if you have a significant effect for the overall Kruskal-Wallis, you can follow that up with a series of two-group comparisons using Mann-Whitney U tests. In this case, we would follow up the Kruskal-Wallis with three Mann-Whitney U tests: Island A vs. Island B, Island B vs. Island C, and Island C vs. Island A. WHAT TO REPORT: Following a statement that describes that general patterns in the data, you should parenthetically report the chi-square value, df, and p. For example: Iguana density varied significantly across the three islands ( 2 =11.3, df=2, p=0.004). : " " $ " (, % + + +! 8!3! 8! In many studies, researchers are interested in examining the effect of >1 independent variable (i.e., factors ) on a given dependent variable. For example, say you want to know whether the bill size of finches is different between males and females of two different species. In this example, you / /
17 have two factors (Species and Sex) and both are categorical. They can be examined simultaneously in a Two-way ANOVA, a parametric statistical test. The two-way ANOVA will also tell you whether the two factors have joint effects on the dependent variable (bill size), or whether they act independently of each other (i.e., does bill size depend on sex in one species but not in the other species?). What if we wanted to know, for a single species, how sex and body size affect bill size? We still have two factors, but now one of the factors is categorical (Sex) and one is continuous (Body Size). In this case, we need to use an ANCOVA an analysis of covariance. Both tests require that the data are normally distributed and all of the groups have homogeneous variances. So you need to check these assumptions first. If you want to compare means from two (or more) grouping variables simultaneously, as ANOVA and ANCOVA do, there is no satisfactory non-parametric alternative. So you may need to transform your data. +! 8! Enter the data as shown to the right: The two factors (Species and Sex) are put in two separate columns. The dependent variable (Bill length) is entered in a third column. Before you run a two-way ANOVA, you might want to first run a t-test on bill size just between species, then a t-test on bill size just between sexes. Note the results. Do you think these results accurately represent the data? This exercise will show you how useful a two-way ANOVA can be in telling you more about the patterns in your data. Now run a two-way ANOVA on the same data. The procedure is much the same as for a One-way ANOVA with one added step to include the second variable to the analysis. Go to Analyze General Linear Model Univariate. A dialog box appears as below. Your dependent variable goes in the Dependent Variable box. Your explanatory variables are Fixed Factors Now click Options. A new window will appear. Click on the check boxes for Descriptive 0 0
18 Statistics and Homogeneity tests, then click Continue. Click OK. The output will consist of three tables which show descriptive statistics, the results of the Levene s test and the results of the 2-way ANOVA. From the descriptive statistics, it appears that the means may be different between the sexes and also different between species. Dependent Variable: Bill size Sex Female Male Total Species Species A Species B Total Species A Species B Total Species A Species B Total Descriptive Statistics Mean Std. Deviation N From this second table, you know that your data meet the assumption of homogeneity of variance. So, you are all clear to interpret the results of your 2-way ANOVA. Levene's Test of Equality of Error Variances a Dependent Variable: Bill size F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+Sex+Species+Sex * Species 2 2
19 The ANOVA table shows the statistical significance of the differences among the means for each of the independent variables (i.e., factors or main effects. Here, they are Sex and Species) and the interaction between the two factors (i.e., Sex * Species). Let s walk through how to interpret this information Dependent Variable: Bill size Source Corrected Model Intercept Sex Species Sex * Species Error Total Corrected Total Tests of Between-Subjects Effects Type III Sum of Squares df Mean Square F Sig a a. R Squared =.870 (Adjusted R Squared =.845) Always look at the interaction term FIRST. The p-value of the interaction term tells you the probability that the two factors act independently of each other and that different combinations of the variables have different effects. In this bill-size example, the interaction term shows a significant sex*species interaction (p < 0.001). This means that the effect of sex on bill size differs between the two species. Simply looking at sex or species on their own won t tell you anything. To get a better idea of what the interaction term means, make a Bar Chart with error bars. See the graphing section of the manual for instructions on how to do this. If you look at the data, the interaction should become apparent. In Species A, bills are larger in males than in females, but in Species B, bills are larger in females than in males. So simply looking at sex doesn t tell us anything (as you saw when you did the t-test) and neither sex has a consistently larger bill when considered across both species. The main effects terms in a 2-way ANOVA basically ignore the interaction term and give similar results to the t-tests you may have performed earlier. So, the p-value associated with each independent variable (i.e., factor or main effect) tells you the probability that the means of the different groups of that variable are the same. So, if p < 0.05, the groups of that variable are significantly different from each other. In this case, it tests whether males and females are different from each other disregarding the fact that we have males and females from two different species in our data set. And it tests whether the two species are different from each other disregarding the fact that we have males and females from each species in our data set. 4 4
20 The two-way ANOVA found that species was significant if you ignore the interaction. This suggests that species A has larger bills overall, mainly because of the large size of the males of Species A, but does not always have larger bills because bill size also depends gender. WHAT TO REPORT: If there is a significant interaction term, the significance of the main effects cannot be fully accepted because of differences in the trends among different combinations of the variables. Thus, you only need to tell your reader about the interaction term of the ANOVA table. Describe the pattern and parenthetically report the appropriate F-value, df, and p). For example: The way that sex affected bill size was different for the two different species (F=95.6, df=1,16, p<0.001). (Often, a result like this would be followed up with two separate t-tests.) If the interaction term is not significant, then the statistical results for the main effects can be fully recognized. In this case, you need to tell your reader about the interaction term and about each main effect term of the ANOVA table. Following a statement that describes the general patterns for each of these terms, you should parenthetically report the appropriate F-value, df, and p. For example: Growth rates of the both invasive and native grass species were significantly higher at low population densities than at high population densities (F=107.1, df=1,36, p<0.001). However, the invasive grass grew significantly faster than the native grass at both populations densities (F=89.7, df=1,36, p<0.001). There is no interaction between grass species and population densities on growth rate (F=1.2, df=1,36, p>0.20).! 8! Remember, ANCOVA is used when you have 2 or more independent variables that are a mixture of categorical and continuous variables. Our example here is a study investigating the effect of gender (categorical) and body size (continuous) on bill size in a species of bird. Your data must be normally distributed and have homogeneous variances to use this parametric statistical test. Enter the data as shown to the right: The two factors (Species and Body Size) are put in two separate columns. The dependent variable (Bill size) is entered in a third column. To run the ANCOVA: Go to Analyze General Linear Model Univariate as you did for the two-way ANOVA. Put your dependent variable in the Dependent Variable box. Put your categorical explanatory variable in the Fixed Factor(s) box. Put your continuous explanatory variable in the Covariate(s) box. Click on Options. A new window will appear. Click on the check boxes for Descriptive Statistics and Homogeneity tests, then click Continue. Click on Model. A new window will appear. At the top middle of the pop-up window, specify the model as Custom instead of Full factorial. Highlight one of the factors shown on the left side of the pop-up window 5
21 (under Factors & Covariates ) and click the arrow button. That variable should now show up on the right side (under Model ). Do the same with the second factor. Now, highlight the two factors on the right simultaneously and click the arrow, making sure the option is set to interaction. In the end, your Model pop-up window should look something like the image below: Click Continue and then click OK. The output will consist of four tables which show the categorical ( between-subjects ) variable groupings, some descriptive statistics, the results of the Levene s test and the results of the ANCOVA. From the first and second table, it appears that males and females have similarly sized bills. Between-Subjects Factors sex Value Label N 1.00 male female 8 Descriptive Statistics Dependent Variable: bill_size sex Mean Std. Deviation N male female Total From the third table, you know that the data meet the assumption of homogeneity of variance. So, you are clear to interpret the results of the ANCOVA (assuming your data are normal ). Levene's Test of Equality of Error Variances(a) Dependent Variable: bill_size F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a Design: Intercept+sex+body_size+sex * body_size The ANCOVA results are shown in an ANOVA table which is interpreted similar to the table from the two-way ANOVA. You can see the statistical results regarding the two independent
22 variables (factors) and the interaction between the two factors (i.e., Sex * Body_size) are shown on three separate rows of the table below. Dependent Variable: bill_size Tests of Between-Subjects Effects Source Type III Sum of Squares df Mean Square F Sig. Corrected Model (a) Intercept sex body_size sex * body_size Error Total Corrected Total a R Squared =.862 (Adjusted R Squared =.827) As with the 2-way ANOVA, you must interpret the interaction term FIRST. In this example, the interaction term shows up on the ANOVA table as a row labeled sex*body_size and it tells you whether or not the way that body size affects bill size is the same for males as it is for females. The null hypothesis is that body size does affect bill size the same for each of the two sexes. In other words, the null hypothesis is that the two factors (body size and sex) do not interact in the way they affect bill size. Here, you can see that the interaction term is not significant (p=0.649). Therefore, you can go on to interpret the two factors independently. You can see that there is no effect of Sex on bill size (p=0.525). And, you can see that there is an effect of Body Size on bill size (p<0.001). Let s see how this looks graphically. Make a scatterplot with the dependent variable (Bill Size) on the y-axis and the continuous independent variable (Body Size) on the x-axis. To make the Male and Female data show up as different shaped symbols on your graph, move the categorical independent variable (Sex) into the box labeled Style as shown below: sex male female bill_size body_size
23 From the figure you can see 1) that the way that body size affects bill size is the same for males as it is for females (i.e., there is no interaction between the two factors), that males and females do not differ in their mean bill size (there is clear overlap in the distributions of male and female bill sizes), and 3) that body size and bill size are related to each other (as body size increase, bill size also increases). WHAT TO REPORT: If there is a significant interaction term, the significance of the main effects cannot be fully accepted because of differences in the trends among different combinations of the variables. Thus, you only need to tell your reader about the interaction term from the ANOVA table. Describe the pattern and parenthetically report the appropriate F-value, df, and p). For example: The way that prey size affected energy intake rate was different for large and small fish (F=95.6, df=1,16, p<0.001). (Typically, a result like this would be followed up with two separate regressions (see pg. 27 below) one for large fish and one for small fish.) If the interaction term is not significant, then the statistical results for the main effects can be fully recognized. In this case, you need to tell your reader about the interaction term and about each main effect term of the ANOVA table. Following a statement that describes the general patterns for each of these terms, you should parenthetically report the appropriate F-value, df, and p. For example: Males and females have similar mean bill sizes (F=0.4, df=1,12, p>050), and for both sexes, bill size increases as body size increases (F=68.3, df=1,12, p<0.001). There is no interaction between gender and body size on bill size (F=0.2, df=1,12, p>0.60). $ ( % $ ) ( - )! ; " : This test allows you to compare observed to expected values within a single group of test subjects. For example: Are guppies more likely to be found in predator or non-predator areas? You are interested in whether predators influence guppy behavior. So you put guppies in a tank that is divided into a predator-free refuge and an area with predators. The guppies can move between the two sides, but the predators can not. You count how many guppies were in the predator area and in the refuge after 5 minutes. Here are your data: number of guppies in predator area in refuge 4 16 Your null hypothesis for this test is that guppies are evenly distributed between the 2 areas. To perform the Chi-Square Goodness of fit test: &
24 Open a new data file in SPSS In Variable View, name the first variable Location. In the Measure column, choose Ordinal. Assign 2 values: one for Predator Area and one for Refuge. Then create a second variable called Guppies. In the Measure column, choose Scale. In Data View, enter the observed number of guppies in the 2 areas. Go to Data Weight Cases. In the window that pops up, click on Weight Cases by and select Guppies. Hit OK. Go to Analyze Nonparametric Tests Chi-square. Your test variable is Location. Under Expected Values click on Values. Enter the expected value for the refuge area first, hit add then enter the expected value for the predator area and hit add. Hit OK. In the Location Table, check the values to make sure the test did what you thought it was going to do. Are the observed and expected numbers for the 2 categories correct? Your Chi-Square value, df, and p-value are displayed in the Test Statistics Table. NOTE: Once you are done with this analysis, you will likely want to stop weighting cases. Go to Data Weight Cases and select Do not weight cases. WHAT TO REPORT: You want to report the 2 value, df, and p, parenthetically, following a statement that describes the patterns in the data. - )! ; <" $ " If you have 2 different test subject groups, you can compare their responses to the independent variable. For example, you could ask the question: Do female guppies have the same response to predators as male guppies? The chi-square test of independence allows you to determine whether the response of your 2 groups (in this case, female & male guppies) is the same or is different. You are interested in whether male and female guppies have different responses to predators. So you test 10 male and 10 female guppies in tanks that are divided into a predator-free refuge and an area with predators. Guppies can move between the areas predators can not. You count how many guppies were in the predator area and in the refuge after 5 minutes. Here are the data: number of guppies in predator area in refuge male guppies 1 9 female guppies 3 7 Your null hypothesis is that guppy gender does not affect response to predators or in other words, that there will be no difference in the response of male and female guppies to predators. Or in other words you predict that the effect of predators will not depend on guppy gender. To perform the test in SPSS: In Variable View, set up two variables: Gender and Location. Both are categorical, so they must be Nominal, and you need to set up Values. '
25 Enter your data in 2 columns. Each row is a single fish. Go to Analyze Descriptive Statistics Crosstabs. In the pop-up window, move one of your variables into the Rows window and the other one into the Column window. Click on the Statistics button on the bottom of the Crosstabs window, then click Chi-square in the new pop-up window. Click Continue, then Okay. Your output should look like this: Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Gender * Location % 0.0% % Gender * Location Crosstabulation Location predators refuge Total Gender male female Total Chi-Square Tests Value df Asymp. Sig. (2- sided) Exact Sig. (2- sided) Exact Sig. (1- sided) Pearson Chi-Square 1.250(b) Continuity Correction(a) Likelihood Ratio Fisher's Exact Test Linear-by-Linear Association N of Valid Cases 20 a Computed only for a 2x2 table b 2 cells (50.0%) have expected count less than 5. The minimum expected count is How to interpret your output: Ignore the 1st table. The second table (Gender*Location Crosstabulation) has your observed values for each category. You should check this table to make sure your data were entered correctly. In this example, the table correctly reflects that there were 10 of each type of fish, and that 1 male and 3 females were in the predator side of their respective tanks. In the 3rd table, look at the Pearson Chi-Square line. Your Chi-square value is 2 = Your p-value is p = This suggests that the response to predators was not different between male and female guppies. WHAT TO REPORT: You want to report the 2 value, df, and p, parenthetically, following a statement that describes the patterns in the data. For example: Male and female guppies did not differ in their response to predators (chi-square test of independence, 2 =1.25, df=1, p>0.20)..
