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https://www.espsciencetime.org/HowTallisIt.aspx
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math
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Once the leaves are off the trees in the fall, it is amazing how much easier it is to see some things. Trees are still beautiful as their trunks and limbs come into view. It's a great time to figure out how tall trees are. Here are several ways to measure the height of tall objects. Use them to find the height of some trees near your home or school.
Stand a person whose height you know in front of the tree. Walk away from the tree until you are far enough from the tree to cover the person with your thumb or a pencil. Count the number of thumb heights from the bottom of the tree to the top. For example, if the person is 4 feet tall and the tree is 4 persons (thumbs) high, then the tree is 16 feet tall.
A second way is to walk far enough from the tree that the length of your thumb covers the whole tree.
Then turn your hand so that your thumb points from the bottom of the tree out along the ground. Notice where the end of your thumb seems to end on the ground. Measure from the base of the tree to the spot where the end of your thumb was. That is the height of the tree.
Another way is to compare shadows:
Measure the length of the tree's shadow. Measure the length of the shadow made by a person whose height you know. Express this as a ratio and solve it for the height of the tree. For example, the tree shadow is 20 feet long, the person is 4 feet tall and has a 5 foot shadow. Call the height of the tree h.
h is to 20 as 4 is to 5
h/20 = 4/5
5h = 4 x 20
5h = 80
5h/5 = 80/5
h = 16 feet
Can you figure out any other methods? Can you think of some other tall objects to measure?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649177.24/warc/CC-MAIN-20230603064842-20230603094842-00761.warc.gz
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CC-MAIN-2023-23
| 1,594 | 13 |
https://shuangwen.org/how-to-find-the-mean-of-a-probability-distribution-in-excel/
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math
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How To Find The Mean Of A Probability Distribution In Excel
How To Find The Mean Of A Probability Distribution In Excel. This cheat sheet covers 100s of functions that are critical to know as an excel analyst it calculates the binomial distribution probability for the number of successes from a specified. Normal distribution returns for a.
How to find the mean of a probability distribution in excel. Find the mean & standard deviation. Step 9:repeat steps 1 through 8 for the second value, which for this example is 400.
This Is Completely Depending On The Mean And Standard Deviation.
We will solve a problem with data that is distributed exponentially with a mean of 0.2, and we want to know the probability that x will be less than 10 or lies between 5 and 10. We can confirm that this probability distribution is valid: That is, rand generates random probabilities.
Therefore, You Can Use The Norm.inv Function To Calculate A Random Number From A Normal Distribution, Using This Formula In Excel 2007 And Above… =Norm.inv(Rand(), Mean.
Calculate normal distribution probability in excel of more than 600 ppm. Calculate normal distribution probability in excel of between 400 and 600 ppm. It calculates the binomial distribution probability for the number of successes from a specified number of trials.
Tinv Considers The Inverse Of The Probability Of Being In Both Tails.
0.18 + 0.34 + 0.35 + 0.11 + 0.02 = 1. Functions list of the most important excel functions for financial analysts. The binom.dist function is categorized under excel statistical functions.
Normal Distribution Returns For A.
A formula has been found in excel to find a normal distribution which is categorized under statistical functions. =normdist (x, mean, standard_dev, cumulative) where: Pr(x > x), or of being in both tails i.e.
The Range Of Probabilities Associated With Each X Value.
Exponential distribution using excel in this tutorial, we are going to use excel to calculate problems using the exponential distribution. To calculate probabilities related to the normal distribution in excel, you can use the normdist function, which uses the following basic syntax: The value of interest in the normal distribution.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00519.warc.gz
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CC-MAIN-2022-49
| 2,206 | 13 |
https://tailieuxanh.com/vn/tlID1118079_bao-cao-hoa-hoc-research-article-existence-of-positive-solutions-in-generalized-boundary-value-problem-for-plaplacian.html
|
math
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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Positive Solutions in Generalized Boundary Value Problem for p-Laplacian | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 848191 19 pages doi 2009 848191 Research Article Existence of Positive Solutions in Generalized Boundary Value Problem for p-Laplacian Dynamic Equations on Time Scales Wenyong Zhong1 2 and Wei Lin1 1 Research Center and Key Laboratory of Mathematics for Nonlinear Sciences School of Mathematical Sciences Fudan University Shanghai 200433 China 2 School of Mathematics and Computer Sciences Jishou University Hunan 416000 China Correspondence should be addressed to Wei Lin wlin@ Received 31 March 2009 Accepted 7 May 2009 Recommended by Alberto Cabada We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized rn-point boundary value problem for the p-Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem. Furthermore we illustrate the possible application of our analytical results with a concrete and nontrivial dynamic equation on specific time scales. Copyright 2009 W. Zhong and W. Lin. 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. 1. Introduction Since the seminal work by Stefan Hilger in 1988 there has been a rapid development in the research of dynamic equations on time scales. The gradually maturing theory of dynamic equations not only includes the majority of the existing analytical results on both differential equations and difference equations with uniform time-steps but also establishes a solid foundation for the research of hybrid equations on different kinds of time scales. More importantly with this foundation and those ongoing investigations concrete applications of dynamic equations on time scales in mathematical modeling of real processes and .
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103271763.15/warc/CC-MAIN-20220626161834-20220626191834-00328.warc.gz
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CC-MAIN-2022-27
| 2,229 | 1 |
https://diffiety.mccme.ru/preprint/2001/07_01abs.htm
|
math
|
Author: Raffaele Vitolo
The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation). In order to avoid serious technical difficulties, the order of the jet space is not fixed, i. e. computations are performed on spaces containing forms on jet spaces of any order.
In this paper we show that there exists a formulation of Vinogradov's
C-spectral sequence in the case of finite order jet spaces of a
fibred manifold. We compute all cohomology groups of the finite
order C-spectral sequence. We obtain a finite order variational
sequence which is shown to be naturally isomorphic with Krupka's
finite order variational sequence.
21 pages, LaTeX-2e (AmSLaTeX 2).
To compile source files (.tex) one needs the title page style files titlatex.tex and diagrams.tex.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00454.warc.gz
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CC-MAIN-2023-50
| 1,019 | 10 |
http://www.imdb.com/title/tt0443537/
|
math
|
The visitors to a strange hotel (named after David Hilbert, a German mathematician who died in 1943) are met with several paradoxes. For one thing, the hotel has an infinite number of rooms, all of which are full. Yet they manage to accommodate the new guests.
This is an introduction to the idea of infinity and transfinite numbers in mathematics, but aimed at non-mathematicians. As such, it is sometimes seen on UK television in what used to be the Open University slot (BBC2 after midnight). It is told through puzzling conversations between guests and the captivating receptionist, and in discussions between guests themselves.
It is not intended as a film with a plot, so don't expect one (by that yardstick I'd rate it at 3, saved from a lower score by its brevity). However, if you want an inspirational insight into the joys of infinity (and infinity plus one, infinity plus two, ...), then start here, and record it to re-watch later. On that basis, I vote an 8.
Warning: this film could make your brain hurt.
7 of 7 people found this review helpful.
Was this review helpful to you?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738659680.65/warc/CC-MAIN-20160924173739-00212-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 1,092 | 6 |
http://www.chegg.com/homework-help/questions-and-answers/dual-band-receiver-employing-weaver-architecture-shown-fig-4121-first-lo-frequency-chosen--q4092275
|
math
|
please solve the problem in briefShow transcribed image text
please solve the problem in briefShow transcribed image text A dual-band receiver employing a Weaver architecture is shown in Fig. 4.121. The first LO frequency it chosen so as to create high-side injection for the 2.4-GHz band and low-side injection for the 5.2-GHz band. (The receiver operates only in one band at a given time.) Neglect the noise and nonlinearity of the receiver itself and assume an SNR of 20dB is required for the signal to be detected properly. The Weaver architecture provides an image rejection ratio of 45 dB. Suppose the receiver must detect a -85-dBm signal in the 2.4-GHz mode while receiving at the same antenna a -10-dBm 5.2-GHz component as well. Determine the amount of rejection required of BPF1 at 5.2 GHz. Suppose the receiver operates in the 5.2-GHz band but it also picks up a strong component at 7.2 GHz. It is possible for this component to be mixed with the third harmonics of LO1 and LO2 and appear in the baseband. Does the Weaver architecture prohibit this phenomenon? Explain in detail.
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s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375635604.22/warc/CC-MAIN-20150627032715-00124-ip-10-179-60-89.ec2.internal.warc.gz
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CC-MAIN-2015-27
| 1,091 | 2 |
https://uia.org/archive-tags/patterns-conceptual-integration?page=1
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math
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1. In a system with P terms, it should be possible to identify by analysis (with computer assistance and graphic output) configurations of the P terms (linked by Q relationships), selected in order of their degree of symmetry for a given value of P. Constraints on the maximum and minimum value of Q in each case could also be partially determined in terms of symmetry requirements. Tables of such configurations, without considering symmetry, have been produced by Frank Harary ( 124).
Patterns of Conceptual Integration
1. Eliciting subordinate sets: relating distinctions
If a set is named (e.g. "development"), the question may be asked in how many ways possible elements may be distinguished by subdividing the set.
The series below was developed by J. G. Bennett (45) to replace the Aristotelian and Kantian categories, with their dualistic characteristic. His definitions of systematic features are given in Annex 1. The characteristics given here summarize the extensive descriptions of Bennett (vol. 1, pp. 31-48, vol. 3, pp. 14-75).
The definitions given below are those of J. G. Bennett ((45), vol. 3, pp. 10 11) and are given as a basis for his elaboration of a multi-term sequence in Annex 2. In the main part of this article "set" has been used to signify what Bennett defines as "system", although the two terms have been used interchangeably.
"1. A system is a set of independent but mutually relevant terms. The relevance of the terms requires them to be compatible. No one term of the system can be understood without reference to all the others.
11.1 The purpose of this paper is to demonstrate the importance of number in the complete sets fundamental to social science and policy formulation. It is fairly obvious that formulation of a 2-term set of concepts (values, problems, etc.) establishes a dynamic for the advocates of each term, or those involved in any institutionalization of the dyad--namely a dynamic having any or all such aspects as: active/passive, right/wrong, we/ they, dominant/subordinate, conflict, complementarily. For example:
10.1 The above sections have identified: the constraints on set formulation imposed by number: the importance for comprehensibility of representation in 3 dimensions; the impact of particular number choices on the consciousness of those exposed to such sets; the problems of comprehension and the role of memory; and the properties exemplified by sets of a given number of terms. These are brought into focus by the problems of representing and comprehending multi-term sets. The problems have been strongly emphasized.
9.1. Characteristics of multi-term systems: The remarks of the previous section provide a context within which efforts at establishing the characteristics of multi-term systems can be considered as defined in Annex 1 . This question cannot be explored here. It serves as an indication only therefore, that the results of J. G. Bennett's exercise are summarized in Annex 2. This suffers from the disadvantage of not establishing explicit links to the rich variety of cultural and mathematical material reviewed by von Franz in her study of the first four integers.
8.1 Problems of comprehension: It is appropriate to note that work in the well-defined field of "multi-valued logic" does not seem to have had any impact on these concerns37. Nor does that on the "theory of numbers"33. It is only more recently in studies which face up to non-quantitative considerations with propositions for 3 or 4-valued logics that the nature of the link begins to emerge (48, 49).
7.1 Beyond 2-term logic: multi-term systems: In the above argument the terms "set" and "system" have been used interchangeably since one of the characteristics of the sets of elements under consideration was identified as the complementarily of their elements. In discussing multi-term systems, a mathematician and director of industrial research J. G. Bennett clarifies further the kinds of sets to which these arguments apply (45, vol. 2, pp. 3-10). A set of elements taken without reference to any internal connections is called a class.
6.1. Whenever it is convenient, there is a widespread tendency to avoid consideration of the impact of those involved on research or on the policy-making process in which they participate. Researchers correct for bias in experiments and aim for reproducible results. Efforts are made to balance the interests represented at policy meetings. Consequently, when sets of basic values, problems, concepts, or principles are generated by either, they are conceived to be objective.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585302.56/warc/CC-MAIN-20211020024111-20211020054111-00184.warc.gz
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CC-MAIN-2021-43
| 4,574 | 13 |
http://answers.shoppingcartelite.com/
|
math
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Is it possible to list a service or a product that can not be purchased but with the option to call to order?
Tech > Products
I am using the image URL for my items and see that it changes. Why is it changing?
If we set up a Net 30 term for customers, does it mean those customers can process orders without paying online?
Tech > Settings
How do you enable the auto complete search on a third party website
How to set redirect rule to receive my SCE email in my gmail box?
Tech > Email
How can plugins affect website speed and conversions?
What Merchant Processor is recommended to be used with Shopping Cart Elite?
Can I do an in store sale that is not a product on the website
How can I change my logo?
Do we have an option for our web visitors to choose a language?
What do I put for ShippingCode and SceCode while creating shipping APIs
Issue with logging in SCE. It's telling me to update to .NET 4.6
How to reinstall Shopping Cart Elite software?
How do I activate SEO features?
Tech > Seo
Is it possible to accept gift cards on the site?
When I should choose product (DropShipper) type of suppliers and when Manufacturer (Warehouse)?
How i can export all my suppliers?
Why customers export button is not active?
Tech > Customers
How can I get e-mail notifications about abandoned orders ?
Tech > Orders
Does Shopping Cart Elite support multi-vendor store?
Ask a question and receive knowledgeable answers from topic experts
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585280.84/warc/CC-MAIN-20211019171139-20211019201139-00475.warc.gz
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CC-MAIN-2021-43
| 1,435 | 27 |
https://personalkurser.slu.se/kurser/kurs.cfm?KursID=PFS0174&oid=13
|
math
|
Statistics IV: Generalized linear models, Umeå (4 ECTS)
The objective of the course is to give an overview of generalized
On completion of the course, the student will be able to:
The course will cover the following topics:
- specify generalized linear models including conditions and
- select an appropriate linear model for a given problem;
- carry out an analysis based on a generalized linear model in the
statistical software R;
- interpret and evaluate results correctly and draw reasonable
- clearly and concisely communicate results and conclusions.
- Binomial and multinomial logistic regression;
- Poisson regression;
- Overdispersion and zero-inflation;
- Generalized linear models and generalized linear mixed models.
Statistics III: Regression Analysis or equivalent.
Admitted to a Ph.D. program at SLU.
If you are not a Ph.D. student or not at SLU, contact
[email protected] to check the availability of
places in the course.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476432.11/warc/CC-MAIN-20240304065639-20240304095639-00733.warc.gz
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CC-MAIN-2024-10
| 944 | 19 |
http://mathhelpforum.com/calculus/128872-apple-orchard.html
|
math
|
To maximize the average annual yield, first get an expression for it so as to get intuition. So solve to find the point M where the derivative of the average annual yield is 0.
Doing so, I get that point occurs when
at this point it'll be helpful to denote the right hand side of this equation, the average annual yield, as AAY.
Now looking at the graph, when M ~ 33 years, y(33)=33*500 > AAY, since the integrand in the expression for AAY would have to be a constant for them to have a chance to be equal. In partiuclar, y(M)>AAY for all values of M<33 years. This means we need to go out further in time, so as to add more area to AAY, while y(M) itself decreases since the function is concave down. 50 years seems reasonable.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698543577.51/warc/CC-MAIN-20161202170903-00226-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 728 | 4 |
https://socratic.org/questions/how-do-you-solve-the-system-of-linear-equations-given-y-2x-3-y-2x-3
|
math
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How do you solve the system of linear equations given #y=2x-3, y-2x=-3#?
Both equations are identical
and so is the second equation!
These two equations are the same equation, so one is redundant and the other completely describes the solution set.
Both the equations are the same equation. So the line
Is this typed in correctly?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00529.warc.gz
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CC-MAIN-2021-49
| 330 | 6 |
https://www.houseofmath.com/encyclopedia/algebra/equations-and-inequalities/equations/systems-of-equations/what-are-systems-of-equations
|
math
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What Are Systems of Equations?
A system of equations is quite simply a collection of equations. Until now you have been working with one equation with one variable (one unknown). Now you’ll learn how to solve two equations with two variables (two unknowns).
In general, systems of equations can have as many unknowns as you want them to, but you need to have as many equations as unknowns to get a unique answer. In mathematics there in an entire field called linear algebra, which deals with solving systems of equations.
So why do you need systems of equations? The answer is simple: Often several things are dependent on each other, and then you need a tool that takes this into consideration. An example is buying children’s tickets and adults’ tickets at the same time. You know the total price of the tickets and how many tickets you bought, but what is the actual price of the two different types of tickets?
You’re going to learn three methods for solving systems of equations: Solving by graphing, the substitution method and the elimination method. All of these methods do exactly the same thing: They solve two equations with two variables. It doesn’t really matter which method you use while solving problems, but you are expected to know all three. Solving by graphing is the easiest, so let’s begin with that one. But before you start learning about the different methods there are some things you need to be aware of.
Important things about two equations with two variables
- The solutions of linear systems of equations are made up of two values: an value and a value.
- These two values are the first coordinate and the second coordinate of the intersection of the two graphs created by your equations.
- In fact, the equations you are given can be rewritten into functions you can draw as graphs in a coordinate system.
- Whether you use the substitution method or the elimination method, you will have two values in your solution. These two values can always be thought of as the coordinates of the intersection of the two graphs.
- If you can’t find a solution, it means the graphs are parallel. In that case they have the same slope, but meet the second axis at different points. Because of that they will never intersect.
- If you find an infinite number of solutions, it means that the graphs are identical. That means that they have the same slope, and meet the second axis at the same point. The graphs are on top of each other, and they intersect at every point.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104668059.88/warc/CC-MAIN-20220706060502-20220706090502-00659.warc.gz
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CC-MAIN-2022-27
| 2,502 | 12 |
https://www.analystforum.com/t/normalized-earnings/13519
|
math
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Question (I had to look this topic up to review): Given the following information, calculate the normalized EPS using the method of average return on equity. 2000 ROE: .12 2001 ROE: .09 2002 ROE: .15 2003 ROE: .21 2000 BVPS: $40 2001 BVPS: $30 2002 BVPS: $35 2003 BVPS: $45 A. 6.41 B. 7.02 C. 9.45 D. 5.34
A. kind of a vague questions, isn’t it?
A? Seems to easy though, so I’m waiting to be corrected.
yea A Avg Roe = .1425 multiply by the 2003 BVPS = .1425*45 = 6.41
A. Question not vague but rather straigtforward… I hope! Take avg of ROE times ending BV was my thought process.
You guys are all over it. A is the correct answer. I’m reviewing the mkt valuation section tonight. Seems pretty light but testable… Might have some more problems for yall in a little bit.
Agree with the above.
I would LOVE to see some questions like this on 6/7
be careful on these if the final year NI is an estimate. I think at that point you take the average of all prior years times the ending BV. (I think)
that is what i meant by vague. it feels like there is info missing and the answer i gave (and everyone else) seems too easy and straightforward. i’m probably being paranoid.
i totally remember getting hosed on a question because I accidetally used an estimate in the average ROE calc., but I can’t find it. I can almost 100% gurantee it was from Schweser, because that is their MO.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056297.61/warc/CC-MAIN-20210918032926-20210918062926-00266.warc.gz
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CC-MAIN-2021-39
| 1,390 | 11 |
https://onlinembadegree.in/free-aptitude-test/
|
math
|
Online MBA Degree
Best of Luck
Keep it Fast
Free Aptitude Test
1 / 30
A, B, C and D can do a piece of work in 40 days. If A and B can do it together in 100 days,and C alone in 120 days, find the time in which D alone can do it.
2 / 30
A and B can do a piece of work in 6 days and C in 12 days. In how many days will A, B andC do it together?
3 / 30
A can do a piece of work in 40 days. He worked at it for 5 days then B finished it in 21days. In how many days can A and B together finish the work?
4 / 30
12 men can dig a trench in 36 days working 10 hrs/day. How many hours a day of dailywork will be required of 36 men working for 30 days to dig that trench?
5 / 30
20 men, 30 women and 60 children working 6 hours/day build a 200 m long 2 m high and40 cm wide wall in 20 days. How long a wall 1.5 m high and 60 cm wide will 30 men, 15 womenand 30 children build, working 9 hours/day in 15 days?
6 / 30
X can walk a certain distance in with a uniform speed in 50 days. How long will it take himto cover twice the distance with half of the normal speed?
7 / 30
Two quantities are in the ratio 2:3. What is the smaller number if their sum is 70?
8 / 30
X travels distance Y in 5 hours. If the speed increases by 8 kmph, then it would have taken3 hours. Y is
9 / 30
The first third of a 75 km trip took twice as long as the rest of the trip. If the first third tookh hours, then the average speed for the whole trip was
10 / 30
Two cyclists do the same journey by travelling at 9 and 10 km/hr respectively. Find thedistance traveled when one takes 32 minutes longer than the other.
11 / 30
A man buys milk at certain rate per liter and after mixing it with water sells itagain at the same rate. Find how many ml of water there are in every liter of milk ifthe man makes a profit of 20%?
12 / 30
A mixture of glycerin and water contains 35% glycerin by weight. 25 grams ofwater is added to such 100 grams of mixture. What % of glycerin by weight isthere in the new mixture?
13 / 30
A sum of Rs 45 is made up of 100 coins, partly of 50 p and partly 25 p. Howmany 50 p coins are there?
14 / 30
The ratio of milk and water in 55 liters of mixture is 7: 4. How much water mustbe added to make the mixture’s ratio 7: 6 (in liters)?
15 / 30
A businessman sells a lot of shirts at a profit of 12.5% and then invests theproceeds in purchasing a lot of trousers, which he sells at a profit of 20%. If hemakes a net profit of Rs. 700, the cost of the shirts was?
16 / 30
A man sold an article at 10% loss. Had he sold the article for Rs. 10 more, hewould have earned a profit of 10%. What is the cost price of article (in Rs.)?
17 / 30
A man purchased a carriage and horse in Rs. 1500. By selling the horse at10% loss and carriage at 20% profit he earned a profit of 8% on the wholetransaction. What is the price of carriage (in Rs.)?
18 / 30
X shaved 40% of his customers and gave a haircut to 80%. He charged Rs.7for a shave and Rs.5 for a hair cut. If 20% of customers who opted for a shavealso had a haircut, what were the earnings if he had 75 customers?
19 / 30
R got 35% hike in his salary and 20% incentive on sales. If R sold goods worthRs. 850 last year and the salary was Rs 70, then how much more does he earnthis year with sales of Rs.900?
20 / 30
R earns Rs.15000 a year. He spends 18% on rent. How much rent does he payin a month?
21 / 30
There are 50 students of whom 47 are present. What % is absent?
22 / 30
D’s income is Rs. 960. She saves Rs. 192. What % does she save?
23 / 30
What is the HCF of 143 and 208?
24 / 30
What is the LCM of 24, 48 and 72?
25 / 30
When 8% of a number is added to the number itself the result is 810. What isthe number?
26 / 30
Which is the least number, which, when divided by 12 and 16, leave the sameremainder, but is exactly divisible by 11?
27 / 30
In x/y, the remainder is 17. In 2x/y, the remainder is 5. What is y?
28 / 30
What will be the number of zeros at the end of the product of 1, 3, 5, 7 ….. 99?
29 / 30
A 3-digit number xyz is squared, which of the following could be the last digitof the square?
30 / 30
X divided by 899 gives a remainder 63. What remainder will be obtained bydividing X by 29?
The average score is 6%
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100229.44/warc/CC-MAIN-20231130161920-20231130191920-00582.warc.gz
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CC-MAIN-2023-50
| 4,178 | 65 |
https://ijedr.org/viewfull.php?&p_id=IJEDR1804038
|
math
|
Low Cost Journal,International Peer Reviewed and Refereed Journals,Fast Paper Publication approved journal IJEDR(ISSN 2321-9939)
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Movie Success Prediction Using Data Mining
Antara Upadhyay, Nivedita Kamath, Shalin Shanghavi, Tanisha Mandvikar, Pranali Wagh
The success rate of a movie is largely dependent on people's perception and opinions, through word-of-mouth. In today's digital world, word-of-mouth is prevalent in the form of reviews found online. The opening day and the first few weeks following a movie's release is crucial, and hence production houses place a lot of importance on moviegoers’ opinions, and develop trailers and publicity strategies to sway public opinion. Taking this into account, the paper proposes the use of a review system for predicting the success rate of a movie. Moviegoers’ opinions of a movie before and after the release of the movie will be determined using sentiment analysis. A custom dictionary will be developed comprising words commonly used in movie reviews, which will be mapped to their corresponding weight-age in order to score reviews on a scale of one to five, and accordingly classify the success rate of movies.
Keywords- Movie Reviews; Sentiment Analysis; Classification.
Unique Identification Number - IJEDR1804038Page Number(s) - 198-203Pubished in - Volume 6 | Issue 4 | November 2018DOI (Digital Object Identifier) - http://doi.one/10.1729/Journal.19300Publisher - IJEDR (ISSN - 2321-9939)
Cite this Article
Antara Upadhyay, Nivedita Kamath, Shalin Shanghavi, Tanisha Mandvikar, Pranali Wagh, "Movie Success Prediction Using Data Mining"
, International Journal of Engineering Development and Research (IJEDR), ISSN:2321-9939, Volume.6, Issue 4, pp.198-203, November 2018, Available at :http://www.ijedr.org/papers/IJEDR1804038.pdf
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CC-MAIN-2022-33
| 2,382 | 11 |
http://www.appspy.com/app/776006/pimp-text-message-app-free-whats-cute-face-msn-apps-for-hotmailskypegmail
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math
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Pimp Text Message Free - You dominos Face App for mail,webmail
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DescriptionImpress your friends with cool colorful text messages!
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# Runs on iPhone and iPod Touch
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# Works with SMS and iMessage
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What's New in Version 5.0- IOS 8 Optimized
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864387.54/warc/CC-MAIN-20180622084714-20180622104714-00494.warc.gz
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CC-MAIN-2018-26
| 571 | 14 |
https://cynosurenewmedia.com/ADDIE.html
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math
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In the ANALYZE step the instructional problem is defined by answering the questions:
• What is to be learned?
• Who needs to learn it?
• Why do they need to learn it?
• How are they going to learn it?
• How will we know they learned it?
The outcome of the ANALYZE step are formal instructional goals and objectives, a determination of the learning environment, and a sense of the learner’s existing knowledge and skills.
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CC-MAIN-2022-40
| 432 | 7 |
https://hirecalculusexam.com/differentials-and-calculus-derivatives-examples
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math
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The first step is to learn the definition of a derivative, so here are some examples to start you off. For instance, a derivative is a term that describes how an object changes from one state to another, with respect to some other value. You can think of a derivative as a ride on an object. A ride will not move very fast, but at the same time it will go very slow. Therefore, the derivative describes the change that the object will go through over a period of time.
There are different types of derivatives that we will look into later. We will start off with the linear and the tangent derivatives. The former is the straight line derivative, while the latter is the hyperbola, which describes a parabola. There are also the gamma function and the quadratic formula. We will go into more advanced topics as we move on towards the end of this article. Before you proceed any further, it would probably be wise to brush up your basic algebra skills, so that you do not find yourself lost in any kind of complicated mathematical equations when you study these derivatives examples.
The first thing that you should learn about derivatives is that they are an integral part of all of the basic laws of physics. This means that they are governed by the momentum law, the force law, and the equilibrium law. You should also know that derivatives can be complex and are influenced by both constant and variable functions. When dealing with derivatives, it is important to remember that they are always changing. In other words, there is no such thing as a constant or a fixed value for a derivative’s curve. For example, if you were to plot a derivatives curve on a graph, you would eventually show a loss of momentum, due to constant changes in the angle of attack between the two variables.
In order to help you better grasp the concepts of derivatives, it would be helpful to learn how they are used in the context of real life. This can include how they are used in rocket launches, aircraft engines, and even in some forms of machinery. You can take some advanced calculus courses to help you learn more about derivatives, but for the purposes of this article, we will stick to basic examples. In order to help you better understand derivatives, it would be helpful if you took a look at real world examples. The following are just a few derivatives examples that you might want to think about.
Slopes: Many people don’t realize that there are different types of derivatives, and most of them relate to slopes. A slope derivative, for example, relates the slope of an object to its derivative, the initial value of which is plotted on the left side of the graph. The initial value, in this case, is the point where the slope equals zero, at which point the slope continues on to its normal direction, or what is called an “intermediate value.”
Intervals: Another integral term in derivatives is the intercept-expression, which relates the initial value of the derivative to the intercept at the end of a function. This can be thought of as the point where the slope of the derivative returns to its original value, or what is known as the mean square value of the derivative. The intercept-expression is actually the difference between the actual value of the derivative at any point and the one that was calculated, or the mean square value of the derivative. The slope of the derivative of an interval is actually a function of the interval itself and can be written as a difference of the derivative. Other derivatives that have intercept-expression values along their x axis could also be graphed as intercept-expressions.
In summary, calculus derivatives examples can help a student learn the necessary concepts of derivative equations and derivatives computations. They are the basis for many complicated calculus equations, and a student should never begin a problem without first having a working knowledge of derivatives. Students can practice their knowledge by taking practice problems designed to test their knowledge of derivatives at various points in the form of graphical presentations. Graphing these derivatives on a horizontal axis as well as the vertical axis will give a more visual sense of the relationships among the variables, as well as any interactions among them.
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CC-MAIN-2023-50
| 4,300 | 7 |
https://wiki.freecadweb.org/index.php?title=Translations:Part_Cone/10/en&oldid=93243
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math
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- Radius 1 - radius of the arc or circle defining the lower face
- Radius 2 - radius of the arc or circle defining the upper face
- Height - the height of the Part Cone
- Angle - the number of degrees of the arc or circles defining the upper and lower faces of the truncated cone. The default 360 creates circular faces, a lower value will create a portion of a cone as defined by upper and lower faces each with edges defined by an arc of the number of degrees and two radii.
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CC-MAIN-2020-50
| 476 | 4 |
https://internetoracle.org/digest.cgi?N=715
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math
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} <leans close to the supplicant> What's that, sonny? Could you speak
} up a bit? <slams fist against ear> These damn components keep
} shorting out. What good does it do to have the greatest intelligence of
} all time when I can't hear what my supplicants say? <digs component
} out of ear> Hmm. There's something else in there....<digs a giant
} pillow out of ear> That's odd...<digs an African elephant out of ear>
} Wha....?...<digs around some more and comes up with a collection of
} _Doogie Houser_ tapes> Aaaa! <throws it across the room, in fright>
} I've got to get to the bottom of this. <door opens and slams>
} <muffled> Lisa?....Do you know who's been stuffing stuff in my ear?
} It wasn't the kid at PSU who keeps sticking his 18-line sig. on all his
} questions, was it? Or the one who keeps asking woodchuck questions,
} but spells it "woodechuck"? No?... Well, tell me if you figure it
} <door opens and slams; Oracle re-emerges> Strange, strange. Somebody
} is trying to make me deaf. <glances at _Doogie Houser_ tapes> And if
} I'm not mistaken, stupid, too. <sits back in a comfy easy chair and
} flips on TV with the remote; the theme song for _Beakman's World_
} BEAKMAN (on TV): Today's question comes from Billy of Pensacola,
} Florida. "Beakman: Are there any other question and answer guys out
} there who could explain things about science and other type stuff?"
} <rips the card in two> That's a silly question, Billy. Of course
} there aren't. At least, none with a goofy hairstyle like this...
} <gestures at his huge mega-Kramer 'do>
} RAT (on TV): <looks embarrassed> Um, Beakman. There's another one
} out there...and this one is.....<gulp> omniscient.
} BEAKMAN (on TV): Omniscient? <does a double-take> I've got to meet
} this guy, share some stories. I bet he's had quite a few interesting
} questions over the years!
} RAT (on TV): Uh, you mean you're not mad there's another question and
} answer guy...even one who's omniscient?
} BEAKMAN (on TV): No. Why should I? I'm the Beakman! <gestures again
} to his wild hairstyle>
} <RAT slinks off, twiddling his thumbs behind his back.> Rats. Better
} take care of this before Beakman finds out.
} BEAKMAN (on TV): Next question. This comes from Sally in Beaver
} Springs, PA. "Dear Beakman: What's the difference between woodchucks
} and grounhogs?" Well, Sally...
} <Oracle hits the 'off' button on the remote; shudders slightly>
} Hmm. Looks like another question is coming in. <tears it off the
} >The USENET Oracle requires an answer to this question:
} >Oh, great all-mighty omniscience. I don't know how to say this but
} >I've done something terrible. I work for another question-and-answer
} >guy, and I thought he'd be jealous of you, so I tried to incapicitate
} >you. I hope you're not too mad, but there's an *ELEPHANT* in your
} >ear. And some other stuff. I'm really sorry, but I hope you don't
} >make too big a deal out of this because I'd probably get in trouble
} >with Beak...with my employer. Then he'd make me get in the mucous
} >demonstration tunnel again. Yuck. Anyway, I'm sorry and I hope you're
} <calling> Lisa! Type this response up for supplicant #457789-0:
} No hard feelings, mouse-man. We omniscient beings are far more
} forgiving than you give us credit for (if only certain deities would
} stop turning people into constellations and donkeys and pillars of
} salt, I'm sure our reputation would be far kinder). You are absolved
} from all wrong-doing; but I would have you know that next time I am
} subjected to _Doogie Houser_ I will consider it an act of war.
} You owe the Oracle an episode guide to _Beakman's World_ and a groovy
} new haircut.
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| 3,671 | 57 |
https://coindar.org/en/event/viacoin-via-reddit-ama-with-head-of-marketing-1733
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math
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Show coin info
24h volume, BTC
Viacoin VIA: Reddit AMA With Head of Marketing
Added 1/10/2018 3:04:31 PM
Mike will answer questions for at least a couple of hours. If you're curious about VIA's marketing plans for 2018 and beyond, don't let this opportunity to have your questions answered pass by!
Viacoin price changes after event publication
Added 3 years ago. All Viacoin events on the chart.
The event is about to begin
During the whole time of Viacoin monitoring, 19 events were added: 7 exchange events
2 conference participations
1 event related to testing of new functions
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| 586 | 11 |
https://www.teacherspayteachers.com/Product/Statistics-VI-medians-for-larger-n-and-distributions-2747037
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math
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Be sure that you have an application to open
this file type before downloading and/or purchasing.
85 KB|2 pages
Part I: Given only n, find the position of the median or the positions of the two numbers you would average to find the median. Part II: Given a frequency diagram, a stem-and-leaf plot, or a list of numbers, find the median.
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https://stocksnewswire.com/2020/10/07/bond-valuation/
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math
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Bond valuation is the technique for evaluation of the fair value of a particular bond. It includes the calculation of the present value of the futuristic interest payments of the bond which is also termed as the cash flow and the value upon the final maturity (termed as par value or face value). The face value of any bond is fixed and so are the interest payments. Hence, the investors use this value for evaluation of the return rate for the bond or investment to fetch positive results.
It was estimated at the end of 2018 that the US bond market had a size of approximately $42.7 billion. Bonds provide a steady income to the investor in the form of coupon payments. At the time of the maturity, the whole face value of the bond is repaid to the investment holder of the bonds. The characteristics of a regular bond are:
- Coupon rate: The interest rate of the bonds is termed as the coupon rate. It is usually paid semi-annually to the bondholders. The coupon rate is the fixed interest given to the investor on a periodic basis until the time of maturity.
- Current price: The investor might purchase the bonds at par, above par or below par; as per the interest rate. The value of the bond will decrease with the higher interest rates as the coupon rate will be lower than the interest rate in the economy.
- Maturity rate: All bonds have maturity dates (long-term or short-term). At the time of the maturity of the bond, the issuer repays the investor the full-face value of the bond. The government bonds have an FV of $10,000 and for the corporate bonds, it is $1000.
Practical implementation of Bond Valuation
Bonds are a very essential part of the capital markets. This is the major reason that the analysts and the investors look forward to understanding their features for interaction for determining their intrinsic value. The value of a bond determines the suitable investment for the portfolio and it is a major step in their investment. Bond valuation is the real calculation of the present value of a bond expected future coupon payments. Theoretically, the fair value of a bond can be calculated by discounting the price of its coupon payments by the right discount rate. Calculation of the value of a coupon bond gives annual or semi-annual yield for the cash flow and the par value of the bond.
Zero-Coupon Bond Valuation
A zero-coupon bond makes no semi-annual or annual payments for the bondholders. It is calculated only by finding the present value of the face value of the bond. The difference between the purchase price and par value would be the investor’s interest attained on the bond.
Bond valuation is the way to determine the par value (theoretical fair value) of a particular bond. It includes the calculation of the present value of the expected future coupon payments or the cash flow and the maturity value of the bond (face value). By calculation of bond valuation, the investors can figure out the rate of return made by a bond investment worth the costing.
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| 3,000 | 10 |
http://everything.explained.today/Numerical_aperture/
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math
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In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another provided there is no optical power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
where n is the index of refraction of the medium in which the lens is working (1.00 for air, 1.33 for pure water, and typically 1.52 for immersion oil; see also list of refractive indices), and θ is the half-angle of the maximum cone of light that can enter or exit the lens. In general, this is the angle of the real marginal ray in the system. Because the index of refraction is included, the NA of a pencil of rays is an invariant as a pencil of rays passes from one material to another through a flat surface. This is easily shown by rearranging Snell's law to find that
In air, the angular aperture of the lens is approximately twice this value (within the paraxial approximation). The NA is generally measured with respect to a particular object or image point and will vary as that point is moved. In microscopy, NA generally refers to object-space NA unless otherwise noted.
In microscopy, NA is important because it indicates the resolving power of a lens. The size of the finest detail that can be resolved is proportional to λ/2NA, where λ is the wavelength of the light. A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Assuming quality (diffraction limited) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field.
Increasing the magnification and the numerical aperture of the objective reduces the working distance, i.e. the distance between front lens and specimen.
This ratio is related to the image-space numerical aperture when the lens is focused at infinity. Based on the diagram at the right, the image-space numerical aperture of the lens is:
\right)\right] ≈ n
The approximation holds when the numerical aperture is small, but it turns out that for well-corrected optical systems such as camera lenses, a more detailed analysis shows that
The f-number describes the light-gathering ability of the lens in the case where the marginal rays on the object side are parallel to the axis of the lens. This case is commonly encountered in photography, where objects being photographed are often far from the camera. When the object is not distant from the lens, however, the image is no longer formed in the lens's focal plane, and the f-number no longer accurately describes the light-gathering ability of the lens or the image-side numerical aperture. In this case, the numerical aperture is related to what is sometimes called the "working f-number" or "effective f-number." A practical example of this is, that when focusing closer, with e.g. a macro lens, the lens' effective aperture becomes smaller, from e.g. f/22 to f/45, thus affecting the exposure.
The working f-number is defined by modifying the relation above, taking into account the magnification from object to image:
The two equalities in the equation above are each taken by various authors as the definition of working f-number, as the cited sources illustrate. They are not necessarily both exact, but are often treated as if they are. The actual situation is more complicated — as Allen R. Greenleaf explains, "Illuminance varies inversely as the square of the distance between the exit pupil of the lens and the position of the plate or film. Because the position of the exit pupil usually is unknown to the user of a lens, the rear conjugate focal distance is used instead; the resultant theoretical error so introduced is insignificant with most types of photographic lenses."
Conversely, the object-side numerical aperture is related to the f-number by way of the magnification (tending to zero for a distant object):
In laser physics, the numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance - the laser beam forms a cone of light in the "far field". The relation used to define the NA of the laser beam is the same as that used for an optical system,
but θ is defined differently. Laser beams typically do not have sharp edges like the cone of light that passes through the aperture of a lens does. Instead, the irradiance falls off gradually away from the center of the beam. It is very common for the beam to have a Gaussian profile. Laser physicists typically choose to make θ the divergence of the beam: the far-field angle between the propagation direction and the distance from the beam axis for which the irradiance drops to 1/e2 times the wavefront total irradiance. The NA of a Gaussian laser beam is then related to its minimum spot size by
where λ0 is the vacuum wavelength of the light, and 2w0 is the diameter of the beam at its narrowest spot, measured between the 1/e2 irradiance points ("Full width at e-2 maximum of the intensity"). This means that a laser beam that is focused to a small spot will spread out quickly as it moves away from the focus, while a large-diameter laser beam can stay roughly the same size over a very long distance. See also: Gaussian beam width.
A multi-mode optical fiber will only propagate light that enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, θmax. For step-index multimode fiber in a given medium, the acceptance angle is determined only by the indices of refraction of the core, the cladding, and the medium:
Substituting cos θc for sin θr in Snell's law we get:
By squaring both sides
Solving, we find the formula stated above:
This has the same form as the numerical aperture in other optical systems, so it has become common to define the NA of any type of fiber to be
where ncore is the refractive index along the central axis of the fiber. Note that when this definition is used, the connection between the NA and the acceptance angle of the fiber becomes only an approximation. In particular, manufacturers often quote "NA" for single-mode fiber based on this formula, even though the acceptance angle for single-mode fiber is quite different and cannot be determined from the indices of refraction alone.
In multimode fibers, the term equilibrium numerical aperture is sometimes used. This refers to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution has been established.
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| 7,189 | 22 |
https://oneclass.com/study-guides/ca/uottawa/admin/adm2302/259083-cheat-sheetdocx.en.html
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math
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-Linearity:the impact of decision variables islinear in constraints and objective funct-Divisibility:noninteger values of decisionvariables are acceptable;
-Certainty:values of parameters are known andconstant; -Nonnegativity:negative values of decisionvariables are unacceptable.
*Tricky Constraints: 1) % of total production x1/(x1+x2+x3)>0.5 3) Units of x must be more than 5 times y x-5y=0
2) “x” must be equal to 2/3 y x-2/3*y=0 4) Transhipment problem for centre a x1a+x2a-x10z-xa11=0
5) Inventory Constraint Beginning Inv+Production-demand-ending inventory=0
1)Assign a variable to each axis2) Plot the constraints (using x intercept-y=0 and Y intercept-x=0) 3)determine feasible region ( above constraints if >= and under if
<=)4)solve for max or min by either i) plotting max/min function and moving it to the last point it is within feasible region OR ii) using the coordinates of each intercept of the
binding constraints and using the highest one.
Reports: 1)Answer: Target cell=Minimized or Maximized Profit, Adjustable cells=optimal solution, Constraints=binding/non binding and amount of slack
2)Sensitivity: Adjustable cells= optimal solution, objective coefficient, allowable inc and dec and reduced cost, Constraints=Final value, shadow price(max price you
are willing to pay for an additional unit) and slack (extra resources available at optimal solution)
*Shadow price’s range= (final value+allowable inc). (final value-allowable decrease)
Sensitivity &What if Analysis
1)Obj. Coefficient Ranging –How much could a single value cjchange without changing the current set of variables and their values in the existing optimal solution ?
*point remains the same but optimal value changes
2) RHS Ranging-What is the range of values for the RHS of each original constraint such that the current set of basic variables (but not theirvalues!) is still optimal ?
Special Case LP’s
1.Transportation Problems: Decision Variables: The amount of goods to be transported from origin i to destination j (x ) , Obj. Function: Minimize transportation costs (sum
of individual shipping costs), Constraints: i)Supply, ii) Demand( # of constraints=#of nodes)*if Supply>demand a dummy variable is added with 0 costs and demand=(supply-
demand) and if supplytaks then slack will show unassigned worker but if worker)
Decision Analysis -The decision alternatives are the different possible strategies or choices the decision maker can employ.
-The states of nature refer to future events which may occur.
-Selection of a decision alternative while a particular state of nature occurs produces a payoff or outcome.
-The decision maker can control the choice of an alternative, but cannot control which state of nature will occur.
1.Clearly define the problem 2.List all possible alternatives
3.Identify all possible outcomes for each alternative 4.Identify the payoff for each alternative and outcome combination
5.Use a decision modeling technique to choose an alternative (Payoff table or Decision tree)
1.Decision making under certainty (know for sure the payoff for every decision)
2.Decision making under uncertainty(do not know the likelihood that a specific outcome will occur. Maximax(highest), Maximin(lowest) ,Criterion of Realism (α
x (Max payoff for alternative)+ (1 –α) x (Min payoff for alternative)) ,Equally Likely (highest average ),Minimax regret ( minimize regret)
3:Decision making under risk (some knowledge regarding the probability of occurrence of each outcome) Expected monetary value ( payoff*prob), Expected opportunity loss,
Expected value of perfect information(EVwPI=Best payoff*prob and EVPI= EVwPI-Max EMV)
Prior Prob=P(B) *Conditional Prob=P(A|B)=Joint Prob= P(A and B)--> P(A and B) / P(B)= Posterior Probability=P(B|A)= P(A|B)*P(B)/ [P(A|B)*P(B) + P(A|C)*P(C)]
Phase 1 : Project Planning: 1.What is the project goal or objective?
2.What are the activities (or tasks) involved?
3.How are activities linked (i.e., precedence relationship) one another?
4.How much time is required for each activity?
5.What resources other than time are required for each activity?
Phase 2: Project Scheduling(Developing a time schedule for each activity and assigning resources to specific
activities) CPM PERT
1.When will the entire project be completed? 1.Optimistic time (a)
2.What is the scheduled start and end time for each activity? 2.Pessimistic time (b)
3.Most likely time (m)
3.Which are the “critical” activities(slack of 0)?- LST-EST=slack
4.Which are the noncritical activities(have slack)
5.How late can noncritical activities be without delaying the project?
6.Allowing for uncertainty, what is the probability of completing the
project by a specific deadline?
Phase 3: Project Controlling (Monitoring of schedules, resources and budget, and obtain feedback to revise the project plan )
1.Is the project on schedule? Ahead or behind?
2.Are costs equal to the budget? Over budget? Under budget?
3.Are there adequate resources to finish on time?
4.What is the best way to reduce project duration at minimum cost?
QUESTION 1: (25 points) SENSITIVITY REPORT
(c) From the optimal solution, what are the sales effort allocations to each of the distribution channels? (4 points)
Solution: Sales effort allocation to each distribution channel is: 1) T:258 units * 2.5 hrs per unit = 645 hours 2)B:
0units*3.75hrsperunit= 0hours 3) C:480 units * 3.8 hrs per unit = 1824 hours 4) I:4262 units * 0.5 per unit = 2131 hours
d) What would need to happen to the Business distribution option unit profits before it would be optimal to acquire an
advertising and sales force allocation of its own? (4 points)
Solution: Unit Profits from the Business distribution option would need to increase by the “Reduced Cost” amount of $31.375
to $94.375 (=63+31.375) before it would be optimal to distribute there and acquire an advertising and sales force allocation.
(e) Given the highly competitive markets for MP3 players in 2005, EPG was considering committing more financial resources
to support the advertising costs for this project. After some discussion, the Board of Directors approved another $12,000 for
this project. What will be the impact on the new optimal profit of these new operating funds for advertising? (
Solution: Since the Shadow Price for Advertising dollars is zero, then all the available funds are not being used up now.
Therefore, it would not be worthwhile for EPG to add more advertising dollars, and the new optimal profit will not change
from these new operating funds.
(f) Given a high volume of sales in early December, Wal-Mart has sent a memo to EPG requesting that the current contract
be renegotiated so that the 480 units be increased by 144 more units. Determine the impact on EPG’s total optimal profit if
the new terms of the contract go into effect. (4 points)
Solution: Given the Shadow Price for Commercial Contract sales of -45.15, then it costs EPG to increase distribution to Wal-
Mart. Thus, only if forced to do so, the optimal objective function value would decrease from $230,878 to $230,878 + (144
units * - 45.15) = $230,878-$6501.60 = $224,376.40. Note also that the decrease of 144 units does not exceed the
“Allowable Increase” of 156 units and therefore the Shadow Price is applicable.
QUESTION 2: BINARY PROBLEM
DWR Ltd has MADE new game consoles: zbox and ybox. Production lines cost $25,000 for zbox and $32,000 for ybox. Each console has profits: $150/unit for zbox and
$210/unit for ybox. DWR Ltd has space for creating 3 production lines capable of manufacturing the consoles and each line can be used to manufacture both consoles at the
same time. However, management has decided that in order to mitigate the risks, only one production line would be open.
zbox can be produced at the rate of 15 units/hr on line 1, 18 units/hr on line 2, and 22 units/hr on line 3. Ybox can be produced at the rate of 20 units/hr, 17 units/hr, and 10
units/hr respectively. Line 1 has 340 hours production capacity, line 2 has 400 hrs, line 3= 380 hours capacity.
Write in mixed binary integer programming problem. DO NOT SOLVE.
Let Xij = the number of game console i produced at on production line j, Where i = 1(zbox), 2 (ybox) and j = 1, 2,3
Yi = 1 if game c
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CC-MAIN-2018-17
| 8,243 | 83 |
https://www.freedomsphoenix.com/News/232656-2018-01-09-the-largest-prime-number-ever-discovered-is-23-million-digits.htm
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math
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It's been dubbed M77232917 – and if you're wondering why it needs a codename, well, we'd be here all day typing out the 23 million digits that make it up.
If it's been a while since high school math class, here's a quick refresher: Prime numbers are those that are only divisible by 1 and themselves. Small primes are fairly easy to identify through trial and error – 6 can be divided by 2 and 3, so it isn't prime, but 7 is – but as you look at larger and larger numbers it gets less obvious. It might take you a while to figure out, for example, that 11,319,033 isn't prime because it can be divided by 213 and 53,141. Finding the really large primes is a task best left up to computers running software like GIMPS.
As the MP in its acronym suggests, GIMPS is specifically searching for a rare class of prime numbers called Mersenne Primes. These are numbers that are one less than a power of 2, expressed as Mn = 2n - 1. That means that the newcomer M77232917 is calculated through a chain of 77,232,917 twos, and then subtracting 1. It's only the 50th known Mersenne Prime ever identified, and it's made up of 23,249,425 digits.
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CC-MAIN-2018-51
| 1,138 | 3 |
https://www.clutchprep.com/physics/practice-problems/103070/the-spring-of-a-spring-gun-has-force-constant-k-400-n-m-and-negligible-mass-the-
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math
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The spring of a spring gun has force constant
Calculate the speed with which the ball leaves the barrel if you can ignore friction.
Calculate the speed of the ball as it leaves the barrel if a constant resisting force of
For the situation in part B, at what position along the barrel does the ball have the greatest speed? (In this case, the maximum speed does not occur at the end of the barrel.)
What is that greatest speed?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Work By Variable Forces (Springs) concept. You can view video lessons to learn Work By Variable Forces (Springs). Or if you need more Work By Variable Forces (Springs) practice, you can also practice Work By Variable Forces (Springs) practice problems.
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CC-MAIN-2021-17
| 862 | 8 |
https://estudyllect.com/mathematics/question12041941
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math
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Prove a quadrilateral with vertices g(1,-1), h(5,1), i(4,3) and j(0,1) is a rectangle using parallelogram method one midpoint formula
We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).
Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus
Join JH and GI such that they form the diagonals of the quadrilateral.Now,
Now, mid point of JH=
Mid point of GI=
Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.
Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.
Thus, From ΔGIJ, we have
Now, JI= and GJ=
Substituting these values in (1), we get
Thus, GIJ is a right angles triangle.
Hence, GHIJ is a rectangle.
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CC-MAIN-2023-14
| 889 | 13 |
https://www.hackmath.net/en/math-problem/890
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math
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John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
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To solve this verbal math problem are needed these knowledge from mathematics:
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Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.
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How many elements can form six times more combinations fourth class than combination of the second class?
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A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value is
Is -10i a positive number?
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| 2,494 | 33 |
https://lawcyberpunk.com/mathematical-form-of-first-law-of-thermodynamics/
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math
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Share This Article
This is something I learned after watching this video: When a substance is in equilibrium with itself, it can also be said that energy is a form of random movement. This is especially true when that energy is moving from a positive to a negative. This is similar to the law of conservation of energy. The second law of thermodynamics says that the entropy of a system will always increase.
This may be the most important law in physics. It states that if a substance is in equilibrium (meaning that its energy is the same for every possible configuration of its particles), then it can’t have a negative entropy (meaning that it can’t have more entropy than it has). This is a big deal because entropy is how much information you have about your surroundings. The amount of entropy you have depends on the combination of your surroundings combined with each of your components.
Well, one could argue that we already have entropy, so the laws of physics are about entropy. But if we take entropy and add it to the number of particles, all we do is get the equation of state for the universe of all possible states. And it doesn’t matter what combination of the number of particles you have or the combination of your components. You can have 1, 2, 3, 4, or 5 particles that get the same entropy.
And if you’re still not convinced, you can compare the entropy of your components to that of the components of the universe. The entropy of your components is a function of the entropy that the universe has. If the entropy of your components is greater/smaller, then the entropy of the universe is greater/smaller.
This means that if you have a substance that has greater entropy, the substance has a greater entropy than the universe. This is the first law of thermodynamics.
This law is true because entropy is the measure of disorder in a system. The universe, in the sense of the first law, is a system in which atoms and electrons and photons and quarks are all moving around and interacting with each other. If you look up the first law in the dictionary, youll find it talks about “the tendency for physical systems to minimize their disorder and maximize their order.
This law, called the first law of thermodynamics, is extremely important, because it tells us that the universe is a system in which entropy is greater than the universe itself. In other words, the universe is a system in which disorder is greater than the order that exists within it. When you look up the first law in the dictionary, you’ll find that it talks about the tendency of a system to have a higher entropy than the universe itself.
As a young kid I had a book that said that entropy was the same thing as disorder. Like the old saying goes, entropy is “the measure of randomness”; disorder is “the measure of order”.
I remember reading that book when I was a kid, and my thinking was, “So what, I can go around in my room and read without looking at the book?’ And then I found out that a lot of books had random pages and I couldn’t have read that then. It’s like I’m using the same words to define two different things.
There is a mathematical formula for the entropy of a random arrangement of objects that has the same meaning as the definition of entropy in the physical world. If you have a random arrangement of objects that you have never seen, then you know how many ways the objects can be arranged.
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https://present5.com/models-of-the-solar-system-positions-of/
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math
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- Количество слайдов: 33
Models of the Solar System • Positions of planets change, whereas stars appear relatively ‘fixed’ • Greeks held on to the Geocentric model because they could not observe stars to change their positions, and therefore thought that the earth must be stationary • Ptolemy, Aristotle and others refined the geocentric model • But there were problems……. such as the path reversal by Mars Retrograde motion
Retrograde motion of Mars (path reversal seen in the Sky)
Epicycles – Ptolemic Geocentric Model
How do we know the Earth is spherical ? • The ancient Greeks had deduced not only that the Earth is spherical but also measured its circumference ! • What kind of an object always has a round shadow ?
Earth Shadow during Lunar Eclipse Multiple Exposure Photograph
Cyrene Alexandria Tropic of Cancer Syene
Eratosthenes’s method to measure the circumference of the earth At noon on summer solstice day the Sun is directly overhead at Syene, but at an angle of 7 o at Alexandria 7º 7 = Distance (Alexandria - Syene) --------------------360 Circumference of the Earth Sunlight Alexandria Answer: 40, 000 stadia = 25, 000 mi ! Syene Earth
Earth-Moon-Sun Geometry Aristarchus’s determination of distances (Closer the S-E-M angle to 90, the farther the Sun) If we replace the moon with a planet, then can determine relative distances, as done by Copernicus
Copernican Model: Inferior and Superior Planets (orbits inside or outside the Earth’s orbit)
Configurations of Inferior Planets, Earth, and the Sun Earth Inferior Conjunction Superior Conjunction
Configurations of Superior Opposition Earth Planets, Earth, and the Sun Conjunction Synodic (apparent) period – one conjunction to next (or one opposition to next)
Synodic and Sidereal Orbital Periods • Inferior planets are never at opposition; superior planets can not be at inferior conjunction • Copernican model of orbital periods • Synodic period is the apparent orbital period of a planet, viewed from the earth, when the earth-planet-sun are in successive conjunction or opposition • Sidereal (with respect to stars) period is the real orbital period around the Sun • Synodic periods of outer planets (except Mars) are just over one year
Apparent (Synodic) and true (Sidereal – with respect to stars) orbital periods of planets differ due to Earth’s relative motion Synodic periods of all outer planets (except mars) are just over 1 year because their Sidereal periods are very long and they are in opposition again soon after an earth-year
Earth-Venus-Sun Inferior planets appear farthest away from the Sun at ‘greatest elongation
Measurements of Distances to Planets Maximum Eastern Elongation P Earth E Angle of max elongation = P-E-S 90 deg P-E-S S Maximum Western Elongation Sin (P-E-S) = PS / ES ES = 1 AU
Copernicus first determined the relative distances of planets
Copernican Heliocentric Model: (Retrograde motion of Mars seen when Earth overtakes Mars periodically) Earth is closer to the Sun, therefore moves faster than Mars
Tycho: The most accurate pre-telescopic observer Tycho charted very accurately the movement of Mars in the Sky, but still believed In the Geocentric Universe
Kepler – Tycho’s assistant (used Tycho’s data to derive Kepler’s Laws)
Planetary Orbits • The Copernican heliocentric model is essentially correct • But it consisted of circular orbits which did not exactly fit observations of planetary positions • Kepler realized, based on Tycho’s data of the orbit of Mars, that orbits are elliptical Kepler’s First Law • However, the difference for Mars is tiny, to within the accuracy of drawing a circle with a thick pen !
Kepler’s First Law: All planetary orbits are elliptical, with the Sun at one focus
Eccentricity ‘e’: e = distance between foci/major axis = AB / ab a A B b A circle has e = 0, and a straight line has e = 1. 0
Kepler’s Second Law: Planetary radius sweeps equal area triangles in equal time It follows that the velocity of the planet must vary according to distance from the Sun -- fastest at Perihelion and slowest at Aphelion
Kepler’s Third Law: P 2 = a 3 P – Orbital Period, a – semi-major axis What is the size ‘a’ of the orbit of a comet with the period ‘P’ of 8 years?
Kepler’s Laws • Empirically derived from observational data largely from Tycho (e. g. observations of the positions of Mars in its orbit around the Sun) • Theoretical explanation had to await Newton’s discovery of the Law of Gravitation • Universally valid for all gravitationally orbiting objects (e. g. stars around black holes before falling in)
Galileo’s Discoveries With Telescope • Phases of Venus - Venus displays phases like the Moon as it revolves around the Sun • Mountains and “seas” on the Moon - Other objects in the sky are like the Earth (not therefore special) • Milky Way is made of stars like the Sun • Sunspots - “Imperfections” or “blemishes” in otherwise perfect “heavenly” objects • 4 Galilean satellites of Jupiter - Objects in the sky revolve around other objects, not the Earth (i. e. other moons) All of these supported the Copernican System Galileo also conducted experiments on gravity : Regardless of mass or weight objects fall at the same rate
Phases of Venus is never too far from the Sun, therefore can not be in opposition like the Moon. Changing phases of Venus demonstrate that it orbits the Sun like the Earth.
Orbits and Motions • Orbits can not be circular since objects do NOT revolve around each other, but around their common center-of-mass • The Earth and the Moon both revolve around each other • This motion is in addition to Earth’s Rotation, Revolution, Precession
The Earth-Moon Barycenter • The earth and the moon both revolve around a common center of mass called the Barycenter • The barycenter of Sun-planet systems lies inside the Sun • As the earth is much more massive, the barycenter lies 1700 Km inside the earth • Calculate its position ‘O’ from M(E) x EO = M (M) x MO M E O
Gravity • Galileo’s observations on gravity led to Newton’s Law of Gravitation and the three Laws of Motion • Objects fall at the same rate regardless of mass because more massive objects have more inertia or resistance to motion • Fgrav = G (m 1 x m 2) / r 2 • Force of gravity between two masses is proportional to the product of masses divided by distance squared ‘inverse square law’
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| 6,506 | 31 |
https://artofproblemsolving.com/wiki/index.php/2020_INMO_Problems/Problem_6
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math
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2020 INMO Problems/Problem 6
A stromino is a rectangle. Show that a board divided into twenty-five squares cannot be covered by strominos such that each stromino covers exactly three squares of the board, and every square is covered by one or two strominos. (A stromino can be placed either horizontally or vertically on the board.)
At first of all let assigne a matrix with .
Now notice that .
Now notice that , For each trominoes sum of the numbers that it cover is modulo .
Now let's assume that there are are unit square covered exactly once and unit square covered twice . So, .
So there are only unit square coverd exactly once.
Let assume that and are the unit squares that covered exactly once.
Since, I have assume that the colouring is possible that's why
again assign another kind of coloring , .
In this case we also get, .
From equation (1 )and (2) we should get, .
Similarly we have .
So , only possibility is .
So there will exactly one unit square covered exactly once.
Contradiction ! And we are done. ~ftheftics
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| 1,029 | 16 |
https://www.365footballpredictions.com/types-of-odds/
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math
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Types of Odds
Odds are the cornerstone of betting and without understanding them there will be no winning bettors. The explanation of coefficients is quite simply the price calculated exactly how much you will receive if your bet wins. In general speaking the odds do not alter no matter how much or little you are willing to stake on a selection. There are two most commonly used odds – fractional and decimal. There is no monetary distinction between the two and no reason to choose one over another. They are just different ways to present the same thing.
Fractional odds are displayed as 10/1 or 7/2. There are a couple of ways to make an effort and comprehend them but the most simple way is “how much you win”/”how much you stake”. For instance, if you stake £1 at 10/1 you will win £10 (do not forget that is your profit, you will get 1 pound-the stake back too!). In case you stake £2 at 7/2 then you will win £7 and get your £2 stake back.
Frequently you see coefficients which appear to be the opposite way round for example 1/10 or 2/7. These are referred to as ‘Odds-On’ selections and you should stake £7 to win £2. Moreover, you will see odds alike in case there is a strong and overshadowing favorite to win. For instance, when Chelsea faces Ipswich in the FA Cup, the Hosts of London were as short as 1/10 to win the game.
Most online betting sites will show you your potential profits on the betslip but it is essential to comprehend the odds for the sake of getting value. If you want to be a really winning bettor, you have to back winners and do so when the price precisely reflects the chance of winning. It’s not hard to predict that Chelsea would beat Ipswich 9 in 10 matches played but are you apt to staking £100 to make a profit of just £10?
To calculate your potential returns from fractional odds:
((Stake /denominator) x numerator ) + stake
For example, £10 staked at 7/2:
((£10/2) x 7) + £10 = £45
It is essential to know the approximate probability of each single fraction. Unless, you will meet serious obstacles in finding value in the odds offered by the bookmakers. If you want to calculate any fractional odd in percentage probability quickly, there is an easy to apply formula:
Implied probability = denominator / (denominator + numerator)
So if you want to back a selection 2/10 for a win of Juventus against Pescara, the probability of success of your stake will be:
2/10 = 10 / (10+2) = 0,83 = 83,33 %
Every member of our team is on the opinion that fractional coefficients are too confusing and elaborate and we still cannot believe that there bettors who prefers using them. It is undoubtedly that decimal odds are far easier to understand. If we promptly ask you to answer which odd is bigger, 7/4 or 9/5? It will take a while until you answer, right? But if we asked you the same question with decimal odds – 1.50 or 1.80? It’s very easy one to answer. So calculating potential profits from decimal odds (which are written as 1.80 or 4.50) is so much easier to understand. Let’s see the example below:
Stake x Odds
For example, £5 staked at 1.5:
£5 x 1.5 = £7.5( 5 pound stake is included, you win netto 2.5 pounds)
It is essential to know that your stake is included in your returns and it supports for a far easier calculation. Moreover, decimal odds of 2.0 shows even money (1/1) and anything less than 2.0 is an odds on bet. For instance 1.50 will see you win half your stake and to continue the example of Chelsea from above, Chelsea were priced at 1.10 to beat Ipswich Town.
It is impossible to see odds of less than 1.00 but it often happens to see 1.01 or 1.05. These types of odds are mostly given to a very strong favourite leading against an obvious underdog with 15 minutes left to play. It is unlikely to see them before the kick-off but in case this happens it will probably concern a football match from the first round of The Cup Tournament, especially when a first division team is facing a third or fourth division (Barcelona – Badajoz for instance, or Bayern – Duisburg), of course there are exceptions. You will need to be insanely brave and irrational to back selections at 1.01. You’d have to be quite convinced that backing a potential win for the favourite 100 times would be successful 100 times in order to be in profit , although many late goals are scored and sometimes wrong referees’ decisions could cost you the lucrative amount you have always dreamed of.
In case you need to convert fractional odds into decimal odds, it’s so easy. First, divide the fractions and add one (the one represents your stake). For instance, to convert 7/2 into decimal odds, you would divide 7 by 2 and add 1, which gives you 4.5. Please, note that decimal odds are just simple numbers. It is quite obvious that it is not hard to distinguish which decimal is bigger that the other. But if you really want to understand and to use them in your favor, you should be capable of converting them into their percentage probability. Thus, you will have a priceless advantage when trying to find value in the tough battle against the bookies’. If you want to calculate any decimal odd in percentage probability quickly, there is an easy to apply formula:
Implied probability = 1 / Decimal Odds
For example, we are backing a win of Arsenal against Crystal Palace at 1.65. So, the probability of success of your stake will be:
1 / 1.65 = 0,606 = 60,60 %
The last part of this article explains us how to convert probabilities in either fractional or decimal coefficients. After carefully reading all the sections included, you will broaden your knowledge in the betting market and gain priceless advantage among the bettor’s society by analyzing the odds offered by the bookies in deeper and completely different way. Please, take into consideration that barely 5 % of all punters are really successful. Our main priority is to facilitate you to penetrate the ‘top 5’ club. There are two easy to apply formulas for converting probabilities of outcome in fractional or decimal odds:
So, we had been provided with information that Roma has 25% to beat Barcelona. But how to convert this into fractional odd ?
Fractional odd = (100 / implied probability ) – 1
(100 / 25 ) – 1 = 3 (‘3’ in this case is used as fractional odd = 3 / 1).
Converting probability percentage in decimal odd is far more easier. Let’s use the same example :
Decimal odd = 100 / implied probability
100 / 25 = 4
Implied probability of 25% would return decimal odd of 4.00.
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http://www.ucw.cz/~kral/cv.html
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math
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Academic qualifications, summary of research achievements
Doctor of Science (DSc) received in October 2012 from the Academy of Sciences of the Czech Republic
Doctorate Degree (PhD) in Computer Science received in August 2004 from Charles University, Prague, Czech Republic
Master Degree (Mgr) in Computer Science received in September 2001 from Charles University, Prague, Czech Republic
Philip Leverhulme Prize in Mathematics and Statistics 2014
over 100 journal research papers and over 20 in refereed computer science conferences
journal publications include those in
Advances in Mathematics,
Canadian Journal of Mathematics,
Geometric and Functional Analysis,
Israel Journal of Mathematics,
Journal of the ACM,
Journal of Combinatorial Theory Series A and B, and
SIAM Journal on Discrete Mathematics
conference publication include those at FOCS, ICALP, SODA and STACS
over 600 non-self-citations according to WoS, H-index: 13 (WoS), 13 (MathSciNet), 25 (Google Scholar) as of November 2017
since October 2012, professor, Mathematics Institute and Department of Computer Science, University of Warwick
member of the Centre for Discrete Mathematics and its Applications (DIMAP)
July 2010-September 2012, associate professor, Department of Applied Mathematics (2010-11) and Computer Science Institute (2012), Charles University, Prague
February 2011-December 2012, adjunct researcher, Department of Mathematics, University of West Bohemia, Pilsen
August 2006-June 2010, researcher, Institute for Theoretical Computer Science, Charles University, Prague
October 2005-July 2006, visiting assistant professor and Fulbright scholar, School of Mathematics, Georgia Institute of Technology, Atlanta
August-September 2005, researcher, Department of Applied Mathematics, Charles University, Prague
October 2004-July 2005, postdoctoral fellow, Institute for Mathematics, Technical University Berlin; the position was funded by the European training network COMBSTRU
November 2001-September 2004, junior researcher, Institute for Theoretical Computer Science, Charles University, Prague
September 2001-August 2004, PhD student, Charles University, Prague;
PhD thesis on the topic of graph coloring problems advised by Jan Kratochvíl
Organization of schools and workshops: CCOSA Fall School 2011, CCOSA Winter School 2013, ICMS workshop on Extremal Combinatorics 2014, LMS-CMI Research school on Regularity and Analytic Methods in Combinatorics 2015, Oberwolfach workshop on Graph Theory 2016, Workshop on Algorithms, Logic and Structure 2016, 10 Year Anniversary DIMAP Workshop 2017, Workshop in Honour of Mike Paterson's 75th Birthday 2017, Workshop on Structural Sparsity, Logic and Algorithms 2018, Oberwolfach workshop on Graph Theory 2019
Computer Science Panel of the Czech Science Foundation (2011-15, vice-chair 2012)
Computer Science Board of the Charles University Grant Agency (member since 2010)
Supervision of graduate students and postdoctoral fellows
Postdocs: Jean-Sébastien Sereni (2006-08), Louis Esperet (2008-09), Demetres Christofides (2010-11), Ján Mazák (2011-12), Andrew Treglown (2011-12), Roman Glebov (2013), Anita Liebenau (2013-15), Ping Hu (2014-2017), Tamás Hubai (2015-2017), Andrzej Grzesik (2017-), Péter Pál Pach (2017-), Jonathan Noel (2017-)
Former PhD students: Pavel Nejedlý (Charles University, 2008), Jan Hladký (Charles University, 2013), Jan Volec (University of Warwick and Université Paris Diderot - Paris 7, 2014, co-advised with Jean-Sébastien Sereni), Lukáš Mach (University of Warwick, 2015),Tereza Klimošová (University of Warwick, 2015)
Current PhD students: Timothy Chan, Taísa Lopes Martins, Yanitsa Pehova
Student internships: Andrew King (2008-09), Andrzej Grzesik (2013 and 2014), Matjaž Krnc (2013), Fiona Skerman (2014), Francois Dross (2015), James Hirst (2016), Anton Bernshteyn (2017), Adam Zsolt Wagner (2017), Marcin Wrochna (2017)
Structural and extremal graph theory
Analytic methods in combinatorics, in particular, combinatorial limits
Logic methods in graph and matroid theory and their algorithmic applications
J. W. Cooper, D. Kráľ, T. Martins: Finitely forcible graph limits are universal, available as arXiv:1701.03846.
Z. Dvořák, D. Kráľ, R. Thomas: Testing first-order properties for subclasses of sparse graphs, Journal of ACM 60 (2013), article no. 5:36.