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CC-MAIN-2018-51
| 49,602 | 25 |
https://www.ifc.ir/market-risk-analysis-quantitative-methods-in-finance-volume-i
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math
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is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis
(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager’s Handbook
(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance.
Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see www.icmacentre.rdg.ac.uk/alexander
List of Figures
List of Tables.
List of Examples.
Preface to Volume 1.
I.1 Basic Calculus for Finance.
I.1.2 Functions and Graphs, Equations and Roots.
I.1.3 Differentiation and Integration.
I.1.4 Analysis of Financial Returns.
I.1.5 Functions of Several Variables.
I.1.6 Taylor Expansion.
I.1.7 Summary and Conclusions.
I.2 Essential Linear Algebra for Finance.
I.2.2 Matrix Algebra and its Mathematical Applications.
I.2.3 Eigenvectors and Eigenvalues.
I.2.4 Applications to Linear Portfolios.
I.2.5 Matrix Decomposition.
I.2.6 Principal Component Analysis.
I.2.7 Summary and Conclusions.
I.3 Probability and Statistics.
I.3.2 Basic Concepts.
I.3.3 Univariate Distributions.
I.3.4 Multivariate Distributions.
I.3.5 Introduction to Statistical Inference.
I.3.6 Maximum Likelihood Estimation.
I.3.7 Stochastic Processes in Discrete and Continuous Time.
I.3.8 Summary and Conclusions.
I.4 Introduction to Linear Regression.
I.4.2 Simple Linear Regression.
I.4.3 Properties of OLS Estimators.
I.4.4 Multivariate Linear Regression.
I.4.5 Autocorrelation and Heteroscedasticity.
I.4.6 Applications of Linear Regression in Finance.
I.4.7 Summary and Conclusions.
I.5 Numerical Methods in Finance.
I.5.3 Interpolation and Extrapolation.
I.5.5 Finite Difference Approximations.
I.5.6 Binomial Lattices.
I.5.7 Monte Carlo Simulation.
I.5.8 Summary and Conclusions.
I.6 Introduction to Portfolio Theory.
I.6.2 Utility Theory.
I.6.3 Portfolio Allocation.
I.6.4 Theory of Asset Pricing.
I.6.5 Risk Adjusted Performance Measures.
I.6.6 Summary and Conclusions.
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CC-MAIN-2021-31
| 2,362 | 49 |
https://www.lawwriters.org/what-is-the-current-price-of-this-preferred-stock-given-a-required-rate-of-return-of-11-6-percent/
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math
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1. Trigen Corp. management will invest cash flows of $331,000, $616,450, $212,775, $818,400, $1,239,644, and $1,617,848 in research and development over the next six years. If the appropriate interest rate is 6.75 percent, what is the future value of these investment cash flows six years from today? (Round answer to 2 decimal places, e.g. 15.25.)
2. You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into their systems and is offering to pay you $500,000 today, plus $500,000 at the end of each of the following six years for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you? (Round answer to the nearest whole dollar, e.g. 5,275.)
3. Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find
Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00%
What is the expected return on Barbara’s investment? (Round answer to 3 decimal places, e.g. 0.076.)
4. Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $1,048.77, what is the yield that Trevor would earn by selling the bonds today? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.)
5. The First Bank of Ellicott City has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 11.6 percent? (Round answer to 2 decimal places, e.g. 15.25.)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153816.3/warc/CC-MAIN-20210729043158-20210729073158-00424.warc.gz
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CC-MAIN-2021-31
| 2,425 | 10 |
https://pipe-fitting.org/article/how-to-calculate-the-size-of-piping-for-underfloor-heating
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math
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To calculate the size of piping for underfloor heating, formulas related to heat transfer and water flow in piping should be used. In the following, the formulas and steps for calculating the piping size for underfloor heating are described:
1 Calculation of heating requirement: First, the heating requirement of the building should be determined based on its dimensions, material and location. For example, for a building with dimensions of 20 x 15 meters and a ceiling height of 3 meters, the heating requirement is about 25 kW.
2 Calculation of the required power for the water heater: To heat the water in the underfloor heating system, the required power for the water heater must be calculated. To calculate the required power for the water heater, you can use the following formula:
Q = m × c × ΔT
In this formula, Q is the required power (watts), m is the mass of water (kilograms), c is the heat capacity of water (4.18 J/g °C) and ΔT is the temperature change (°C). For example, to heat 10 liters of water from 20°C to 60°C, the power required for the water heater is about 2000 watts.
3 Calculation of water flow rate: After determining the required power for the water heater, the water flow rate in the piping must be calculated. To calculate the water flow rate, you can use the following formula:
V = Q / (A × 3600, where in this formula, V is the speed of water flow (meters per second), Q is the power required for the water heater (watts), A is the internal surface area of the piping (square meters) and 3600 is the number of seconds in an hour. Is.
4 Choosing the piping size: After calculating the water flow rate in the piping, you can use the piping size table to determine the appropriate size for the piping for underfloor heating. This table is determined based on the speed of water flow and the amount of piping pressure loss.
5 Checking the performance of the system: after choosing the appropriate size of the piping, the performance of the underfloor heating system should be checked using various simulations and operational tests to ensure that the system works properly and meets the building's heating needs. he does.
In general, to calculate the size of piping for underfloor heating, one should pay attention to the principles of heat transfer and water flow in piping and choose the appropriate size by using relevant formulas and tables.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474715.58/warc/CC-MAIN-20240228112121-20240228142121-00639.warc.gz
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CC-MAIN-2024-10
| 2,386 | 10 |
http://www.catalystathletics.com/forum/showpost.php?p=47449&postcount=1
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math
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i have 1 day a week to do this exercise, so i try to combine endurance as well as strength. i warm up with 10 reps 60#, another set of 10 with 100#. then go to 150# 20 reps, then 170# 10 reps, then 200# 5 reps, 200# 5 reps again, then 220# a single, then 230# a single. a good workout, or are changes needed? just building strength/endurance.
my best is 360# at 145#, but i dont wanna lift that heavy anymore, as i'm afraid of injuries. i did those weights when i was playing ice hockey in the 1970's..
53 years old, 6' 145#
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824995.51/warc/CC-MAIN-20160723071024-00087-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 524 | 3 |
https://www.enotes.com/homework-help/how-many-unpaired-electrons-present-phosphorous-600856
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math
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The ground state electron configuration of a phosphorous atom has three unpaired electrons. They're in the 3p sublevel. The electron configuration is:
`1s^2 2s^2 2p^6 3s^2 3p^3` , for a total of 15 electrons. According to Hund's Rule, when a sublevel isn't full each orbital will contain one electron before any contain two. In other words, electrons don't pair up until they have to.
The image below is the orbital diagram for phosphorous. It illustrates Hund's Rule. Sulfur, for example, which has 16 electrons, will have another electron in the first 3p orbital and therefore only have two unpaired electrons. This is a periodic trend. Elements in the same group have the same number of unpaired electrons.
The opposite directions of the arrows in the orbital diagram represent the Pauli Exclusion principle, which states that a maximum of two electrons can occupy one orbital and they must have opposite spin.
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CC-MAIN-2023-06
| 913 | 4 |
https://physics.stackexchange.com/questions/171056/different-voltages-between-same-point/171061
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math
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In this circuit, we determine that the emf needs to be reversed and that its value is 108.75 V.
My confusion is that I thought the voltage between any two points must be the same irrespective of the path taken.
For instance, in the parallel group of 15.0 and 20.0 resistors, let's call the point on the right a and left b. From the top branch, V_ab = 108.75 - 15(4.25) = +45V. From the bottom branch, V_ab = (-2.25)20 = -45V.
I see how this is true from Kirchoff's loop rule, but it violates my previous intuition.
(A copy of the problem can be found in (PPT file): physics.wku.edu/~womble/phys260/ch26exp1.ppt)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057158.19/warc/CC-MAIN-20210921041059-20210921071059-00412.warc.gz
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CC-MAIN-2021-39
| 611 | 5 |
https://scholaron.com/homework-answers/acalculate-the-scrap-cost-reprocessing-time-10177
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math
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Question : (a)Calculate the scrap cost, reprocessing time, and productivity per hour. : 10177
(a)Calculate the scrap cost, reprocessing time, and productivity per hour. Productivity should be calculated in terms of conforming units per hour of resource input.
(b)A quality improvement program has recently been successfully introduced. For each 100 units manufactured, the process now yields 95 conforming units, one to be scrapped, and four for reprocessing. Repeat the calculations of paragraph (a). What are the quantitative benefits of the quality effort to costs, to delivery schedules, and to productivity?
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CC-MAIN-2020-50
| 612 | 3 |
https://newfieldschools.org/districtpage.cfm?pageid=1071
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math
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This course is a dual credit course where students earn both high school and college credit.
Concurrent Enrollment Course Outline
High School Name: Newfield Senior High School, Newfield, NY
Date Proposal Submitted/Prepared: Wednesday, June 13, 2012
Revised: Saturday, August 6, 2016
Instructor: Kristopher Williamson
TC3 Course #: Math 135
TC3 Course Title: Pre-Calculus
Credit Hours: 3 hours
Student Audience – Grade Level(s): 11th and 12th Grade students
Semester(s) Offered: Fall 2016 Semester
Instructor e-mail and/or phone #: Mr. Williamson (607) 564-9955 x3210 (school)
Course Description: Math 135 is a college level course which students learn key concepts to prepare them for Calculus 1. Topics that are covered include Introductions to Functions (definition, domain, range, graphs), Linear Functions, Quadratic Functions, Polynomial Functions, Rational Functions, Exponential Functions, Logarithmic Functions, Absolute Value Functions, Trigonometric Functions, Conic Sections, an Introduction to Calculus using Polynomial Functions (informal limits, definition of derivative, applying the derivative to graph functions, approximating the area under a curve, exact area using summation formula, integration and derivative shortcut methods), and additional topics, if time permits (polar coordinates, vectors).
Course Prerequisites: High School Algebra 2/Trigonometry
Minimal Basic Skills Needed to Complete Course Successfully: Students must know how to factor polynomials and know the basics of functions. They also need to have strong organizational skills.
Course Objectives: Learn mathematics topics at the college level that will prepare students to take Calculus 1. Develop an organized approach to problem solving.
Required Texts and Materials/Optional Materials as Appropriate: Precalculus Functions and graphs: A Graphing Approach. By Larson, Hostetler, and Edwards
Class Modalities/Alternative Learning Strategies: Lecture, discussions, individual practice, use of computer technology.
Required Readings, Presentations, Written Assignments, etc.: Homework, quizzes, tests. Some selected readings from textbook.
Course Content Presented in Units or Segments: Class meets 5 days a week for 43 minute periods. See the Course Outline for a list of topics in the order that they are planned to be taught.
Evaluation/Grading System: Homework assignments will not be collected or graded; however, students are expected to complete their homework assignments and seek assistance where necessary. Grades will consist only of quizzes and tests, which will be averaged within each of the three marking periods. The final exam will count as a fourth grade. The overall course grade will be calculated by averaging the three marking periods with the final exam. Final grades will be issued as numbers for high school credit and as letters for college credit.
Statement of Academic Integrity: In addition to TC3's Statement of Academic Integrity below, late work will only be accepted on occasion and by specific deadlines. If a student misses a quiz or test, they are responsible to take the quiz or test within 2 days of their return to school; afterward the student will earn a zero for their score.
Tompkins Cortland Community College's Statement of Academic Integrity
Every student at Tompkins Cortland Community College is expected to act in an academically honest fashion in all aspects of his or her academic work: in writing papers and reports, in taking examinations, in performing laboratory experiments and reporting the results, in clinical and cooperative learning experiences, and in attending to paperwork such as registration forms.