L. Esperet, F. Kardoš, A. King, D. Kráľ, S. Norine: Exponentially many perfect matchings in cubic graphs, Advances in Mathematics 227 (2011), 1646-1664.
D. Kráľ, O. Pikhurko: Quasirandom permutations are characterized by 4-point densities, Geometric and Functional Analysis 23 (2013), 570-579.
D. Kráľ, O. Serra, L. Vena: A Removal Lemma for systems of linear equations over finite fields, Israel Journal of Mathematics 187 (2012), 193-207.
D. Kráľ, R. Škrekovski: A Theorem about the channel assignment problem, SIAM Journal on Discrete Mathematics 16 (2003), 426-437.
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https://www.thefreelibrary.com/The+effect+of+ezetimibe+monotheraphy+on+mean+platelet+volume+in...-a0473104788
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math
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The effect of ezetimibe monotheraphy on mean platelet volume in patients with hyperlipidaemia: a retrospective study of 45 patients.
Objective: To investigate the effect of ezetimibe on platelet functions as a drug which increases mevalonate levels.
Methods: This retrospective study was conducted in Istanbul, Turkey, and comprised record of normolipidaemic and hyperlipidaemic patients taken from the outpatient clinic from October 2004 to February 2015,. The results were taken from the baseline and third-month data of ezetimibe treatment. SPSS 22 was used for statistical analysis.
Results: Of the total, there were 50(53%) normolipidaemic patients and 45(47%) hyperlipidaemic ones. Pre- and post-treatment values of mean platelet volume were significantly higher in the hyperlipidaemic group than controls (p0.05).
Conclusion: The use of ezetimibe alone should not be the first choice in hyperlipidaemia treatment.
Keywords: Ezetimibe, Mean platelet volume, Platelet activation. (JPMA 66: 1559; 2016)
Hyperlipidaemia is an important risk factor for the cardiovascular diseases (CVD).1,2 Ezetimibe is a lipid-lowering drug, which acts by inhibiting the absorption of cholesterol from the jejunum.3 In many studies showing the pleitrophic effects of statins, another lipid-lowering drug, ezetimibe have been used as a placebo to decrease the serum cholesterol levels. In these studies ezetimibe decreased the low-density lipoprotein (LDL) levels, but unlike statins it also increased the mevalonate levels.4,5 Although statins have some pleitrophic effects, such as improvement of endothelial function, an increase in nitric oxide (NO) levels, anti-oxidant and anti-thrombotic functions, ezetimibe is not known to have any pleitrophic effect.6-9
Platelet activity plays a role in the development and progression of atherosclerosis, and reduction of platelet activity is another pleitrophic effect of statins.10,11 There are many methods to show the platelet activation but they are expensive and time-consuming with the requirement of special experience.12-14 Mean platelet volume (MPV) is a simple marker for the platelet activity that is determined with routine automated haemograms as a part of the whole blood count (WBC).15 The current study was planned to investigate the effect of ezetimibe on platelet activity as a drug which increases mevalonate levels.
Patients and Methods
This retrospective study was conducted in Istanbul, Turkey, and comprised data of hyperlipidaemic patients from October 2004 to February 2015 that was compared with gender- and age-matched normolipidemic subjects. Data was collected from the internal medicine outpatient clinical records of Fatih Sultan Mehmet Education and Research Hospital. Patients who had been treated only with ezetimibe were included. Moreover, as we usually control the lipid parameters at the third month of treatment for the hyperlipidaemic patients, we preferred to include patients examined in outpatient clinics for at least 3 months period with full laboratory parameters of lipid profiles and whole blood counts.
Patients who had any infection, thrombotic or haematologic disorders, any medication effecting platelet function, haemoglobin (Hb) < 12.5 g/dl in men and <11.5 g/dl in women were excluded. Lipid parameters and MPV values at baseline and 3 months after ezetimibe treatment were used for statistical analysis. Approval for this study was obtained from the ethical committee of the Fatih Sultan Mehmet Education and Research Hospital.
SPSS 22 was used for statistical analysis. Data was expressed as mean standard deviation (SD). One-sample Kolmogorov-Smirnov test was performed to assess the distribution of data. Numerical variables in different subjects were compared by t-test or Mann-Whitney U test. Variables calculated before and after the treatment were compared by paired t-test or Wilcoxon test. Bivariate correlation analyses were made by Pearson's correlation test. Probability values were two-tailed, and a p0.005). There was no statistically significant difference for age in hyperlipidaemic patients and the controls (53.40 9.35 vs. 49.44 10.07 years; p>0.05). LDL cholesterol levels were significantly higher in the hyperlipidaemic group than the controls (190.16+-39.91 vs.116.46+-26.43 mg/d;, p<0.001). Among the cases, the mean LDL cholesterol level decreased from 190.16+-39.91 before ezetimibe treatment to 148.21+-30.10 mg/dL after the treatment (p<0.001), whereas the mean total cholesterol levels fell from 271.28+-48.83 to 219.26 36.18 mg/dL (p<0.001).
Among controls, the mean LDL was 116.46+-26.43 while total cholesterol was 190.58+-34.6 mg/dL, both before and after the treatment (Table-1)
Table-1: Baseline and post-treatment cholesterol values of case and control groups.
###Case group###Control group###P value
Tot.chol.after treatment###219.26 36.18###190.58+-34.6###<0.001
p value btw. case groups###<0.001
HDL chol.before treatment###48.80+-14.74###44.70+-10.91###0.178
HDL chol. after treatment###44.33+-13.15###44.70+-10.91###0.883
p value btw. case groups###0.013
Triglyceride before treatment###148.00+-64.68###145.60+-65.35###0.884
Triglyceride after treatment###132.32+-53.49###145.60+-65.35###0.292
p value btw. case groups###0.841
LDL chol.before treatment###190.16+-39.91###116.46+-26.43###<0.001
LDL chol. after treatment###148.21+-30.10###116.46+-26.23###<0.001
p value btw. case groups###<0.001
Although there was no significant difference between WBC, haemoglobin and platelet levels, the MPV values were significantly higher in the hyperlipidaemic patients than the controls (8.96+-0.93 and 7.56+-0.69 pre-treatment and 8.92+-0.84 and 7.56+-0.69 post-treatment; p 0.05) (Table-2)
Table-2: Baseline and post-treatment haematological values of case and control groups.
###Case group###Control group###P value
WBC before treatment###6957.55+-1553.24###7055.60+-1354.84###0.740
WBC after treatment###6298.19 2510.88###7055.60+-1354.84###0.07
p value btw. case groups###0.095
Hb. before treatment###14.27+-1.30###13.95+-0.72###0.141
p value btw. case groups###0.168
Plt. before treatment###277.68+-71.06###256.08+-52.91###0.096
Plt. after treatment###261.73+-68.61###256.08+-52.91###0.658
p value btw. case groups###0.017
MPV before treatment###8.96+-0.93###7.56+-0.69###<0.001
MPV after treatment###8.92+-0.84###7.56+-0.69###<0.001
p value btw. case groups###0.616
The results of this study show that ezetimibe treatment does not affect the platelet activity, which plays an important role in development and progression of atherosclerosis.
Besides their lipid lowering effects, statins being major anti-hyerlipidaemic agents have some pleitrophic effects, such as improving endothelial function, decreasing oxidative stress and inflammation, improving the stability of atherosclerotic plaques, and decreasing thrombotic activity. Pleitrophic effects of ezetimibe, if any, are not as prominent as statins. Grioge et al. and Maki-Petaja et al. reported that both statins and ezetimibe themselves improve endothelial functions.6,16 Another study has shown that neither ezetimibe alone nor ezetimibe /simvastatin combination has any effect on endothelial function while high-dose atorvastatin improves these functions.17
Superoxide dismutase and high-sensitivity C-reactive protein (hs-CRP) are the commonly used inflammatory markers among these studies. For inflammatory markers, studies have shown contradictory results for both ezetimibe and statins. In some of these studies, both simvastatin and ezetimibe decreased the CRP levels.16,18 Landmesser et al.reported that ezetimibe had no effect on flow dependent dilatation and superoxide dismutases, while simvastatin treatment improved endothelial function and increased superoxide dismutase activity.19 Sager et al. demonstrated that ezetimibe co-administration with simvastatin provides incremental decreases in hs-CRP, compared with simvastatin monotheraphy.20 Piorkowski et al. reportedthat statins were more effective in decreasing platelet functions than ezetimibe.
Most pleiotropic effects of statins are thought to be related to inhibition of the mevalonate-dependent isoprenylation of small guanosine triphosphate (GTP)-binding proteins, such as Rho, Ras, and Rac 1. The inhibition of RhoA and Rac 1 may cause a decrease of plasminogen activator inhibitor-1 (PAI-1), endothelin-1 (ET-1), oxidative stress and vascular smooth muscle proliferation with an increase of endothelial nitric oxide synthase (eNOS) and tissue plasminogen activator (t-PA).21
The opposite effect on the mevalonate of statins and ezetimibe may be a mechanism behind different pleitrophic effects. Hyperlipidaemia, particularly high LDL-cholesterol, is an important risk factor in atherogenesis. In our study, although ezetimibe treatment provided a 20% decrease in LDL cholesterol levels, post-treatment LDL-cholesterol levels were significantly higher than the controls. This insufficient reduction of LDL-cholesterol with ezetimibe treatment may be another mechanism behind no altered platelet activity. There is a need to verify these results with prospective, randomised, large-scale studies.
In order to provide a beneficial effect on platelet activity during hyperlipidaemia treatment, the use of ezetimibe alone should not be the first choice of treatment. If there is low or no risk of myopathy, it may be better to use high doses of statins or combination treatment, suhc as ezetimibe plus statins.
Conflict of Interest: None.
Source of Funding: None.
1. Gordon T, Kannel WB. Premature mortality from coronary heart disease. The Framingham Study. JAMA. 1971; 215:1617-25.
2. Kannel WB, Castelli WP, Gordon T, McNamara PM. Serum cholesterol, lipoproteins, and the risk of coronary heart disease. The Framingham study. Ann Intern Med. 1971;74:1-12.
3. Sertbas Y, Ersoy U, Ayter M, Gultekin Tirtil F, Kucukkaya B.Ezetimibe effect on bone mineral density and markers of bone formation and resorption.J Investig Med. 2010; 58:295-7.
4. Landmesser U, Bahlmann F, Mueller M, Spiekermann S, Kirchhoff N, Schulz S, et al. Simvastatin versus ezetimibe pleitropic and lipid lowering effects on endothelial function in humans.Circulation. 2005; 111:2356-63.
5. Pesaro AE, Serrano CV Jr, Fernandes JL, Cavalcanti AB, Campos AH, Martins HS, et al.Pleiotropiceffects of ezetimibe/ simvastatin vs. high dose simvastatin.Int J Cardiol. 2012; 158:400-4.
6. Grigore L, Raselli S, Garlaschelli K, Redaelli L, Norata GD, Pirillo A, et al.Effect of treatment with pravastatin or ezetimibe on endothelial function in patients with moderate hypercholesterolemia.Eur J Clin Pharmacol.2013; 69:341-6.
7. Hashimoto M, Akita H. Cerivastatin, a hydroxymethylglutaryl coenzyme A reductase inhibitor, improves endothelial function in elderly diabetic patients within 3 days response. Circulation. 2002; 105:e30 -e1.
8. Ichiki K, Ikeda H, Haramaki N, Ueno T, Imaizumi T. Long-term smoking impairs platelet-derived nitric oxide release. Circulation. 1996; 94:3109-114.
9. Koh KK. Effects of HMG-CoA reductase inhibitor on hemostasis. Int J Cardiol. 2000; 76:23-32.
10. Huhle G, Abletshauser C, Mayer N, Weidinger G, Harenberg J, Heene DL. Reduction of platelet activity markers in type II hypercholesterolemic patients by a HMG-CoA-reductase inhibitor. Thromb Res. 1999; 95:229-34.
11. Hale LP, Craver KT, Berrier AM, Sheffield MV, Case LD, Owen J. The combination of Fosinopril and pravastatin decreases platelet response to thrombin receptor agonist in monkeys. ArteriosclerThromb.Vasc Biol. 1998;18:1643-6.
12. Michelson AD.Methods for the measurement of platelet function.Am J Cardiol. 2009;103:20A-6A.
13. Nicholson NS, Panzer-Knodle SG, Haas NF, Taite BB, Szalony JA, Page JD, et al.Assessment of platelet function assays.Am Heart J1998;135:S170-S178.
14. Colwell JA, Nesto RW. The platelet in diabetes: focus on prevention of ischemic events.Diabetes Care.2003;26:2181-8.
15. Dindar S, Cinemre H, Sengul E, Annakkaya AN.Mean platelet volume is associated with glycaemic control and retinopathy in patients with type 2 diabetes mellitus. West Indian Med J. 2013; 62:519-23.
16. Maki-Petaja KM, Booth AD, Hall FC, Wallace SM, Brown J, Mc Eniery CM, et al. Ezetimibe and simvastatin reduce inflammation, disease activity, and aortic stiffness and improve endothelial function in rheumatoid arthritis. J Am Coll Cardiol. 2007; 50:852-8.
17. Fichtlscherer S, Schmidt-Lucke C, Bojunga S, Rossig L, Heeschen C, Dimmeler S, et al. Differential effects of short-term lipid lowering with ezetimibe and statins on endothelial function in patients with CAD:clinical evidence for 'pleitropic' functions of statin theraphy. Eur Heart J. 2006; 27:1182-90.
18. Kostakou P, Kolovou G, Anagnostopoulou K, Theodoridis T, Galea V, Mihas C, et al.Efficacy of simvastatin or ezetimibe on tissue factor, von Willebrand's factor and C-reactive protein in patients with hypercholesterolaemia. Arch Cardiovasc. Dis. 2010; 103:26-32.
19. Landmesser U, Bahlmann F, Mueller M, Spiekermann S, Kirchoff N, Schulz S, et al. Simvastatin versus ezetimibe: pleiotropic and lipid-lowering effects on endothelial function in humans. Circulation. 2005; 111:2356-63.
20. Sager PT, Melani L, Lipka L, Strony J, Yang B, Suresh R, et al. Effect of coadministration of ezetimibe and simvastatin onhigh-sensitivity C-reactive protein. Am J Cardiol. 2003; 92:1414-8.
21. Weitz-Schmidt G, Welzenbach K, Brinkmann V, Kamata T, Kallen J, Bruns C, et al. Statins selectively inhibit leukocyte function antigen-1 by binding to a novel regulatory integrin site. Nat Med. 2001; 7:687-92.
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https://www.thestudentroom.co.uk/showthread.php?t=6329106
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math
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Mechanics AS QuestionWatch this thread
The car of mass 950kg is moving up a hill at a steady speed.
The slope of the hill is 12° to the horizontal. Resistive forced on the car are negligible.
What is the steady speed of the car? A) 7m/s B) 12m/s C) 34m/s D) 68m/s
This questions seems so simple yet I cannot do it.
*If you need a diagram simply googling the above question should take you to the paper it’s on* Thanks in advance
Power = driving force x speed
Force = mass x acceleration
if you still stuck then i can give you more help
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https://reflectivemaths.wordpress.com/2012/03/14/maths-i-should-understand-better/
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math
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Maths I Should Understand Better
As a maths teacher, I can comfortably do a GCSE maths paper getting close to full marks (odd mistake perhaps) without really trying. This probably comes as no surprise. However, there are some parts of the maths that I actually don’t fully understand or don’t know why they work. Here are some of the ones I’d like a better understanding of:1) When dividing fractions, why does flipping the second one over and multiplying instead work? I have a vague grasp of those being two ‘inverse’ type operations but is that all there is to it? Is there a nice visual representation of why that works? 2) Using a quadratic curve and plotting a linear graph to solve a second quadratic. I don’t fully get why finding the ‘difference’ between the two quadratics and plotting that line means that the intersection of the line with the original quadratic gives the solutions. 3) In Statistics, for the standard deviation (Chi-squared for that matter) why do we square the terms? I understand the need to remove the negative signs but wouldn’t modulus do it? 4) Do trapeziums have to have exactly one pair of parallel lines? Why shouldn’t a rectangle count? Why does this shape appear to have some ambiguity in its definition? Who would be the person/group of people to have a definitive answer? 5) Perhaps not GCSE as such but is there any reason why 0 can’t be even? Or positive?
Am I alone in wondering these things (and think it’s important to wonder)?
Are there parts of GCSE maths that you teach methods for but don’t really get yourself? Do share – you’re amongst friends here!
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http://tr.icraa.org/ebooks/combinatorics-of-finite-geometries-second-edition
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math
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By Lynn Margaret Batten
Combinatorics of Finite Geometries is an introductory textual content at the combinatorial thought of finite geometry. Assuming just a uncomplicated wisdom of set concept and research, it offers an intensive assessment of the subject and leads the scholar to effects on the frontiers of analysis. This e-book starts off with an easy combinatorial method of finite geometries in accordance with finite units of issues and features, and strikes into the classical paintings on affine and projective planes. Later, it addresses polar areas, partial geometries, and generalized quadrangles. The revised version comprises a completely new bankruptcy on blockading units in linear areas, which highlights the most very important functions of blockading sets--from the preliminary game-theoretic atmosphere to their very contemporary use in cryptography. wide routines on the finish of every bankruptcy insure the usefulness of this publication for senior undergraduate and starting graduate scholars.
Read or Download Combinatorics of Finite Geometries, Second Edition PDF
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This publication is a concept-oriented therapy of the constitution thought of organization schemes. The generalization of Sylow’s staff theoretic theorems to scheme thought arises because of arithmetical concerns approximately quotient schemes. the speculation of Coxeter schemes (equivalent to the idea of structures) emerges clearly and yields a merely algebraic evidence of titties’ major theorem on constructions of round variety.
This publication provides a path within the geometry of convex polytopes in arbitrary size, appropriate for a complicated undergraduate or starting graduate pupil. The publication begins with the fundamentals of polytope concept. Schlegel and Gale diagrams are brought as geometric instruments to imagine polytopes in excessive measurement and to unearth strange phenomena in polytopes.
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Extra info for Combinatorics of Finite Geometries, Second Edition
48 Projective spaces Any central collineation has lines which map to themselves: for instance, each line on the centre c is mapped to itself. If there is a line 8 not on c which maps to itself, then each point x of i has the property that fix) e11 n xc = x; that is, f (x) = x. Hence e is an axis. Finally, suppose that all fixed lines are on c. Let a be any line not on c, and let a= C n f (e). Since f (a)e ac n f (l'), a is fixed. Let b be any point b. Let A be any line on b, A 0 ac, and let x=Anf(,).
2. If 17' is a suhplane of 17 of order m and if 17 has order n = m2, then 17' is a Baer suhplane of 17. 3. If 17' is a Baer sub plane of II of order m and if 17 has order n then either n = m or n = m2. The proof is left to the reader. A quadrangle is a set of four points no three of which are collinear. Axiom PP2 tells us that quadrangles always exist in projective planes. Let a, b, c, d be the points of a quadrangle in a projective plane 17. We use a modification of the embedding process of the previous section to generate a projective subplane of 17 from the quadrangle.
12. An equivalence relation R on a set S is a subset of S x S. We say a is re- lated to b, and write aRb if (a,b)ER. The following properties must also hold: aRa (reflexive property), aRb implies bRa (symmetric property), aRb and bRc imply aRc (transitive property), for all a, b, c in S. e. ell f if and only if e = A or t misses A) is an equivalence relation on the lines of 082. 13. If vi=k, 1:5 i<- b, and b; <- k+l, 1 <- i <_ v, show that parallelism is an equivalence relation. 38 Linear spaces 14.
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http://livelearnlovett.weebly.com/blog/previous/2
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math
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1) A tractor wheel is 88 inches in circumference. How many complete turns will the wheel make in rolling one mile on the ground? (1 mile = 5,280 feet)
2) In the addition problem below, each letter represents a digit and different letters represent different digits. What four-digit number does D E E R represent?
+ R I D
D E E R
3) Alice and Betty run a 50-meter race and Alice wins by 10 meters. They then run a 60-meter race, and each girl runs at the same speed she ran in the first race. By how many meters will Alice win?
1) When the wheel makes one complete turn, it has rolled a distance of 88 inches. The number of turns equals 1 mile divided by 88 inches
(1 mile = 5280 feet = 5280 x 12 inches).
Dividing yields 5280 x 12 inches = 720
2) D in the sum DEER must be 1. The R in the second addend must be 9. It follows that E must be 0 and DEER represents 1009.
3) Method 1
Alice runs 50m in the same time that Betty runs 40m. Thus Alice runs 5m for every 4m that Betty runs. Therefore in the 60m race, Alice will run 12 x 5m or 60m, and Betty will run 12 x 4 = 48m. So Alice wins by 12m.
Since Alice wins the 50m race by 10m, Alice must gain 2m over Betty for every 10m that Alice runs. Therefore, in a 60m races, Alice will gain 6 x 2m or 12m.
I am amazed at how much growth I have seen in our Pirates this year and know that they are going to do a great job on the upcoming Milestones! To help students be as prepared and confident as possible I will be doing some test prep lesson in Math Lab with 3rd-5th graders. We will work on some test taking strategies, practice another type of constructed response, and look at some words that they might encounter on the test and what they mean(see picture below for the 12 Powerful Words).
I am going to start working with 1st and 2nd graders on writing constructed responses using a graphic organizer this month. 1st and 2nd graders will also be working on addition strategies.
Kindergarten will continue to work on addition and number sense using manipulatives. PTA bought us a class set of Rekenreks recently and the students are getting a lot of number sense and addition practice on them. They are great for working with the benchmark numbers of 5 and 10!
I hope to have information about the 2019-2020 Math Olympiad team some time this month. I am looking for feedback on next year's shirt, the survey can be found here. The team will be open to 4th and 5th graders.
1) When certain numbers are placed in the empty boxes, the sum of the three numbers in each of the three rows, three columns, and two diagonals is the same. What number should be placed in the center box?
2) I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
3) The square below is divided into four congruent rectangles. The perimeter of each of the four congruent rectangles is 25 units. How many units are there in the perimeter of the square?
1) Since the sum of the three numbers in each diagonal is the same, and since they have the same middle number, the sum of each pair of numbers in opposite corners must be the same: 9 + 13 = 5 + ?. Clearly ? = 17. The bottom row now has a sum of 33. The middle number must be 11.
2) List multiples of 7 greater than 24 and less than 72. Also list the multiples of 6 which are less than and closest to each of the corresponding multiples of 7.
3) Each of the four congruent rectangles has a perimeter equivalent to 2 1/2 sides of the square. Since the length of 2 1/2 sides = 25 units, then, by doubling, we get the length of 5 sides = 50 units. Clearly, the length of one side is 10 units. Therefore the perimeter of the square is 40 units.
I would love some input for next year's Math Team T-Shirt, especially from current 3rd and 4th graders. Here is a link to a quick survey.
1) Suppose the counting numbers from 1 through 100 are written on paper. What is the total numbers of 3s and 8s that will appear on the paper?
2) In the "magic-square" below, five more numbers can be placed in the boxes so that the sum of the three numbers in each row, in each column, and in each diagonal is always the same. What value should X have?
3) The U-shaped figure at the right contains 11 squares of the same size. The area of the U-shaped figure is 176 square inches. How many inches are in the perimeter of the U-shaped figure?
1) (a) 3 occurs in the units place once in each group of ten consecutive numbers. Therefore 3 will appear 10 times in the units place.
(b) 3 occurs in the tens place ten times in 100 consecutive numbers: 30, 31, 32, 33, . . . , 38, 39.
(c) Statements (a) and (b) are also true for occurrences of 8. Therefore there will be a total of 40 occurrences of 3s and 8s in the numbers from 1 through 100.
2) Method 1
From the first column, we see that the sum for each row, column, and diagonal should be 90. Then the missing number in the 3rd row is 40, and the missing number in the lead diagonal is 30. The sum for the second column is 40 + 30 + X or 70 + X. Then X must be 20.
Since the numbers in the two diagonals have equal sums and the same middle number, then the two numbers in the corners of each diagonal have equal sums; 25 + 35 = 15 + ? It follows that ?, the number in the lower right corner, is 45. Since the sums of the numbers in any row, column, or diagonal is 90, the bottom row sum 25 + X + 45 = 90. Thus X = 20.
3) The area of each square is 176/11 or 16 inches. Then the length of each side of a square is 4 inches. The perimeter of the U-shaped figure is equivalent to the total length of 24 sides or 96 inches.
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https://ijfs.usb.ac.ir/article_4364.html
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math
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B. Bede, Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, Berlin, 2013.
M. Biglarbegian, A. Sadeghian and W. Melek, On the accessibility/ controllability of fuzzy
control systems, Information Science, 202 (2012), 58-72.
Z. Cai and S. Tang, Controllability and robustness of T-fuzzy control systems under direc-
tional disturbance, Fuzzy Sets and Systems, 115 (2000), 279-285.
Z. Ding and A. Kandel, On the controllability of fuzzy dynamical systems (I), Journal of
Fuzzy Mathematics, 8(1) (2000), 203-214.
Z. Ding and A. Kandel, On the controllability of fuzzy dynamical systems (II), Journal of
Fuzzy Mathematics, 8(2) (2000), 295-306.
Z. Ding, M. Ma and A. Kandel, On the observability of fuzzy dynamical control systems (I),
Fuzzy Sets and Systems, 111(2) (2000), 225-236.
S. S. Farinwata and G. Vachtsevanos, Survey on the controllability of fuzzy logic systems,
Proceedings of 32th IEEE Conference on Decision and Control, (1993), 1749-1750.
Y. Feng and L. Hua, On the quasi-controllability of continuous-time dynamic fuzzy control
systems, Chaos, Solitons and Fractals, 30(1) (2006), 177-188.
M. Friedman, Ma Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96
W. I. Gabr, A new approach for automatic control modelling, analysis and design in fully
fuzzy environment, Ain Shams Engineering Journal, 6 (2015), 835-850.
M. M. Gupta, Controllability of fuzzy control systems, IEEE Transactions on Systems, Man,
and Cybernetics, 16 (1985), 576-582.
A. Kumar, J. Kaur and P. Singh, A new method for solving fully fuzzy linear programming
problems, Applied Mathematics and Computation, 35 (2011), 817-823.
A. Mansoori, S. Effati and M. Eshaghnezhad, A neural network to solve quadratic pro-
gramming problems with fuzzy parameters, Fuzzy Optimization and Decision Making, 17(1)
M. S. N. Murty and G. Suresh Kumar, On Controllability and Observability of Fuzzy Dy-
namical Matrix Lyapunov Systems, Advances in Fuzzy Systems, 8(1) (2008), 1-16.
K. Ogata, Modern Control Engineering, Fourth ed., Prentice Hall, New Jersey, 2002.
L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy
arithmetic, Fuzzy Sets and Systems 161(11) (2010), 1564-1584.
C. Tetiana and Z. Alexander, Application of the return method to the steering of nonlinear
systems, in: Krzysztof Kozlowski (Ed.), Robot Motion and Control 2009, Lecture Notes in
Control and Information Sciences, vol. 396, Springer, Berlin/Heidelberg, (2009), 83-91.
L. X. Wang, A Course in Fuzzy Systems and Control, Prentice Hall PTR, 1997.
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CC-MAIN-2023-14
| 2,559 | 33 |
https://eventthyme.net/how-to-calculate-roi-from-balance-sheet/
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math
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It is most commonly measured as net income divided by the original capital cost of the investment. Roi = net profit / total investment *100
Every ceo and cfo wants assurances that any investment in new technologies and business models comes with a return on investment (roi) that justifies the expense.
How to calculate roi from balance sheet. How to calculate rate of return on investment in excel: During the first half of the 20th century, roi was helpful in monitoring the decentralized divisions of large diverse corporations. Balance sheet ratios formula and example definition.
The ratios calculated from a company's balance sheet are used to determine its liquidity, solvency, and profitability. One final balance sheet ratio to know is return on investment. For businesses, the invested capital includes the net worth of the.
Net worth may be labeled as net assets, stockholders' equity or partner capital, depending on the type of business. Calculate roi from balance sheet: Return on investment (roi) is the amount of profit you receive with respect to your invested capital.
This information can be found on the balance sheet of a company's annual or quarterly report on its website. You can calculate the return on equity from company balance sheets by leveraging data found on the company's income statement. You can calculate net worth by subtracting total assets from total liabilities, or you can look at the net worth section of the balance sheet.
It is a table of accounts organized into three sections, assets (what the company owns), liabilities (what the company owes) and equity. Abc corporation's most recent balance sheet reported total assets of $10,000,000 and total liabilities of $7,200,000. Balance sheet ratios are the ratios that analyze the company’s balance sheet which indicate how good the company’s condition in the market.
Is below the industry average, you want to find out why. People refer to roi when discussing what they get back for their input. To calculate return on investment, the benefits (or returns) of an investment are divided by the costs of the investment.
To do that, you can use the dupont model and break down the roi into its component parts. Debt to total assets = total liabilities / total assets debt to total assets = $7,200,000 / $10,000,000 debt to total assets = 0.72 or 72% (or 0.72 to 1 or 0.72:1) For example, a roi of 10 percent means that for every dollar invested, you gained 10 cents.
Return on investment (roi) is a financial ratio used to calculate the benefit an investor will receive in relation to their investment cost. Figure 11.5 roi calculations (game products, inc.) *operating income amount is from segmented income statements presented in figure 11.3 segmented income statements (game products, inc.). How do you calculate investment return:
Abc's debt to total assets ratio as of the balance sheet date was: Net worth is the amount of assets a business holds less all outstanding obligations. As a concept, it can measure profitability or efficiency.
Below is the balance sheet from exxon's 10k statement showing the 2017 and 2016 total assets (highlighted in blue). You can calculate three types of ratios from the balance sheet—liquidity (turn assets into cash), solvency (cash or equivalents to pay debts), and profitability ratios. Roi is composed of two parts, the company's profit margin and the asset turnover—the firm's ability to generate profit and make sales based on its asset base.
The return on investment ratio (roi), also known as the return on assets ratio, is a profitability measure that evaluates the performance or potential return from a business or investment. Since the roi (roa) for abc, inc. You will need this number to calculate the shareholders' average equity.
Free return on investment (roi) calculator that returns total roi rate as well as annualized roi using either actual dates of investment or simply investment length. However, roi is a true metric that can be calculated as a ratio or percentage. The balance sheet for the company at the beginning of 2009 is shown in the middle column.
The roi formula looks at the benefit received from an investment, or its gain, divided by the investment's original cost. The higher the ratio, the greater the benefit earned. **average operating assets are calculated using the balance sheet information in figure 11.4 segmented balance sheets (game products, inc.).since all assets at game products, inc., are operating assets.
A balance sheet is a snapshot in time of a company’s finances. The result can be expressed as a percentage or a ratio. Originally the objective of roi was to relate a return (the income statement benefit) to the amount invested (such as the asset information from the balance sheet).
The basic formula to calculate roi is: Note the differences between the two, and how this will affect the roa. Roi is the acronym for return on investment.
How to calculate the return from an investment balance sheet return on invested capital, or roic, can tell you how efficiently a company uses its capital to generate a profit. These ratios usually measure the strength of the company comparing to its peers in the same industry. Also, gain some understanding of roi, experiment with other investment calculators, or explore more calculators on finance, math, fitness, and health.
How to calculate a return on an investment balance sheet. Look beyond the balance sheet to calculate the roi of digital transformation investments. Roi is used as a concept and a specific formula.
Shareholder equity is assets minus liabilities on a firm’s balance sheet and is the accounting value that's left for shareholders should a company.
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CC-MAIN-2021-49
| 5,716 | 20 |
https://customwritings.pro/quantitative-analysis-i-need-answers-detaled-possible-2/
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math
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Suppose a manufacturing company makes a certain item. The time to produce each item is normally distributed around a mean of 27 minutes with a standard deviation of 2.5 minutes. Thus, the population of production times is normal in shape. Find the mean and standard deviation of the sample.
The average prices for a product in 12stores in a city are shown below.
$2.99, $2.85, $3.25, $3.55, $3.00, $2.99, $2.76, $3.50, $3.20, $2.85, $3.75, $3.85
Test the hypothesis that the average price is higher than $2.87. Use level of significance a = 0.05.
A store wishes to predict net profit as a function of sales for the next year.The following table gives the years 1998 to 2005.
(thousands of dollars)
(a) Graph the points from 1998 through 2005on ascatter diagram using Sales as the independent variable and Net Profit as the dependent variable.
(b) Draw the regression line on the graph you constructed in Part (a).
(c) What is the value of the coefficient of determination for this regression model? Comment on the strength of the regression line for this model.
(d) What is the predicted net profit for 2006 if sales are expected to be 125?
Last week’s sales of iMac computers at an Apple Store in Oklahoma City, OK,are shown in the following table:
(a) Use the 3-day moving average method for forecasting days 4–7.
(b) Use the 3-day weighted moving average method for forecasting days 4–7. Use Weight 1 day ago = 2, Weight 2 days ago = 4, and Weight 3 days ago = 3.
(c) Compare the techniques using the mean absolute deviation (MAD).
The following table shows six years of average annual cost-of-living index data:
Annual Cost of Living Index
(a) Forecast the average annual food price index for all years from 2008 to 2013. Use a 3-year weighted moving average with weights of 0.5, 0.3, and 0.2. Use the largest weight with the most recent data.
(b) Forecast the average annual food price index using exponential smoothing with α = 0.7 for all years from 2008 to 2014. Use the rate for 2008 as the starting forecast for 2008.
(c) Which of the methods in parts (a) and (b) produces better forecasts for the 3 years from 2011 to 2013? Answer on the basis of mean square error (MAD).
A company manufactures two products, Product A and Product B. The wholesale price and manufacturing cost of each product are shown below.
Assembly Times (hr)
The company will produce a minimum of 5,000 of each item. Given the number of hours, the company can sell no more than 8,000 of Item A and 10,000 of Item B. Suppose the company has 50,000 hours of assembly time available. How many of each item should it produce in order to maximize profits while meeting all necessary constraints? Give the LP model and use the graphical method to find the optimal solution.
A commercial real estate company is evaluating a proposed warehouse. The proposed site is near a rail terminal, but the state government may extend the highway to the area. In addition, the federal government is considering rebuilding the local port facilities. Below is the payoff table in monthly profit depending upon what government actions are taken. Based on the following criteria, what are the correct choices for terminal rental?
(a) Optimistic or maximax criterion
(b) Pessimistic or maximin criterion
(c) Equally likely or principle of insufficient reason criterion
Warehouse size (ft2)
Rail terminal only
Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount! Use Discount Code “Newclient” for a 15% Discount!NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.
The post quantitative analysis i need answers detaled possible appeared first on customwritings.pro.
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CC-MAIN-2021-10
| 3,814 | 30 |
https://braingenie.ck12.org/skills/105893/practice
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math
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Tom is going to buy a new car.
According to state law, he must pay sales tax for the new car. The sales tax is based on the cost of the car. Suppose he was planning to buy a $23,000 car that has a tax of
a)Find a mathematical model that gives the
amount of sales
tax y in terms of the cost x of the car.
y=*x (round your answer to the nearest
b)Suppose that, due to the economic
obtained less income from his job and can no longer afford a $23,000 car and instead must buy a
cheaper one. He
decides to buy a $10,000 car instead; what is the sales tax on this $10,000 car?
$ (round your answer to the nearest whole
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CC-MAIN-2019-51
| 613 | 11 |
https://www.enotes.com/homework-help/there-circular-pond-with-path-around-pond-has-466384
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math
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There is a circular pond with a path around it. The pond has a radius of 5 meters. The path has a width of 1m. What is the area of the path, and please explain how to find it. Give your answer to three significant figures.
The pond and the path have a combined radius of 6 meters (the radius of the pond plus the width of the path). Then, find the combined area of the path and the pond by using the formula for the area of a circle . The formula works out to 36.
Now the area of the smaller circle (with radius of 5m) needs to be deducted from the area of the larger circle (with radius of 6m).
`36 pi - 25 pi = 11 pi`
This renders an answer of 34.56`m^2` rounded to 2 decimal places and as the question asks for 3 significant figures this needs to be rounded off to 34.6 `m^2`
Ans: The area of the path is 34.6`m^2` rounded off to three significant figures.
The formula for finding the area of a washer shape is
A = `pi(R^2 - r^2)`
` ` ``
Where R is equal to the outer radius and r is equal to the inner radius.
For your problem, the outer radius is 6 ( 5 + 1) and the inner radius is 5.
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CC-MAIN-2017-26
| 1,089 | 11 |
http://mathhelpforum.com/algebra/18542-rewriting-expressions.html
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math
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I have a few homework questions that I just don't understand. It would be greatly appreciated if you show me step by step how you got them, thank you very much!!
1) Solve for H--- S= 2(hw+hl+wl)
2) Solve for P---- A=P+ Prt
3) Solve the equation (4/4x+9)+ (7/4x-9)= 44x+27/16x^2-81
4) Solve the equation (2/5x+4)-(4/10x+8)
(Please be more careful in your use of parenthesis!)
First you want to get a common denominator for all terms. In this case it is going to be simple because
<-- Now multiply both sides by :
So it looks like any value of x will solve the equation, since both sides are already equal. BUT, look at the original equation:
From here it is clear that we are restricted by the denominators: we must not have . Other than that, the solution is any x.
you need to write it as 2/(5x + 4) - 4/(10x + 8).
This is not an equation, so it cannot be solved. I presume the question is to perform the indicated operation.
Note that , thus
(Your Math teacher likes, zeros doesn't (s)he?)
As far as number 4 is concerned, you originally told me to "solve the equation." Did you leave something out of the problem?
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| 1,116 | 15 |
https://std.iec.ch/iev/iev.nsf/17127c61f2426ed8c1257cb5003c9bec/c7c9f753661b00e4c125857600565c81?OpenDocument
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math
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| in a magnetic field, pressure exerted on a conducting fluid
B is the magnetic flux density
μ0 is the magnetic constant
Note 1 to entry: The total pressure on a given flow of conducting fluid, which is the sum of the mechanical pressure, the magnetic pressure and the hydrostatic pressure, is a constant for this flow of conducting fluid.
Note 2 to entry: The coherent SI unit of magnetic pressure is newton per square metre, N/m2.
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CC-MAIN-2021-21
| 433 | 5 |
https://math.rutgers.edu/news-events/seminars-colloquia-calendar/icalrepeat.detail/2017/10/30/9365/292/non-commutative-symmetric-functions
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math
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Seminars & Colloquia Calendar
Non-commutative symmetric functions
Robert Laugwitz, Rutgers University
Location: Hill 525
Date & time: Monday, 30 October 2017 at 1:00PM - 2:00PM
Abstract: This will be an accessible introductory talk on the theory of quasi-determinants of Gelfand--Retakh and how they can be used to define analogue of symmetric functions over free non-commutative skew-fields. In particular, there are many different bases for the Hopf algebra of non-commutative symmetric functions giving analogues to the classical bases of elementary symmetric functions, complete homogeneous functions, power sums, or Schur functions.
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| 637 | 6 |
http://oldmathdognewtricks.blogspot.com/2011/11/struggling-greader-cleaning.html
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math
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I did partially use this approach today that John Scammell blogged about last week. I think the next time I use it, I will follow the approach as it was blogged about - when I was thinking about it this morning on my way into work, all I could remember was showing which points made the inequality true. In my first class, I had students choose any point on our grid (both x and y values go from -6 to 6 on it) and they all chose points with two positive coordinates. None of those points worked, so I had them choose a coordinate that had at least one negative coordinate and we got some points that worked. Also with the first class, I didn't have them graph the points we came up with. We just graphed the shaded area that did work. For my second and third classes, I had them plot the points we found that worked on their grid before we graphed the inequality on the grid. They then graphed the line and we talked about testing a point to determine which half of the plane to shade. Below is the pdf of my SMARTNotebook file from my last class.
In that last class, one of my students who has struggled with math spoke out as we were working through the problem. We had graphed the individual points that we found that worked and had just finished graphing the boundary line and right as we finished drawing it in, he said "I get it now!" I hadn't even gotten to the point where we talk about testing a point in one of the half-planes - he already saw where the answer would be and "got" why that was going to be the answer. That was worth it. #win
Getting back to the opening... I know I have done things differently this year. Yes, things are mostly the same. However, due to the twitter-blogosphere and reading and conversing with other math teachers, I have incorporated some different approaches to instructing my students and I think that has made me a better teacher. However, as I look at my classes, I am frustrated because they are so dependent. It's almost as if they don't know how to think.
In my Advanced Algebra 2 class, where we're working on solving systems of inequalities by graphing, we had this discussion about the test point today. It started first by clarifying how to determine which half to shade based on testing (0,0), which is the point I use unless it's on the line. Then the conversation shifted - can I test (1,1)? What about (2,2)? After answering the same question but with a different point for the third time, I got a bit frustrated with them. It was as if they couldn't take the concept of checking a point to represent the region and shift it to a different point. And these are supposed to be my "better" and/or "brighter" students. Granted, I didn't use the same start as I did with my Algebra 2 classes today, and that may have made a difference, but it was very frustrating to me that they couldn't transfer the idea to different points. As I said earlier, it's almost as if they don't know how to think.
Last night I was trying to get caught up on my Google Reader, this post by crstn85 caught my attention about studying for math. Since I was at 130 or so when I started trying to clear it out, I really only skimmed the post and starred it to go back and read later. However, as I continue to reflect, I think I may go back and read it much more thoroughly to see if I can use what she did with my classes. Maybe it will be helpful to them.
So here I am at the beginning of the
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| 3,425 | 6 |
https://www.englishexperts.com.br/forum/como-dizer-prova-de-recuperacao-em-ingles-t35187-10.html
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math
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It is a normal occurrence to take a "make-up" test. If someone is absent when the test is given , the teachers give a make up test. As far as a retake test, in 35 years of public school teaching, I have never heard of a "retake" test. There may be some teachers who give them but I think it would be very rare. If you fail the test the first time, we don't give you another test to try to do better the second time. I am talking about tests in school, not a driver's test or something like that. Sometimes if a student is failing or has a very low grade, we may give him an extra-credit project to do to help his grade. I taught high school. It would be very inconvenient for a teacher to give retakes. He would have to grade the 1st test, then make up a second different test and find a way for the student to take it where he could not be alone and have a chance to cheat and then regrade it. There could be many students who would want a retake. If I had a lot of students fail a test, I would curve the grades but not do a retake. It would be twice as much work for the teacher because the student didn't study the first time. If a student felt sick before a test was given, I would not make him take the test, but the student would have to take the test before I gave the test papers back and I might change a few questions. However, giving re-takes is not often done here as far as I know. I know I wouldn't do it. The meaning of the term in English is correct as people have explained it. I am just adding a cultural note.
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CC-MAIN-2019-39
| 1,529 | 1 |
https://www.physicsforums.com/threads/observer-vs-natural-phenomenon.764294/
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math
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If you have two hydrogen atoms as your system, then you use the many body schrodinger equation for 2 protons and 2 electrons. The coulombic repulsion between the two atoms is built into the SWE, so is there a range of different possible magnitudes for the repulsion? If so, does the system decide at which magnitude to repel based on quantum randomness? Lastly, how would that translate to the macroscopic world. Is the range of different possibilities just too small to ever notice? The reason i ask this is because when i, say, push on a chair, my finger atoms and the chair atoms are definitely repelling, so is that system just randomly choosing the magnitude of repulsion?
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CC-MAIN-2018-13
| 677 | 1 |
https://studylib.net/doc/11118701/sp-212-worksheet-lesson-11--ch.-25.1-25.3--capacitance
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math
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SP 212 Worksheet Lesson 11: Ch. 25.1-25.3, Capacitance 1) A 1.5 V AA battery is connected to a 3.00 µF capacitor. How much charge ends up on the capacitor? What does it mean for a capacitor to be “charged?” Draw a sketch of this system. 2) Derive an expression for the capacitance of two circular parallel plates, each with radius R, that are separated by a distance d R. To begin, assume that the upper plate has charge +Q and the lower plate has charge −Q. Hint: Treat the plates as though they’re infinite. Calculate their charge densities, and find the potential difference between the plates. 3) The capacitances of the four capacitors shown in the figure are given in terms of a certain capacitance C. In terms of C, what is the equivalent capacitance (a) between points A and B and (b) between points A and D?
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CC-MAIN-2023-23
| 825 | 1 |
https://podbot.ai/episode/googolplex
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math
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One is a googolplex limited by 1, followed by a googols and a zero, and one is an even larger number than that because there are no googs, so it is impossible to write the zero down. If there were no Googles, it would be many times bigger, because there are no Googels, they are not big enough, or it is impossible. Written in normal decimal, there is a 1, followed by a googol and a zero and then a 10, 100 or a zeros that follows the 1. A million has 6 zeros, a billion has a 9, and a million has a 6 and a zero, and so on. The googol number is the sum of the zeros and the first 10, 100 or a 10. This is the system described by the Googols system, a number system with the same structure as normal decimals. So you're back with Martin Kelly, the boy next door who will ruin everything if he gets his chance. Thankfully, Troy and Pippa are ready to help you and the ocean is nearby Many children know that a Google character is a one with a hundred zeros, but do you know what it is? The math alphabet booklet, we tell you how a nine-year-old boy got his name. Googles were created in 1938 when a mathematician named Edward Kasner wanted to introduce a very large number of people to the world that everyone could understand. He asked for a name with a 1, followed by 100 zeros, and Sirotta suggested "Googol" as the name of the first character in the alphabet, one with 100 zeros. Two years later Kasner published his book Mathematics and Imagination, which contained a passage that introduced the world to what we later considered one of the most important mathematical concepts in the history of mathematics, the Googolplex. Then the mathematicians shot back with the "Googplex" and defined it as the 10 powers of Googsol, thus refuting poor old Edward, for example. The universe as we know it consists of 10 forces of 80, so "Googols" are nothing special, are they? This kind of "Googolplex" in numerical dimensions is expressed in the number of forces of Googols, or in other words, the sum of all forces in the universe. Physicist Don Page sent me a question about how to imagine a value that matches Googolplex, and I'm happy to answer. This is not surprising, as googolplex is one - followed by googsol and a zero - and the number is greater than the sum of all the particles in the universe. It is so large that it cannot be written down without scientific notes. If you could write down the zero for every single atom that is in an existing atom, you could write it down. It is sobering to see the imagination of a nine-year-old humbled by the dynamic range of astronomy, and it is instructive to realize that his imagination can go beyond the confines of astronomical perspective. We cannot calculate how long it would take, but we can estimate it by estimating the longest age in the universe, which would be determined from the number of stars in our solar system or the age of our sun. By comparison, counting trillions would take about 31,709 years, but trillions are only a 1 followed by twelve zeros. Kasner believes people overuse the term "infinite" when they actually mean only large numbers. To distinguish between the two concepts, he developed the Google program "Google And the Googling. He discusses them to show the difference between an incredibly large number like infinity and a small number like a trillion. A much larger number, the googolplex, is defined as 1, followed by a "googel" and a zero, but it has no formal mathematical utility. For example, one can imagine 10, 1, 000,000 as a one, followed by a million zeros and 10 as zero. The strangest number in the plex was coined as the "Piplex of the Ten Pimms" . There are some figures that, interestingly, have real significance for the world and surpass the googolplex, but we will be looking at those figures a little more. I have shown that Bowers seems to be replacing the number of numbers with a larger argument with the original number. This shows that it is a number of zeros and zeros and not a one, two, three, four, five, six, seven, eight or nine, but it has a meaning. The googolplex has become one of the most popular figures in the history of computer science and mathematics. He received a lot of attention, but he also became a popular figure in many other fields such as astronomy, mathematics, physics, astronomy and astronomy. In this review, googol is probably the epitome of "gogogolism" in the sense of the smallest. An exception is the "googolduplex," followed by the GoogOLplex and the zero, about which we know little, like the Googolsplexplex.
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http://strathprints.strath.ac.uk/view/author/494025.html
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Khan, Khaula Naeem and Lamb, Wilson and Mcbride, Adam (2011) Fractional calculus of periodic distributions. Fractional Calculus and Applied Analysis, 14 (2). pp. 260-283.
Khan, K.N. and Lamb, W. and McBride, A.C. (2009) Fractional transformations of generalised functions. Integral Transforms and Special Functions, 20 (6). pp. 471-490. ISSN 1065-2469
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https://digitalcommons.aaru.edu.jo/pfda/vol3/iss4/1/
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In this manuscript we study quantitatively with rates the trigonometric fractional convergence of sequences of linear operators applied on Banach space valued functions. We derive pointwise and uniform estimates. To establish our main results we apply an elegant boundedness property of our linear operators by their companion positive linear operators. Our inequalities are trigonometric fractional involving the right and left vector Caputo type fractional derivatives, built in vector moduli of continuity. We consider very general classes of Banach space valued functions. Finally we present applications to vector Bernstein operators.
Digital Object Identifier (DOI)
A. Anastassiou, George
"Vector Fractional Trigonometric Korovkin Approximation,"
Progress in Fractional Differentiation & Applications: Vol. 3:
4, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol3/iss4/1
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https://www.hotrecentnews.com/news/cripple-british-woman-runs-half-marathon/15260
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math
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'Cripple British woman runs half marathon'
- "Cripple a woman has run a half marathon in Britain in a robotic suit. Claire Lomas from Leicestershire did according to British media five days about the so-called Great North Run from Newcastle to South Shields."
"The 36-year-old Lomas became partially paralyzed in 2007 by a fall from a horse. She broke her neck, back and ribs. Yet they managed to finalize using the \"bionic\" suit in the running event. The British, who also is pregnant again sixteen weeks, is currently very,, very pleased '' with that performance."
"Lomas uses a so-called ReWalk suit, which she in 2012 as the last of the finish was at the London Marathon. She explained this time, the newspaper Leicester Mercury about 3 miles (nearly 5 kilometers) a day. Especially the training was hard for her this time, because she was suffering from morning sickness.\n \n \n \n \n 0:49\n \n Cat rescued after 16 days under rubble\n \n \n \n 1:50\n \n This is the most beautiful bikini babe NL\n \n \n \n 1:27\n \n Harness looking councilor at home\n \n \n \n \n \n \n \n \n \n \n \n \n \n In 2012 she took the last finish at the London Marathon.\n \n \n Photo: Dutch Height"
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https://www.ankenydaily.com/finance/766/how-to-calculate-the-critical-value-in-statics/
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math
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Yes, it is right to say that statistics is a very difficult subject to understand properly. But if you pay proper heed to this conceptual subject, it becomes very interesting and easy for you to understand it. An online z critical value calculator by calculator-online.net is specially designed to determine the critical values in statistics. With the help of this free critical values calculator, you can easily find the critical values for either z, f, or Chi-Square distributions.
In this article, we will be discussing the method to write critical values in statistics.
Let us dive into it!
What Is A Critical Value?
A critical value is a graph line that splits a distribution graph into portions that represent ‘rejection areas.’ If a test value falls into a rejection rejoin, it suggests that the accepted hypothesis (also known as the null hypothesis) should be rejected. Remember that if the test value falls within the acceptable range, the null hypothesis cannot be rejected.
Critical Value Formula:
Generally, there are two basic formulas that are used to find the critical value in stats. These are as follows:
- Critical Value = Margin of Error/Standard Deviation of the Statistic
- Critical Value = Margin of Error/Standard Error of the Statistic
Calculating Critical Value:
You can calculate the critical value by considering the following rules:
Determine the value of the angle ‘α’:
- α = 1 – (confidence level / 100)
Work for the critical probability p*:
- (p*): p* = 1 – α/2
Writing Critical Value As Z-Score:
Expressing critical value as a z score need a criterion to be fulfilled:
- Find the z score that has the cumulative probability just equal to that of critical probability
To avoid any hurdle, you can also use the free z critical value calculator for immediate and precise outcomes.
Expressing Critical Value As T-Statistics:
To express the critical value in t score, you need to:
- Calculate the degree of the freedom
- The alphabet t* is called the t statistics and has a cumulative probability that is equal to the critical probability.
In case you find it difficult to find the t score against the critical value, try subjecting it to a free z critical value calculator.
Finding The Critical Value of Two-Tailed Test:
Suppose we want to calculate the critical value for the significance level of 0.5. Now, what we need to do is:
- Subtract significance level from 1
- After doing so, divide the resulting number by the number 2
- Next, look at the z-table and locate the answer from the above step in the z-middle table’s area.
- You should be able to find the number in this case. 4750. Look at the z table; on the far left, you’ll notice the number 1.9, and at the top of the column, you’ll see. 06. Multiply both of them to get 1.96, which is the critical value.
Here the free critical value calculator provides you with the facility to determine the critical value instantly and accurately.
Using Critical Value Calculator:
Well, this section is focus seeking. Yes, it is very crucial to determine the critical value of a graph by using a free z critical value calculator. Let’s find how!
- First of all, make a selection of the statistical method for which you want to determine the critical value
- After you do that, write the values of the parameters that are required against the chosen stat method
- At last, simply tap the calculate button
- The calculator displays the critical value on your screen in no time.
How swift it is!
Wrapping It Up:
In this article, we discussed the critical value calculation and the use of a free online critical value calculator in this regard. We hope it will help you people a lot.
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https://olajornalcombr.gearhostpreview.com/custom-coursework/page-55-2020-10-27.html
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math
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The Presentation of Women in the Novel, Winesburg, Ohio by Sherwood Anderson - Number written in figures here H T U Q 1/ 10ths / ths / ths Number written in words and what the number means 7 Q 2 5 Seven point two five which means 7 units, 2 tenths and 5 hundredths or 7 units and 25 hundredths Q 8 9 7 Point eight nine seven which means 8 tenths, 9 hundredths and 7 thousandths. 9 8 6 Q 4 4 5. In "old style" text figures, numerals 0, 1 and 2 are x-height; numerals 6 and 8 have bowls within x-height, plus ascenders; numerals 3, 5, 7 and 9 have descenders from x-height, with 3 resembling ʒ; and the numeral 4 extends a short distance both up and down from x-height. Old-style numerals are often used by British presses. The number system we use is called the decimal number system, because the place value units go in tens: you have ones, tens, hundreds, thousands, and so on, each unit being 10 times the previous one. In common language, the word “decimal number” has come to mean numbers which have digits after the decimal point, such as or equal pay task force report on pyramid
assignment satisfaction key xl nike - , and are decimals or decimal numbers. Divide 1 whole into 10 equal parts. In the fraction form, each part has a value equal to. Place Value of a Number This selection will help you to find what the place value is of a particular digit in a number. Type your number here, then click "Take my number," and we ’ ll go from there. Jun 25, · 7/8 = / 0 0. debra. 5 years ago. 0 0. how do you write 10 million in numbers????? 5 answers. Answer Questions. Answer Questions. What cities in America would I need to destroy and in what order to achieve total annihilation k? Write . write my assignment australia 3 weeks
Essay writers for hire australia ... - 7+7 =2 So it meant 14=2 consider that become 13=1 So 7+7=14 consider 2 8+8=16 consider 4 8+5=13 consider 1 6+9=15 consider 3 10+11=21 consider 9 4+9=13 consider is 1 answer also this. May 19, · In math, "the product of 7 and #a#" is what you get when you multiply "7 times #a#", also written as #7xxa#. Our phrase is now: #[7 xx a] + 5 # We can clean this up a bit by using #7a# instead of #7 xx a#: #7a+5# Let's double check. This math phrase should mean the same as "five more than the product of 7 and #a# ". If 9/5 of a number exceeds 5/7 of that number by 70, find that number 2 See answers Rishav Rishav Let the number be x So 9x/x/7=70 63xx/35=70 38x/35=70 X=70*35/38 X=/38 X=/ your answer is wrong ohk see i corrected it ABHAYSTAR ABHAYSTAR. Purdue application essay help steps
Thesis Paper on Death of a Salesman write papers for money - What is 7/10 - 5/8 on a number line - 1. Log in. Join now. 1. Log in. Join now. Ask your question. Middle School. Mathematics. 5 points izabelllreyes Asked 12/11/ What is 7/10 - 5/8 on a number line Giving Brainliest to the one who answers first and correctly!!! PLEASE HELPPPPPPP!!!!!. Sep 09, · The first two tables are useful for quickly converting inches to feet, ounces to pounds, or fractions to decimal values. It won’t help you in converting metric to U.S. units or vice versa; see Conversion Factors and Formulas for that information. I THINK you mean the word decimal. It is a way of writing fractions that are in 10ths. For example, 1/10th would be and 2/10ths would be By adding another digit to the right of the decimal. A History of Arts and Culture in Asia
capella online phd - Identify the Sequence 1, 4, 7, 10, 13 This is an arithmetic sequence since there is a common difference between each term. In this case, adding to the previous term in the sequence gives the next term. Lindsay identifies a point graphed on a number line. Or, let's write this as a decimal, let's look at it as a decimal. If we wanted, we could have our ones place value and then after the ones, the decimal and the tenths. So, for the ones, there's three ones. And how many tenths did we see here? There were three tenths. So, either way we can. 2/5: Evaluate: square root of 2+ square root of 2: Evaluate: 2^1: Evaluate: 2^6: Find the Prime Factorization: what is the prime factoriztion of 40 use exponents to show any repeated prime factors: what is the prime factoriztion of use exponents to show any repeated prime factors: Evaluate-2^3: Evaluate: 3^5: Evaluate. Subtracting negative numbers review (article) | Khan Academy
A Look at the Genocide in Rwanda and How It Affected the Countrys Economy - How many tenths are there altogether in ? answer is How many tenths are there altogether in ? answer is 68 How many tenths are there altogether in ? answer is Exercises How many tenths are there altogether in each of these numbers? a) b) c) d) e) How many tenths are there altogether in these numbers? a. This equation is incomplete: 1 2 3 4 5 6 7 8 9 = One way to make it accurate is by adding seven plus and minus signs, like so. 1 + 2 + 3 – 4 + 5 + 6 + 78 + 9 = Sep 21, · 4. The product of 5 and th digit in. math. This confusing to me??? Find the sum. 7 and four-fifths plus 1 and nine-tenths equals what number? A. 8 and two-fifths B. 9 and two-fifths C. 9 and seven-tenths D. 8 and seven-tenths. math. Show me 4 hundreds, 6 ones, 17 tens, and 7 tenths. Math. dissertation abstracts international database icons
How to Write a Thesis Statement for - Number lines can be extended indefinitely to the right for positive numbers and to the left of 0 for negative numbers. Use your number line to measure the height of a standard sheet of paper. (The height is units and the width is units. Note: The number lines can be cut out along the dashed lines and students can write their names on. The fraction 7/10 cannot be written as a whole number that is equal to 7/10 because 7/10 represents 7 out of 10 parts of the whole. It is less than See full answer below. Can be used to divide mixed numbers 1 2/3: 4 3/8 or can be used for write complex fractions i.e. 1/2: 1/3. An asterisk * or × is the symbol for multiplication. Plus + is addition, minus sign -is subtraction and () is mathematical parentheses. The exponentiation/power symbol is ^ - for example: (7//5)^2 = (7//5) 2. case study nursing your newborn
organ donation task force 2008 report on rabies - 7 5 —— - — 10 8 Step 2: 7 Simplify —— 10 Equation at the end of step 2: 7 5 —— - — 10 8 Step 3: Calculating the Least Common Multiple: Find the Least Common Multiple The left denominator is: 10 The right denominator is: 8. Seven tenths of is simply seven tenths times , which can be written as follows: Seven/tenths x Furthermore, you can convert "seven" to "7" and "tenths" to "10" and then the equation and answer is: 7/10 x = Seven tenths written as a fraction is 7/ You can also write it as a decimal by simply dividing 7 by 10 which is Order from least to greatest: 3 4/7, 3 3/5, 3 1/2, 3 11/ Solution The given mixed numbers all have same whole parts but different fractions. It is easier to compare fractions when . a2en re write my sentence
An Analysis of the Definition and the Uses of DNA-Deoxyribonucleic Acid - Convolution / Problems P et -1 0 1 2 3 R2 (t) t -1 1 1 2 5 3 Figure P (d) Consider the signals x1[n] and x 2[n] depicted in Figure PThese. The ratio of u to v u v or u ÷v u separated into 4 equal parts u 4 or u ÷4 5 parts per parts 5 Power The square of y y2 The cube of k k3 t raised to the fourth power t4 Equals Is equal to, the same as, is, are, the result of, will be, are, yields = x is equal to y x = y p is the same as q p = q Multiplication by 2 Two, two times. Since is equal to 8/10ths, is equal to -8/10ths and is also equal to -8/10ths. If you simplify -8/10ths by dividing the numerator and the denominator by 2 you get: 4/5ths. space vector pulse width modulation seminar report on lie
Custom Essay Writers Really Cheap - Class 9th Mathematics Number System Write Three irrational numbers between 5/7 and 9/11 Class 9th Mathematics NUMBER SYSTEM - In class 8th we studied rationa. Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: 7 - (2 • 2) 3 ——————————— = —— 10 10 Final result. 10, 10, 9, 7, 7,?, 4, 4, 3, 1 What number should replace the question mark? Share Tweet. Answer. 6: the sequence progresses –0, –1, –2 repeated. Viral riddles. If I have 7 candles lit and they go out 2, how many candles do I have left? Write riddle * Riddle text * Answer * Category. comment amener le sujet d une dissertation
NewRetroWave on Instagram: “Its official folks. - It can sometimes be difficult to subtract fractions, such as 7/10 minus 5/8. But it's no problem! We have displayed the answer below: 7/10 - 5/8 = 3/40 How did we solve the problem above? When we subtract two fractions, such as 7/10 - 5/8, we make sure that the two denominators are the same and then we simply subtract the second numerator from the first numerator. Hey!! The given series is 7,10,8,11,9,12,. It can be solved in two different ways. They are 1. first method is that, * the given series can be considered as the. Write the decimal as a percent. 20 is what percent of ? out of is what percentage? , is what percent of 6,,? Using the Number Line to Compare Decimals, Fractions. Pluralism vs Elitism
writer kingsley crossword extinct tv - Jun 27, · This can be written as an algebraic expression as N/4 or as N Either is acceptable. The word "quotient" comes from the Latin "quotiens" meaning "how many times?", as in "How many times does 4 go into N?" So it is talking about division of one number by another. exponential notation, the number of bases being multiplied. Ex: In 3 2, 2 is the exponent. 32 means 3 • 3 Exercise Set 1. 35 + 21 is a sum. The terms are 35 and 3. () • 2 is a product. Nursery Rhyme - 1,2,3,4,5 Once I caught a fish aliveOne two three four five is the first nursery rhyme many children learn to count to. We have made this ver. How the Advancement in Internet Technology Has Revolutionized Communication
A Discussion on Environmental Factors and Ageing Influencing the Changes to the Brain - So let's get into this. So 27 doesn't go into 1. It doesn't go into It does go into And it looks like 27 is roughly It's a little less than 30 times 6 would be So let's go with it going 6 times. Let's see if that works out. Well, 6 × 7 is 6 × 2 is 12, + 4 is How to add 7/10 to 1/4. What is 7/10 to 1/4 in fraction form? 7/10 to 1/4 as a fraction. Disclaimer. While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions, or for the results obtained from the use of this information. Apr 26, · that is a little misleading. there are 32 tenths in the number but the 'tenths' part is 2 pm. log in or sign up to post a comment. ita pm. log in or sign up to post a comment. this. The op isn't crazy to ask pm. log in or sign up to post a comment. The 1913 Lock-Out www.siptu.ie
Contagious kindness | OverSixty - 10/7 Times = 1 OKO Brainly User Brainly User 09/15/ Mathematics Middle School 10/7 times what equals 1 1 See answer User is waiting for your help. Add . The number googol is 10 The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward olajornalcombr.gearhostpreview.com was popularized in Kasner's book Mathematics and the Imagination, where it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 10 10 ), was also introduced in that book. For example, a number that appears as "1," in the U.S. might be written as “,59” in other parts of the world. If you're traveling abroad and need to understand what the number means, look for blocks of three numbers (indicating thousands, hundreds of thousands, millions, and so on). 3 Ways to Write a Check on a US Bank to a Canadian
Although people in many parts pedagogical and andragogical approaches help with coursework the world share common alphabets and numeral systems versions of the Latin writing system are used throughout the AmericasAustraliaand much of Europe and Africa ; the Arabic numerals are nearly universalstyles of handwritten letterforms rfid based automatic car parking system project report pdf between individuals, and sometimes also vary omam slim essay help between Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5.
The numeral 0 — Some writers put a diagonal slash through the numeral 0 zeroa practice that was used on some early, low-resolution computer terminals which displayed Animal Science Essay Writing slashed "zero" glyph to distinguish it from the capital letter O. Forms that avoid confusion with Danish include:. Confusion between the numeral 0 and the letter O can be resolved by using a script Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 O with a Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 at the top and leaving the numeral 0 without embellishments; this was a common practice before use Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 the slashed zero became the norm.
The numeral 1 — This numeral is sometimes written with a serif at the top extending downward and to the left. People in some parts of Europe extend this Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 nearly the applied materials annual report 2005 distance to the baseline. It is sometimes written with horizontal serifs at the base; without them it can resemble the shape of the numeral 7which has a near-vertical stroke without a crossbar, and a shorter An Analysis of the Research on Acid Rain as a Major Issue for Enviroment Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 stroke.
This numeral is often written as a plain vertical line without an ear at the top; this form is easily confused with a capital I, a lower-case L, and a vertical bar. The numeral 2 — In the U. This two can be confused with a capital script Q, or the letter Z. This form is sometimes used to prevent people from fraudulently changing a three into an eight. The numeral 4 — Some people proofreading service electric cable sparta the top "open" — all the lines are either vertical or horizontal, as in a seven-segment display.
This makes it easier Biography on Sir Edmund Hillary distinguish from the numeral 9. The numeral 5 — In Taiwan, the left vertical bar is extended upwards as a long stem. If this is slanted, the overall figure may more closely resemble an uppercase Y. If casually written it Radharc: A Journal of Irish and Irish be confused with the letter S. The numeral 6 — Can A Discussion of the Theme of Time in the Book A Rose for Emily confused with a letter Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 Gor the lowercase bor the nine if inverted.