Any written work submitted by a student must be his or her own. If the student uses the words or ideas of someone else, he or she must cite the source by such means as a footnote. Our guiding principle is that any honest evaluation of a student's performance must be based on that student's work. Any action taken by a student that would result in misrepresentation of someone else's work or actions as the student's own — such as cheating on a test, submitting for credit a paper written by another person, or forging an advisor's signature — is intellectually dishonest and deserving of censure.
Make-Up Policy/Late Work: Late work will only be accepted on occasion and by specific deadlines, usually within 2 days of the due date. Students are responsible to approach the teacher for any notes and work missed when absent from school. Please visit the course website.
Attendance Policy: Missing multiple days of class will result in a lower average. Students who miss an excessive amount of school and who do not make the effort to seek missed work could be removed from the class.
Student Responsibilities: Students are responsible for maintaining a neat and organized binder that contains all notes taken in class as well as homework assignments, quizzes, and tests. If students have difficulty with certain topics, they are responsible for seeking extra help outside of class where necessary. Students are responsible for turning in all assignments by the specified due-dates.
Course Outline – Math 135: Pre-Calculus
The following course outline matches closely with your textbook. It is suggested that you at least skim over the section in the textbook for the next day's lesson before you come to class. Some lessons are not in the textbook.
There will be a test at the end of each chapter. Longer chapters could have a quiz half-way through the chapter.
Chapter P: Prerequisites
P.1 Polynomials and Special Products
P.3 Fractional Expressions
P.4 The Cartesian Plane
Chapter 1: Introduction to Functions
1.1 Lines in the Plane and Angle Between Lines
1.2 Distance from a Point to a Line
1.4 Graphs of Functions
1.5 Shifting, Reflecting, and Stretching Graphs
1.6 Combinations of Functions
1.7 Inverse Functions
Chapter 2: Solving Equations
2.1 Solving Equations Graphically
2.2 Complex Numbers
2.3 Solving Equations Algebraically (2 days)
2.4 Solving Inequalities Algebraically and Graphically
Chapter 3: Polynomial Functions
3.1 Quadratic Functions
3.2 Polynomial Functions of Higher Degree
3.3 Real Zeros of Polynomial Functions
3.4 Complex Zeros and the Fundamental Theorem of Algebra
Chapter 4: Rational Functions
4.1 Rational Functions and Asymptotes
4.2 Graphs of Rational Functions
4.3 Partial Fractions
4.4 Mixed Rational Functions Problems
4.5 Solving Rational Inequalities Algebraically
Chapter 5: Exponential and Logarithmic Functions
5.1 Exponential and Logarithmic Functions
5.2 Properties of Logarithms
5.3 Solving Exponential and Logarithmic Equations
5.4 Applications of Exponential and Logarithmic Functions
5.5 Mixed of Exponential and Logarithmic Problems
Chapter 6: Trigonometric Functions
6.1 Trigonometric Identities
6.2 Evaluating Trigonometric Expressions
6.3 Solving Trigonometric Equations
6.4 Trigonometric Formulas
6.5 Mixed Trigonometry Problems
6.6 Graphs of Sine and Cosine Functions
6.7 Graphs of Other Trigonometric Functions
6.8 More Practice Graphing Trigonometric Functions
Chapter 7: Derivatives
7.1 Introduction to Limits
7.2 Definition of Derivative
7.3 More Practice with Definition of Derivative
7.4 More Limits and Review
7.5 Derivative Shortcut Method and Applications of Derivatives
7.6 Derivative Rules
7.7 More Applications of Derivatives and Review
Chapter 8: Integration
8.1 Midpoint Rule and Trapezoid Rule
8.2 Summation Formula for Finding Exact Area
8.3 Mixed Area Problems
8.4 Introduction to Integration
8.5 Practice with Integration
8.6 Integration Using Partial Fractions
8.7 Mixed Integration Problems
Chapter 9: Conic Sections
9.1 Circles and Ellipses
Review for Final Exam
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CC-MAIN-2021-04
| 7,702 | 92 |
https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/21/
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math
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Applied Mathematics & Information Sciences
On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls
In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional condition in the form of the system of inequalities. Sufficient conditions for the existence of a unique solution of the problem of nonlinear optimization are given, and algorithm of its construction has been developed.
Digital Object Identifier (DOI)
Kerimbekov, Akylbek; Abdyldaeva, Elmira; Nametkulova, Raihan; and Kadirimbetova, Aisha
"On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls,"
Applied Mathematics & Information Sciences: Vol. 10:
1, Article 21.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/21
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| 1,453 | 9 |
http://fontstruct.com/gallery/tag/Move
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math
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The Gallery: Browse and find FontStructions
We found 2 FontStructions tagged with “Move”. Hide Options
Last edit: 09.11.20095%20downloads553%20glyphs53I%20was%20interested%20by%20the%20movement%20and%20vibrations%20created%20from%20sound%20for%20this%20typeface%20as%20part%20of%20my%20first%20year%20of%20Graphic%20Design.%0D%0AI%20experimented%20with%20speakers%20with%20paint%20and%20corn%2C%20taking%20photographs%20of%20the%20movement%20throughout.%0D%0A%0D%0AThis%20is%20a%20simple%20sans%20serif%20typeface%2C%20using%20different%20sized%20cubes%20to%20create%20the%20effect%20of%20noise%20or%20vibration%20flowing%20out%20of%20the%20type.
Some fonts you just can’t FontStruct. Try a non-modular typeface from FontShop.com
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707437545/warc/CC-MAIN-20130516123037-00086-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 735 | 4 |
https://britam.org/stats/GDPall.html
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math
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Movement of the Lost Ten Tribes
The Lost Ten Tribes
Identified and the Relevant Statistics.
An Ongoing Series: Previous Articles
Total GDP per Country and the Israelite Peoples Amongst Them.
Basic statistics Followed by Notes Concerning the Significance for Israelite Identification Brit-Am Studies.
Economy Statistics > Gross National Income (most recent) by country
Showing latest available data.
Rank Countries Amount
Brit-Am Note: We see in another article the GDP figures per head of population. Isrtaelite Nations took nine of the top ten places and seven of the ten after that. This accounted for most of the Israelite Peoples as identified by Brit-Am Reseach Studies.
The article below lists TOTAL GDP per country so naturally countries with more people are liable to top the list.
# 1 United States: $9,780,000,000,000.00
# 2 Japan: $4,520,000,000,000.00
# 3 Germany: $1,940,000,000,000.00
# 4 United Kingdom: $1,480,000,000,000.00
# 5 France: $1,380,000,000,000.00
# 6 China: $1,130,000,000,000.00
# 7 Italy: $1,120,000,000,000.00
# 8 Canada: $682,000,000,000.00
# 9 Spain: $588,000,000,000.00
# 10 Mexico: $550,000,000,000.00
# 11 Brazil: $529,000,000,000.00
# 12 India: $477,000,000,000.00
# 13 Netherlands: $390,000,000,000.00
# 14 Australia: $386,000,000,000.00
# 15 Switzerland: $277,000,000,000.00
# 16 Argentina: $260,000,000,000.00
# 17 Russia: $253,000,000,000.00
# 18 Belgium: $245,000,000,000.00
# 19 Sweden: $226,000,000,000.00
# 20 Austria: $195,000,000,000.00
# 21 Saudi Arabia: $181,000,000,000.00
# 22 Turkey: $167,000,000,000.00
= 23 Poland: $164,000,000,000.00
= 23 Denmark: $164,000,000,000.00
# 25 Norway: $161,000,000,000.00
# 26 Indonesia: $145,000,000,000.00
# 27 Finland: $123,000,000,000.00
# 28 South Africa: $122,000,000,000.00
# 29 Greece: $121,000,000,000.00
# 30 Thailand: $118,000,000,000.00
# 31 Portugal: $109,000,000,000.00
# 32 Israel: $107,000,000,000.00
# 33 Singapore: $88,812,300,000.00
# 34 Ireland: $87,735,600,000.00
# 35 Colombia: $81,551,500,000.00
# 43 New Zealand: $51,000,100,000.00
# 44 United Arab Emirates: $49,205,100,000.00
# 47 Puerto Rico: $42,052,000,000.00
# 62 Lebanon: $17,585,000,000.00
# 63 Luxembourg: $17,571,000,000.00
# 64 Syria: $17,260,500,000.00
# 79 Cyprus: $9,372,210,000.00
# 80 Jordan: $8,784,960,000.00
# 107 French Polynesia: $4,063,640,000.00
Notes of Brit-Am Significance:
Of the first 10 spots, four (USA, UK, France, Canada) are occupied by nations we identify as dominated by Israelites.
Of the spots 11 to 20, five (Netherlands, Australia, Switzerland, Belgium, Sweden) are taken by Israelite nations.
Partly Edomite countries (Japan, Germany, China, Italy, Spain, Mexico) are also in the top 10 and in the second 10 (Argentina, Russia, Austria) after that.
Israelite and Edomite nations occupy most of the top 20 spots.
Amongst Israelites nations the wealth is spread more equitably though the stronger the Edomite eement is (as in Germanyand Austria) the closer the standard approaches that of the Israelites.
Israelite Nations not in the top 20 include Denmark (23), Norway (25) Finland (27), Israel (32), Ireland (34), New Zealand (43), and Luxembourg (63). The figure for French Polynesia should probably have been added to that of France.
We wish to emphasize the facor of population in these figures. The figures DO NOT give GDP per capita but the total for all of the nation. As an example let us compare Finland to Indonesia. The Total GDP figures of Finland (27) and Indonesia (26) are similar. Finland with little natural resources has ca. 5,367,188 people and ranks population-wise 111th compared to other countries.
[Finland is a world leader in international comparisons of national performance.]
Indonesia possesses natural resources, has a population of ca.240,271,522, and ranks 4th in the number of people it has.
The State of Israel (32) is in the same league as Ireland (34).
Here too, the figures may be misleading since the military potential of Israel is not on the whole included in the GDP.
Israelite Statistics _ List of Contents.
Pleased with what you read?
PHYSICAL ANTHROPOLOGY OF
THE HEBREW PEOPLES
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CC-MAIN-2022-49
| 4,117 | 71 |
https://www.pharmacy-tech-study.com/question-about-hourly-rate-of-infusion.html
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math
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question about hourly rate of infusion
A bag of saline with an infusion apparatus is labeled 15 gtt/ml. The flow rate is 60 gtt/min. What is the hourly rate of infusion?
Help! Is this the formula to use?
F = V/T
Then solve 15/60 ? I am really stuck on this one. Thanks so much.
Reply (keith) : I'm not sure what formula you're trying to use there? I have a feeling that trying to put a formula on it may be getting in your way. Let's just look at it in practical terms...
O.K., so in this case:
You know that every minute- 60 drips will drop
You also know that each time 15 drops fall = 1mL
So, how many mL are infused in one minute?
60 ÷ 15 = 4mL per minute
How many minutes in 1 hour?
60 (min) X 4 (mL) = 240ml
Formulas are great and you need to learn them eventually, but sometimes while learning it's better to just work it out on paper. Thanks for the question.
For more practice on IV infusion calculations, go to This Page
Click here to post comments.
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Simply click here to return to Pharmacy math questions.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817158.8/warc/CC-MAIN-20240417142102-20240417172102-00819.warc.gz
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CC-MAIN-2024-18
| 1,070 | 18 |
https://www.inbetter.com/Industry-news/what-does-it-mean-to-divide-the-needle-type-paper-into-two-equal-parts-and-three-equal-parts
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math
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What does it mean to divide the needle type paper into two equal parts and three equal parts
Needle-type printing paper, commonly used in invoices, invoices, etc., is a kind of computer printing paper commonly used by enterprises and factories. However, people often say that the needle-type printing paper is divided into two equal parts, the needle-type printing paper is divided into three equal parts, and so on. So, what does "equally divided" mean here?
Divide is smaller than A4 paper. 241mm*279mm
The second half is 241mm*140mm (the second half is half of the first half)
The third is 241mm*93mm (the third is one third of the first)
These formats are available in the sample delivery note printing software, and the formats are also ready-made. very good.
The specification of the paper refers to that after the paper is made, it is trimmed and trimmed to a certain size. In the past, how many "opens" (such as 8 open or 16 open, etc.) were used to indicate the size of the paper. I adopted the international standard and stipulated that the marks such as A0, A1, A2, B1, B2, A4, A5. Specification. The standard stipulates that the proportional relationship between the width (represented by X) and the length (represented by Y) of the paper is X:Y=1:n.
According to the basic area of paper format, the format specifications are divided into A series, B series and C series. The format size of A0 is 841mm×1189mm, and the format area is 1 square meter; the format size of B0 is 1000mm×1414mm, and the format The area is 2.5 square meters; the format size of C0 is 917mm×1279mm, and the format area is 2.25 square meters; the format specifications of copy paper only use A series and B series.
If A0 paper is halved along the length, it becomes A1 size, and A1 paper is halved along the length direction, it becomes A2 size, and so on to A8 size; B8 paper is also bisected to B8 size in this way Specification. The format sizes of A0~A8 and B0~B8 are listed in the table below. Among them, there are 7 formats of A3, A4, A5, A6, B4, B5, B6, etc., which are commonly used for copy paper.
For example, "A4" paper means that the basic size of A-type paper is folded 4 times, so the area of a piece of A4 paper is 1/16 of the 4th power of 2 of the basic paper area. And so on for the rest.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100632.0/warc/CC-MAIN-20231207022257-20231207052257-00552.warc.gz
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CC-MAIN-2023-50
| 2,296 | 10 |
https://www.coursehero.com/tutors-problems/Statistics-and-Probability/11731519-1-In-order-to-estimate-the-proportion-of-office-workers-who-liste/
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math
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1. In order to estimate the proportion of office workers who listen to streamed music on a work computer on a regular basis, a sample of 1200 office workers who work at a computer was taken. Of them, 543 listen to steamed music on the computer at work. A 99% confidence interval for the proportion of all office workers who listen to streamed music at work is about:
The mean monthly salary of a random sample of 20 college graduates under the age of 30 was found to be $3120 with a standard deviation of $67. Assume that the distribution of salaries for all college graduates under the age of 30 is normally distributed.
(a) Construct a 90% confidence interval for the population mean of monthly salaries of all college graduates under the age of 30.
(b) All other information remaining unchanged, which of the following will produce a wider interval than the 90% confidence interval constructed above?
A sample with a standard deviation of 52 instead of 67
An 80% confidence interval rather than a 90% confidence interval
A sample of size 28 instead of 20
A sample of size 24 instead of 20
A sample with a standard deviation of 72 instead of 67
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CC-MAIN-2018-30
| 1,562 | 13 |
http://www.merriam-webster.com/medical/molecular%20formula
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math
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molecular formula noun
: a chemical formula for a compound existing as discrete molecules that gives the total number of atoms of each element in a molecule <the molecular formula for water is H2O>—see structural formula; compare empirical formula
Seen & Heard
What made you want to look up molecular formula? Please tell us where you read or heard it (including the quote, if possible).
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CC-MAIN-2015-06
| 389 | 4 |
https://www.thebsps.org/short-reads/laws-and-initial-conditions-jacobs/
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math
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A theory consists of a formalism and an interpretation. The formalism is just a piece of mathematics, and the interpretation tells us what that formalism means. In her book Interpreting Quantum Theories, Laura Ruetsche () cashes out interpretation in terms of ‘what the world could be like […] if the theory were true’ (in the words of Bas van Fraassen’s , p. 242). In slightly more formal terms, an interpretation maps each of the theory’s observables to a physical quantity, such as position or spin, and each of the theory’s states to a possible world. In this way, an interpretation delineates a space of worlds, which are called ‘physically possible’: they are ways the world could be if the theory were true.
This account of interpretation entails a distinction between initial conditions and laws of nature. In short, the laws of nature are whatever remains constant across all physically possible worlds. From the perspective of the theory in question, the laws are immutable. The initial conditions, meanwhile, are allowed to vary across the possible worlds. They concern particular matters of fact that are not already determined by the laws of nature—the particular spin or location of a particle, for example. Ruetsche dubs this view the ‘ideal of pristine interpretation’. Behind this ideal lies the thought that the laws of nature are philosophically interesting, whereas the initial conditions are only relevant to the special sciences (to ‘the astronomer, geographer, geologist, etc.’, as Ruetsche quotes Houtappel et al. (, p. 596)).
However, Ruetsche’s () book contains a sustained criticism of pristinism. In particular, Ruetsche argues that pristinism fails in the context of infinite-dimensional quantum theories, such as quantum field theory (QFT) and quantum statistical mechanics (QSM). Taking the latter as an example, Ruetsche argues that the occurrence of ‘unitarily inequivalent representations’ spells trouble for pristinism. Leaving the mathematical details aside, the problem Ruetsche pinpoints is that theories such as QSM allow for more than one space of physically possible worlds and no mathematically sound way to ‘glue’ these spaces together. This means that the interpreter of such a theory has to choose a space of possible worlds on the basis of ‘geographical’ considerations, such as the particular state of a system under study, or even the particular aims and interests of the scientists in question. But this blurs the distinction between laws and initial conditions: while some physical fact may appear to be a law from the perspective of a single space of possibilities—as it is constant across this space—that same fact may vary across distinct spaces. On her alternative, the coalescence approach:
[…] there can be an a posteriori, even a pragmatic, dimension to content specification, and […] physical possibility is not monolithic but kaleidoscopic. Instead of one possibility space pristinely associated with a theory from the outset, many different possibility spaces, keyed to and configured by the many settings in which the theory operates, pertain to it. (Ruetsche , p. 147)
In my article, I argue that Ruetsche’s criticism of the pristine ideal is not limited to infinite-dimensional quantum theories, but equally applies to classical mechanics, classical statistical mechanics, and ordinary (non-infinite) quantum mechanics. On the one hand, this means that Ruetsche is mistaken in claiming that the pristine ideal fails specifically because of the mathematical nature of infinite-dimensional quantum theories. Instead, I claim, the pristine ideal was too simplistic from the start, far removed from the reality of physical interpretation. On the other hand, my article ultimately provides further support for Ruetsche’s coalescence approach. In that sense, it is a friendly amendment to her own work. But the version of the coalescence approach that I defend is a slightly attenuated form of Ruetsche’s own. In particular, it does not pose a threat to scientific realism, pace Ruetsche’s claims to the contrary.
In order to see the coalescence approach in action in a non-quantum context, consider classical particle mechanics. The space of possibilities for this theory is represented by a 6N-dimensional ‘phase space’, where N is the number of particles in the world. For each particle, this phase space specifies six observables: three positions (one for each of the three x, y, and z axes) and three velocities. For example, if the actual system of interest contains ten particles, then classical particle mechanics models this system via a sixty-dimensional phase space. However, if we consider one such phase space, it seems that the number of particles is fixed across each state. Put differently, each ‘point’ in a phase space represents the exact same number of particles. From the ideal of pristine interpretation, which identifies laws with whatever remains constant across the space of possibilities, it would follow that it is a law that the universe contains a certain number of particles. This conflicts with our intuitions that the world could have contained a bigger or smaller number of particles, without any change in the laws that govern these particles.
In response, one might suggest that we ‘glue’ the phase spaces for each N together to create one massive phase space, which contains points for each state for a variable number of particles. The problem with this suggestion is that it violates a principle of parsimony: for any given system, this ‘universal’ phase space contains many observables that are simply irrelevant. For example, if we study a universe with ten particles, then it doesn’t make sense to ask what the velocity of the twelfth particle in the y-direction is. This is why physicists in practice never work with such a monstrous phase space—indeed, the very idea of such a space seems slightly horrifying.
The alternative offered by the coalescence approach is to allow interpreters a degree of flexibility. Which phase space is appropriate depends on the number of degrees of freedom of the actual system under study, but the choice of one phase space does not mean that all other spaces are immediately unphysical. Instead, we can imagine the collection of all classical phase spaces as a reservoir of possibility spaces, from which physicists choose one as particularly relevant to the situation at hand. In Ruetsche’s (, p. 1340) words, ‘other […] states aren’t impossible; they’re simply possibilities more remote from the present application of the theory’. This approach has consequences for the nature of lawhood. In fact, we allow laws of varying strength. Whatever is true across a single phase space most relevant to the application at hand is law-like in a narrower sense, whereas whatever is true across all phase spaces of possible interest is a law in a much stronger sense. Which notion of lawhood to use depends on the circumstances. For example, if we are interested in conservation laws (such as the conservation of mass or of the number of particles), it is not so crazy to consider the number of particles in the universe as a fixed law. But if we want to know whether space is an independent substance—and hence whether empty space could exist—it is appropriate to consider phase spaces of varying N. The strength of the coalescence approach is that it allows us the flexibility to use the same theory for both circumstances.
Finally, let’s return to the issue of scientific realism, briefly mentioned above. Ruetsche argues that the coalescence approach stymies the no miracles argument (NMA) for realism. The NMA states that a theory’s empirical virtues warrant our belief in its (approximate) truth. Ruetsche’s claim is that the NMA requires that all of a theory’s virtues accrue to a single interpretation, whereas on the coalescence approach different interpretations may display different virtues. I respond that this depends on how one construes the coalescence approach. I distinguish between a ‘modest’ and a ‘radical’ version, and argue that neither my case studies nor Ruetsche’s own require any recourse to the latter. But the modest version of the coalescence approach can sustain the NMA, as follows: instead of thinking of different choices of phase space as different interpretations of the theory, we think of these as different applications of the same theory. Put differently, an interpretation consists not of a single space of possibilities, but of a whole array of spaces, indexed to particular circumstances. Ruetsche uses the metaphor of a Swiss army knife, which seems to capture the spirit of the modest coalescence approach. The idea is that each blade of the knife represents a particular phase space, and which blade is used depends on the circumstances. But the Swiss knife as a whole corresponds to the theory, so it is not the case that each application of the knife requires a different interpretation. Rather, the multiple applications are already there, within the theory. The aim of the (modest) coalescence approach is to allow scientists to realize their theory’s full potential.
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CC-MAIN-2022-21
| 9,255 | 9 |
https://lexique.netmath.ca/en/position-parameter/
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math
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Value in a distribution of a quantitative
chosen for its representativeness of a tendency in this distribution, whether it is its centre, dominant frequency, or median position in the set of values.