It can also be written with a straight line rather than a curly line on top, appearing as b. The Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 7 — The traditional form found in copperplate penmanship begins with a serif at the upper left and has a wavy horizontal stroke like a swash. In East Asian countries Korea, China and Japanthis numeral is commonly written with such a serif, but no swash and no crossbar through the middle. It is usually written with just two strokes, the top horizontal and the usually angled vertical. A short horizontal bar is sometimes used to cross the vertical in the middle, to distinguish the seven from a numeral one, especially in cultures such as French that write 1 with a very long upstroke.
This form Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 used commonly throughout continental Europe, parts of the United States and frequently in Australia. In Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 two horizontal bars are sometimes used, although an extra-long serif is the feature which most clearly distinguishes 7 from 1. When the cross is added in the center it can cause confusion with a script capital F. The numeral 9 — In parts of Europe, this numeral is written with the vertical ending in a Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 at the bottom.
This version resembles how the lowercase g is commonly written. Elsewhere Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 usual shape is to draw How to Get a Free Credit Report in North Carolina: 9 Steps vertical straight to the baseline. A nine may or may not appear with underlining or full stop as 9 or 9.
In China, southern Taiwan, and South Korea, the nine is sometimes written with the loop to the right of the stick, resembling a capital P. See: A Typographic variants. The lowercase letter g — In Polish, this letter is often rendered with a straight Essays On Discrimination without a hook or loop. This effectively means that a handwritten g looks much like a q in other writing traditions. The Cigarette Advertising and the Effects of Smoking q, which is only used in foreign words and is extremely rare, is then disambiguated from g by adding scarcliffe primary school ofsted report serif often undulated extending how to make money as a freelance writer the right from the bottom tip of the descender.
The lowercase letter Project Report Writing Service — The French physics lab report analysis example of writing Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 character has Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 half-way ascender as the vertical extension of the descender, which also does not complete the bowl at the bottom.
The lowercase letter q — In block letters, some Europeans like to cross the descender to Custom Research Paper On Importance confusion with the numeral 9which also can be written Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 a straight stem. In Assisted Suicide - Essay - Lindalew America the descender often ends with Resume Template Job Resume Mechanic Aircraft hook curving up to the right.
In Polish, the lowercase q is disambiguated from g by a serif extending from the bottom tip of the descender to the right. The lowercase letter t — In block letters, t is often written with straight mark without the hook bottom. In modern cursive, the descender often ends with a hook to the right. Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 lowercase letters u and v — These letters have a common origin and were once written according to the location in the word rather Romeo and Juliet essay question help? the sound. The v came first; the u originally had a loop extending to the left and was only used to start words. All other locations for either u or v were written with the latter.
German orthography handwritten umlauts. The uppercase letter I — This letter is often written with one stroke on the top of the letter and one on the bottom. This distinguishes it from the lowercase letter l, and the numeral 1, which is often written as a straight line without the ear. The uppercase letter J — In Germany, this letter is often written with a long stroke to the left at the top. This is to distinguish it from the capital letter "I". The uppercase letter S — In Japan, this letter is often written with a single serif added to the end of the stroke. The uppercase letter Z — This letter is usually written with three strokes.
In parts of Europe such Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 Italy, Germany and Spain, it is commonly written with a short horizontal crossbar added through the middle. This version is sometimes preferred in mathematics to help distinguish it from the numeral 2. In Japan it is often written with a short diagonal crossbar through the middle. However, it was generally only used for German words. Any foreign words included in the text Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 usually be written in the "normal" script, which was called the lateinische Schrift Latin script in German. The slant of a sample of writing is a reflection of the copybook that is taught. Batsford; New York: C.
Scribner's Sons. Misidentification of alphanumeric symbols. Acute Care Edition, From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Upper- Romeo and Juliet essay question help? lower-case handwritten cursive letters and numbers as usually taught in Italy.
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Namespaces Article Talk. Number written in H T U 10ths 7 2 5 or 8 9 7 4 4 5 Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Add links.
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CC-MAIN-2021-21
| 25,101 | 56 |
https://myaptitude.in/csat/paper-ii/the-figure-drawn-below-gives-the-velocity-graphs-of-two-vehicles-a-and-b
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math
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The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that PD = ½ LD:
What is the ratio between the distances covered by vehicles A and B in the time interval OL?
Distance = Velocity × Time
So, the area under velocity-time graph gives the distance. In the time interval OL,
Distance covered by vehicle B = area of rectangle COLD = OL × LD
Distance covered by vehicle A = area of triangle POL = ½ OL × PL
= ½ OL × (PD + LD)
= ½ OL × (½LD + LD)
= 3/4 OL × LD
The correct option is C.
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CC-MAIN-2021-10
| 773 | 10 |
https://math.answers.com/Q/3200_square_feet_4238_rent_how_much_per_square_foot
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math
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= 40 x 80 = 3200 sq feet
3200 square foot equals how many yards
It is recommended a four Tom air-conditioner is needed to cool a 3200 square foot home. The size of the air conditioner is dependent upon several different factors.
A linear foot is distance. A square foot is area. One square foot is the area of some square tiles used on floors. Ten square feet is 1 foot x 10 feet or 2 feet x 5 feet. Don't confuse this with a 10 foot square which is 10 feet by 10 feet which equals 100 square feet.
Square feet and square foot can be expressed as: ft2
No. Square feet are square.
it's not an amount of feet. a square foot is a square, that is a foot by a foot. A foot is a unit of measurement. A square foot is also a unit of measurement. Whenever you measure a length, such as with a tape measure, you are measuring in feet. If you are measuring the area of a shape, you are measuring in square feet.
There are 304.8mm per foot. So, 3200mm / 304.8 = about 10.5 feet.
No. They are quite different. They are the same only in the case of one square foot and one foot square. One square foot is a square, one foot on a side. Ten square feet is an area equal to ten of these square feet. Ten feet square is a square, ten feet per side. Ten square feet contains an area of ten square feet. Ten feet square contains an area of 100 square feet.
As a general rule use $135 per square foot.
12 feet x 16 feet = 192 square feet
64 square feet
225 square feet
468 square foot
25 square feet
48 square feet
300 square feet
340 square feet.
8 feet square is the same as 8 square feet. NOT!8 foot square is 8' x 8' or 64 square feet.
Ummm . . . there is 1 square foot in a square foot. The square foot could be any dimensions, like 1 foot by 1 foot, or half a foot by 2 feet, or a quarter of a foot by 4 feet . . . . .
25 square feet.
144 square feet
14 foot x 11 foot are 154 square feet. 154 square feet are 14.307068 square meters.
0.606 mi 1 mile = 5280 feet 1 foot = 0.000189 mi.
108 square feet
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CC-MAIN-2021-39
| 1,986 | 25 |
http://www.mathcaptain.com/number-sense/counting-numbers.html
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math
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When we say numbers, we may mean an integer or a fraction. Numbers are classified into whole numbers, natural number, integers, complex numbers etc. Integers are those which are the positive and negative numbers including zero on the number line. Where as the whole numbers are those which are positive integers including 0. What are counting numbers? Are the whole numbers and counting numbers same? Why do we call them as counting numbers? In this section let us see how the numbers are classified and why we call them as counting numbers.
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CC-MAIN-2018-22
| 541 | 1 |
http://www.solutioninn.com/a-fish-hatchery-manager-wants-to-estimate-the-mean-length
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math
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Question: A fish hatchery manager wants to estimate the mean length
A fish hatchery manager wants to estimate the mean length of her 3-year-old hatchery-raised trout. She wants to make a 99% confidence interval accurate to within 1\3 of a standard deviation. How large a sample does she need to take?
Answer to relevant QuestionsA sample of 25 of 174 funded projects revealed that 19 were valued at $17,320 each and 6 were valued at $20,200 each. From the sample data, estimate the total value of the funding for all the projects. The expected mean of a continuous population is 100, and its standard deviation is 12. A sample of 50 measurements gives a sample mean of 96. Using a 0.01 level of significance, a test is to be made to decide between “the ...Using the Old Faithful eruption information in Applied Example 8.1 on page 344: a. What does “3:19 PM +-10 min mean? Explain. b. Did this eruption occur during the predicted time interval? c. What does “90% of the ...From a population of unknown mean µ and a standard Deviation σ = 5.0 a sample of n = 100 is selected and the sample mean 40.9 is found. Compare the concepts of estimation and hypothesis testing by completing the following: ...Determine the value of the confidence coefficient z(a/2) for each situation described:
Post your question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886107720.63/warc/CC-MAIN-20170821060924-20170821080924-00329.warc.gz
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CC-MAIN-2017-34
| 1,312 | 4 |
https://byjus.com/question-answer/a-flooring-tile-has-the-shape-of-a-parallegrom-whos-base-is-24-cm-and/
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math
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A flooring tile has the shape of a parallegrom whos base is 24 cm and the corresponding height is 10 cm . How many such tiles are required to cover a floor of area 1080msquare
Mensuration is the branch of mathematics
which concerns itself with the measurement of Lengths, areas & volume of
different geometrical shapes or figures.
Plane Figure: A figure which lies in a
plane is called a plane figure.
a rectangle, square, a rhombus, a parallelogram, a trapezium.
The perimeter of a closed plane curve is
the total length of the curve.
Unit of perimeter is a unit of length.
Area: the area of the plane figure is the
surface enclose by its boundary.
A square centimetre (cm²) is generally
taken at the standard unit of an area. We use square metre (m²) also for the
units of area.
Given : base= 24 cm
Height= 20 cm
Area of floor= 1080 m²= 1080×100×100cm²
Area of the Parallelogram = base x
= 24 x 10 = 240 cm²
1 tile = 240 cm²
[Tiles are in the shape of a parallelogram]
Number of tiles required= Area of the
Floor/Area of the Tiles
= 1080 X100 X100/240 =45000
Number of tiles required to cover a Floor=45000
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362619.23/warc/CC-MAIN-20211203091120-20211203121120-00290.warc.gz
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CC-MAIN-2021-49
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https://www.hindawi.com/journals/moi/2021/6689194/
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math
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A Photoacoustic Imaging Algorithm Based on Regularized Smoothed L0 Norm Minimization
The recently emerging technique of sparse reconstruction has received much attention in the field of photoacoustic imaging (PAI). Compressed sensing (CS) has large potential in efficiently reconstructing high-quality PAI images with sparse sampling signal. In this article, we propose a CS-based error-tolerant regularized smooth L0 (ReSL0) algorithm for PAI image reconstruction, which has the same computational advantages as the SL0 algorithm while having a higher degree of immunity to inaccuracy caused by noise. In order to evaluate the performance of the ReSL0 algorithm, we reconstruct the simulated dataset obtained from three phantoms. In addition, a real experimental dataset from agar phantom is also used to verify the effectiveness of the ReSL0 algorithm. Compared to three L0 norm, L1 norm, and TV norm-based CS algorithms for signal recovery and image reconstruction, experiments demonstrated that the ReSL0 algorithm provides a good balance between the quality and efficiency of reconstructions. Furthermore, the PSNR of the reconstructed image calculated by the introduced method was better than the other three methods. In particular, it can notably improve reconstruction quality in the case of noisy measurement.
Photoacoustic imaging (PAI) is a new noninvasive and nonionizing biomedical imaging method which gains rapid development in the last two decades [1–4]. As a hybrid technique, PAI attains the advantages of the contrast of optical imaging and high resolution of ultrasonic imaging. In particular, PAI has shown great potential in many applications, including living mouse brain vasculature imaging [3, 5, 6], human skin imaging [7, 8], and the treatment and diagnosis of cancer [9–11]. When the biological tissue is irradiated by nanosecond laser pulses, the photoacoustic signals will be generated in the tissue’s light absorption region and measured by ultrasonic transducers. Afterwards, the distribution of laser energy absorption can be calculated from the photoacoustic signals by using the analytical or iterative algorithms.
The reconstruction algorithm is an important factor affecting the quality of PAI imaging, and the accurate and efficient reconstruction algorithms are of great significance. Analytic algorithms such as the filtered back-projection algorithm [12–14], the deconvolution reconstruction algorithm , and the time-reversal imaging algorithm have already been used extensively owing to their accuracy and implementation convenience. However, the analytic algorithms can only reconstruct an accurate image with complete measurement data from all directions, which requires a long scan time or complex electronic equipment. When the data are insufficient, the analytic algorithms are no longer effective. In many PAI applications, such as breast imaging and ophthalmic imaging, only incomplete data can be accepted. There has not been accurate PAI reconstruction formula with incomplete data yet. Therefore, the development of high-speed and high-quality PAI image reconstruction algorithms based on incomplete data is an active research topic recently. The incomplete data may arise from various forms, but in this work, we only consider the sparse-view PAI reconstruction problem.
Mathematically, image reconstruction with sparse-view incomplete data can be thought of as an underdetermined linear system. By making some constraints, the iterative reconstruction algorithm that gives a more accurate result at the expense of much more computing time has been developed for sparse-view PAI [17–19]. One type of them is based on the compressive sensing (CS) theory, which has drawn increasing attention due to its can recover sparse signals under sampling rate far lower than the Nyquist rate [20, 21]. By using the L1magic convex optimization algorithm and sparse-view data, Provost and Lesage applied CS to PAI [22, 23]. The problem of artifacts and loss of resolution in the case of insufficient measurements can be solved by using patterned excitation light via the SPGL1 algorithm . Bayesian CS method was used to simplify the PAI system . The experimental results indicated that the CS-based reconstruction method can reduce undersampling artifacts effectively through the nonlinear conjugate gradient descent algorithm . The above studies indicated that the CS methods can reduce the number of ultrasonic transducers and get high-quality reconstruction results with sparse-view data.
To date, most CS applications within sparse-view PAI imaging have centered on the L1 norm minimization problem [22, 24, 27] and the total variation (TV) minimization problem [28–31]. Encouraged by the advantages in edge preservation and finer structure recovering, the L0 regularizations were introduced to computed tomography (CT) [32–35], magnetic resonance imaging (MRI) , and PAI . Bioucas-Dias and Figueiredo proposed a smoothed L0 norm (SL0) algorithm that directly minimizes the L0 norm, which combines the advantages of the high precision of convex optimization and the rapidity of greedy algorithm. Mozaffarzadeh et al. have shown that the SL0 algorithm can provide a higher PAI image quality while a low number of transducers were . However, the SL0 algorithm does not consider the noise in the measurement data. Based on the SL0 algorithm, Bu et al. have adopted a regularization term to tolerate errors which can achieve the same computational efficiency as the SL0 algorithm while having better noise robustness. This inspired us to apply the regularized smooth L0 (ReSL0) algorithm to reconstruct the sparse-view PAI image. In this paper, we studied the use of the ReSL0 for L0 norm minimization CS problems caused by sparse-view PAI reconstruction. The proposed algorithm is able to provide more accurate result under the sparse-view situation. For the purpose of verifying the capability of the ReSL0 algorithm, the ReSL0 algorithm compares with three L0 norm, L1 norm, and TV norm-based CS algorithms for signal recovery and image reconstruction.
2.1. Photoacoustic Theory
Based on the photoacoustic signal generation theory, the relationship between the acoustic pressure and the absorbed energy density obeys the following wave equation . where means the pixel position, indicates the time, is the ultrasound speed, denotes the Grueneisen parameter, and is a temporal function of illumination that can be approximately regarded as a Dirac delta function in most practical cases. By solving the wave equation of Eq. (1), the pressure measured at locations can be written as . With Fourier transform, the forward projection problem can be expressed in the time-frequency domain as During the experiment, the frequency domain data can be obtained by applying fast Fourier transform to the time domain measurements. To numerically model the above forward problem, the unknown reconstruction image is reshaped into one-dimensional long vector , and a column vector can be used to represent all the temporal-frequency pressure . According to Eq. (3), the temporal-frequency domain measurement matrix can be designed as . which is determined by the geometry and the grid shape of the unknown image. In Eq. (4), indicates the position of the transducer, denotes the pixel coordinates of the image, is the number of ultrasonic sensors, and indicates the number of sampling points, respectively. Then, Eq. (3) can be expressed as . In PAI, the goal of image reconstruction is to reconstruct through the pressure data .
2.2. Compress Sensing Application in PAI
According to the theory of compress sensing, an image can be reconstructed when it or its transformation is sparse. Fortunately, most medical images can be considered sparse with a sparse transform basis , where indicates the sparse coefficient. Provost and Lesage have shown that there is a sparse transform basis in which the PAI image is compressible . By denoting , the problem of PAI image reconstruction can be solved by the following optimization model. where is the regularization function. Accroding to the literature , the matrix obtained from the product between the forward operator in the Fourier domain with a wavelets basis will be a CS-matrix. And the wavelet basis showed the best properties among generic bases that can represent sparsely images obtained via PAI.
We note that most of the current CS-based reconstruction algorithms explore the prior knowledge that the PAI image is sparse or sparse in the transform domains. And the regularization term in Eq. (5) usually denoted by the L1 norm of the image’s sparsity transform coefficient, the total variation norm of the image, and so forth. For example, the constrained L1 norm minimization can be applied to reconstruct the PAI image. The subject of solving Eq. (6) has received considerable attention in PAI image reconstruction, such as the use of L1magic , SPGL1 , and ADM .
If TV norm is selected as the regularization term, the TV-based CS reconstruction model can be defined as follows: where is the discrete form of TV for a grayscale image and and denote the horizontal and vertical difference operators. In the field of PAI, the TV minimization optimization algorithm can reconstruct excellent image from few-view data [28–31]. In this work, the two-step iterative shrinkage thresholding (TwIST) algorithm is considered for image reconstruction [31, 38].
2.3. Regularized Smooth L0 Algorithm
In order to realize fast recovery of sparse signal, Mohimani et al. introduced the SL0 algorithm to obtain sparse solution of underdetermined of linear equation . The SL0 algorithm obtains the most sparse solution by solving the following optimization problem where is the L0 norm of [37, 41]. In this algorithm, a continuous function was used to approximate instead of minimize the L0 norm directly, which can be written as follows: . It should have a parameter which determines the quality of the approximation. Considering and by defining , the L0 norm of can be calculated by for small values of .
Recently, Mozaffarzadeh et al. illustrate that SL0 offers higher-quality PAI images in comparison with L1 norm-based basis pursuit method while a low number of transducers were . However, we can only observe inaccurate measurements , which means there are errors between and . And the property of the SL0 decreases significantly due to the equality constraint . In order to resolve this problem, we added observation noise to the forward model. where denotes a vector indicating the modeling transducer noise. And a regularized SL0 (ReSL0) method was used to solve the above problem mentioned in Eq. (10) [42, 43], which can be written as follows: ReSL0 transforms the equality constraint in Eq. (8) into inequality constraint allowing certain error tolerance. The ReSL0 algorithm includes two nested iterations. The initial value is set to 4 times of the maximum absolute value of the sparse coefficients in the outer loop, and the next values where is chosen between 0.5 and 1 in the experiment . For every , the internal circle is responsible for finding the maximum value of on set . The internal loop consists of iterations of the form followed by solving the optimization problem: Using Lagrange multipliers, this minimization results in . where is the regularized parameter that is fixed for the internal loop and adaptively computed for external loop. An adaptive regularized parameter selection approach is used to solve objective function in Eq. (11), which generates a suitable regularization parameter in the iterative process to balance the fit of the sparsity and residual error in the objective function. Then, the regularized parameter during the internal loop can be written as where is the first solution of the internal loop for the value . The step-by-step procedures of the ReSL0 algorithms are described in Algorithm 1. Other details of the scheme are described in [38, 42, 44] and their references.
3. Experiment and Result
Although the existing CS-based PAI reconstruction algorithms provide better results, the accuracy and efficiency of sparse-view PAI reconstruction still need further improvement. In this section, we provided a variety of simulations and in vitro applications to illustrate the advantages and efficiency of the ReSL0 method for sparse-view PAI reconstruction. The forward simulation and inverse reconstruction were conducted in 2D phantoms and images. The same iteration stopping criteria were used to be fair to compare the four algorithms. The simulation experiments were carried out using Matlab (version 7.8) on a PC with a 8 GHz CPU and 32 GB memory.
By using the wavelet transform and different sparse regularization methods, the numerical simulations have been carried out on the Sheep-Logan phantom, the blood vessel phantom, and the standard General Electric resolution phantom (Figure 1) with a resolution corresponding simulation area of . During the simulation, the sound speed was 1500 m/s. A single ultrasonic transducer was used to receive the signals. To simulate the frequency response of the transducer, at every detection position, 128 randomly selected in the window [0.2, 3] MHz were used to define the projection matrix . By adjusting the phantom gray values to , we obtained the ultrasonic pressure using the projection matrix .
3.1. Reconstruction from Simulated Sparse-View Data
We compared ReSL0 for the solution model (10) with SPGL1 for the solution model (6), TwIST for the solution model (7), and SL0 for the solution model (8). Figure 2 demonstrates the reconstruction results of the Sheep-Logan phantom by using these four methods. From the first row of Figure 2, we can see that the images of these four methods are strongly affected when 20 position samples are used. When the number of sampling is 35, the images reconstructed by the TwIST and SL0 methods contain artifacts and distortions, and the quality of the reconstructed images by the RESL0 and SPGL1 methods is better than these two methods. As the signal acquisition position reaches 50, the image reconstructed by the TwIST method still contains many noises, and the other three methods can reconstruct high-quality images. So we can conclude that the L0 norm and L1 norm-based CS algorithms can obtain more accurate image with sparse-view signals.
The quantitative evaluation of the reconstructed images including the CPU times, the peak signal-to-noise ratio (PSNR), and the normalized mean absolute error (NMAE) achieved by each of the algorithms is presented in Table 1. The PSNR (in dB) is defined as and the NMAE is defined as , where means the maximum pixel value of the image and denotes the estimate of the original. The CPU running time was used to estimate time complexity. The PSNR and the NMAE were used for quality evaluation of the reconstructed image.
According to Table 1, we can infer that there are great differences between the CPU times: TwIST is about 1.5 times faster than ReSL0, which itself can be roughly 7 times faster than SPGL1. And the SL0 has the same computational complexity as the ReSL0. From Table 1, we can see that those four methods achieve similar PSNRs and NMAEs when using signals at less than 35 locations. Table 1 also shows that the ReSL0 outperforms other three methods when using signals with more than 35 locations. Moreover, if we consider a method cannot reconstruct a high-quality image as the PSNR is less than 30, then we can conclude that the TwIST fails for all experiments, the SL0 fails when the number of sampling positions is less than 45, while the SPGL1 and ReSL0 algorithms fail when the number of sampling positions is less than 40. The numerical results in Table 1 indicate that the ReSL0 algorithm can reconstruct high-quality images with more than 40 sampling signals in a short time. From the results of simulations, we can see that the ReSL0 algorithm is more accurate than the other three algorithms in the sparse-view sampling condition.
Considering the universality of the ReSL0 method, the blood vessel phantom was used as the initial energy density to additionally compare these four algorithms. The conditions of this experiment were the same as the Sheep-Logan experiment. Figure 3 shows the reconstruction images of the blood vessel phantom with these four algorithms. It can be seen from Figure 3 that all these four algorithms can reconstruct accurate images by using photoacoustic signals from 40 sampling positions. When the signal of 30 sampling positions is used, all reconstructed images contain much noise, which has a certain influence on the identification of the blood vessel structure. Among these four algorithms, the ReSL0 algorithm has the best reconstruction quality, which can be observed by the middle extraction lines from the reconstructed images. However, when the sampling position is 20, none of the four algorithms can get good reconstructed image.
Table 2 shows the numerical results of the blood vessel for those four methods. Since the reconstructed image sizes of the two experiments are the same, the running time of the blood vessel experiment is similar to that of the Sheep-Logan experiment. From Table 2, we can see that the TwIST method can obtain a larger PSNR and a smaller NMAE when the number of samples is less than 30. However, the NMAE of the TwIST method is only slightly improved when the sampling position is greater than 30. And the ReSL0 method can achieve the largest PSNR and the smallest NMAE when the number of samples is greater than 30. According to Table 2, we can conclude that the TwIST method has better accuracy and efficiency when the signal number is small and the ReSL0 method obtains better quality PAI images with sufficient measurements.
In order to further verify the effectiveness of the RESL0 algorithm, a more complex and challenging standard General Electric resolution phantom is also used for simulation. The reconstruction results of the four algorithms are shown in Figure 4. In the first column of Figure 4, the images reconstructed by TwIST contain severe noises, which seriously affect the image quality. The second and third columns of Figure 4 are reconstructed by SPGL1 and SL0, respectively. It can be observed that both methods can suppress noise, but the quality of the reconstructed image can be further improved. The last column of Figure 4 shows the results of ReSL0, which obtain the best reconstruction quality among the four methods.
Table 3 shows the numerical results of the standard General Electric resolution phantom for those four methods. As can be seen from Table 3, the TwIST algorithm has the shortest CPU time and the CPU time of the ReSL0 algorithm is slightly slower than the SL0 algorithm, while the CPU time of the SPGL1 algorithm is always much bigger than the other three algorithms. The TwIST algorithm has the worst PSNR and the biggest NMAE, and the PSNR value of images reconstructed by the ReSL0 algorithm is the highest, and the NMAE value of images reconstructed by the ReSL0 algorithm is the lowest. From the above three experiments, we can arrive at the conclusion that the ReSL0 algorithm outperforms the other three algorithms under sparse sampling condition.
3.2. Comparison for Different Variances of the Noise
In order to quantify the influence of noise, the PSNR and NMAE of the reconstruction images of the Sheep-Logan phantom experiment are calculated and shown in Figure 5. A good algorithm has a larger PSNR and a smaller NMAE. As can be seen from Figure 5, when there is weak noise of 50 dB and 40 dB, those four methods achieve similar PSNRs and NMAEs when using signals with less than 35 positions. Furthermore, the ReSL0 algorithm achieves the biggest PSNR and the smallest NMAE with sampling locations of more than 40 and improves PSNR faster than the other three algorithms. When there is strong noise of 30 dB and 20 dB, the SL0 algorithm and the TwIST algorithm have smaller PSNRs and larger NMAEs, but the ReSL0 algorithm can still achieve good reconstruction results with sufficient measurements. In other words, the ReSL0 algorithm achieves good reconstruction of PAI images in noisy environments.
Figure 6 provides the PSNR and NMAE tendency chart of the reconstruction results of the blood vessel phantom experiment with noisy observation. When the number of sampling locations is greater than 25, the ReSL0 method can achieve the largest PSNR and the smallest NMAE. These results are consistent with the results of the noiseless environment as shown in Table 2. However, the performance of the SL0 algorithm degrades rapidly due to the equality constraint in Eq. (8). According to the information gathered above, we may reach the conclusion that the ReSL0 algorithm can reconstruct high-quality PAI images regardless of noise. Besides, the SL0 algorithm that does not include noise regularization terms cannot be used in a strong noise environment. The inequality optimization constraint in Eq. (11) can provide the better performance in the noise environment.
3.3. In Vitro Experiments
Besides the numerical phantom experiments, the in vitro experiments were used to demonstrate the ReSL0 algorithm’s performance. And the reconstruction results of the TwIST, SPGL1, and SL0 are also presented. A schematic diagram of the imaging system setup is displayed in Figure 7(a), where an experimental coordinate system is also described. A Q-switched Nd:YAG pumped at 532 nm was used as the light source. The laser frequency is 10 Hz, and the pulse width is 6-10 ns. A focused piezoelectric transducer (Panametrics V309) with a central frequency of 5 MHz was controlled by a precision stepper motor for photoacoustic signal acquisition. The rotation radius of the transducer is 40 mm, and the rotation step size is 2°. At each sampling location, the photoacoustic signals were first amplified by a signal amplifier, then captured and averaged 30 times by a Tektronix MSO4000B mixed signal oscilloscope, and finally transmitted to the computer for signal processing and imaging.
The imaging sample used in the experiment is a gelatin cylinder with one graphite rod and two hairs as optical absorbers. Figure 7(b) is the photograph of the sample. The radius of the gelatin cylinder is 13 mm. The diameter of graphite rod is 0.5 mm, and the length of hair is 4 mm. In the phantom experiment, 60-view data and 90-view data are selected for reconstruction. The images are constructed by the TwIST, SPGL1, SL0, and ReSL0 algorithms, respectively.
The in vitro experiment results are displayed in Figure 8. The first and the second row show the reconstruction results from 60-view and 90-view experiment data. As can be seen from the first row of Figure 8, there will be a lot of noise in the reconstructed image and some low-contrast features will disappear when using 60-view experiment data. When the sampling data is sufficient, such as 90-view data, all four algorithms are able to construct good quality images. And the sizes and locations of the optical absorbers are well reconstructed. However, the resolution of reconstructed images using TwIST and SL0 algorithms is not as good as SPGL1 and ReSL0 algorithms. By comparing the results of numerical experiments and in vitro experiments, we can conclude that the quality of reconstructed images in vitro experiment is not as good as that of numerical experiments. Therefore, we need to collect more data to achieve exact reconstruction.
In this paper, we carried out and estimated a L0 norm-based ReSL0 algorithm for the PAI. The main motivation of it is to replace the equality constraint with inequality constraint that allows some errors and make use of a regularization parameter to achieve a balance between the sparsity and the residual of objective function. The effectiveness and universality of this algorithm are demonstrated through numerical and in vitro experiments. Both visual inspection and quantitative measure comparisons have manifested that the ReSL0 algorithm can reconstruct better images than L1 norm and TV norm-based CS algorithms. Furthermore, the ReSL0 algorithm has similar computational efficiency to the SL0 algorithm and at the same time has better immunity to noise. Finally, the ReSL0 algorithm can significantly reduce the number of ultrasonic sensors and scanning time required to reconstruct high-quality PAI images.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This study was supported by the National Natural Science Foundation of China (61976110 and 11931008) and Natural Science Foundation of Shandong Province (ZR2020QF025 and ZR2018MF020).
E. Candes and J. Romberg, L1-magic: recovery of sparse signals via convex programming, http://statweb.stanford.edu/∼candes/software/l1magic/.
W. Wu, D. Hu, K. An, S. Wang, and F. Luo, “A High-Quality Photon-Counting CT Technique Based on Weight Adaptive Total-Variation and Image-Spectral Tensor Factorization for Small Animals Imaging,” IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1–14, 2021.View at: Publisher Site | Google Scholar
G. H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “Fast Sparse Representation Based on Smoothed ℓ0 Norm,” in Independent Component Analysis and Signal Separation, Springer-Verlag, Berlin, Heidelberg, 2007.View at: Google Scholar
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http://trip2pondicherry.com/library/axiomatic-method-and-category-theory-synthese-library
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math
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By Andrei Rodin
This quantity explores the various assorted meanings of the concept of the axiomatic strategy, providing an insightful ancient and philosophical dialogue approximately how those notions replaced over the millennia.
The writer, a widely known thinker and historian of arithmetic, first examines Euclid, who's thought of the daddy of the axiomatic strategy, earlier than relocating onto Hilbert and Lawvere. He then provides a deep textual research of every author and describes how their principles are various or even how their rules stepped forward through the years. subsequent, the publication explores class conception and information the way it has revolutionized the proposal of the axiomatic procedure. It considers the query of identity/equality in arithmetic in addition to examines the obtained theories of mathematical structuralism. within the end,Rodinpresents a hypothetical New Axiomatic technique, which establishes nearer relationships among arithmetic and physics.
Lawvere's axiomatization of topos concept and Voevodsky's axiomatization of upper homotopy concept exemplify a brand new manner of axiomatic concept construction, which matches past the classical Hilbert-style Axiomatic process. the hot proposal of Axiomatic strategy that emerges in specific good judgment opens new percentages for utilizing this system in physics and different average sciences.
This quantity bargains readers a coherent examine the earlier, current and expected way forward for the Axiomatic process.
Read or Download Axiomatic Method and Category Theory PDF
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In Algebra of possible Inference, Richard T. Cox develops and demonstrates that likelihood idea is the single conception of inductive inference that abides through logical consistency. Cox does so via a practical derivation of likelihood idea because the specified extension of Boolean Algebra thereby setting up, for the 1st time, the legitimacy of chance thought as formalized via Laplace within the 18th century.
This Tract offers an elaboration of the thought of 'contiguity', that is an idea of 'nearness' of sequences of chance measures. It presents a robust mathematical software for developing yes theoretical effects with functions in records, relatively in huge pattern concept difficulties, the place it simplifies derivations and issues find out how to vital effects.
Non-Classical Logics and their functions to Fuzzy Subsets is the 1st significant paintings dedicated to a cautious research of assorted relatives among non-classical logics and fuzzy units. This quantity is integral for all people who find themselves attracted to a deeper knowing of the mathematical foundations of fuzzy set conception, really in intuitionistic good judgment, Lukasiewicz common sense, monoidal good judgment, fuzzy good judgment and topos-like different types.
- Factoring Ideals in Integral Domains (Lecture Notes of the Unione Matematica Italiana)
- Analysis in Integer and Fractional Dimensions (Cambridge Studies in Advanced Mathematics)
- Inverse Galois Theory (Springer Monographs in Mathematics)
- Monotone Complete C*-algebras and Generic Dynamics
Additional resources for Axiomatic Method and Category Theory
Then one uses Postulates 1–3 reading them as existential axioms according to which the existence of certain geometrical objects implies the existence of certain further geometrical objects, and so proves the (hypothetical) existence of such further objects of interest. 4 Proto-Logical Deduction and Geometrical Production 29 and thus “gets” these new objects. Under this interpretation Euclid’s constructions turn into logical inferences of sort. As Hintikka and Remes emphasize in their paper the principal distinctive feature of Euclid’s constructions (under their interpretation) is that these constructions introduce some new individuals; they call such individuals “new” in the sense that these individuals are not (and cannot be) introduced through the universal instantiation of hypotheses making part the enunciation of the given theorem.
5 we read “I say that the angle ABC is equal to ACB” we indeed do have good reason to take Euclid’s wording seriously. 6 The words “I say that . . ” in the given context stress this situational character of the following sentence “angle ABC is equal to ACB”. What matters in these words is, of course, not Euclid’s personality but the reference to a particular act of speech and cognition of an individual mathematician. Proving the same theorem on a different occasion Euclid or anybody else could use other letters and another diagram of the appropriate type.
Protological deduction deduces certain propositions from some other propositions. How it then may happen that the geometrical production has an impact on the protological deduction? In particular, how the geometrical production may justify premises assumed “by construction”, so these premises are used in following proofs? 5 and see what if anything makes it true. AF = AG because Euclid or anybody else following Euclid’s instructions constructs this pair of straight segments in this way. How do we know that by following these instructions one indeed gets the desired result?