Measure of central tendency
Median of a distribution
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CC-MAIN-2023-23
| 334 | 7 |
https://mustangsandmore.com/ubb/DanJonesTorqueVsHP.html
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math
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Torque Versus Horsepower - More Than You Really Wanted to Know by Dan Jones Every so often, in the car magazines, you see a question to the technical editor that reads something like "Should I build my engine for torque or horsepower?" While the tech editors often respond with sound advice, they rarely (never?) take the time to define their terms. This only serves to perpetuate the torque versus horsepower myth. Torque is no more a low rpm phenomenon than horsepower is a high rpm phenomenon. Both concepts apply over the entire rpm range, as any decent dyno sheet will show. As a general service to the list, I have taken it upon myself to explode this myth once and for all. To begin, we'll need several boring, but essential, definitions. Work is a measurement that describes the effect of a force applied on an object over some distance. If an object is moved one foot by applying a force of one pound, one foot-pound of work has been performed. Torque is force applied over a distance (the moment-arm) so as to produce a rotary motion. A one pound force on a one foot moment-arm produces one foot-pound of torque. Note that dimensionally (ft-lbs), work and torque are equivalent. Power measures the rate at which work is performed. Moving a one pound object over a one foot distance in one second requires one foot-pound per second of power. One horsepower is arbitrarily defined as 550 foot-pounds per second, nominally the power output of one horse (e.g. Mr. Ed). Since, for an engine, horsepower is the rate of producing torque, we can convert between these two quantities given the engine rate (RPM): HP = (TQ*2.0*PI*RPM)/33000.0 TQ = (33000.0*HP)/(2.0*PI*RPM) where: TQ = torque in ft-lbs HP = power in horsepower RPM = engine speed in revolutions per minute PI = the mathematical constant PI (approximately 3.141592654) Note: 33000 = conversion factor (550 ft-lbs/sec * 60 sec/min) In general, the torque and power peaks do not occur simultaneously (i.e. they occur at different rpm's). To answer the question "Is it horsepower or torque that accelerates an automobile?", we need to review some basic physics, specifically Newton's laws of motion. Newton's Second Law of Motion states that the sum of the external forces acting on a body is equal to the rate of change of momentum of the body. This can be written in equation form as: F = d/dt(M*V) where: F = sum of all the external forces acting on a body M = the mass of the body V = the velocity of the body d/dt = time derivative For a constant mass system, this reduces to the more familiar equation: F = M*A where: F = sum of all the external forces acting on a body M = the mass of the body A = the resultant acceleration of the body due to the sum of the forces A simple rearrangement yields: A = F/M For an accelerating automobile, the acceleration is equal to the sum of the external forces, divided by the mass of the car. The external forces include the motive force applied by the tires against the ground (via Newton's Third Law of Motion: For every action there is an equal and opposite re-action) and the resistive forces of tire friction (rolling resistance) and air drag (skin friction and form drag). One interesting fact to observe from this equation is that a vehicle will continue to accelerate until the sum of the motive and resistive forces are zero, so the weight of a vehicle has no bearing whatsoever on its top speed. Weight is only a factor in how quickly a vehicle will accelerate to its top speed. In our case, an automobile engine provides the necessary motive force for acceleration in the form of rotary torque at the crankshaft. Given the transmission and final drive ratios, the flywheel torque can be translated to the axles. Note that not all of the engine torque gets transmitted to the rear axles. Along the way, some of it gets absorbed (and converted to heat) by friction, so we need a value for the frictional losses: ATQ = FWTQ * CEFFGR * TRGR * FDGR - DLOSS where: ATQ = axle torque FWTQ = flywheel (or flexplate) torque CEFFGR = torque converter effective torque multiplication (=1 for manual) TRGR = transmission gear ratio (e.g. 3 for a 3:1 ratio) FDGR = final drive gear ratio DLOSS = drivetrain torque losses (due to friction in transmission, rear end, wheel bearings, torque converter slippage, etc.) During our previous aerodynamics discussion, one of the list members mentioned that aerodynamic drag is the reason cars accelerate slower as speed increases, implying that, in a vacuum, a car would continue to rapidly accelerate. This is only true for vehicles like rockets. Unlike rockets, cars have finite rpm limits and rely upon gearing to provide torque multiplication so gearing plays a major role. In first gear, TRGR may have a value of 3.35 but in top gear it may be only 0.70. By the above formula, we can see this has a big effect on the axle torque generated. So, even in a vacuum, a car will accelerate slower as speed increases, because you would lose torque multiplication as you went up through the gears. The rotary axle torque is converted to a linear motive force by the tires: LTF = ATQ / TRADIUS where: TRADIUS = tire radius (ft) ATQ = axle torque (ft-lbs) LTF = linear tire force (lbs) What this all boils down to is, as far as maximum automobile acceleration is concerned, all that really matters is the maximum torque imparted to the ground by the tires (assuming adequate traction). At first glance it might seem that, given two engines of different torque output, the engine that produces the greater torque will be the engine that provides the greatest acceleration. This is incorrect and it's also where horsepower figures into the discussion. Earlier, I noted that the torque and horsepower peaks of an engine do not necessarily occur simultaneously. Considering only the torque peak neglects the potential torque multiplication offered by the transmission, final drive ratio, and tire diameter. It's the torque applied by the tires to the ground that actually accelerates a car, not the torque generated by the engine. Horsepower, being the rate at which torque is produced, is an indicator of how much *potential* torque multiplication is available. In other words, horsepower describes how much engine rpm can be traded for tire torque. The word "potential" is important here. If a car is not geared properly, it will be unable to take full advantage of the engine's horsepower. Ideally, a continuously variable transmission which holds rpm at an engine's horsepower peak, would yield the best possible acceleration. Unfortunately, most cars are forced to live with finitely spaced fixed gearing. Even assuming fixed transmission ratios, most cars are not equipped with optimal final drive gearing, because things like durability, noise, and fuel consumption take precedence to absolute acceleration. This explains why large displacement, high torque, low horsepower, engines are better suited to towing heavy loads than smaller displacement engines. These engines produce large amounts of torque at low rpm and so can pull a load at a nice, relaxed, low rpm. A 300 hp, 300 ft-lb, 302 cubic inch engine can out-pull a 220 hp, 375 ft-lb, 460 cubic engine, but only if it is geared accordingly. Even if it was, you'd have to tow with the engine spinning at high rpm to realize the potential (tire) torque. As far as the original question ("Should I build my engine for torque or horsepower?") goes, it should be rephrased to something like "What rpm range and gear ratio should I build my car to?". Pick an rpm range that is consistent with your goals and match your components to this rpm range. So far I've only mentioned peak values which will provide peak instantaneous acceleration. Generally, we are concerned about the average acceleration over some distance. In a drag or road race, the average acceleration between shifts is most important. This is why gear spacing is important. A peaky engine (i.e. one that makes its best power over a narrow rpm) needs to be matched with a gearbox with narrowly spaced ratios to produce its best acceleration. Some Formula 1 cars (approximately 800 hp from 3 liters, normally aspirated, 17,000+ rpm) use seven speed gearboxes. Knowing the basic physics outlined above (and realizing that acceleration can be integrated over time to yield velocity, which can then be integrated to yield position), it would be relatively easy to write a simulation program which would output time, speed, and acceleration over a given distance. The inputs required would include a curve of engine torque (or horsepower) versus rpm, vehicle weight, transmission gear ratios, final drive ratio, tire diameter and estimates of rolling resistance and aerodynamic drag. The last two inputs could be estimated from coast down measurements or taken from published tests. Optimization loops could be added to minimize elapsed time, providing optimal shift points, final drive ratio, and/or gear spacing. Optimal gearing for top speed could be determined. Appropriate delays for shifts and loss of traction could be added. Parametrics of the effects of changes in power, drag, weight, gearing ratios, tire diameter, etc. could be calculated. If you wanted to get fancy, you could take into account the effects of the rotating and reciprocating inertia (pistons, flywheels, driveshafts, tires, etc.). Relativistic effects (mass and length variation as you approach the speed of light) would be easy to account for, as well, though I don't drive quite that fast. Later, Dan Jones >Please put this in perspective for me, using this example: > >Two almost identical Ford pickups: > >1. 300ci six, five spd man---145 hp@3400rpm----265ft-lbs torque @2000 rpm >2. 302ciV8, five spd man----205 hp@4000rpm----275ft-lbs torque @3000 rpm > >Conditions: Both weigh 3500#, both have 3.55 gears, both are pulling a 5000# >boat/trailer. Both are going to the lake north of town via FWY. There is a >very steep grade on the way. They hit the bottom of the grade side by side >at 55mph. What will happen and why? This theoretical situation has fascinated >me, so maybe one of the experts can solutionize me forever. In short, the V8 wins because it has more horsepower to trade for rear wheel torque, using transmission gear multiplication. What really accelerates a vehicle is rear wheel torque, which is the product of engine torque and the gearing provided by the transmission, rear end, and tires. Horsepower is simply a measure of how much rear wheel torque you can potentially gain from gearing. My previous posting provides all the necessary equations to answer this question, but we need a few more inputs (tire size, transmission gear ratios, etc.) and assumptions. I'll fill in the details as we go along. To do this properly would require a torque (or horsepower) curve versus rpm, but for illustration purposes, let's just assume the torque curve of the I6 is greater than that of the V8 up to 2500 rpm, after which the V8 takes over. Using the horsepower and torque equations, we can fill in a few points. 300 I6 302 V8 RPM Tq Hp Tq Hp --- ------- -------- 4000 269 205 3400 224 145 3000 275 157 2000 265 100 where: TQ = torque in ft-lbs HP = power in horsepower RPM = engine speed in revolutions per minute Assume both trucks have 225/60/15 tires (approximately 25.6 inches in diameter) and transmission ratios of: Gear Ratio RPM @ 55 MPH ---- ----- ------------ 1st 2.95 7554 2nd 1.52 3892 3rd 1.32 3386 4th 1.00 2560 5th 0.70 1792 I determined engine rpm using: K1 = 0.03937 K2 = 12.*5280./60. PI = 3.141592654 TD = (K1*WIDTH*AR*2.+WD) TC = TD*PI TRPM = K2*MPH/TC OGR = FDGR*TRGR ERPM = OGR*TRPM where: K1 = conversion factor (millimeters to inches) K2 = conversion factor (mph to inches) WIDTH = tire width in millimeters AR = fractional tire aspect ratio (e.g. 0.6 for a 60 series tire) WD = wheel diameter in inches TC = tire circumference in inches TD = tire diameter in inches MPH = vehicle speed in mph for which engine rpm is desired TRGR = transmission gear ratio (e.g. 3 for a 3:1 ratio) FDGR = final drive gear ratio OGR = overall gear ratio (transmission gear ratio * final drive ratio) TRPM = tire RPM ERPM = engine RPM In fifth gear, both trucks are at 1792 rpm (55 mph) as they approach the hill. Running side-by-side, the drivers then floor their accelerators. Since the I6 makes greater torque below 2500 rpm, it will begin to pull ahead. The V8 driver, having read my earlier posting, drops all the way down to second gear, putting his engine near its 4000 rpm power peak. Responding, the I6 driver drops to third gear which also puts his engine near its power peak (3400 rpm). The race has begun. Since the engines are now in different gears, we must figure in the effects of the gear ratios to determine which vehicle has the greater rear wheel torque and thus the greater acceleration. We can determine axle torque from: ATQ = FWTQ * CEFFGR * TRGR * FDGR - DLOSS where: ATQ = axle torque FWTQ = flywheel (or flexplate) torque CEFFGR = torque converter effective torque multiplication (=1 for manual) TRGR = transmission gear ratio (e.g. 3 for a 3:1 ratio) FDGR = final drive gear ratio DLOSS = drivetrain torque losses (due to friction in transmission, rear end, wheel bearings, torque converter slippage, etc.) Assuming there are no friction losses, the equation reduces to: ATQ = FWTQ*TRGR*FDGR = 269*1.52*3.55 = 1452 ft-lbs for the V8 at 4000 rpm = 224*1.32*3.55 = 1050 ft-lbs for the I6 at 3400 rpm Since the V8 now makes considerably more rear axle torque, it will easily pull away from the I6. Falling behind, the I6 driver might shift down a gear to take advantage of second gear's greater torque multiplication. He will still lose the contest because his I6 engine, now operating at close to 4000 rpm, is making less torque than the V8. If he shifts up to a gear that places his engine at its maximum torque output, he will lose the torque multiplication of the lower gear ratio and fall even farther behind. Note that I picked the gear ratios so both engines can operate near their respective horsepower peaks at 55 mph by shifting to a lower gear (second gear for the V8 and third gear for the I6). This was necessary to make the contest equal. I could have manipulated the gear ratios to favor one engine or the other, but that would not have been a fair comparison. In any case where both engines are optimally geared, the V8 will win because it simply has more horsepower to trade for rear wheel torque. Q.E.D. Dan Jones P.S. Since we know the weights and the tire diameter, we can convert this rotary torque to a linear tire force and, given the angle of the hill, compute the linear accelerations of the two trucks using F=MA. This computation is left as an exercise for the reader.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711045.18/warc/CC-MAIN-20221205200634-20221205230634-00056.warc.gz
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CC-MAIN-2022-49
| 14,784 | 1 |
https://m.hugendubel.de/de/buch/martin_vath-integration_theory-3795876-produkt-details.html
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math
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Integration Theory - A Second Course
Lieferbar innert 2 Wochen
BeschreibungThis book presents a very general approach to integration theory, as well as some advanced topics of the theory. It includes some new results but is also a self-contained introduction suitable for a graduate student doing self-study or an advanced course on integration theory.The book is divided into two parts. In the first part, integration theory is developed from the beginning in a general setting and for vector-valued functions which can hardly be found in other textbooks. The second part covers various topics related to integration theory, such as spaces of measurable functions, convolutions, famous paradoxes in connection with set theory, and extensions of formulas from elementary calculus to the setting of the Lebesgue integral.
InhaltsverzeichnisContents: Basic Integration Theory: Abstract Integration; Adding a Topological Structure: The Radon Measure; Adding a Group Structure: The Haar Measure; Advanced Topics: Spaces of Measurable Functions; Convolutions; Connections with Logic and Set Theory; Special Properties of the Lebesgue Measure; Miscellaneous.
Pressestimmen?Because of the original treatment and selection of topics, the book stands out among other books on the same subject."
Untertitel: Sprache: Englisch.
Verlag: WORLD SCIENTIFIC PUB CO INC
Erscheinungsdatum: August 2002
Seitenanzahl: 288 Seiten
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s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607963.70/warc/CC-MAIN-20170525025250-20170525045250-00039.warc.gz
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CC-MAIN-2017-22
| 1,408 | 9 |
http://www.usablestats.com/askstats/question/920/
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math
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Question 920:The average service time at CheesePlate Restaurant is 3.5 minutes with a standard deviation of .04 minutes. A new order system claims it can improve service time. A sample of 49 orders revealed a mean service time of 3.4 minutes. Does the claim about the new order system hold true?
Need more than just an answer? Download the Easy t Excel T-test Calculator Package which gets you the answer with the detailed calculations.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119080.24/warc/CC-MAIN-20170423031159-00285-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 436 | 2 |
https://metamoracarriagedriving.org/odds-and-ends/
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math
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Sleighs Marathon Times – v4.0 Level/Class Set default Speeds—————-Training VSETraining Small PonyTraining PonyTraining Horse—————-Preliminary VSEPreliminary Small PonyPreliminary PonyPreliminary Horse—————-Intermediate VSEIntermediate Small PonyIntermediate PonyIntermediate Horse—————-Advanced/FEI PonyAdvanced/FEI Horse (in meters or km) (kph) (minutes) Section A Distance Speed Window T/W Section Distance Speed Midpoint: 500m from Beginning 1/2 Distance 500m from End Section B Distance Speed Window Distributed across Window (average target/minimum speed) Include Target Times Include Minimum Times Km-Time minus window Include Target Times (1/2 window) Include Minimum Times Allowed column on: Left Right Generated Text: A A A *To suppress generation of a section, blank out the distance Last Updated: 31Dec18 Cones Split Times Set default Speed—————-Training VSE Single/PairTraining VSE Tandem/FourTraining Horse & Pony Single/PairTraining Horse & Pony Tandem/Four—————-Preliminary VSE Single/PairPreliminary VSE Tandem/FourPreliminary Horse & Pony Single/PairPreliminary Horse & Pony Tandem/Four—————-Intermediate VSE Single/PairIntermediate VSE Tandem/FourIntermediate Horse & Pony Single/PairIntermediate Horse & Pony Tandem/Four—————-Advanced/FEI Pony SingleAdvanced/FEI Pony PairAdvanced/FEI Pony TandemAdvanced/FEI Pony Four—————-Advanced/FEI Horse SingleAdvanced/FEI Horse PairAdvanced/FEI Horse TandemAdvanced/FEI Horse Four (in meters) (mpm) (minutes) Total Distance* Speed Time** * The Total Distance & Time are used to calculate the splits. The distance can be specified in any unit, for example if you step off the total distance and your split locations, then you could specify a distance in steps and the time provided by the event. Specify each split distance in steps too, the calculation will give you the split times. ** If the Time is left blank, it will be calculated using the distance & speed, if specified (since this is the only number that counts), that value will be used for split calculations. Split 1 Distance Comment Split 2 Distance Comment Split 3 Distance Comment Split 4 Distance Comment Split 5 Distance Comment Note: Only fill in as many splits as you need. For comments/corrections/updates contact Support ([email protected]).