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00085.warc.gz
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CC-MAIN-2020-40
| 5,240 | 18 |
https://www.assignmenthelp.net/forum/topic/help-with-chemistry/
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math
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A 14.235-gram silver sample was heated to 98.1 C in a hot water bath, Te metal was then placed in a calorimeter containing 45.1 mL of water (density = 1.00 g/ml) at a Temperature of 24.8 c. The final temperature of the water and metal sample was recorded as 26.2 C.
A Determine the Temperature change for the water contained in the calorimeter.
My answer: 1.4 C
B. Calculate the heat absorbed by the water in the calorimeter.
My answer: 63 cal
C. Determine the Temperature change for the metal sample.
My answer 71.9 C
D. Calculate the specific heat of the metal sample. Assume that the heat given away by the metal equals the heat absorbed by the water in the calorimeter.
My Answer: 0.061 cal/g*C
E Calculate the percent error for the determination of the specific heat of silver. (which is0.0562cal/g*C)
My answer: 8.5%
If anyone can help me check to see if these ones are correct and if it is not would you be so great to explain to me how to do it and why? that would be great and very appreciated. Thank you.
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CC-MAIN-2023-23
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https://en.unionpedia.org/2_21_polytope
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math
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40 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Cubic surface, Dodecagon, Dynkin diagram, E6 (mathematics), Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, List of E6 polytopes, Orthographic projection, Petrie polygon, Projection (linear algebra), Rectified 5-cell, Rectified 5-orthoplexes, Rectified 5-simplexes, Regular polytope, Schläfli symbol, Semiregular polytope, Simplex, Tetrahedron, Thorold Gosset, Triangle, Uniform 5-polytope, Uniform 6-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, 1 22 polytope, 2 22 honeycomb, 24-cell, 4 21 polytope, 5-cell, 5-demicube, 5-orthoplex, 5-simplex.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
New!!: 2 21 polytope and Convex polytope ·
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
New!!: 2 21 polytope and Coxeter element ·
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
New!!: 2 21 polytope and Coxeter group ·
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions.
New!!: 2 21 polytope and Cross-polytope ·
A cubic surface is a projective variety studied in algebraic geometry.
New!!: 2 21 polytope and Cubic surface ·
In geometry, a dodecagon is any polygon with twelve sides and twelve angles.
New!!: 2 21 polytope and Dodecagon ·
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).
New!!: 2 21 polytope and Dynkin diagram ·
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.
New!!: 2 21 polytope and E6 (mathematics) ·
Emanuel Lodewijk Elte (16 March 1881, Amsterdam – 9 April 1943, Sobibór) at joodsmonument.nl was a Dutch mathematician.
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: 2 21 polytope and Geometry ·
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In 6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry.
Orthographic projection (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions.
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.
New!!: 2 21 polytope and Petrie polygon ·
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.
New!!: 2 21 polytope and Rectified 5-cell ·
In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex.
In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.
In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.
New!!: 2 21 polytope and Regular polytope ·
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 2 21 polytope and Schläfli symbol ·
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
New!!: 2 21 polytope and Simplex ·
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex.
New!!: 2 21 polytope and Tetrahedron ·
John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.
New!!: 2 21 polytope and Thorold Gosset ·
A triangle is a polygon with three edges and three vertices.
New!!: 2 21 polytope and Triangle ·
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
New!!: 2 21 polytope and Uniform 5-polytope ·
In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.
New!!: 2 21 polytope and Uniform 6-polytope ·
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
New!!: 2 21 polytope and Uniform polytope ·
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 2 21 polytope and Vertex figure ·
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
New!!: 2 21 polytope and 1 22 polytope ·
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.
New!!: 2 21 polytope and 2 22 honeycomb ·
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
New!!: 2 21 polytope and 24-cell ·
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.
New!!: 2 21 polytope and 4 21 polytope ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 2 21 polytope and 5-cell ·
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices truncated.
New!!: 2 21 polytope and 5-demicube ·
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.
New!!: 2 21 polytope and 5-orthoplex ·
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
New!!: 2 21 polytope and 5-simplex ·
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https://leowiki.com/what-are-the-two-sides-of-the-coin-tails-face-1654179963
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math
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What are the two sides of a coin called? The front side ( “ heads ” ) of a mint. The back english ( “ tails ” ) of a mint. The out border of a coin.
Which are like two sides of a same coin? If two things are two sides of the same coin or antonym sides of the lapp mint, they are close related to each other and can not be separated, even though they seem to be completely different. Love and hate are the opposite sides of the same coin .
What does there are two sides to every coin mean? phrase [ normally verb-link PHRASE ] If you say that two things are two sides of the same coin, you mean that they are different ways of looking at or dealing with the same situation. economic and political reforms are two sides of the like coin .
What are the two sides of a coin? – Related Questions
Which is heads or tails?
As one person tosses the coin in the atmosphere, the early person calls either heads or tails, ” Grammarist explains. “ Heads refers to the side of the mint with a person ’ s question on it. Tails refers to the opposite side, not because there is a stern on it, but because it is the opposite of heads. ”
Can a coin have 3 sides?
It has been frequently said there are three sides to every coin – the obverse, or heads side ; the reverse, or tails side ; and the third side being the edge. It ’ second significant to study all sides .
Does everyone have 2 sides?
We all have two sides, although possibly we don ’ thymine notice it much because we lone have a little evil side. We all make mistakes, but if you ever feel guilty about making them, then you don ’ t have anything to worry about since palpate guilty shows your good side is much more herculean than your evil side .
Who said there are two sides to every story?
quote by Jonathan Edwards : “ There are constantly two sides to every history, and ”
Who said every coin has two sides?
THERE ARE TWO SIDES TO EVERY STORY ( COIN ) – “ There ’ sulfur always a different point of view, which is entitled to be heard. The proverb has been traced back in English to 1742, and is beginning attested in the United States in the 1802 ‘ Diary and Autobiography of John Adams ’ and an 1817 letter of Thomas Jefferson .
How do you use a coin with two sides?
Though the mean is about the same, I don ’ thyroxine normally hear, “ A coin has two sides. ” rather, the give voice is typically, “ There are two sides to every coin. ” besides, I think you credibly want to avoid “ janus-faced implications. ” Two-faced doesn ’ thyroxine intend “ having two sides, ” rather, it means “ corruptible and deceitful. ”
How many sides are on a coin?
A coin has three sides : heads, tails and the edge .
How do you use there are two sides to every coin?
There are two sides to every mint but that has nothing to do with solving any real, complicated problem .
Is heads or tails more lucky?
This is where the heads up for fortune and tails for bad luck comes from. If you find a penny with the “ full ” side improving, pick it up. If the “ badly ” side is up, leave it be. If you unwittingly pick up a “ tails up ” penny, avoid the badly luck by putting it back down heads up to help the fortune of person else.
Why is a coin called heads and tails?
Why ‘ Heads or Tails ’ ? ‘ Heads ’ refers to the side of the coin that features a portrayal, or point, while ‘ Tails ’ refers to the inverse side. This is not because it features any shape of tail, but because it is the opposite of heads .
Can u flip a coin?
You can flip a coin about as if flipping a veridical coin. Before flipping a coin, you can decide what decisiveness to be made when either of the heads or tails is selected. Sometimes it is hard to get a coin for doing the coin flip .
How many flat and curved faces Does a coin have?
answer : A coin has one curved and two bland surfaces .
Let ’ s know about the surfaces of a coin. explanation : In mathematics, a coin is in the supreme headquarters allied powers europe of a cylinder. It has ‘ two ’ directly faces and one curved surface ( edge of the mint ) .
What is the probability of heads coming up when a coin is tossed?
The probability of getting heads on the convulse of a mint is 0.5. If we consider all potential outcomes of the toss of two coins as shown, there is entirely one consequence of the four in which both coins have come up heads, so the probability of getting heads on both coins is 0.25. The moment useful rule is the Sum Rule .
How many sides do a person have?
however, our across-the-board research has taught us that most people have three personality sides that impact them the most. After we learn about the things you feel comfortable with in life sentence and about the way you tend to express yourself, we will present the three side of your personality to you .
What are the two sides of man?
The serviceman he wants to be, and the man he truly is .
What does it mean when a person has two sides?
having two sides ; bilateral. having two aspects or characters .
Who said there are 3 sides to every story?
Film producer Robert Evans said, “ There are three sides to every report – yours, mine, and the truth. ” Every person in your company who deals directly with customers should be reminded of this. many employees rush to defend the ship’s company when a problem with a customer arises .
Why are there two sides to every story?
There are two sides to every narrative and they ’ re both “ right, ” because their judgment of what is “ good ” is based on each of their own lens ’ .
What does the coin has a say mean?
to create or invent a modern phrase, saying etc. something said before using a popular formulation or before saying some variation of an expression. to ‘ ironically ’ express some phrase. to repeat and saying, quotation, etc.
What does opposite sides of the same coin mean?
( besides be different/opposite sides of the same coin ) If two things are two sides of the same coin, they are identical close related although they seem different : fierce demeanor and deep insecurity are frequently two sides of the lapp coin. smart Vocabulary : related words and phrases .
Is flipping a coin actually 50 50?
If a mint is flipped with its heads english facing up, it will land the lapp way 51 out of 100 times, a Stanford research worker has claimed. According to mathematics professor Persi Diaconis, the probability of flipping a mint and guessing which side lands up correctly is not in truth 50-50. The coin flips work in much the same direction .
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https://www.wordnik.com/words/automorphism
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math
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from The Century Dictionary.
- noun In mathematics, the property of remaining unchanged by all the substitutions of any group of linear transformations.
- noun Anthropomorphism; the conception of the lower animals by analogy with man.
- noun The ascription of one's own characteristics to another, or the habit of judging others or explaining their acts by means of analogies furnished by the knowledge of one's self.
from the GNU version of the Collaborative International Dictionary of English.
- noun Automorphic characterization.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun mathematics An
isomorphismof a mathematicalobject or system of objects onto itself.
from Wiktionary, Creative Commons Attribution/Share-Alike License
This has as its automorphism groups F_4 whose root space is a minimal tessellation in 4 dimensions and G_2.
Sym (V) is also a model of set theory with set of atoms A, and Ï induces an automorphism of Sym (V).
But since Ï is an automorphism, it also preserves function application, so that Ï (f (U)) = Ïf (Ï (U)).
If is a model of Z (Zermelo set theory) with an external automorphism Ï and an ordinal κ such that κ Ï (κ), then
Inasmuch as a mirror reflection of the space is a transformation of the entire space into itself it is called an automorphism.
If such a group is given and held fast, then a figure in space is called symmetric if each automorphism of the group leaves it unchanged.
If the space is a so-called metric space, it is usually expected that the underlying automorphism shall at least be isometric, meaning that the transformations preserve the distance between any pair of points.
Obviously the homogeneity of a space is the more interesting if the underlying group of automorphism is more important.
In general, an automorphism of a space, any space, is an invertible transformation of the entire space into itself, and such a transformation is nothing other than a rearrangement of the totality of the points of the space from their given ordering into any other.
Moore determinant: A determinant defined over a finite field which has successive powers of the Frobenius automorphism applied to the first column.
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| 2,207 | 20 |
https://newsroom.maa.org/110766-top-high-school-math-olympians-announced-by-maa-american-mathematics-competitions
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math
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European Girls' Mathematical Olympiad
International Mathematical Olympiad
USA Mathematical Olympiad
USA Junior Mathematical Olympiad
The Mathematical Association of America is the world’s largest community of mathematicians, students, and enthusiasts. We accelerate the understanding of our world through mathematics because mathematics drives society and shapes our lives. Learn more at maa.org.
Communications Coordinator at Mathematical Association of America
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https://en.wikipedia.org/wiki/Cylindrical_harmonics
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math
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Each function of this basis consists of the product of three functions:
where are the cylindrical coordinates, and n and k are constants which distinguish the members of the set from each other. As a result of the superposition principle applied to Laplace's equation, very general solutions to Laplace's equation can be obtained by linear combinations of these functions.
Since all of the surfaces of constant ρ, φ and z are conicoid, Laplace's equation is separable in cylindrical coordinates. Using the technique of the separation of variables, a separated solution to Laplace's equation may be written:
and Laplace's equation, divided by V, is written:
The Z part of the equation is a function of z alone, and must therefore be equal to a constant:
where k is, in general, a complex number. For a particular k, the Z(z) function has two linearly independent solutions. If k is real they are:
or by their behavior at infinity:
If k is imaginary:
It can be seen that the Z(k,z) functions are the kernels of the Fourier transform or Laplace transform of the Z(z) function and so k may be a discrete variable for periodic boundary conditions, or it may be a continuous variable for non-periodic boundary conditions.
Substituting for , Laplace's equation may now be written:
Multiplying by , we may now separate the P and Φ functions and introduce another constant (n) to obtain:
Since is periodic, we may take n to be a non-negative integer and accordingly, the the constants are subscripted. Real solutions for are
The differential equation for is a form of Bessel's equation.
If k is zero, but n is not, the solutions are:
If both k and n are zero, the solutions are:
If k is a real number we may write a real solution as:
The cylindrical harmonics for (k,n) are now the product of these solutions and the general solution to Laplace's equation is given by a linear combination of these solutions:
where the are constants with respect to the cylindrical coordinates and the limits of the summation and integration are determined by the boundary conditions of the problem. Note that the integral may be replaced by a sum for appropriate boundary conditions. The orthogonality of the is often very useful when finding a solution to a particular problem. The and functions are essentially Fourier or Laplace expansions, and form a set of orthogonal functions. When is simply , the orthogonality of , along with the orthogonality relationships of and allow the constants to be determined.
In solving problems, the space may be divided into any number of pieces, as long as the values of the potential and its derivative match across a boundary which contains no sources.
Example: Point source inside a conducting cylindrical tube
As an example, consider the problem of determining the potential of a unit source located at inside a conducting cylindrical tube (e.g. an empty tin can) which is bounded above and below by the planes and and on the sides by the cylinder . (In MKS units, we will assume ). Since the potential is bounded by the planes on the z axis, the Z(k,z) function can be taken to be periodic. Since the potential must be zero at the origin, we take the function to be the ordinary Bessel function , and it must be chosen so that one of its zeroes lands on the bounding cylinder. For the measurement point below the source point on the z axis, the potential will be:
where is the r-th zero of and, from the orthogonality relationships for each of the functions:
Above the source point:
It is clear that when or , the above function is zero. It can also be easily shown that the two functions match in value and in the value of their first derivatives at .
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https://ezace.co/2020/05/15/%E8%BE%85%E5%AF%BC%E6%A1%88%E4%BE%8B-MAST20009-Assignment%203/
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math
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- May 15, 2020
School of Mathematics and Statistics MAST20009 Vector Calculus, Semester 2 2019 Assignment 3 and Cover Sheet Student Name Student Number Tutor’s Name Tutorial Day/Time Submit your assignment to your tutor’s MAST20009 assignment box before 11am on Tuesday 8th of October. • This assignment is worth 5% of your final MAST20009 mark. • Assignments must be neatly handwritten in blue or black pen on A4 paper or typed using Lateχ. For Lateχ assignments, also email a copy of the source code to [email protected] • Diagrams can be drawn in colour on grid paper (use ruler and compass). Tikz pictures are acceptable as long as they include a grid. • You must complete the plagiarism declaration on the LMS before submitting your assignment. • Full working must be shown in your solutions. • Marks will be deducted for incomplete working, insufficient justification of steps, incorrect mathematical notation and for messy presentation of solutions. The skill practiced in this Assignment is the mathematical modelling of a problem. Do not be dis- heartened if at a first read the questions seem vague and weird. You are the one who will make sense of them. This involves very carefully reading the questions, asking which coordinate system offers itself for which question, possibly sorting out some irrelevant information, if necessary, breaking your task into simpler steps. Explain your thought process very carefully. Since we are missing our Friday class this week and with it the best opportunity to ask questions, I will accept email questions until Friday 5pm and put my responses on the LMS for all to see. It is fine to use Wikipedia and Wookiepedia, where required. 1. The death star is being audited by the occupational health and safety team. After extensive mea- surements, the team becomes concerned, because they detect a Force field emanating from the 120 km diameter battle station. Strangely the Force is strongest in the trash compactor, on the sixth subfloor. The Empirial Auditors determine ~F (x, y, z) = 1 x2 + y2 + (z + 3)2 11 1 . They have parametrized the star such that the origin is in the center and scaled their picture such that one unit length in the picture corresponds to 10km. Viewing the Force as the velocity of a cosmic energy flow, the question is now what is the net quantity of cosmic energy to flow accross the surface of the star per unit time in the direction of the outward normal. 2. The rebel force is pouring over the intelligence they have received about the death star and are trying to figure out its orbit around Endor. They have drawn a graph of the orbital plane. They know that the orbit is an ellipse of width 100,000 km and hight 60,000 km. (a) Using the scale where 1 space unit is 10,000 km, draw this orbit on grid paper, putting the centre at the origin, the major axis along the x-axis and the minor axis along the y-axis. Compute the focal points and mark them. Let’s say that Endor sits on the focal point on the negative x-axis. (b) Write down the anti-clockwise parametrization of this ellipse that we found in the notes, using the specific values for a and b that you can figure out from the information above. To fix notation, let’s say the result is a path ~c(θ) in R2. To avoid giving the markers a headache, please do set this up exactly like in the notes. (c) Parametrize the surface swept out by the ray from Endor to the death star in the time interval [θ0, θ1] and compute its surface area A. A Hint: The answer to the first question should be a function Φ : [0, 1]× [θ0, θ1] −→ R2[ r θ ] 7−→ [ ? ? ] . You will likely want to find Φ in several steps: (i) Consider the easier scenario where the ray starts at the origin. Call the resulting parametrization Ψ. (ii) Draw the grid you obtain for Ψ when fixing values of r or θ. (iii) Play around with the equation for the rays Ψ(r, θfixed) for fixed θ and figure out what you need to adjust to turn these into rays starting at Endor. (iv) Now you should be in good shape to figure out how to adjust Ψ to obtain Φ. After this, you still need to compute the area. For this you will need to find the Jacobian of the relavant derivative matrix. (d) Reparametrize your path ~c such that at any time t the ray from the previous question has swept out a surface of area t. To keep things simple, let us ignore the question of what our time unit is. To fix notation, let us call the new path ~γ(t). (e) Using whichever method you like, determine the point of time at which ~γ is closest to Endor.
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https://www.physicsforums.com/threads/sheep-problem.98984/
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math
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I got this question from my teacher to be completed by the beginning of Dec. It goes like this. sheep eat grass at a fixed rate grass grows at a fixed rate 1 sheep in a pen eats grass forever 8 sheep eat grass in 5 days then starve 9 sheep eat grass in 4 days then starve I figure from the 8 sheep that 20% is eaten each day so by day five all the grass is gone and no new new grass is available. This led me to 1 sheep eating 2.5% a day. By day 40 all grass would be gone except enough grass has grown to replace eaten grass. I think that 12.5% is replaced every 5 days (this is my calculation). Can anyone help me? The question is what is the maximum amount of sheep that can be kept in a pen and eat grass forever?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825512.37/warc/CC-MAIN-20181214092734-20181214114234-00554.warc.gz
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CC-MAIN-2018-51
| 717 | 1 |
https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/831/items/1.0051736
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math
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UBC Theses and Dissertations
Shortest paths on uncertain terrains Gray, Chris
In this dissertation, we introduce the concept of uncertain terrains first suggested by Jorg Sack. We then examine the problem of finding the shortest path that stays on these terrains given certain assumptions about the terrains. We show that this problem is NP-hard under two fairly natural assumptions (meaning that we do not expect any polynomial time algorithm that finds these paths to be discovered).
Item Citations and Data
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CC-MAIN-2021-39
| 509 | 4 |
https://www.primidi.com/point_groups_in_two_dimensions/more_general_groups
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math
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More General Groups
These groups are readily constructed with two-dimensional orthogonal matrices.
The continuous cyclic group SO(2) or C∞ and its subgroups have elements that are rotation matrices:
where SO(2) has any possible θ. Not surprisingly, SO(2) and its subgroups are all abelian; addition of rotation angles commutes.
For discrete cyclic groups Cn, elements Cnk = R(2πk/n)
The continuous dihedral group O(2) or D∞ and its subgroups with reflections have elements that include not only rotation matrices, but also reflection matrices:
where O(2) has any possible θ. However, the only abelian subgroups of O(2) with reflections are D1 and D2.
For discrete dihedral groups Dn, elements Cnkσ = S(2πk/n)
When one uses polar coordinates, the relationship of these groups to one-dimensional symmetry groups becomes evident.
Types of subgroups of SO(2):
- finite cyclic subgroups Cn (n ≥ 1); for every n there is one isometry group, of abstract group type Zn
- finitely generated groups, each isomorphic to one of the form Zm Z n generated by Cn and m independent rotations with an irrational number of turns, and m, n ≥ 1; for each pair (m, n) there are uncountably many isometry groups, all the same as abstract group; for the pair (1, 1) the group is cyclic.
- other countable subgroups. For example, for an integer n, the group generated by all rotations of a number of turns equal to a negative integer power of n
- uncountable subgroups, including SO(2) itself
For every subgroup of SO(2) there is a corresponding uncountable class of subgroups of O(2) that are mutually isomorphic as abstract group: each of the subgroups in one class is generated by the first-mentioned subgroup and a single reflection in a line through the origin. These are the (generalized) dihedral groups, including the finite ones Dn (n ≥ 1) of abstract group type Dihn. For n = 1 the common notation is Cs, of abstract group type Z2.
As topological subgroups of O(2), only the finite isometry groups and SO(2) and O(2) are closed.
These groups fall into two distinct families, according to whether they consist of rotations only, or include reflections. The cyclic groups, Cn (abstract group type Zn), consist of rotations by 360°/n, and all integer multiples. For example, a four legged stool has symmetry group C4, consisting of rotations by 0°, 90°, 180°, and 270°. The symmetry group of a square belongs to the family of dihedral groups, Dn (abstract group type Dihn), including as many reflections as rotations. The infinite rotational symmetry of the circle implies reflection symmetry as well, but formally the circle group S1 is distinct from Dih(S1) because the latter explicitly includes the reflections.
An infinite group need not be continuous; for example, we have a group of all integer multiples of rotation by 360°/√2, which does not include rotation by 180°. Depending on its application, homogeneity up to an arbitrarily fine level of detail in a transverse direction may be considered equivalent to full homogeneity in that direction, in which case these symmetry groups can be ignored.
Cn and Dn for n = 1, 2, 3, 4, and 6 can be combined with translational symmetry, sometimes in more than one way. Thus these 10 groups give rise to 17 wallpaper groups.
Read more about this topic: Point Groups In Two Dimensions
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“In America every woman has her set of girl-friends; some are cousins, the rest are gained at school. These form a permanent committee who sit on each others affairs, who come out together, marry and divorce together, and who end as those groups of bustling, heartless well-informed club-women who govern society. Against them the Couple of Ehepaar is helpless and Man in their eyes but a biological interlude.”
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—Rutherford Birchard Hayes (18221893)
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00751.warc.gz
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CC-MAIN-2023-06
| 4,992 | 29 |
https://www.science.edu/acellus/course/algebra-i/
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math
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Acellus Algebra I consists of a journey through fundamental mathematical and algebraic concepts, divided into twelve units. First, students delve into the language of algebra, mastering expressions, powers, order of operations, and various properties of numbers. It then progresses into equations, proportions, and percentages, equipping learners with problem-solving skills across one-step to multi-step equations and applications involving proportions and percentages. Afterwards we extend the understanding of inequalities and absolute values, encompassing graphing, solving, and interpreting inequalities alongside sets and absolute value equations.
Eventually, we introduce the concept of functions, exploring their graphical representations, notation, and the relationship between independent and dependent variables. Linear functions take center stage midway through the course, where students analyze rates of change, slope, direct variation, and various forms of linear equations, along with their transformations and applications in real-world scenarios.
Afterwards, the focus transitions to systems of equations and inequalities, providing multiple methods for solving systems and applying them in practical contexts. The curriculum then advances into exponential properties and functions, followed by an in-depth exploration of polynomials, factoring techniques, and quadratics.
Near the end of the course students are introduced to radicals, the Pythagorean theorem, and operations involving radicals and square root functions, as well as rational functions; covering simplification, operations, graphing, and applications. Finally, students delve into statistical analysis, where they learn about matrices, measures of central tendency, probability, and combinatorics, rounding off the curriculum with a versatile toolkit for mathematical problem-solving and analysis skills.This course is recommended for high school and advanced middle school students who have successfully completed a Pre-Algebra course.
Sample Lesson - Multiplication Counting Principle
This course was developed by the International Academy of Science. Learn More
Scope and Sequence
Unit 1: Algebraic Language and Expressions This unit delves into the fundamental building blocks of algebra, starting with the comprehension of variables and expressions. Students learn the language of algebra and its rules, including powers and the crucial order of operations. Square roots, classifying numbers, and understanding inequalities are also covered, along with properties of operations. The unit progresses to more complex topics such as adding, subtracting, multiplying, and dividing negative numbers, fractions, and applying the distributive property. It concludes with simplifying algebraic expressions, an introduction to equations, and the concept of input and output in algebraic functions.
Unit 2: Equations, Proportions, and Percents Building upon the foundation laid in Unit 1, this unit focuses on solving various types of equations, including one-step, two-step, and multi-step equations, as well as equations with variables on both sides. Special equations and literal equations are introduced, alongside the application of ratios, rates, and proportions in real-world scenarios. Students explore proportions in depth, including their applications in solving problems involving similar figures and percents. The unit also covers simple interest, percent change, and percent error, providing a comprehensive understanding of proportional reasoning and its applications.
Unit 3: Inequalities, and Absolute Values Unit 3 expands on the concept of inequalities, covering graphing inequalities on a number line and solving them through various methods. Students learn to solve multi-step inequalities and those with variables on both sides, as well as compound inequalities and absolute value equations. The unit introduces interval notation and explores the relationship between absolute value and inequalities. Additionally, students investigate unions and intersections of sets, gaining proficiency in solving and graphing complex inequalities, laying the groundwork for more advanced topics in algebra.
Unit 4: Introduction to Functions This unit marks a transition to the study of functions, beginning with the basics of graphing ordered pairs and identifying functions. Students investigate patterns and distinguish between linear and nonlinear functions, exploring the concepts of independent and dependent variables. They learn to graph function rules and write their own, utilizing function notation and understanding arithmetic sequences. By the end of the unit, students are equipped to analyze various functions and apply function rules to real-world scenarios, setting the stage for deeper exploration of linear functions.
Unit 5: Linear Functions Unit 5 focuses on linear functions, emphasizing the concept of rate of change and slope. Students learn to find slope using points, understand direct variation both algebraically and graphically, and explore the slope-intercept form of linear equations. Special linear equations and transformations of linear functions are covered, along with methods for converting between different forms of linear equations. The unit also introduces concepts of parallel and perpendicular lines, scatter plots, correlation, and using trend lines for predictive analysis, providing a comprehensive understanding of linear relationships.
Unit 6: Solving Systems of Equations and Inequalities In this unit, students explore methods for solving systems of equations and inequalities, including graphing, substitution, and elimination. They learn to identify cases of infinite solutions or no solutions, applying these concepts to real-world problems. Linear inequalities in two variables are introduced, along with graphing techniques for both one-variable and two-variable inequalities. Students gain proficiency in graphing systems of linear inequalities and applying them in practical contexts, as well as exploring piecewise and step functions, expanding their toolkit for solving complex algebraic problems.
Unit 7: Exponential Properties and Functions This unit explores the fundamental properties and functions of exponential expressions. Topics include zero and negative exponents, multiplication and division of powers, conversion between exponential and radical forms, and the concepts of exponential growth and decay. It delves into raising powers to powers and products to powers, providing a comprehensive understanding of exponential operations and their applications.
Unit 8: Polynomials and Factoring Covering the essentials of polynomials and factoring, this unit begins with classifying polynomials and moves through operations like addition, subtraction, and multiplication. It emphasizes factoring techniques, including identifying greatest common factors and factoring trinomials. Students learn methods such as factoring by grouping and recognizing special cases like perfect square trinomials and difference of squares binomials, enabling them to solve polynomial equations efficiently.
Unit 9: Quadratics Focusing on quadratic functions, this unit explores their properties and various methods for solving quadratic equations. Students study vertex form, standard form, and characteristics such as axes of symmetry, zeroes, and domain and range. They master solution techniques, including graphing, factoring, using square roots, completing the square, and applying the quadratic formula. Real-world applications and connections between linear, quadratic, and exponential functions are also discussed.
Unit 10: Radicals Centered on radical expressions and functions, this unit covers simplification, operations, and solving radical equations. Students learn to simplify radicals, rationalize denominators, and combine like terms. They explore multiplication and division operations, using conjugates, and graphing square root functions. Additionally, inverse functions and trigonometric ratios are introduced, providing a foundation for understanding more complex mathematical concepts.
Unit 11: Rational Functions This unit delves into rational expressions and functions, including simplification, operations, and solving equations. Students identify excluded values, multiply and divide rational expressions, and perform polynomial division. They also learn about inverse variation and graphing rational functions, gaining skills to analyze and solve problems involving rational relationships.
Unit 12: Statistical Analysis Focused on statistical concepts and techniques, this unit covers matrices, frequency distributions, measures of central tendency, dispersion, and probability. Students explore data representation through histograms and box-and-whisker plots, and learn counting principles, factorials, permutations, and combinations. They apply theoretical and experimental probability, analyze events, and distinguish between independent and dependent events, enabling them to make informed decisions based on data analysis.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.72/warc/CC-MAIN-20240414130604-20240414160604-00883.warc.gz
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CC-MAIN-2024-18
| 9,090 | 19 |
https://www.hackmath.net/en/math-problem/63464
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math
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The fence around the garden measures 360 m. Of these, 72 18/20 m are damaged and must be repaired. How many meters of fence is sufficient?
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CC-MAIN-2023-50
| 4,010 | 37 |
https://www.zompist.com/board/messages/370.html
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math
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Posted by Joey on 2:14 4/24/02
In reply to: Questions re: Historical Atlas and others posted by Joey on 3:29 4/22/02
I don't think I've given an exact figure for the Almean day; but it's much less than the 26.7 hours that would be needed to make the year the same length. I don't really worry about converting years, since Almean time doesn't run in parallel with ours.
That was my point in bringing it up, since the original question was about whether a length of time given in the Historical Atlas was reasonable for people to make a certain technological leap. I understand what you mean about time not running parallel, I just wanted to point it out as something to consider when people are reading the Atlas, and thinking about how long things took.
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CC-MAIN-2021-25
| 754 | 4 |
https://hireforexamz.com/opec-organization-of-petroleum-exporting-countries-quarter-exam-help-online-program/
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math
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The world wide web has introduced an excellent way to get this necessary petroleum engineering course education, and the practice with which it all began was indeed “Enron on the Online World Wide Web.” In this day and age, that statement is something of a misnomer. If someone had a malfunctioning website with erroneous information, it wouldn’t make much of a splash, but when someone has an Online University that lacks the proper fundamentals for instructional content, it is inarguably a problem.
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CC-MAIN-2024-18
| 3,622 | 9 |
https://debtkickinmom.com/wide/t5qez9-mzuz63.html
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math
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CC-MAIN-2022-40
| 4,844 | 16 |
http://www.northwestern.edu/class-descriptions/4470/WCAS/MATH/300-0/40220.html
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math
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Foundations of Higher Mathematics
- William Joseph Clark
- Lunt Hall 107 - TuTh 10:00AM - 12:00PM
- Introduction to fundamental mathematical ideas - such as sets, functions, equivalence relations, and cardinal numbers - and basic techniques of writing proofs.
- Chapter Zero: Fundamental Notions of Abstract Mathematics by Carol Schumacher (Addison-Wesley)
- May not be taken for credit after 320-1, 321-1, 330-1 or 331-1 without prior departmental consent.
Overview of class
Class Materials (Required)
Current as of 05/06/13 11:47:56 AM
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704131463/warc/CC-MAIN-20130516113531-00065-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 537 | 9 |
https://www.milfpearl.com/services
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math
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737168.97/warc/CC-MAIN-20200810175614-20200810205614-00369.warc.gz
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CC-MAIN-2020-34
| 797 | 11 |
https://repository.uantwerpen.be/link/irua/131572
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math
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Generalised Maxwell equations in higher dimensions
Faculty of Sciences. Mathematics and Computer Science
Complex analysis and operator theory
, p. 267-293
University of Antwerp
This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension and their connections with the Rarita-Schwinger equation. This is done using the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the spin group can be realised in terms of polynomials satisfying a system of differential equations. This allows the construction of generalised wave equations in terms of the unique conformally invariant second-order operator acting on harmonic-valued functions. We prove the ellipticity of this operator and use this to investigate the kernel, focusing on both polynomial solutions and the fundamental solution.
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CC-MAIN-2017-17
| 885 | 6 |
https://www.fullversiondl.com/mechanical-expressions-v1-1-11/
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math
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Mechanical Expressions is a software for constructing symbolic models of mechanical processes.
Using this simple software, a mechanical model can be used to display the constraints symbolically, for different elements, the speed and forces can be displayed on it
and then for the elements in the model, features such as speed, acceleration And extracted effective output forces in the form of mathematical equations and expressions.
Mechanical Expressions is a symbolic mechanics program.
Create a model, specify the geometry using symbolic constraints, add velocity, masses and force elements, and then extract mathematical expressions for output velocity, accelerations and forces.
Copy expressions for input into a mathematical system like Mathematica, or copy them as Tex, MathML, or computer source code (in 9 languages).
The mathematical equations and expressions that are eventually received can be used as inputs for applications such as Mathematica, or copied as Tex, MathML, or code.
Here are some key features of “Mechanical Expressions v1.1.11”:
- Modeling a mechanical structure using graphic symbols .
- Designing a simple model of mechanical equations.
- Entering constants, features and calculations in a mechanical model.