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473738.92/warc/CC-MAIN-20240222093910-20240222123910-00804.warc.gz
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CC-MAIN-2024-10
| 2,388 | 1 |
https://total-guitar-lessons.com/beginner/beginner-guitar-notes.php
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math
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In the last beginner guitar lesson we learned the notes of the six 'open' strings E - A - D - G - B - E and some may wonder 'what happened to C and F?'. The strings on a guitar are tuned so that fingerings of chords and scales are 'playable' and to find all the notes we'll have to use the fingers of our left hand on the various frets.
Every fret corresponds to a Half Tone interval (see the Theory section) which is the interval between two consecutive piano keys, black and white.
So there is a half tone between B and C or E and F and two Half tones between C and D, D and E, F and G, G and A and A and B.
So, starting on the 6th string (E) we will find an F on the first fret, a G on the 3rd and an A on the fifth. This is also the pitch of the 5th string, so we can move to it and find a B on the 2nd fret a C on the 3rd and a D on the 5th and so on.
Obviously, seeing we have at least 20 frets, we can also go on on a single string and find all the notes on it and it would be a nice thing to memorize all the notes on all the frets.
It's interesting to see that we can find notes with the same pitch on different strings like the C on the 3rd string, 5th fret and the C on the 2nd string, 1st fret. It may be confusing at first but, actually, is a big bonus: it sempifies fingerings and scales in a big way compared to a keyboard instrument.
On the 'free' frets between the notes we find the 'black keys' notes, sharps and flats. On the 1st string 2nd fret we have Fsharp (F#), on the 4th G# (or A flat, it's actually the same pitch) and so on.
This concludes our lesson on notes: the next step is to learn about chords.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473738.92/warc/CC-MAIN-20240222093910-20240222123910-00569.warc.gz
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CC-MAIN-2024-10
| 1,628 | 8 |
https://brainmass.com/business/weighted-average-cost-of-capital/relationship-wacc-cost-equity-121204
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math
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Dilbert has recently taken a course in financial management and has learned the following: The cost of debt, rd, is normally less than the cost of equity, rs. Consider a firm which has no debt. If the firm is an all equity firm (i.e. it has no debt), (1) what is the relationship between the weighted average cost of capital (WACC) and the cost of equity ( rs)?. A diagram may help explain your answer.
Dilbert further recognizes that there are costs associated with debt. For example, if the firm issues debt (and with the proceeds of the debt, repurchases equity,) it will be adding to its financial distress and agency costs. This means that the there will be (1)an increase in expected value of bankruptcy costs, as well as (2)additional costs due to the restrictions likely to appear in bond covenants and (3) additional costs in monitoring these restrictions in the bond covenants. Consequently, Dilbert reasons that to avoid these, the firm should keep its debt to a minimum. In this way, Dilbert believes that the firm will be choosing the D/E ratio that maximizes the value of the firm.
(2) Do you agree with Dilbert? Why or why not?
Please see the attached file.
Dilbert is correct. The trade off model of the capital structure decisions says that a firm has to make a trade off between the benefits of debt and costs of debt. The benefit of tax is ...
The computations and explanations are given to determine the relationship between the WACC and the cost of equity.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687255.13/warc/CC-MAIN-20170920104615-20170920124615-00194.warc.gz
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CC-MAIN-2017-39
| 1,477 | 6 |
https://fens.sabanciuniv.edu/tr/announcement-detail?nid=81634
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math
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Turgay Bayraktar received the "Ikeda Research Award (2019)"10-03-2020
Ikeda Research Award (2019) is given to Turgay Bayraktar
Associate Professor Turgay Bayraktar has been awarded with 'Masatoshi Gündüz Ikeda Research Award' given by the Mathematics Foundation for his contributions to mathematics. This award will be given to Turgay Bayraktar on 26 March 2020 15:30 at ODTU Mathematics Department, Masatoshi Gündüz Ikeda Seminar Room at a ceremony. At the specified day and time, Bayraktar will give a seminar on "Stochastic Kähler Geometry and Random Holomorphic Sections".
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400206133.46/warc/CC-MAIN-20200922125920-20200922155920-00005.warc.gz
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CC-MAIN-2020-40
| 581 | 3 |
http://antonymueller.blogspot.com/2011/01/known-and-unknown.html
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math
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In his own words:
"Reports that say that something hasn't happened are always interesting to me, because, as we know, there are known knowns; there are things we know that we know. There are known unknowns. That is to say, there are things that we now know we don't know. But there are also unknown unknowns. There are things we do not know we don't know."
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660877.4/warc/CC-MAIN-20190118233719-20190119015719-00412.warc.gz
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CC-MAIN-2019-04
| 356 | 2 |
https://baandek.org/posts/the-decanomial-square/
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math
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Montessori Encyclopedia: The Decanomial Square
How do you use this material?
This is one of the most beautiful materials in the classroom, and it requires a high level of patience, attention to detail, and logic. First a child gets out a large rug. A child brings the box containing the Decanomial Square to the rug. There are 10 squares, ranging from 12 to 102, as well as pairs of rectangles with the proportions of the square and all the squares that came before. For instance, the square 4×4 also has three pairs of rectangles, measuring 4×3, 4×2, & 4×1. The colors of the squares and rectangles correspond to the colors in the bead cabinet.
The child removes only the squares, stacking to create a pyramid. Starting with the smallest square, a red square measuring 1×1, the child begins to build the Decanomial Square.
The child places the first square at the top left corner of the rug. The next square, a green square measuring 2×2, is placed diagonally adjacent to the first, and two rectangles measuring 2×1 are placed with the side measuring 2cm against the green square, and the side measuring 1cm against the red square. A larger square has been formed.
The child places the third square, a pink square measuring 3×3, diagonally adjacent to the green square. The two pairs of rectangles measure 3×2 & 3×1. The wider pair is placed on either side of the pink square, with the 3cm side touching the pink square, and the 2cm side touching the sides of the green square. The narrower pair is placed next, with the 3cm side matching with the first pair of rectangles, and the 1cm side touching the green rectangles measuring 2×1. A new, larger square has been formed.
This pattern continues as increasingly larger squares are formed.
After this first activity has been mastered, a child will explore with this material, building squares using just the rectangles, and using the smaller squares to create larger squares (for instance, building the 8×8 square using the 2×2 square, the 6×6 square, and the pair of 6×2 rectangles.
What is the child learning?
A child is learning to build squares. This material is very beautiful and precise, and creating order with the tiles, placing them in sequence to build increasingly larger rectangles, is immensely satisfying.
What does a child not know they’re learning?
In addition to the logical patterning the child is developing, the child is preparing for mathematics, specifically for geometry, algebra, and squaring.
Written by:Charlotte Snyder
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474690.22/warc/CC-MAIN-20240228012542-20240228042542-00075.warc.gz
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CC-MAIN-2024-10
| 2,514 | 13 |
https://studylib.net/doc/17779485/use-axioms--proposition-1--mauney%E2%80%99s-postulate--and-congru...
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math
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Use Axioms, Proposition 1, Mauney’s Postulate, and Congruence Theorems SAS and SSS to bisect a given line segment. Also, construct a line perpendicular to a given line segment. How do we define a right angle, today? According to Euclid, what is a right angle? Why did Euclid define right angle in such a strange way? When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. C A B D C A B D C O A B D C A B C A O B Math/lLogic Homework for Monday, May 2 1. Mauney’s Postulate 2. Area Workshop 3. Polished perpendicular bisector proof 4. Formal deduction from some Holmes book.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989030.87/warc/CC-MAIN-20210510033850-20210510063850-00317.warc.gz
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CC-MAIN-2021-21
| 752 | 1 |
http://www.lancaster.ac.uk/maths/about-us/history/50th-anniversary-special-lectures/
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math
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50th Anniversary Special Lectures
In 2014, Lancaster University celebrated the 50th anniversary of its foundation. To honour this occasion, the department organised two special Anniversary Lectures on Friday 26th September.
The first lecture was given by Professor E. Brian Davies, FRS, of King's College, London. Brian was the President of the London Mathematical Society from 2007 to 2009; he is the author of many papers and seven books.
His talk, based on a joint paper with Michael Levitin, was devoted to an easily stated question: what are the eigenvalues of a specific, elementary, non-self-adjoint n by n matrix (with n large)? The answer, however, is not easily found.
Elementary estimates give some rough bounds, and impressive numerical calculations, shown on attractive slides, lead to conjectures on other bounds. The latter have been verified in some cases, using surprisingly advanced mathematics. Brian illustrated beautifully the elusive nature of this approach by showing a short video indicating how the eigenvalue distribution varies with n.
We are far from a secure theory that explains the numerical phenomena, even in this specific example. But the audience was surely convinced that the conjectures of Davies and Levitin must be true, even if nobody could prove them.
The second lecture was given by Professor W. Hugh Woodin. Hugh now holds a joint position in the Departments of Mathematics and of Philosophy at Harvard University; he was previously Professor at the University of California, Berkeley, from 1989 to 2014. He is surely one of the leaders in our era in the quest to understand the fundamental nature of sets and the real numbers, taking forward the journey of Gödel and Tarski into the far reaches of higher cardinals.
His lecture (almost) also marked the 50th anniversary of Gödel's Incompleteness Theorem. By 1964, we knew that the Continuum Hypothesis (CH) is independent of the axioms ZFC of set theory; now we know that very many statements, including many in mainstream mathematics, are independent. How satisfactory is this? Could (necessarily detailed) examination of higher cardinals lead to a further compelling axiom that 'resolves' CH and other questions? Is 'ultra-L' such an axiom? These were very challenging ideas, very clearly articulated.
The two lectures kept a large audience engrossed for the afternoon; we are very grateful to the speakers. A gallery of photos from the event is available.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945660.53/warc/CC-MAIN-20180422212935-20180422232935-00085.warc.gz
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CC-MAIN-2018-17
| 2,454 | 9 |
http://jylyoi.kz/?query=look+and+say+sequence+c
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math
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The Look and say sequence is a recursively defined sequence of numbers studied most notably by John Conway. Sequence Definition. Take a decimal number. Look at the number, visually grouping consecutive runs of the same digit.
In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... (sequence A005150 in OEIS). To generate a member of the sequence from the previous member, read off the digits of the previous member...
Find the n’th term in Look-and-say (Or Count and Say) Sequence. The look-and-say sequence is the sequence of below integers: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211
The look and say sequence is a basic form of run length encoding. The sequence starts with the number 1 and each additional number encodes the number of digits that are repeated before each digit sequence.
qiwihui/look-and-say_sequence.c. Created Sep 10, 2014. Embed.
Puts automatically appends a newline. If that's not what you want, you can fputs your string to stdout or use printf. Fputs(x=a,stdout); Or. Printf("%s ",a)...
Перед нами так называемая Look-and-Say sequence, начинающаяся с 0. Чтобы получить последующий член последовательности, нам потребуется обратиться к предыдущему и выполнить следующее
Look and say sequence. Problem 419. Published on Saturday, 16th March 2013, 10:00 pm; Solved by 322; Difficulty rating: 50%.
A005150. Look and Say sequence: describe the previous term! (method A - initial term is 1). (Formerly M4780).
The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic scale) tend to straight lines whose slopes coincide with Conway's constant.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540563.83/warc/CC-MAIN-20161202170900-00510-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 1,946 | 10 |
https://www.math.uic.edu/seminars/view_seminar?id=4931
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math
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Quantum Topology / Hopf Algebra Seminar
University of Liverpool, UK
Quantum Mechanics from a Double Vector Space
Abstract: This talk will be a discussion of the foundations of physics from the speaker's unique point of view. See "Foundations of Physical Law" by Peter Rowlands, World Scientific Pub. Co. (2015).