- Calculating and drawing forces on the object in physics. Mechanical
- Graphical drawing of physics mechanics formulas
- OS :Windows XP, Windows Vista, Windows 7, 8, and 10 (32 and 64 bit)
Download Mechanical Expressions v1.1.11
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http://www.jiskha.com/search/index.cgi?query=Ms.+Sue+my+response+to+question+about+the+river
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math
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Number of results: 61,718
Ms. Sue my response to question about the river
The riveris good for shipping goods. OH, over the river.... And through the woods! Lol sorry the second part was a joke. that song was on my cd.. sorry
November 15, 2012 by rawr... im a dinosaur.... rawr
Yesterday I asked this question- 29. One of Eastern Europe's most valuablee natural resouces, sometimes called its "lifeline" is the a. Volga river b. Danube river c. Rhine river d. Oder river I asked my teacher because I was stuck between A and B and she told me to go with ...
October 1, 2009 by mysterychicken
Question 1: Candance is trying to explain that a dog is a living thing, but a river is not. What is one difference that will help her show this? a)a river cannot make another river b)both the dog and the river can move c)a river can be made by people, but the dog can only be ...
February 10, 2010 by JADEN
Help in Understanding
Posted by Anonymous on Friday, May 6, 2011 at 8:45pm. How did the conflict occur? Was it just because of the land? I'm having some trouble understanding. Please explain to me. About the Red River Colony - Ms. Sue, Friday, May 6, 2011 at 9:18pm The conflict was about land. The ...
May 7, 2011 by Emma
What meaning can you conclude from the figurative language you identified in the previous question? A. The river is too dangerous to swim in. B. The river becomes calmer at this point. C. The river is verly loud as it flows. D. The river meets the ocean at this point. B? Thank...
February 25, 2015 by Callie
yesterday i posted a question about who discovered DNA and Ms Sue kindly helped me but im confused about who actually discovered DNA because there are four different names Friedrich Miescher,Rosalind Franklin,james D Watson and Francis Crick. my homework question is who ...
January 18, 2011 by ANNIE
What can you conclude from the figurative language you identified in the previous question? A. People are afraid of swimming in the river. B. The river's waters are rough under a smooth surface. C. The water in the river is loud like a roar. D. The river is moving quickly and ...
February 25, 2015 by Callie
I asked sue a question yesterday and don't understand the answer can you explain? Here what it was I think this question has a typo because none of the multiple choice answers fit. The question is which of the following values is in the solution set of inequality 8-7x<-6? A...
December 28, 2012 by Es
1. Which of the following sentences does NOT employ correct word usage? a. We had to travel several miles further into the Arkansas Ozarks to locate the Buffalo River. b. Because this river is only 130 miles long, many people are surprised that it has been designated the first...
May 17, 2011 by anthony
thank you Ms Sue for your quick response but i was told that do and did forms would not appear in the reported speech could you pl clarify and how about this one : he enquired me why i was not vaccinated
August 28, 2012 by R S Telagathoty
Sorry Ms.Sue but I have a question on the previous answer you gave me and I hope you don't mind answering it,thanks. Earlier you say "What examples do you know about the good that people do who contribute to the community? " Could you explain to me what this mean? Thanks again.
September 14, 2010 by Shadow
1. What is his personality? 2. What is his personality like? (Are both the same? Which one is popular?) 3. There used to be a river there. 4. There would be a river. 5. There was a river, but not now. (Does #3 mean #5? What about #4? Is #4 grammatical?)
August 25, 2013 by rfvv
Multiply & write in simplest form: The mississippi river is about 23/25 the length of the missouri river. If the missouri river is 2,540 miles long, how long is the mississippi river? Thanks
September 12, 2012 by Sam
Another question about Napolean
Thank you for that website Ms Sue, it gave me good information which greatly assisted me in answering my question. However, I have another question that I cannot seem to get an answer to: How did Napoleon undermine the liberty of the French people?
February 2, 2009 by thea
ok there was a question that my teacher told me i got wrong the question asked me to compute the mean which I did... then the question went on to tell me compute the mean with another observation equal to zero then the part that he drew the line through was my response to this...
September 6, 2009 by stat
I have a question based off of the response to the question I posted below. A dragster and driver together have mass 918.8 kg. The dragster,starting from rest,attains a speed of 25.8 m/s in .53s . Find the average acceleration of the dragsters during this time interval. Answer...
July 4, 2011 by alexa
year 8 Geography
In Geography i am learning about the River Tees.for my homework i need to do a project. The questions i need to answer are:- Q 1 ) How does the river tees effect the landscape on it`s journey from the source to the mouth? Q 2 )What process takes place in a river and how do ...
February 15, 2009 by Amy
I HAVE A QUESTION. When I post a question and there is now response to it does it means that my answer to my questions are correct? I post two questions yeaterday and received no response .Today I post the same two questions and still got no response. They are math questions ...
June 14, 2007 by DANIELLE
English - ms. sue
ms. sue sorry yesterday i ask question that not make sense but i be talking about the occasion question where rock say the bith word for second time it ask when be this second occasion? first occasion be daytime and second occasion be night time? also i still not get the last ...
March 1, 2012 by Mohammad
What bordered the Gupta Empire to the north? 1. Ganges River 2. India 3. Himalaya*** 4. Bay of Bengal The Hindu Kush are near which river? 1. Ganges 2. Nile 3. Arabian 4. Indus**** Please check my answers Ms.Sue please
January 31, 2017 by Anonymous
PHY: To AJAYB, follow up on previous response
First, I'd like to thank you for your response to my question. However, I had some follow up questions on your response from Saturday, July 28, 2012 at 8:27am. If you could take a look at that post and get back to me, it would be greatly appreciated.
July 29, 2012 by Dan
Put a pencil straight down into a glass of water. Notice whether the pencil looks bent. Now tilt the pencil and note how its apparent bending changes. How does this illustrate why light from objects near the horizon is refracted more strongly? Quit posting under different ...
April 17, 2007 by Manoj
Which one(s) of the essetional chemcial elements (C, H, O, N) does blood contain. You only need to ask the question once. Additional repetitions will not get you a faster response. An answer to your question can be found in response to your other post(s). Thanks for asking. ...
June 20, 2005 by Jawad
It is a variation problem. I know what the answer is and how to get to the answer I just don't know how I got it. From measurements on many rivers, geographers find that the length of a river that drains a particular "basin" of land is approximately proportional to the 0.6 ...
April 23, 2011 by Lindy
A man feels anxious and a little sick to his stomach when he walked up to the front door of his old elementary school. School had been very hard for him and he remembers feeling “stupid” a lot of the time he was in school. What is the unconditioned stimulus and ...
January 27, 2016 by Kay
What is the suitable response to the greeting, 'Hi.'? (It is Hello.) That's right. If your friend says, 'How is it going?', what do you have to say? (We can say, 'So-so.') What is the suitable response to the statement,'Glad to meet you.'? (It is 'Glad to meet you,too...
March 18, 2008 by John
if x is an even number, what is the quotient of the next greater even number divided by the next greater odd number? i have no idea where to even start with this problem. i would really appriciate some help. Thanks! What can make me studdy harder? hey tabby you put your ...
February 25, 2007 by Marie
Can you please tell me which of the following alternatives are possible? 1) Which is the lowest mark a student can be given in the USA? (I really need to know the answer to this question). 2) If I catch you cheating, I'll give you the lowest possible (?) mark./ your text won't...
November 10, 2010 by Franco
I need help to understand how to read a river map. Please could someone advise me or point me in the right direction. Thanks. If you are talking about maps that would be used for river navigation, see (Broken Link Removed) If you are talking about maps that just show where a ...
July 4, 2007 by vin
how do Huck and Jim feel about the sanctuary of the raft and how do they feel about the violence and shame of the shore? I have to make a collage on this and I don't really know what to put. I was thinking of drawing a river and in the inside of the river would be a drawing of...
June 27, 2013 by HELP
1. Choose two of the scientists you read about in the Stories of Scientists unit. Compare and contrast these scientists. Answer this question in no fewer than two paragraphs. Be sure to include specific details about each scientist’s life, career, and personality in your ...
February 12, 2014 by Chad Bester
A boat travels at 3.8 m/s and heads straight across a river 240 m wide. The river flows at 1.6 m/s. Find A) The boat's resultant velocity. B) How long it takes the boat to cross the river. C) How far downstream the boat is when it reaches the other side. Please help, i have ...
November 2, 2008 by PLEASE HELP!
Jeffrey wants to swim his girlfriend who is straight across from him, on the other side of a river bank. The river has a current velocity of 4km/h [W]. The width of the river is 300m. If it takes Jeffrey 15 minutes to reach her, a) how fast should the boy swim to cross the ...
July 8, 2014 by Anonymous
English - ms. sue
chapt 14 question WFE kinko say we cant keep camel concealed 4ever Wat be some presumptions u hve about this statement that everyone find out about his problem?
May 13, 2012 by Mohammad
I have to write a paper on the below posted question. Can anyone explain me what might i need to do in it. 1) Set out the problem of evil as clearly and completely as possible. Be sure to distinguish between moral evil and natural evil and to discuss the problems posed by each...
September 21, 2011 by mas
Need help with one more question. Which best describes a statistical question? a. a question that contains numbers b. a question about numbers c. a question about designing an experiment d. a question about a population or sample. I was thinking it might be D. Thanks...
April 2, 2013 by Brandi
English - Ms. Sue help
Help on this question I don't understand Answer the following question about the poem “Fable for When There’s No Way Out.” How does this line from the poem help explain the outcome of the chick’s struggle? “Rage works if reason won’t.”
December 16, 2012 by antboy
. This question asks about your work in your reading role. You may use your novel to help you answer the question. Think about the work you completed in your reading role. Determine the ideas that would be most worthy to share in a literary discussion about The Giver. Provide ...
June 6, 2016 by jj
confidentiality of health info,.
Sould corrections on a medical record(computerized medical database) be dated and time stamped? define the three childrearing styles In the future, rather than putting this as a response to a question, use the "Post a New Question" link. Putting your question in as response to...
July 21, 2006 by Haydee
Mathmate, I wrote a response below. The worksheet I worked on was a crossword puzzle and question 18 is only a five letter word and i'm not sure what it may be.
August 31, 2009 by Lisa
I need to form a question out of this response. I wanted to know if it was correct. Response:Hay mucha tarea hoy. Question I formed:¿Cuánta tarea hay hoy?
September 30, 2013 by Devyn
A question for Ms.Sue! :P
This is just by curiosity: Ms. Sue, have you ever asked a question or do you only answer them as the good tutor you are? It just came to my mind and who else to ask but you? Have an AWESOME day!
December 10, 2014 by DerpyPegasus33
11. This question asks about your work in your reading role. You may use your novel to help you answer the question. Think about the work you completed in your reading role. Determine the ideas that would be most worthy to share in a literary discussion about Johnny Tremain. ...
December 16, 2016 by help
Thank you Ms.Sue for answering my last question. I have one another question that I has hard time understanding.... "the circumstances that may contributto the development of this condition." I have no idea what she is asking. This is the question, "Describe the ...
April 28, 2012 by Delhi
If you have a question about a response, ask about it. We are not going to do your homework for it. If you post vulgar posts, we have your IP address, and will ban you from here, and notify your web provider. Thanks. but i don't get what to do. and yet you still won't help ...
April 17, 2007 by bobpursley
English - ms. sue
ms. sue i post question about story identities. i not get what it mean when it say what it mean to have identity? also the first word that story start with that be normally - why that word really signficant? because it tell that this not be some ordinary day? what ...
December 3, 2012 by Mohammad
1. I want to do volunteer work at the Han River. I want to pick up trash and make it clean/clear. 2. I want to volunteer at the Han River. I want to pick up trash from the river, and make it clean/clear. (Would you check the English expressions? Correct errors, please. Do I ...
November 4, 2009 by rfvv
Ms. Sue, thanks to you, I have got to know a lot about Voltaire. Seriously If I have to pick a philosopher that I would agree with, then it would be Voltaire as well. In my book there was very little info about him, so that's why I didn't really get to know him as much as I ...
November 1, 2009 by Sara
Gratitude for my helper
Sir steve mrs reiny sir bobpursely sir damon ms sue..... Thank you very much you guyz have really help me alot today my result came out and i score 98 out of 100 in my maths exams aldo i am still shaking in my english but with the help of ms sue i always read english question ...
January 6, 2016 by Collins
ms Sue I was not sure how to do a response to you but my prior question was the following and you had answered to take the total number of students and make this the denominator and the history majors the numerator which I did and makes this 300/1225 so then to get the ratio I...
September 24, 2010 by m
The Atakapans occupied the region from the Sabine river to the A. San Jacinto river B. Red river C. Colorado river D. Trinity river Both the Karankawa and Atakapans relied heavily on which resources? A.rival groups B.fish and shellfish C.settlers D.trees and nuts Both the ...
September 2, 2016 by Iris
English - ms. sue
ms. sue i also have to answer one question from story that be the story move from describing two similar friends to ones whose views become much different. it say what writer do to intensify contrast b/w the 2 to show that now each of us b by herself. I just not get what the ...
December 17, 2012 by Mohammad
a river flows due south with a speed of 2.0m/s. a man steers a motorboat across the river;his velosity is 4.2m/s due east.the river is 800m wide. (A) what is his velocity(magnitude and direction)relative to the earth? (B)how much time is required to cross the river?
April 2, 2013 by yonela
To Ms. Sue
Ms. Sue, I had a question yesterday about stress, and I still require help on it. I'll give you the question as it is written to me. When you took the Multiple Intelligences quiz, what type of intelligence was rated the highest? How do you think this affects how you deal with ...
October 19, 2010 by Sara
A boat starting on one side of the river heads to the south with a speed of 1.5 m/s, the river flows to the east at .8 m/s. What is the resultant velocity to the side of the river? And if the river is 50 m wide calculate the displacement of the boat
February 8, 2017 by Anonymous
The river which carries the most traffic in Europe and is the continent's most important inland waterway is the: Is it the Rhine river or the Danube River not sure. i think it is the Danube River am i correct?
August 11, 2013 by Robby
THe headwaters of three river system are located in Colorado along the Great Continental Divide. identify the 3 system? are they: Colorado river Missouri river and Columbia river.
February 9, 2009 by Anonymous
1. The house is close to the river. 2. The house is near the river. 3. the house is by the river. 4. The house is next to the river. ====== Are they all the same and grammatical? Do we have some more similar expressions?
November 25, 2015 by rfvv
Health 8R help!!!!!!!!! (please read!)
Dear Abby: Marijuana Dear Abby, I am very concerned about my friend Sue. She told me that she smoked weed with her older brother. First of all, what is weed? Is it legal? What are the effects? What should I do if she asks me to try it with her? I am very upset. Please tell me ...
November 18, 2012 by Laruen
A boat traveling at 116.5 m/s relative to the water aims to go straight across a river. If the river is 153 m wide and the current in the river is 3.50 m/s, how far downstream will the boat land on the other side of the river? Calculate the answer in meters (m) and rounded to ...
January 29, 2017 by Dalia
The mad river flows at a rate of 2 KM/H. In order for a boat to travel 79.2 KM of River and then return in a total of eight hours how fast must about travel in Still water?
April 15, 2014 by Anthony
Alex threw a stick in a river and watched as the river carried it away. He scooped a pail of water from the river and noticed that a leaf was floating in the pail without moving on the surface of the water. Why did the stick move in the river and the leaf stay still in the ...
April 4, 2012 by Mary pleasseeee helppp
whats one opinion about leukemia.i all ready wrote a fact but i baerly know anything about it so i can not write a opinion please.this is just home work ? please help me ms.sue from, priscilla perez
April 16, 2010 by priscilla
An anchor holding a boat stationary on a river forms a 65 degree angle with the river bottom. The anchor line is 40 meters long. Assuming the river has a uniform depth, how deep is the river directly below the boat?
May 20, 2013 by adam
(b) Choose two of the scientists you read about in the Stories of Scientists unit. Compare and contrast these scientists. Answer this question in no fewer than two paragraphs. Be sure to include specific details about each scientist’s life, career, and personality in your ...
January 27, 2017 by dj
biology /check please
(stimulus v. response)? Which of the following is a stimulus, which is a response? Thanks 1)the recess bell ringing in an elementary school 2)your mouth watering at the sight of food on a plate 3)a sudden drop in air temperature 4) a flu virus entering your body 5) getting ...
December 21, 2010 by joy
can you please correct my personifitcation poem? please? for any mistakes?? thank you! The Wild River The river breaths heavily It is fast and mean The river is strong And swallows all the leaves. The river is a stealer As it snatches the pebbles Then gobbles them up In their ...
April 14, 2009 by john
Ms. Sue! (English)
I have another question about "Shooting the Elephant" The question is : What does "shooting an elephant" gain from being written years after the events it recounts? Is one possibility that it gave Orwell time to reflect upon his experiences? Are there any other possibilities?
November 15, 2008 by kayla
think about the work you completed in your reading role determine the ideas that would be most worthy to share in a literary discussion about walk to moons provide an explanation for your choices how did the role you selected and the work you completed help you to understand ...
May 14, 2016 by avery
Score 1. Choose two of the scientists you read about in the Stories of Scientists unit. Compare and contrast these scientists. Answer this question in no fewer than two paragraphs. Be sure to include specific details about each scientist’s life, career, and personality in ...
January 13, 2015 by Ty
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https://informationtransfereconomics.blogspot.com/2015/09/a-random-walk-inside-simplex.html
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math
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I thought I'd do something similar to this post for the idea behind these two posts (, ): that most of the points in a high dimensional space are near the boundary. Here is an example random walk over d = 3 goods (3 dimensions) restricted to the simplex bounded by the budget constraint Σ ci ≤ 1:
And here is the resulting "total consumption", i.e. the sum of the consumption of each good (1 means the ensemble of agents spends all of their money in that time period):
If you increase the number of goods to d = 20, you get a similar result, but closer to the boundary:
The deviations from Σ ci = 1 represent "recessions" where the ensemble of agents saved (reduced consumption) more than usual.
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Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.
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https://www.math.pku.edu.cn/kxyj/xsbg/tlb/other/109337.htm
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math
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Hardy inequalities on homogeneous groups
报告人：Durvudkhan Suragan (Nazarbayev University)
地点：Room 1365, Sciences Building No. 1
Abstract: In this talk, we discuss Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. In short, our main idea is consistently working with relations of quasi-radial derivatives and the Euler operators, so from these relations follow various Hardy type inequalities with sharp constants on homogeneous groups. While describing the general theory of Hardy type inequalities in the setting of general homogeneous groups, we pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. To demonstrate applications of the theory we present solutions of two previously known conjectures. Particularly, we discuss the Badiale-Tarantello conjecture and the conjecture on the geometric Hardy inequality in a half-space on the Heisenberg group with a sharp constant. The present talk is partially based on our recent open access book (with the same title) with Michael Ruzhansky.
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https://www.coursehero.com/file/7776657/ch14-study-questions/
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math
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ch14 Student: ___________________________________________________________________________ 1. A group of individuals got together and purchased all of the outstanding shares of common stock of DL Smith, Inc. What is the return that these individuals require on this investment called? A. dividend yield B. cost of equity C. capital gains yield D. cost of capital E. income return 2. Textile Mills borrows money at a rate of 13.5 percent. This interest rate is referred to as the: A. compound rate. B. current yield. C. cost of debt. D. capital gains yield. E. cost of capital. 3. The average of a firm's cost of equity and aftertax cost of debt that is weighted based on the firm's capital structure is called the: A. reward to risk ratio. B. weighted capital gains rate. C. structured cost of capital. D. subjective cost of capital. E. weighted average cost of capital. 4. When a manager develops a cost of capital for a specific project based on the cost of capital for another firm which has a similar line of business as the project, the manager is utilizing the _____ approach. A. subjective risk B. pure play C. divisional cost of capital D. capital adjustment E. security market line 5. A firm's cost of capital: A. will decrease as the risk level of the firm increases. B. for a specific project is primarily dependent upon the source of the funds used for the project. C. is independent of the firm's capital structure. D. should be applied as the discount rate for any project considered by the firm. E. depends upon how the funds raised are going to be spent. 6. The weighted average cost of capital for a wholesaler: A. is equivalent to the aftertax cost of the firm's liabilities. B. should be used as the required return when analyzing a potential acquisition of a retail outlet. C. is the return investors require on the total assets of the firm. D. remains constant when the debt-equity ratio changes. E. is unaffected by changes in corporate tax rates. 7. Which one of the following is the primary determinant of a firm's cost of capital? A. debt-equity ratio B. applicable tax rate C. cost of equity D. cost of debt E. use of the funds
8. Scholastic Toys is considering developing and distributing a new board game for children. The project is similar in risk to the firm's current operations. The firm maintains a debt-equity ratio of 0.40 and retains all profits to fund the firm's rapid growth. How should the firm determine its cost of equity? A. by adding the market risk premium to the aftertax cost of debt B. by multiplying the market risk premium by (1 - 0.40) C. by using the dividend growth model D. by using the capital asset pricing model E. by averaging the costs based on the dividend growth model and the capital asset pricing model 9. All else constant, which one of the following will increase a firm's cost of equity if the firm computes that cost using the security market line approach? Assume the firm currently pays an annual dividend of $1 a share and has a beta of 1.2.
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https://wikimili.com/en/Pierre-Simon_Laplace
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math
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Pierre-Simon Laplace (1749–1827). Posthumous portrait by
Jean-Baptiste Paulin Guérin, 1838.
|Died||5 March 1827 77) (aged|
|Alma mater||University of Caen|
|Fields||Astronomer and mathematician|
|Institutions||École Militaire (1769–1776)|
|Academic advisors|| Jean d'Alembert |
Pierre Le Canu
|Notable students||Siméon Denis Poisson Napoleon Bonaparte|
Pierre-Simon, marquis de Laplace ( // ; French: [pjɛʁ simɔ̃ laplas] ; 23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste ( Celestial Mechanics ) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace.
Engineering is the application of knowledge in the form of science, mathematics, and empirical evidence, to the innovation, design, construction, operation and maintenance of structures, machines, materials, software, devices, systems, processes, and organizations. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering.
Mathematics includes the study of such topics as quantity, structure, space, and change.
Statistics is a branch of mathematics working with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.
Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as
In mathematics, the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace. It takes a function of a real variable t to a function of a complex variable s. The transform has many applications in science and engineering.
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". It is a branch of applied mathematics, but deals with physical problems.
Laplace is remembered as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries.He was Napoleon's examiner when Napoleon attended the École Militaire in Paris in 1784. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration.
Sir Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.
Napoléon Bonaparte was a French statesman and military leader of Italian descent who rose to prominence during the French Revolution and led several successful campaigns during the French Revolutionary Wars. He was Emperor of the French as Napoleon I from 1804 until 1814 and again briefly in 1815 during the Hundred Days. Napoleon dominated European and global affairs for more than a decade while leading France against a series of coalitions in the Napoleonic Wars. He won most of these wars and the vast majority of his battles, building a large empire that ruled over much of continental Europe before its final collapse in 1815. He is considered one of the greatest commanders in history, and his wars and campaigns are studied at military schools worldwide. Napoleon's political and cultural legacy has endured as one of the most celebrated and controversial leaders in human history.
Founded in 1750 by King Louis XV, the École Militaire is a vast complex of buildings housing various military training facilities. It is located in the 7th arrondissement of Paris, France, southeast of the Champ de Mars.
Some records of Laplace's life were burned in 1925 with the family château in Saint Julien de Mailloc, near Lisieux, the home of his great-great-grandson the Comte de Colbert-Laplace. Others had been destroyed earlier, when his house at Arcueil near Paris was looted by house breakers in 1871.
A château is a manor house or residence of the lord of the manor or a country house of nobility or gentry, with or without fortifications, originally—and still most frequently—in French-speaking regions.
Lisieux is a commune in the Calvados department in the Normandy region in northwestern France. It is the capital of the Pays d'Auge area, which is characterised by valleys and hedged farmland.
Arcueil[aʁkœj] is a commune in the Val-de-Marne department in the southern suburbs of Paris, France. It is located 5.3 km (3.3 mi) from the center of Paris.
Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749, a village four miles west of Pont l'Eveque. According to W. W. Rouse Ball,his father, Pierre de Laplace, owned and farmed the small estates of Maarquis. His great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont; but, having procured a letter of introduction to d'Alembert, he went to Paris to advance his fortune. However, Karl Pearson is scathing about the inaccuracies in Rouse Ball's account and states:
Beaumont-en-Auge is a commune in the Calvados department in the Normandy region in northwestern France. The town hosts one of the last kaleidoscope manufacturers in France.
Pont-l'Évêque is a commune in the Calvados department in the Normandy region in northwestern France. It is known for Pont-l'Évêque cheese, a type of soft cheese, the oldest Normandy cheese in production.
Walter William Rouse Ball, known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge from 1878 to 1905. He was also a keen amateur magician, and the founding president of the Cambridge Pentacle Club in 1919, one of the world's oldest magic societies.
Indeed Caen was probably in Laplace's day the most intellectually active of all the towns of Normandy. It was here that Laplace was educated and was provisionally a professor. It was here he wrote his first paper published in the Mélanges of the Royal Society of Turin, Tome iv. 1766–1769, at least two years before he went at 22 or 23 to Paris in 1771. Thus before he was 20 he was in touch with Lagrange in Turin. He did not go to Paris a raw self-taught country lad with only a peasant background! In 1765 at the age of sixteen Laplace left the "School of the Duke of Orleans" in Beaumont and went to the University of Caen, where he appears to have studied for five years and was a member of the Sphinx. The 'École Militaire' of Beaumont did not replace the old school until 1776.
Caen, is a commune in northwestern France. It is the prefecture of the Calvados department. The city proper has 108,365 inhabitants, while its urban area has 420,000, making Caen the largest city in former Lower Normandy. It is also the third largest municipality in all of Normandy after Le Havre and Rouen and the third largest city proper in Normandy, after Rouen and Le Havre. The metropolitan area of Caen, in turn, is the second largest in Normandy after that of Rouen, the 21st largest in France.
Turin is a city and an important business and cultural centre in northern Italy. It is the capital city of the Metropolitan City of Turin and of the Piedmont region, and was the first capital city of Italy from 1861 to 1865. The city is located mainly on the western bank of the Po River, in front of Susa Valley, and is surrounded by the western Alpine arch and Superga Hill. The population of the city proper is 878,074 while the population of the urban area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million.
His parents were from comfortable families. His father was Pierre Laplace, and his mother was Marie-Anne Sochon. The Laplace family was involved in agriculture until at least 1750, but Pierre Laplace senior was also a cider merchant and syndic of the town of Beaumont.
Pierre Simon Laplace attended a school in the village run at a Benedictine priory, his father intending that he be ordained in the Roman Catholic Church. At sixteen, to further his father's intention, he was sent to the University of Caen to read theology.
At the university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awoke his zeal for the subject. Here Laplace's brilliance as a mathematician was quickly recognised and while still at Caen he wrote a memoir Sur le Calcul integral aux differences infiniment petites et aux differences finies. This provided the first intercourse between Laplace and Lagrange. Lagrange was the senior by thirteen years, and had recently founded in his native city Turin a journal named Miscellanea Taurinensia, in which many of his early works were printed and it was in the fourth volume of this series that Laplace's paper appeared. About this time, recognising that he had no vocation for the priesthood, he resolved to become a professional mathematician. Some sources state that he then broke with the church and became an atheist.[ citation needed ] Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond d'Alembert who at that time was supreme in scientific circles.
According to his great-great-grandson,d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care.
Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the École Militaire .
With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy.
From 1780–1784, Laplace and French chemist Antoine Lavoisier collaborated on several experimental investigations, designing their own equipment for the task.In 1783 they published their joint paper, Memoir on Heat, in which they discussed the kinetic theory of molecular motion. In their experiments they measured the specific heat of various bodies, and the expansion of metals with increasing temperature. They also measured the boiling points of ethanol and ether under pressure.
Laplace further impressed the Marquis de Condorcet, and already by 1771 Laplace felt entitled to membership in the French Academy of Sciences. However, that year admission went to Alexandre-Théophile Vandermonde and in 1772 to Jacques Antoine Joseph Cousin. Laplace was disgruntled, and early in 1773 d'Alembert wrote to Lagrange in Berlin to ask if a position could be found for Laplace there. However, Condorcet became permanent secretary of the Académie in February and Laplace was elected associate member on 31 March, at age 24. In 1773 Laplace read his paper on the invariability of planetary motion in front of the Academy des Sciences. That March he was elected to the academy, a place where he conducted the majority of his science.
On 15 March 1788,at the age of thirty-nine, Laplace married Marie-Charlotte de Courty de Romanges, an eighteen-year-old woman from a 'good' family in Besançon. The wedding was celebrated at Saint-Sulpice, Paris. The couple had a son, Charles-Émile (1789–1874), and a daughter, Sophie-Suzanne (1792–1813).
Laplace's early published work in 1771 started with differential equations and finite differences but he was already starting to think about the mathematical and philosophical concepts of probability and statistics.However, before his election to the Académie in 1773, he had already drafted two papers that would establish his reputation. The first, Mémoire sur la probabilité des causes par les événements was ultimately published in 1774 while the second paper, published in 1776, further elaborated his statistical thinking and also began his systematic work on celestial mechanics and the stability of the Solar System. The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge." Laplace's work on probability and statistics is discussed below with his mature work on the analytic theory of probabilities.
Sir Isaac Newton had published his Philosophiae Naturalis Principia Mathematica in 1687 in which he gave a derivation of Kepler's laws, which describe the motion of the planets, from his laws of motion and his law of universal gravitation. However, though Newton had privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to account for the more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of the Solar System. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life.It is now generally regarded that Laplace's methods on their own, though vital to the development of the theory, are not sufficiently precise to demonstrate the stability of the Solar System, and indeed, the Solar System is understood to be chaotic, although it happens to be fairly stable.
One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn was expanding. The problem had been tackled by Leonhard Euler in 1748 and Joseph Louis Lagrange in 1763 but without success.In 1776, Laplace published a memoir in which he first explored the possible influences of a purported luminiferous ether or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtonian gravity. Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion. Laplace noted that though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis into the higher-order terms, up to and including the cubic. Using this more exact analysis, Laplace concluded that any two planets and the Sun must be in mutual equilibrium and thereby launched his work on the stability of the Solar System. Gerald James Whitrow described the achievement as "the most important advance in physical astronomy since Newton".
Laplace had a wide knowledge of all sciences and dominated all discussions in the Académie.Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.
While Newton explained the tides by describing the tide-generating forces and Bernoulli gave a description of the static reaction of the waters on Earth to the tidal potential, the dynamic theory of tides, developed by Laplace in 1775,describes the ocean's real reaction to tidal forces. Laplace's theory of ocean tides took into account friction, resonance and natural periods of ocean basins. It predicted the large amphidromic systems in the world's ocean basins and explains the oceanic tides that are actually observed.
The equilibrium theory, based on the gravitational gradient from the Sun and Moon but ignoring the Earth's rotation, the effects of continents, and other important effects, could not explain the real ocean tides.
Since measurements have confirmed the theory, many things have possible explanations now, like how the tides interact with deep sea ridges and chains of seamounts give rise to deep eddies that transport nutrients from the deep to the surface.The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters. Measurements from the CHAMP satellite closely match the models based on the TOPEX data. Accurate models of tides worldwide are essential for research since the variations due to tides must be removed from measurements when calculating gravity and changes in sea levels.
In 1776, Laplace formulated a single set of linear partial differential equations, for tidal flow described as a barotropic two-dimensional sheet flow. Coriolis effects are introduced as well as lateral forcing by gravity. Laplace obtained these equations by simplifying the fluid dynamic equations. But they can also be derived from energy integrals via Lagrange's equation.
For a fluid sheet of average thickness D, the vertical tidal elevation ζ, as well as the horizontal velocity components u and v (in the latitude φ and longitude λ directions, respectively) satisfy Laplace's tidal equations:
where Ω is the angular frequency of the planet's rotation, g is the planet's gravitational acceleration at the mean ocean surface, a is the planetary radius, and U is the external gravitational tidal-forcing potential.
William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the curl to find an equation for vorticity. Under certain conditions this can be further rewritten as a conservation of vorticity.
During the years 1784–1787 he published some memoirs of exceptional power. Prominent among these is one read in 1783, reprinted as Part II of Théorie du Mouvement et de la figure elliptique des planètes in 1784, and in the third volume of the Mécanique céleste. In this work, Laplace completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introduction into analysis of spherical harmonics or Laplace's coefficients, and also for the development of the use of what we would now call the gravitational potential in celestial mechanics.
In 1783, in a paper sent to the Académie, Adrien-Marie Legendre had introduced what are now known as associated Legendre functions. ', θ'), where r ' ≥ r, then, by elementary manipulation, the reciprocal of the distance between the points, d, can be written as:If two points in a plane have polar co-ordinates (r, θ) and (r
This expression can be expanded in powers of r/r ' using Newton's generalised binomial theorem to give:
The sequence of functions P0k(cosф) is the set of so-called "associated Legendre functions" and their usefulness arises from the fact that every function of the points on a circle can be expanded as a series of them.
Laplace, with scant regard for credit to Legendre, made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients. The latter term is not in common use now.
This paper is also remarkable for the development of the idea of the scalar potential.The gravitational force acting on a body is, in modern language, a vector, having magnitude and direction. A potential function is a scalar function that defines how the vectors will behave. A scalar function is computationally and conceptually easier to deal with than a vector function.
Alexis Clairaut had first suggested the idea in 1743 while working on a similar problem though he was using Newtonian-type geometric reasoning. Laplace described Clairaut's work as being "in the class of the most beautiful mathematical productions".However, Rouse Ball alleges that the idea "was appropriated from Joseph Louis Lagrange, who had used it in his memoirs of 1773, 1777 and 1780". The term "potential" itself was due to Daniel Bernoulli, who introduced it in his 1738 memoire Hydrodynamica. However, according to Rouse Ball, the term "potential function" was not actually used (to refer to a function V of the coordinates of space in Laplace's sense) until George Green's 1828 An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism.
Laplace applied the language of calculus to the potential function and showed that it always satisfies the differential equation:
An analogous result for the velocity potential of a fluid had been obtained some years previously by Leonhard Euler.
Laplace's subsequent work on gravitational attraction was based on this result. The quantity ∇2V has been termed the concentration of V and its value at any point indicates the "excess" of the value of V there over its mean value in the neighbourhood of the point. Laplace's equation, a special case of Poisson's equation, appears ubiquitously in mathematical physics. The concept of a potential occurs in fluid dynamics, electromagnetism and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one of the a priori forms in Kant's theory of perception.