Thursday August 31, 2017 at 3:00 PM in SEO 612
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376831715.98/warc/CC-MAIN-20181219065932-20181219091932-00595.warc.gz
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CC-MAIN-2018-51
| 358 | 5 |
https://wikivisually.com/wiki/Orbit_phasing/show-videos-only
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math
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In astrodynamics, orbit phasing is the adjustment of the time-position of spacecraft along its orbit, usually described as adjusting the orbiting spacecrafts true anomaly. Orbital phasing is primarily used in scenarios where a spacecraft in a given orbit must be moved to a different location within the same orbit. The change in position within the orbit is defined as the phase angle, ϕ. To gain or lose time, the spacecraft must be subjected to a simple two-impulse Hohmann transfer which takes the spacecraft away from. The first impulse to change the orbit is performed at a specific point in the original orbit. The impulse creates a new orbit called the “phasing orbit” and is larger or smaller than the original orbit resulting in a different period time than the original orbit. The difference in time between the original and phasing orbits will be equal to the time converted from the phase angle. When complete, the spacecraft will be in the final position within the original obit. To find some of the orbital parameters, first one must find the required period time of the phasing orbit using the following equation. Total change of velocity required for the maneuver is equal to two times ∆V. Orbit phasing can also be referenced as co-orbital rendezvous like an approach to a space station in a docking maneuver. Orbital maneuver Docking maneuver Hohmann transfer orbit General Curtis, Howard D, sellers, Jerry Jon, Marion, Jerry B. Understanding Space An Introduction to Astronautics, http, //arc. aiaa. org/doi/pdf/10. 2514/2.6921 Minimum-Time Orbital Phasing Maneuvers - AIAA, CD Hall -2003 Phasing Maneuver
Image: Phase angle
If the target (satellite) is behind the spacecraft (shuttle) in the same orbit, the spacecraft must speed up to enter a larger, slower phasing orbit to allow the target to catch up.
If spacecraft is behind the final position on the same orbit, the spacecraft must slow down to enter a smaller, faster phasing orbit to catch up to final position.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160400.74/warc/CC-MAIN-20180924110050-20180924130450-00445.warc.gz
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CC-MAIN-2018-39
| 1,998 | 4 |
https://www.aotg.com/nattress-levels-and-curves-plugins-for-fcpx/
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math
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December 3, 2012, 07:55 AM
This time we’re focusing on the Nattress Levels and Curves Plugins for FCPX from FxFactory. Hope you guys enjoy it. Also, you can hire us for your project or for consulting. More info is available...#fcpx#plugins#final cut pro#nle#nattress levels#curves
Gordon Sits down with Nick Carew to discuss The Girlfriend Experience Season 03.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488551052.94/warc/CC-MAIN-20210624045834-20210624075834-00401.warc.gz
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CC-MAIN-2021-25
| 363 | 3 |
https://www.algebra-answer.com/algebra-help/adding-matrices/algebra-2-on-line.html
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math
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Hello Math experts ! I am a starting at algebra 2 on line. I seem to understand the lectures in the class properly , but when I begin to solve the problems at home myself, I commit errors . Does anyone know of any website where I can get my solutions checked before submitting them for grading? Or any resource where I can get to see a step by step solution?
Algebra Helper is what you are looking for. You can use this to enter questions pertaining to any math topic and it will give you a step-by-step answer to it. Try out this software to find answers to questions in reducing fractions and see if you get them done faster.
From: the wastelands between insomnia and clairvoyance
Posted: Friday 06th of Aug 18:46
My parents could not afford my college fees, so I had to work in the evening, after my classes. Solving equations at the end of the day seemed to be difficult for me at those times. A colleague introduced Algebra Helper to me and since then I never had any problem solving my questions .
I’m glad you’re really interested to use this program . It’s the best program I ever tried and I don’t want you to miss using this . Try going to http://www.algebra-answer.com/features.shtml. Good luck with your test pal!
I am a regular user of Algebra Helper. It not only helps me get my homework faster, the detailed explanations given makes understanding the concepts easier. I strongly suggest using it to help improve problem solving skills.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860041.64/warc/CC-MAIN-20180618031628-20180618051628-00407.warc.gz
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CC-MAIN-2018-26
| 2,634 | 33 |
https://smartech.gatech.edu/handle/1853/29474
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math
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A Backward Point Shifted Levelset Method for Highly Accurate Interface Computation
We propose a technique that could significantly improve the accuracy of the levelset method and has the potential for fully conservative treatment. Level set method uses the levelset function, usually an approximate signed distance function Φ to indirectly represent the interface by the zero set of Φ. When Φ is advanced to the next time level by an advection equation, it is no longer a signed distance function any more, therefore the uneven numerical dissipation associated with the discretization of the advection equation could distort the interface particularly in places where the radius of curvature of the interface changes dramatically or two segments of the interface are getting close. Also an auxiliary equation is usually solved at each time level to restore Φ into a signed distance function, which could further shift the interface position. We address the second problem by using an analytic point shifted algorithm to locally perturb the mesh without geometric reconstruction of the interface so that the zero set of Φ is located at grid nodes and therefore solving the auxiliary equation will not move the interface. Our strategy for solving the first problem is that when applying the advection equation for Φ, it does not initiate from a signed distance function, but ends up with one, which can be achieved by solving the advection equation backward in time. These two techniques are combined with an iterative procedure.
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http://wunderstudio.fr/2020/12/10/icc-agreement-interpretation/
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math
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In summary, CCI is a reliability index that reflects both the degree of correlation and the consistency between the measures. It has often been used in conservative care medicine to evaluate interrater, test-retest and intrarater reliability of numerical or continuous measurements. Given that there are 10 different forms of the ICC and that each form contains different hypotheses in their calculations and will give rise to different interpretations, it is important for researchers and readers to understand the principles of selecting an appropriate form of the ICC. Since the CCI estimate from a reliability study is only an expected value of the true CCI, it is preferable to assess the level of reliability based on the 95% confidence interval of the CCI estimate, not the ICC estimate itself. If you tested the same number of advisors (and the same themes) among the two models, you will see that the estimates are identical in the table under both models. However, as I have already said, the interpretation is distinguished by the fact that the conclusion of the agreement on the entire population of councillors can only be generalized with a random bipartisan model. You can also see a footnote indicating that the mixed model assumes that there is no missing-subject interaction; To be clear, this means that rats lack individual biases in relation to the characteristics of subjects that are not relevant to the task being evaluated (for example. B for an examiner`s hair color). (1) When the data sets are the same, all ICC estimates are equal to 1. (2) As a general rule, the « average K-Rater value » TYPE of CCI is larger than the corresponding type of « individual collector. » (3) The definition of « absolute agreement » generally gives a lower estimate of CCI than « coherence. » (4) Single-use random effects model generally gives a smaller CCI estimate than two-way models. (5) For the same definition of CCI (for example.
B absolute agreement), CCI estimates are identical between both two-way models and mixed effects, as they use the same formula for the calculation of CCI (Table 3). This has an important fact that the difference between random two-track models and mixed effect models lies not in the calculation, but in the experimental design of the reliability study and in the interpretation of the results. We need to understand that there are no defaults for acceptable reliability with ICC. A low CCI could not only reflect the low degree of tingling or measurement agreement, but also relate the lack of variability between the subjects studied, the small number of subjects and the small number of tyingers tested.2, 20 As a general rule, researchers should strive to obtain at least 30 heterogeneous samples and, if possible, to include at least 3 in a reliability study.
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http://stackexchange.com/users/2950828/benjamin-steinberg?tab=accounts
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math
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I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, self-similar groups (aka automaton groups), profinite groups and random walks on semigroups and groups. I've been particularly interested in interactions between these areas and Computer Science and am fond of algorithmic questions. I've also dabbled with operator algebras associated to etale groupoids and inverse semigroups. Currently, I am interested in applications of finite semigroup theory to finite state Markov chains.
Q&A for professional mathematicians
Q&A for people studying math at any level and professionals in related fields
Q&A for meta-discussion of the Stack Exchange family of Q&A websites
Q&A for users of TeX, LaTeX, ConTeXt, and related typesetting systems
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https://www.physicsforums.com/threads/concavity-of-parametric-equations.743933/
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math
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1. The problem statement, all variables and given/known data Find dy/dx and d^y/dx^2 x=e^t; y=te^(-t) For which values of t are concave upward? (write your answer in interval notation). 2. Relevant equations 3. The attempt at a solution I used the formula to find d^2y/dx^2. d^2y/dx^2= e^(-3t)*(2t-3) Set it to zero: e^(3t)*(2t-3)>0 I solved it and got t>3/2, but the computer told me it was wrong. What am I doing wrong here?
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http://www.faadooengineers.com/threads/439-MATHEMATICAL-METHODS-Ebook-presentation-and-lecture-notes-covering-full-semester-syllabus
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math
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MATHEMATICAL METHODS Ebook, presentation and lecture notes covering full semester syllabus
The topics covered in the attached e-books are:
UNIT I - Matrices and Linear systems of equations: Elementary row transformations-Rank-Echelon form, Normal form Solution of Linear Systems Direct Methods- LU Decomposition- LU Decomposition from Gauss Elimination Solution of Tridiagonal Systems-Solution of Linear Systems
UNIT II - Eigen values, eigen vectors properties Cayley-Hamilton Theorem - Inverse and powers of a matrix by Cayley-Hamilton theorem Diagonolization of matrix. Calculation of powers of matrix Modal and spectral matrices.
UNIT III - Real matrices Symmetric, skew - symmetric, orthogonal, Linear Transformation Orthogonal Transformation. Complex matrices: Hermitian, Skew-Hermitian and Unitary forms- Reduction of quadratic form to canonical form.
UNIT IV - Solution of Algebraic and Transcendental Equations: Introduction The Bisection Method The Method of False Position The Iteration Method Newton-Raphson Method.
UNIT V - Curve fitting
UNIT VI - Numerical solution of Ordinary Differential equations
UNIT VII - Fourier Series
UNIT VIII - Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions
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https://www.prep4usmle.com/forum/thread/120954/
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math
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|Prep for USMLE|
| Forum | Resources||New Posts | Register | Login||» |
I'm having a problem, my university hasn't received the Form 327-A from ECFMG? (Form 327-A is the form that ECFMG sends to your medical school to request verification of your final medical school diploma and a final medical school transcript)
I know that i can open a Fedex account and ask ECFMG to send it through my account. As i live in Venezuela, Fedex won't allow me to open an account, also i don't have a US address.
What can i do in this case? Can i use a Fedex's account under a friend name? or how can i open one?
Thank you very much!
This thread is closed, so you cannot post a reply.
| Similar forum topics|
Form 327 A resent...any help.
My 327 form is accepted?
frustrated with the 327-form
| Related resources|
Advertise | Support | Premium | Contact
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http://perplexus.info/show.php?pid=2174&cid=16640
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math
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I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?
What if each distance must be unique?
When the sides are allowed to be non-distinct, there is a solution with radius 7/sqrt(3) = 4.01415...
the hexagon has side lengths 3,5,3,5,3,5, and diagonals of length 7 and 8. Labelling the vertices A-F, the distances are as follows:
working on the distinct sides version. initial results suggest the radius > 500. For a quadrilateral with distinct chord lengths, the smallest radius is 12.8102523...., and for a pentagon the smallest radius is 39.2938971....
Posted by sundberg
on 2004-08-19 01:29:47
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https://www.daretoaks.com/forums/topic/Black-Christians/
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math
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- January 23, 2000 at 12:00 am #2782
How do black Christians feel about the fact that their ancestors in Africa were predominantly followers of Islam?
User Detail :Name : Greg P., Gender : M, Sexual Orientation : Straight, Race : White/Caucasian, Religion : Catholic, Age : 22, City : Los Angeles, State : CA Country : United States, Occupation : Student, Education level : 2 Years of College, Social class : Middle class, January 28, 2000 at 12:00 am #27034
It’s strange that so many black Americans embrace Islam as a way of reclaiming their “African” roots, because Islam is not an African religion at all. Islam is an Asian religion, just as Christianity is. Moreover, virtually none of the black slaves brought to America were Moslims. The great majority practiced traditional African pagan/ spirit religions. When you look at Voodoo in Haiti or Santeria in Cuba, you see how many African slaves learned to mix Christianity with their traditional paganism. Even today, Islam is not the dominant religion in sub-Saharan Africa. Nigeria is one of the few black African countries in which Islam is the dominant religion. Interestingly, Catholicism is growing rapidly in Africa. It’s ironic that so many black Christians in America are turning to Islam, at the same time that millions of black Africans are embracing Christianity!
My feeling is, study Islam and Christianity, then decide whether you believe the basic teachings of either religion. Embrace a religion because you believe in it, not because you think (wrongly) that it was the religion of your ancestors.
User Detail :Name : Astorian, Gender : M, Sexual Orientation : Straight, Race : White/Caucasian, Age : 38, City : Austin, State : TX Country : United States, Education level : 4 Years of College, January 28, 2000 at 12:00 am #27375
Actually, all three of the Judeo-Christian religions were born in Africa and the original followers of each were African. The original Jews, the original Christians (even Jesus), as well as the original Muslims are all of the same continent. This is something that all three of those religions seem to suppress rather than embrace. When you look at them objectively, all three religions have a lot in common, especially when you contrast them to Buddhism, for example. It saddens me when so many dwell on differences rather than finding common ground.
User Detail :Name : Laura-H, Gender : F, Sexual Orientation : Straight, Race : White/Caucasian, Religion : Christian, Age : 25, City : Schaumburg, State : IL Country : United States, Education level : Over 4 Years of College, Social class : Middle class, January 28, 2000 at 12:00 am #40244
I’m pretty sure that no where near the majority of black Africans were Muslim. The vast majority were Animist – a polytheistic system in which living (and some non-living) things are endowed with sacredness, deserving of worship, responsible for good and evil occurrences, etc. I am also pretty sure that Muslim black Africans were bestowed that religion, by inheritance or force by Arab slave traders. (See Henry Louis Gates’ PBS program on Africa for more.) This same method is how American blacks became predominately Christian.
User Detail :Name : David25891, City : Parsippany, State : NJ Country : United States, January 28, 2000 at 12:00 am #45166
How do white Christians feel about their ancestors from Europe being barbarians and other brutish types? That was then, this is now. We all strive to thrive.
User Detail :Name : Jean, Gender : F, Sexual Orientation : Straight, Race : White/Caucasian, Religion : Lutheran, Age : 45, City : Milwaukee, State : WI Country : United States, Occupation : Managerial/technical, Education level : Over 4 Years of College, Social class : Middle class, April 23, 2000 at 12:00 am #40799
Islam didn’t originate in Africa, but rather in the Middle East. It is worth noting, however, that huge chunks of African culture became part and parcel Islamic in ancient times. The Hausa, Fulani, and parts of the Yoruba are responsible for large parts of Western Africa being Muslim, while the Swahili extended the religion and associated culture as far south as Mozambique, transforming the whole East Coast. It is true thatthe interiors of all countries south of and including Congo are mainly animist, but it’s also worth noting that most Afro-American slaves were captured in Muslim Western Africa. It is also worth noting that Sub-Sahara and Southeast Asia are famous for having converted to Islam through trade and not through invasion or slavery, as many people in America believe. Middle-Eastern people never colonized the Sub-Sahara except for the English-Egyptian Sudan colonies.
User Detail :Name : Karim, Gender : M, Age : 23, City : Los Angeles, State : CA Country : United States, Social class : Middle class, January 5, 2003 at 12:00 am #31262
That is a false hood , first of all the christian religon was in existence first ,mohammed wrote the quoran , after christ, that said , judaism, and christianity came first, and they were the foremost religons of people in north africa were they were given birth ,
User Detail :Name : Chuck D, Gender : M, Sexual Orientation : Straight, Race : Black/African American, Religion : Christian, Age : 32, City : Baltimore, State : MD Country : United States, Education level : 2 Years of College,
- You must be logged in to reply to this topic.
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https://researchportal.bath.ac.uk/en/publications/wavenumber-explicit-analysis-for-the-helmholtz-h-bem-error-estima
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math
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We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber k to have the error in the iterative solution bounded independently of k as k→∞ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wavenumber for an integral equation used to solve a scattering problem. We also prove new bounds on how h must decrease with k to maintain k-independent quasi-optimality of the Galerkin solutions as k→∞ when the obstacle is nontrapping.
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
FingerprintDive into the research topics of 'Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem'. Together they form a unique fingerprint.
- Department of Mathematical Sciences - Professor
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching
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https://pure.psu.edu/en/publications/on-the-assumption-of-cubic-graphs-of-vascular-networks
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math
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A vascular network is often represented by a Reeb graph, which is a topological skeleton, and graph theory has been widely applied to analyze properties of a vascular network. A Reeb graph model for a vascular network is obtained by assigning the branch points of the network to be the vertices of the graph and the vessels between branch points to be the edges of the graph. Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Vascular networks develop by way of two biological mechanisms of vessel sprouting (budding) and splitting (intussusception). According to a graph theory modeling of two vascular network growth mechanisms, all nodes in the Reeb graph must be cubic in degree except for two special nodes: the afferent (A) and efferent (E) nodes. We define that a vascular network is cubic if all internal nodes are cubic in degree. We consider six normal adult rat renal glomerular networks and use their reeb graphs already constructed and published in the literature. We observe that five of them contain internal vertices of degree higher than three. Branch points in vascular networks may appear to be of a higher degree if the imaging resolution cannot differentiate between blood vessels that are very close in proximity. Here, we propose a random graph theory model that edits a non-cubic vascular network into a cubic graph. We observe that the edited cubic graph from a non-cubic vascular network has the similar size and order as the one cubic vascular network. Renal glomerular network, random graph process, graph degree, graph invariants, pattern matching.
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https://crazyproject.wordpress.com/2011/09/19/finitely-generated-modules-over-r-are-precisely-the-module-homomorphic-images-of-r%E2%81%BF/
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Let be a ring. Prove that is a finitely generated module over if and only if is a module-homomorphic image of .
Suppose first that is a finitely generated -module – say by . Let denote the th standard basis vector in , and define by , and extend linearly. Certainly then is a surjective module homomorphism.
Conversely, suppose is a surjective module homomorphism, and for each let . Since is surjective, and since the generate , the set generates over as desired.
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https://apps.dtic.mil/sti/citations/AD0661663
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math
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FAILURE DISTRIBUTIONS WITH DECREASING MEAN RESIDUAL LIFE.
SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
Pagination or Media Count:
It is well known that the class of distributions with decreasing mean residual life DMR contains the class of distributions with increasing hazard rate IHR. The study of DMR distributions has received little attention in the literature. Starting with a random variable T 0, which has all its moments, and with distribution function F sub 0 x, we can construct a sequence of distribution functions with the following properties 1 F sub o x is DMR implies that F sub k x is DMR, k1,2,... . 2 F sub 0 x is DMR implies that F sub k x converges either to a singular distribution or to an exponential distribution. 3 The members of the sequence F sub k x are all identically exponentially distributed if and only if for some k or 1, F sub k t F sub k-1 t. Author
- Statistics and Probability
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https://nrich.maths.org/2352/solution?nomenu=1
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math
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Copyright © University of Cambridge. All rights reserved.
The answer is 6 students. I numbered each of the students, 1 for the front and 25 for the back. Julia was obviously no. 19. I counted from 25 back 14 places (starting with 25 so the solution would be right). I found that Urvisha was no. 12. Then I counted the numbers between 12 and 19 and got 6.Chiu drew a diagram to help answer the problem:
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http://picdeer.com/tag/diversity
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The Google Walkout is the latest demonstration of the power that employees have when coming together to voice concerns on an issue. As the movement gathered pace so too did the pressure on the company to review its policies and put in better protections for employees. With an estimated 35% of women globally experiencing sexual harassment at work its important that major companies lead the way with ensuring a safe working environment for everyone. In the aftermath we’re left with more questions about gender equality, not just in tech but the business community in general. @worldeconomicforum suggests that if we carry on moving at current rates of progression then the economic gender gap will take more than 200 years to close. What should we be doing to bring about true equality at a faster pace? - - - - - - - - - #gendergap#equality#metoo#feminism#empowerment#startup#tech#inspiration#diversity#protest#unite#movement#peoplepower#harrassment#workplace#culture
Shout out to @blackpaintstudios for creating this thorough guide. We're way past the point of leaders throwing up their hands and saying they don't know how to address issues that stunt #diversity and #inclusion. Download it and share with your agency.
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https://www.omnicalculator.com/math/sphere-equation
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math
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Equation of a Sphere Calculator
Our equation of a sphere calculator will help you write the equation of a sphere in the standard form or expanded form if you know the center and radius of the sphere. Alternatively, you can find the sphere equation if you know its center and any point on its surface or if you know the end-points of any of its diameters. This calculator can also find the center and radius of a sphere from its equation.
Are you wondering what is the standard equation of a sphere or how to find the center and radius of a sphere using its equation? Have you perhaps come across a sphere equation that doesn't look like the general equation? Are you curious how knowing the diameter's end-points or the center and a point on the sphere can help you find the sphere's equation? Grab your favorite drink and keep reading this article; we'll tackle these questions together!
This calculator can also determine a sphere's surface area and volume from its equation. Want to calculate them without bothering with the sphere equation? Head to our sphere calc!
What is the equation of a sphere?
The equation of a sphere in the standard form is given by:
- – Coordinates of any point lying on the surface of the sphere;
- – Coordinates of the center of the sphere; and
- – Radius of the sphere.
If we know the center and radius of the sphere, we can plug them into this standard form to obtain the equation of the sphere. For example, consider a sphere with a radius of and its center at . By inserting this into the equation above, we get the standard equation of the sphere:
Similarly, you can use the standard form of the sphere equation to find the radius and center of the sphere. For example, a sphere with the equation would have its center at , and its radius is given by:
❗ Note that you have to be careful regarding the signs of the center coordinates in the standard equation. If the sphere equation in the above example was instead , then its center would be .
How to derive the equation of a sphere
Now that we know the standard equation of a sphere, let's learn how it came to be:
- First thing to understand is that the equation of a sphere represents all the points lying equidistant from a center point. In other words, any point that lies at a distance from a point lies on the sphere. Sound familiar? A circle equation works the same way! Go to our equation of a circle calculator and see if you can uncover more similarities!
- Consider a point that lies at a distance from the center . Using distance formula, we get:
- Squaring on both sides and rearranging this equation, we get:
And, voila! Just like that, we got the standard equation of a sphere! It bears repeating that every point that satisfies this equation lies on the surface of the sphere.
Expanded form of the sphere equation
Sometimes, you may come across a sphere equation that appears different from the standard form we've discussed so far. Generally, such equations should look like the following:
- – Sum of all coefficients of the terms;
- – Sum of all coefficients of the terms;
- – Sum of all coefficients of the terms; and
- – Sum of all constants terms.
This equation may seem intimidating at a glance, but if you take a closer look; it is simply the expanded version of the standard form we're used to. Let's use the completing the squares method to backtrack our way from the expanded version to the simpler, standard form:
- Rearrange the equation for clarity:
- To write in the format, we need to identify and . Clearly, . If , we get:
- Adding and subtracting the quantity to the equation, we get:
- Similarly, we complete the squares for the y-terms and z-terms by adding and subtracting the quantities and to get:
- Rearrange the equation to group all the constant terms on the right-hand side:
- Comparing this equation with the standard form of the sphere equation
- Extracting the center point and radius of the sphere from this equation, we get:
Need help completing the squares? Our completing the square calculator will serve you.
In this sphere equation calculator, you can simply select the expanded form option as the type of the equation and enter the corresponding , , and values to obtain the equation in the standard form, its center and radius, and other relevant information.
Equation of a sphere from the end-points of any diameter
Now that you know what the equation of a sphere is, let's discuss how to obtain it in cases where you don't have the necessary parameters readily available. Suppose you only know the end-points of any one of the diameters of the sphere and have no information on the center point or radius. You still have a way to frame its equation.
Say the diameter of the sphere has the endpoints and . Clearly, the center is given by the mid-point of , which is given by:
Once we know the center, we can obtain the radius as the distance or , through the distance formula:
We can then insert this center and radius in the standard sphere equation.
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http://oemscorp.com/2016/01/1032/
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math
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EQuaLS is the acronym for the “Expository Quantum Lecture Series”, a lecture series hosted by the Institute for Mathematical Research (INSPEM) at Universiti Putra Malaysia (UPM). This year, EQuaLS 8, was held successfully on January 18-22, 2016, jointly organized by Laboratory of Computational Sciences & Mathematical Physics, Institute for Mathematical Research, Universiti Putra Malaysia; Department of Physics, Faculty of Science, Universiti Putra Malaysia; and Department of Mathematical Sciences, Politecnico di Torino.
Being one of the event sponsors, the team of OEMS IntiPakar Corporation Sdn Bhd, was pleased to meet some of the familiar friends of Wolfram Mathematica again, including Assoc. Prof. Dr. Hishamuddin Zainuddin, Dr. Nurisya Mohd Shah, Mr. Kathiresan Gopal & etc. The persons in the picture from the right was Dr. Chan Kar Tim, Mr Ganesh a/l Subramaniam from INSPEM, Peter & Desmond from OEMS IntiPakar Corporation Sdn Bhd.
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https://collegephysicsanswers.com/openstax-solutions/calculate-wavelength-light-has-its-second-order-maximum-450circ-when-falling-0
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math
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Calculate the wavelength of light that has its second-order maximum at $45.0^\circ$ when falling on a diffraction grating that has 5000 lines per centimeter.
This is College Physics Answers with Shaun Dychko. This formula tells us where the maximum are for light going through a diffraction grating. We're given the separation between slits in the diffraction grating, the angle to the maximum, the order of the maximum m and the wavelength of the light lambda. Now we have to figure out what lambda is in this question and we're told that the angle to the second order maximum which means that m is two, is 45 degrees and the separation between slits we have to figure out given the information that there are 5,000 lines per centimeter. So we want to know how many centimeters there are between each line. And so I've written the reciprocal of the 5000 lines per centimeter here and I have one centimeter per 5000 lines and this works out to one times ten to the minus two meters for every 5,000 lines which is 2.00 times ten to the minus six meters between each line. And so that's what we're gonna substitute in for d and we'll solve this for lambda by dividing both sides by m, the order of the maximum and so lambda is d sine theta over m that's two times ten to the six meters times sine of 45 degrees divided by the order of two which is 707 nanometers must be the wavelength of the light.
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CC-MAIN-2022-21
| 1,397 | 2 |
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