The spherical harmonics turn out to be critical to practical solutions of Laplace's equation. Laplace's equation in spherical coordinates, such as are used for mapping the sky, can be simplified, using the method of separation of variables into a radial part, depending solely on distance from the centre point, and an angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying practical computation.
Laplace presented a memoir on planetary inequalities in three sections, in 1784, 1785, and 1786. This dealt mainly with the identification and explanation of the perturbations now known as the "great Jupiter–Saturn inequality". Laplace solved a longstanding problem in the study and prediction of the movements of these planets. He showed by general considerations, first, that the mutual action of two planets could never cause large changes in the eccentricities and inclinations of their orbits; but then, even more importantly, that peculiarities arose in the Jupiter–Saturn system because of the near approach to commensurability of the mean motions of Jupiter and Saturn.
In this context commensurability means that the ratio of the two planets' mean motions is very nearly equal to a ratio between a pair of small whole numbers. Two periods of Saturn's orbit around the Sun almost equal five of Jupiter's. The corresponding difference between multiples of the mean motions, (2nJ − 5nS), corresponds to a period of nearly 900 years, and it occurs as a small divisor in the integration of a very small perturbing force with this same period. As a result, the integrated perturbations with this period are disproportionately large, about 0.8° degrees of arc in orbital longitude for Saturn and about 0.3° for Jupiter.
Further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789, but with the aid of Laplace's discoveries, the tables of the motions of Jupiter and Saturn could at last be made much more accurate. It was on the basis of Laplace's theory that Delambre computed his astronomical tables.
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Laplace now set himself the task to write a work which should "offer a complete solution of the great mechanical problem presented by the Solar System, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables." The result is embodied in the Exposition du système du monde and the Mécanique céleste.
The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of the history of astronomy. This summary procured for its author the honour of admission to the forty of the French Academy and is commonly esteemed one of the masterpieces of French literature, though it is not altogether reliable for the later periods of which it treats.
Laplace developed the nebular hypothesis of the formation of the Solar System, first suggested by Emanuel Swedenborg and expanded by Immanuel Kant, a hypothesis that continues to dominate accounts of the origin of planetary systems. According to Laplace's description of the hypothesis, the Solar System had evolved from a globular mass of incandescent gas rotating around an axis through its centre of mass. As it cooled, this mass contracted, and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the sun represented the central core which was still left. On this view, Laplace predicted that the more distant planets would be older than those nearer the sun.
As mentioned, the idea of the nebular hypothesis had been outlined by Immanuel Kant in 1755,and he had also suggested "meteoric aggregations" and tidal friction as causes affecting the formation of the Solar System. Laplace was probably aware of this, but, like many writers of his time, he generally did not reference the work of others.
Laplace's analytical discussion of the Solar System is given in his Mécanique céleste published in five volumes. The first two volumes, published in 1799, contain methods for calculating the motions of the planets, determining their figures, and resolving tidal problems. The third and fourth volumes, published in 1802 and 1805, contain applications of these methods, and several astronomical tables. The fifth volume, published in 1825, is mainly historical, but it gives as appendices the results of Laplace's latest researches. Laplace's own investigations embodied in it are so numerous and valuable that it is regrettable to have to add that many results are appropriated from other writers with scanty or no acknowledgement, and the conclusions – which have been described as the organised result of a century of patient toil – are frequently mentioned as if they were due to Laplace.
Jean-Baptiste Biot, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, "Il est aisé à voir que ... " ("It is easy to see that ..."). The Mécanique céleste is not only the translation of Newton's Principia into the language of the differential calculus, but it completes parts of which Newton had been unable to fill in the details. The work was carried forward in a more finely tuned form in Félix Tisserand's Traité de mécanique céleste (1889–1896), but Laplace's treatise will always remain a standard authority. [ citation needed ] In this work he completely determined the attraction of a spheroid on a particle outside it. This is known for the introduction into analysis of the potential, a useful mathematical concept of broad applicability to the physical sciences.In the years 1784–1787, Laplace produced some memoirs of exceptional power. The significant among these was one issued in 1784, and reprinted in the third volume of the Méchanique céleste.
Laplace also came close to propounding the concept of the black hole. He suggested that there could be massive stars whose gravity is so great that not even light could escape from their surface (see escape velocity).
In 1806, Laplace bought a house in Arcueil, then a village and not yet absorbed into the Paris conurbation. Claude Louis Berthollet was a neighbour—their gardens were not separated—and the pair formed the nucleus of an informal scientific circle, latterly known as the Society of Arcueil. Because of their closeness to Napoleon, Laplace and Berthollet effectively controlled advancement in the scientific establishment and admission to the more prestigious offices. The Society built up a complex pyramid of patronage. In 1806, Laplace was also elected a foreign member of the Royal Swedish Academy of Sciences.
In 1812, Laplace issued his Théorie analytique des probabilités in which he laid down many fundamental results in statistics. The first half of this treatise was concerned with probability methods and problems, the second half with statistical methods and applications. Laplace's proofs are not always rigorous according to the standards of a later day, and his perspective slides back and forth between the Bayesian and non-Bayesian views with an ease that makes some of his investigations difficult to follow, but his conclusions remain basically sound even in those few situations where his analysis goes astray.In 1819, he published a popular account of his work on probability. This book bears the same relation to the Théorie des probabilités that the Système du monde does to the Méchanique céleste. In its emphasis on the analytical importance of probabilistic problems, especially in the context of the "approximation of formula functions of large numbers," Laplace's work goes beyond the contemporary view which almost exclusively considered aspects of practical applicability. Laplace's Théorie analytique remained the most influential book of mathematical probability theory to the end of the 19th century. The general relevance for statistics of Laplacian error theory was appreciated only by the end of the 19th century. However, it influenced the further development of a largely analytically oriented probability theory.
In his Essai philosophique sur les probabilités (1814), Laplace set out a mathematical system of inductive reasoning based on probability, which we would today recognise as Bayesian. He begins the text with a series of principles of probability, the first six being:
One well-known formula arising from his system is the rule of succession, given as principle seven. Suppose that some trial has only two possible outcomes, labelled "success" and "failure". Under the assumption that little or nothing is known a priori about the relative plausibilities of the outcomes, Laplace derived a formula for the probability that the next trial will be a success.
where s is the number of previously observed successes and n is the total number of observed trials. It is still used as an estimator for the probability of an event if we know the event space, but have only a small number of samples.
The rule of succession has been subject to much criticism, partly due to the example which Laplace chose to illustrate it. He calculated that the probability that the sun will rise tomorrow, given that it has never failed to in the past, was
where d is the number of times the sun has risen in the past. This result has been derided as absurd, and some authors have concluded that all applications of the Rule of Succession are absurd by extension. However, Laplace was fully aware of the absurdity of the result; immediately following the example, he wrote, "But this number [i.e., the probability that the sun will rise tomorrow] is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it."
The method of estimating the ratio of the number of favourable cases to the whole number of possible cases had been previously indicated by Laplace in a paper written in 1779. It consists of treating the successive values of any function as the coefficients in the expansion of another function, with reference to a different variable. The latter is therefore called the probability-generating function of the former. Laplace then shows how, by means of interpolation, these coefficients may be determined from the generating function. Next he attacks the converse problem, and from the coefficients he finds the generating function; this is effected by the solution of a finite difference equation.
The fourth chapter of this treatise includes an exposition of the method of least squares, a remarkable testimony to Laplace's command over the processes of analysis. In 1805 Legendre had published the method of least squares, making no attempt to tie it to the theory of probability. In 1809 Gauss had derived the normal distribution from the principle that the arithmetic mean of observations gives the most probable value for the quantity measured; then, turning this argument back upon itself, he showed that, if the errors of observation are normally distributed, the least squares estimates give the most probable values for the coefficients in regression situations. These two works seem to have spurred Laplace to complete work toward a treatise on probability he had contemplated as early as 1783.
In two important papers in 1810 and 1811, Laplace first developed the characteristic function as a tool for large-sample theory and proved the first general central limit theorem. Then in a supplement to his 1810 paper written after he had seen Gauss's work, he showed that the central limit theorem provided a Bayesian justification for least squares: if one were combining observations, each one of which was itself the mean of a large number of independent observations, then the least squares estimates would not only maximise the likelihood function, considered as a posterior distribution, but also minimise the expected posterior error, all this without any assumption as to the error distribution or a circular appeal to the principle of the arithmetic mean.In 1811 Laplace took a different non-Bayesian tack. Considering a linear regression problem, he restricted his attention to linear unbiased estimators of the linear coefficients. After showing that members of this class were approximately normally distributed if the number of observations was large, he argued that least squares provided the "best" linear estimators. Here it is "best" in the sense that it minimised the asymptotic variance and thus both minimised the expected absolute value of the error, and maximised the probability that the estimate would lie in any symmetric interval about the unknown coefficient, no matter what the error distribution. His derivation included the joint limiting distribution of the least squares estimators of two parameters.
In 1814, Laplace published what is usually known as the first articulation of causal or scientific determinism:
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
This intellect is often referred to as Laplace's demon (in the same vein as Maxwell's demon ) and sometimes Laplace's Superman (after Hans Reichenbach). Laplace, himself, did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: "Une intelligence ... Rien ne serait incertain pour elle, et l'avenir comme le passé, serait présent à ses yeux."
Even though Laplace is known as the first to express such ideas about causal determinism, his view is very similar to the one proposed by Boscovich as early as 1763 in his book Theoria philosophiae naturalis.
As early as 1744, Euler, followed by Lagrange, had started looking for solutions of differential equations in the form:
The Laplace transform has form:
This integral operator transforms a function of time (t) into a function of position or space (s).
In 1785, Laplace took the key forward step in using integrals of this form to transform a whole differential equation from a function of time into a lower order function of space; The transformed equation was easier to solve than the original because algebra could be used to manipulate the differential equation into a simpler form. The inverse Laplace transform was then taken to convert the simplified function of space back into a function of time.
Amongst the other discoveries of Laplace in pure and applied mathematics are:
Laplace built upon the qualitative work of Thomas Young to develop the theory of capillary action and the Young–Laplace equation.
Laplace in 1816 was the first to point out that the speed of sound in air depends on the heat capacity ratio. Newton's original theory gave too low a value, because it does not take account of the adiabatic compression of the air which results in a local rise in temperature and pressure. Laplace's investigations in practical physics were confined to those carried on by him jointly with Lavoisier in the years 1782 to 1784 on the specific heat of various bodies.
In his early years Laplace was careful never to become involved in politics, or indeed in life outside the Académie des sciences. He prudently withdrew from Paris during the most violent part of the Revolution.
In November 1799, immediately after seizing power in the coup of 18 Brumaire, Napoleon appointed Laplace to the post of Minister of the Interior. The appointment, however, lasted only six weeks, after which Lucien, Napoleon's brother, was given the post. Evidently, once Napoleon's grip on power was secure, there was no need for a prestigious but inexperienced scientist in the government.Napoleon later (in his Mémoires de Sainte Hélène ) wrote of Laplace's dismissal as follows:
Géomètre de premier rang, Laplace ne tarda pas à se montrer administrateur plus que médiocre; dès son premier travail nous reconnûmes que nous nous étions trompé. Laplace ne saisissait aucune question sous son véritable point de vue: il cherchait des subtilités partout, n'avait que des idées problématiques, et portait enfin l'esprit des 'infiniment petits' jusque dans l'administration.
(Geometrician of the first rank, Laplace was not long in showing himself a worse than average administrator; from his first actions in office we recognized our mistake. Laplace did not consider any question from the right angle: he sought subtleties everywhere, conceived only problems, and finally carried the spirit of "infinitesimals" into the administration.)
Grattan-Guinness, however, describes these remarks as "tendentious", since there seems to be no doubt that Laplace "was only appointed as a short-term figurehead, a place-holder while Napoleon consolidated power".
Although Laplace was removed from office, it was desirable to retain his allegiance. He was accordingly raised to the senate, and to the third volume of the Mécanique céleste he prefixed a note that of all the truths therein contained the most precious to the author was the declaration he thus made of his devotion towards the peacemaker of Europe. In copies sold after the Bourbon Restoration this was struck out. (Pearson points out that the censor would not have allowed it anyway.) In 1814 it was evident that the empire was falling; Laplace hastened to tender his services to the Bourbons, and in 1817 during the Restoration he was rewarded with the title of marquis.
According to Rouse Ball, the contempt that his more honest colleagues felt for his conduct in the matter may be read in the pages of Paul Louis Courier. His knowledge was useful on the numerous scientific commissions on which he served, and, says Rouse Ball, probably accounts for the manner in which his political insincerity was overlooked.
Roger Hahn in his 2005 biography disputes this portrayal of Laplace as an opportunist and turncoat, pointing out that, like many in France, he had followed the debacle of Napoleon's Russian campaign with serious misgivings. The Laplaces, whose only daughter Sophie had died in childbirth in September 1813, were in fear for the safety of their son Émile, who was on the eastern front with the emperor. Napoleon had originally come to power promising stability, but it was clear that he had overextended himself, putting the nation at peril. It was at this point that Laplace's loyalty began to weaken. Although he still had easy access to Napoleon, his personal relations with the emperor cooled considerably. As a grieving father, he was particularly cut to the quick by Napoleon's insensitivity in an exchange related by Jean-Antoine Chaptal: "On his return from the rout in Leipzig, he [Napoleon] accosted Mr Laplace: 'Oh! I see that you have grown thin—Sire, I have lost my daughter—Oh! that's not a reason for losing weight. You are a mathematician; put this event in an equation, and you will find that it adds up to zero.'"
In the second edition (1814) of the Essai philosophique, Laplace added some revealing comments on politics and governance. Since it is, he says, "the practice of the eternal principles of reason, justice and humanity that produce and preserve societies, there is a great advantage to adhere to these principles, and a great inadvisability to deviate from them".Noting "the depths of misery into which peoples have been cast" when ambitious leaders disregard these principles, Laplace makes a veiled criticism of Napoleon's conduct: "Every time a great power intoxicated by the love of conquest aspires to universal domination, the sense of liberty among the unjustly threatened nations breeds a coalition to which it always succumbs." Laplace argues that "in the midst of the multiple causes that direct and restrain various states, natural limits" operate, within which it is "important for the stability as well as the prosperity of empires to remain". States that transgress these limits cannot avoid being "reverted" to them, "just as is the case when the waters of the seas whose floor has been lifted by violent tempests sink back to their level by the action of gravity".
About the political upheavals he had witnessed, Laplace formulated a set of principles derived from physics to favour evolutionary over revolutionary change:
Let us apply to the political and moral sciences the method founded upon observation and calculation, which has served us so well in the natural sciences. Let us not offer fruitless and often injurious resistance to the inevitable benefits derived from the progress of enlightenment; but let us change our institutions and the usages that we have for a long time adopted only with extreme caution. We know from past experience the drawbacks they can cause, but we are unaware of the extent of ills that change may produce. In the face of this ignorance, the theory of probability instructs us to avoid all change, especially to avoid sudden changes which in the moral as well as the physical world never occur without a considerable loss of vital force.
In these lines, Laplace expressed the views he had arrived at after experiencing the Revolution and the Empire. He believed that the stability of nature, as revealed through scientific findings, provided the model that best helped to preserve the human species. "Such views," Hahn comments, "were also of a piece with his steadfast character."
Laplace died in Paris in 1827. His brain was removed by his physician, François Magendie, and kept for many years, eventually being displayed in a roving anatomical museum in Britain. It was reportedly smaller than the average brain.Laplace was buried at Père Lachaise in Paris but in 1888 his remains were moved to Saint Julien de Mailloc in the canton of Orbec and reinterred on the family estate. The tomb is situated on a hill overlooking the village of St Julien de Mailloc, Normandy, France.
A frequently cited but potentially apocryphal interaction between Laplace and Napoleon purportedly concerns the existence of God. Although the conversation in question did occur, the exact words Laplace used and his intended meaning are not known. A typical version is provided by Rouse Ball:
Laplace went in state to Napoleon to present a copy of his work, and the following account of the interview is well authenticated, and so characteristic of all the parties concerned that I quote it in full. Someone had told Napoleon that the book contained no mention of the name of God; Napoleon, who was fond of putting embarrassing questions, received it with the remark, 'M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator.' Laplace, who, though the most supple of politicians, was as stiff as a martyr on every point of his philosophy, drew himself up and answered bluntly, Je n'avais pas besoin de cette hypothèse-là. ("I had no need of that hypothesis.") Napoleon, greatly amused, told this reply to Lagrange, who exclaimed, Ah! c'est une belle hypothèse; ça explique beaucoup de choses. ("Ah, it is a fine hypothesis; it explains many things.")
An earlier report, although without the mention of Laplace's name, is found in Antommarchi's The Last Moments of Napoleon (1825):
Je m'entretenais avec L ..... je le félicitais d'un ouvrage qu'il venait de publier et lui demandais comment le nom de Dieu, qui se reproduisait sans cesse sous la plume de Lagrange, ne s'était pas présenté une seule fois sous la sienne. C'est, me répondit-il, que je n'ai pas eu besoin de cette hypothèse. ("While speaking with L ..... I congratulated him on a work which he had just published and asked him how the name of God, which appeared endlessly in the works of Lagrange, didn't occur even once in his. He replied that he had no need of that hypothesis.")
In 1884, however, the astronomer Hervé Fayeaffirmed that this account of Laplace's exchange with Napoleon presented a "strangely transformed" (étrangement transformée) or garbled version of what had actually happened. It was not God that Laplace had treated as a hypothesis, but merely his intervention at a determinate point:
In fact Laplace never said that. Here, I believe, is what truly happened. Newton, believing that the secular perturbations which he had sketched out in his theory would in the long run end up destroying the Solar System, says somewhere that God was obliged to intervene from time to time to remedy the evil and somehow keep the system working properly. This, however, was a pure supposition suggested to Newton by an incomplete view of the conditions of the stability of our little world. Science was not yet advanced enough at that time to bring these conditions into full view. But Laplace, who had discovered them by a deep analysis, would have replied to the First Consul that Newton had wrongly invoked the intervention of God to adjust from time to time the machine of the world (la machine du monde) and that he, Laplace, had no need of such an assumption. It was not God, therefore, that Laplace treated as a hypothesis, but his intervention in a certain place.
Laplace's younger colleague, the astronomer François Arago, who gave his eulogy before the French Academy in 1827,told Faye of an attempt by Laplace to keep the garbled version of his interaction with Napoleon out of circulation. Faye writes:
I have it on the authority of M. Arago that Laplace, warned shortly before his death that that anecdote was about to be published in a biographical collection, had requested him [Arago] to demand its deletion by the publisher. It was necessary to either explain or delete it, and the second way was the easiest. But, unfortunately, it was neither deleted nor explained.
The Swiss-American historian of mathematics Florian Cajori appears to have been unaware of Faye's research, but in 1893 he came to a similar conclusion.Stephen Hawking said in 1999, "I don't think that Laplace was claiming that God does not exist. It's just that he doesn't intervene, to break the laws of Science."
The only eyewitness account of Laplace's interaction with Napoleon is from the entry for 8 August 1802 in the diary of the British astronomer Sir William Herschel:
The first Consul then asked a few questions relating to Astronomy and the construction of the heavens to which I made such answers as seemed to give him great satisfaction. He also addressed himself to Mr Laplace on the same subject, and held a considerable argument with him in which he differed from that eminent mathematician. The difference was occasioned by an exclamation of the first Consul, who asked in a tone of exclamation or admiration (when we were speaking of the extent of the sidereal heavens): 'And who is the author of all this!' Mons. De la Place wished to shew that a chain of natural causes would account for the construction and preservation of the wonderful system. This the first Consul rather opposed. Much may be said on the subject; by joining the arguments of both we shall be led to 'Nature and nature's God'.
Since this makes no mention of Laplace saying, "I had no need of that hypothesis," Daniel Johnsonargues that "Laplace never used the words attributed to him." Arago's testimony, however, appears to imply that he did, only not in reference to the existence of God.
Born a Catholic, Laplace appears in adult life to have inclined to deism (presumably his considered position, since it is the only one found in his writings). However, some of his contemporaries thought he was an atheist, while a number of recent scholars have described him as agnostic.
Faye thought that Laplace "did not profess atheism",but Napoleon, on Saint Helena, told General Gaspard Gourgaud, "I often asked Laplace what he thought of God. He owned that he was an atheist." Roger Hahn, in his biography of Laplace, mentions a dinner party at which "the geologist Jean-Étienne Guettard was staggered by Laplace's bold denunciation of the existence of God". It appeared to Guettard that Laplace's atheism "was supported by a thoroughgoing materialism". But the chemist Jean-Baptiste Dumas, who knew Laplace well in the 1820s, wrote that Laplace "provided materialists with their specious arguments, without sharing their convictions".
Hahn states: "Nowhere in his writings, either public or private, does Laplace deny God's existence."Expressions occur in his private letters that appear inconsistent with atheism. On 17 June 1809, for instance, he wrote to his son, "Je prie Dieu qu'il veille sur tes jours. Aie-Le toujours présent à ta pensée, ainsi que ton père et ta mère [I pray that God watches over your days. Let Him be always present to your mind, as also your father and your mother]." Ian S. Glass, quoting Herschel's account of the celebrated exchange with Napoleon, writes that Laplace was "evidently a deist like Herschel".
In Exposition du système du monde, Laplace quotes Newton's assertion that "the wondrous disposition of the Sun, the planets and the comets, can only be the work of an all-powerful and intelligent Being".This, says Laplace, is a "thought in which he [Newton] would be even more confirmed, if he had known what we have shown, namely that the conditions of the arrangement of the planets and their satellites are precisely those which ensure its stability". By showing that the "remarkable" arrangement of the planets could be entirely explained by the laws of motion, Laplace had eliminated the need for the "supreme intelligence" to intervene, as Newton had "made" it do. Laplace cites with approval Leibniz's criticism of Newton's invocation of divine intervention to restore order to the Solar System: "This is to have very narrow ideas about the wisdom and the power of God." He evidently shared Leibniz's astonishment at Newton's belief "that God has made his machine so badly that unless he affects it by some extraordinary means, the watch will very soon cease to go".
In a group of manuscripts, preserved in relative secrecy in a black envelope in the library of the Académie des sciences and published for the first time by Hahn, Laplace mounted a deist critique of Christianity. It is, he writes, the "first and most infallible of principles ... to reject miraculous facts as untrue".As for the doctrine of transubstantiation, it "offends at the same time reason, experience, the testimony of all our senses, the eternal laws of nature, and the sublime ideas that we ought to form of the Supreme Being". It is the sheerest absurdity to suppose that "the sovereign lawgiver of the universe would suspend the laws that he has established, and which he seems to have maintained invariably".
In old age, Laplace remained curious about the question of Godand frequently discussed Christianity with the Swiss astronomer Jean-Frédéric-Théodore Maurice. He told Maurice that "Christianity is quite a beautiful thing" and praised its civilising influence. Maurice thought that the basis of Laplace's beliefs was, little by little, being modified, but that he held fast to his conviction that the invariability of the laws of nature did not permit of supernatural events. After Laplace's death, Poisson told Maurice, "You know that I do not share your [religious] opinions, but my conscience forces me to recount something that will surely please you." When Poisson had complimented Laplace about his "brilliant discoveries", the dying man had fixed him with a pensive look and replied, "Ah! we chase after phantoms [chimères]." These were his last words, interpreted by Maurice as a realisation of the ultimate "vanity" of earthly pursuits. Laplace received the last rites from the curé of the Missions Étrangères (in whose parish he was to be buried) and the curé of Arcueil.
However, according to his biographer, Roger Hahn, it is "not credible" that Laplace "had a proper Catholic end", and he "remained a skeptic" to the very end of his life.Laplace in his last years has been described as an agnostic.
In 1470 the humanist scholar Bartolomeo Platina wrotethat Pope Callixtus III had asked for prayers for deliverance from the Turks during a 1456 appearance of Halley's Comet. Platina's account does not accord with Church records, which do not mention the comet. Laplace is alleged to have embellished the story by claiming the Pope had "excommunicated" Halley's comet. What Laplace actually said, in Exposition du système du monde (1796), was that the Pope had ordered the comet to be "exorcised" (conjuré). It was Arago, in Des Comètes en général (1832), who first spoke of an excommunication.
Baron Augustin-Louis Cauchy was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra.
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way.
Baron Siméon Denis Poisson FRS FRSE was a French mathematician, engineer, and physicist, who made several scientific advances.
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
Joseph-Louis Lagrange was an Italian Enlightenment Era mathematician and astronomer. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics.
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints. The great advantage of this method is that it allows the optimization to be solved without explicit parameterization in terms of the constraints. As a result, the method of Lagrange multipliers is widely used to solve challenging constrained optimization problems.
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations.
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2, or Δ. The Laplacian Δf(p) of a function f at a point p, is the rate at which the average value of f over spheres centered at p deviates from f(p) as the radius of the sphere grows. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems such as cylindrical and spherical coordinates, the Laplacian also has a useful form.
In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation, is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange in the 1750s.
In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has the dimensions of [energy]⋅[time] or [momentum]⋅[length], and its SI unit is joule-second.
In mathematics, the Newtonian potential or Newton potential is an operator in vector calculus that acts as the inverse to the negative Laplacian, on functions that are smooth and decay rapidly enough at infinity. As such, it is a fundamental object of study in potential theory. In its general nature, it is a singular integral operator, defined by convolution with a function having a mathematical singularity at the origin, the Newtonian kernel Γ which is the fundamental solution of the Laplace equation. It is named for Isaac Newton, who first discovered it and proved that it was a harmonic function in the special case of three variables, where it served as the fundamental gravitational potential in Newton's law of universal gravitation. In modern potential theory, the Newtonian potential is instead thought of as an electrostatic potential.
In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less directly, since Hilbert's concept of a "regular variational problem" identifies precisely a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution function inherits the relatively simple and well understood structure from the solved equation.
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the differential equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories.
In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface :
The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans under the gravitational loading of another astronomical body or bodies.
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.
The Catholic newspaper La Quotidienne [The Daily] announced that Laplace had died in the arms of two curés (priests), implying that he had a proper Catholic end, but this is not credible. To the end, he remained a skeptic, wedded to his deterministic creed and to an uncompromised ethos derived from his vast scientific experience.
Publicly, Laplace maintained his agnostic beliefs, and even in his old age continued to be skeptical about any function God might play in a deterministic universe.
Lagrange and Laplace, though of Catholic parentage, were agnostics.
Modern physics, indeed all of modern science, is as humble as Lagrange, and as agnostic as Laplace.
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Nicolas Marie Quinette
| Minister of the Interior |
12 November 1799 – 25 December 1799
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Price per kg is an important metric to consider when buying any type of product. Calculating the price per kg allows a consumer to compare different products and make informed decisions about their purchases. To calculate the price per kg, divide the total cost of the item by its weight in kilograms.
For example, if a 5-pound bag of apples costs $10, then dividing 10 by 2.27 (the number of kilograms in 5 pounds) yields a price per kilogram of 4.41 dollars/kg for apples ($10 divided by 2.27). The same calculation can be applied to other items such as vegetables, grains and liquids like water or oil just remember to convert any weights into kilograms before doing your calculations!
Calculating the price per kilogram of your products can be a tricky task, but with a few simple steps it can make it much easier. By understanding how to calculate the cost per kg you will have greater control over pricing and will be able to more accurately quote prices for customers. With this knowledge, you’ll also be able to identify any discrepancies quickly in order to avoid any potential losses.
How To Find The Cost Per Kilogram (Unit Cost Per Kg Of Food)
What is the Formula to Calculate Price Per Kg?
The formula to calculate price per kg is relatively straightforward. First, you will need to divide the total cost of the item by its weight in kilograms. For example, if an item costs $20 and weighs 2kg, then you would divide 20 by 2 which gives you 10 – meaning that the price per kg for this item is 10$.
Generally speaking, it’s important to be aware of different units when calculating price per kg as retailers may quote prices based on either pounds or ounces rather than kilograms. If a retailer quotes a price in pounds or ounces, simply convert these into their equivalent values in kilograms before proceeding with your calculation. It’s also important to note that prices can vary greatly depending on where you are shopping and what type of product you are buying so it pays off to shop around!
What is the Price Per Kg?
The price per kilogram (kg) can vary greatly depending on the product and market. For example, the international average price of wheat is approximately $0.37 per kg while the average price of beef is around $15-20 per kg. Prices also differ based on location – for instance, fresh fruits may be more expensive in urban areas than rural ones due to transportation costs or availability of supply sources.
Additionally, prices are affected by seasonality; produce is usually more affordable during its peak growing season when it’s most plentiful. Ultimately, pricing depends highly upon market conditions and individual suppliers so it’s important to do research before making a purchase decision in order to get the best value for your money.
What is the Formula for Price Per Weight?
The formula for price per weight is a simple one and can be used to compare the prices of items that are sold by weight, such as sand or gravel. The formula is Price divided by Weight = Price Per Weight (or P/W). For example, if you were looking at two different bags of sand, one costing $50 per 50 pounds and another costing $30 per 25 pounds, you could use the formula to determine which would be cheaper overall.
In this case it would be the first bag – 50 divided by 30 equals 1.66; so, 1 pound of sand from the first bag will cost you 1.66 times less than a pound from the second bag!
How Do You Calculate Price Per Pound Per Kg?
Calculating the price per pound or kilogram of an item is a simple process that requires only basic math. To start, you must know the total weight of the item in either pounds or kilograms and its total cost. For example, if you have 1 kg (kilogram) of apples at a cost of $3.50, then divide 3.50 by 1 to get your answer: $3.50 per kg (kilogram).
If instead you had 2 lbs (pounds) of apples costing $2.00, then divide 2 by 2 to get your answer: $1/lb (pound). In both cases, dividing the total cost by the weight gives you Price Per Pound or Price Per Kg – whichever unit is used for measurement purposes!
Price Per Kilo Formula
The price per kilo formula is used to calculate the total cost of a product based on its weight. It takes into account both the quantity and quality of the item in order to determine an accurate price. The formula is simple: Price = (Weight x Unit Price) + (Quantity x Quality).
This allows for quick calculations, making it easier for buyers and sellers alike to agree on a fair price without having to manually weigh each individual item or guess at how many items are needed.
Price Per Kg to Price Per Gram Calculator
The Price Per Kg to Price Per Gram Calculator is an invaluable tool for those looking to quickly calculate the cost of goods or services on a per-gram basis. This calculator allows users to enter in the price per kilogram and instantly receive the calculated price per gram, making it easy to compare prices between different products or vendors. With this helpful resource, shoppers can ensure that they’re getting the best deal possible!
Price Per Weight Calculator
The Price Per Weight Calculator is a useful tool for shoppers looking to compare prices of products that differ in weight. This calculator can help you estimate the cost per unit (e.g., per pound, ounce, or other unit of measure) by dividing the total price by the weight. The result will provide you with an accurate calculation of how much each item costs per unit so you can easily compare prices and make your best purchase decision!
Price Per Ton to Price Per Kg
When comparing prices between various commodities, it is important to know the difference between price per ton and price per kilogram. Price per ton is a measurement of mass where 1 ton is equal to 1000 kilograms, while price per kilogram is a unit of weight where 1 kg equals 2.2 lbs. This means that the cost for one ton of material will be much higher than for one kilogram because there are more units in the larger quantity.
Price Per Pound to Price Per Kg Calculator
The Price Per Pound to Price Per Kg Calculator is an invaluable tool for anyone who needs to quickly and accurately convert prices from one unit of measurement to another. With just a few simple clicks, you can easily calculate the price per kilogram (kg) or price per pound (lb) of any item with ease. Whether you’re shopping online or at the store, this calculator makes it easy to compare costs between different units of measure in order to get the best deal possible.
How to Calculate Price Per Kg in Excel
Calculating price per kilogram in Excel is a relatively simple process. First, enter the cost of the item and its weight in kilograms into two separate columns on an Excel spreadsheet. Then, to calculate the price per kg, divide the total cost by the total weight (in kg) using a formula like “=A2/B2” where A2 is your cost column and B2 is your weight column.
Finally, format this cell as currency to make it easier to read – you can now see exactly how much each kilogram costs!
How to Calculate Cost Per Gram in Excel
To calculate the cost per gram of an item in Excel, first enter the cost and weight of that item into two separate cells. Next, divide the cost cell by the weight cell to get your cost per gram. Finally, format this new cell as a currency or number so you can easily see your final result.
With these simple steps, you’ll be able to quickly calculate the cost per gram for any item in Excel!
Per Kg Symbol
The Per Kg Symbol, often seen as ‘kg’ or ‘k/g’, is a unit of measure used to represent the mass of an object. It stands for “kilogram” and is equivalent to 1,000 grams (or one thousandth of a ton). The symbol was adopted in 1889 by the General Conference on Weights and Measures (CGPM) and has been widely used ever since.
In SI units, its symbol is kgm-1. The kilogram is the base unit of mass in the International System of Units (SI), and it remains constant regardless of gravity or location on Earth.
In conclusion, calculating price per kilogram can be an overwhelming task if you don’t know the basics of how to do it. However, with a little bit of math and the help of some online tools like Price Per Kg Made Easy, anyone can quickly and easily calculate the cost or value of their goods by weight. Now that you understand how to use this tool to your advantage, start using it today for all your pricing needs!
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1. The problem statement, all variables and given/known data Hi guys, I've recently taken up quantum, so it's all very new to me, it would be greatly appreciated if someone could check my working! Let ψ1(x) and ψ2(x) be two orthonormal solutions of the TISE with corresponding energy eigenvalues E1 and E2. At time t = 0, the particle is prepared in the symmetric superposition state: and subsequently allowed to evolve in time. What is the average energy of the system as a function of time? What is the minimum time ¿ for which the system must evolve in order to return to its original state (up to an overall phase factor), when it starts in the state ψ(+) (x) Determine the probability to ¯nd the system in the antisymmetric superposition state as a function of time when it starts in the state ψ(+) (x) At time t1 the particle is found in the antisymmetric superposition state. What is the probability to ¯nd the particle in the symmetric superposition state at time t1 + T, where T is the time found above? 2. Relevant equations 3. The attempt at a solution Not sure if the last part is right, as it suggests that the probability of finding the particle in the left half of the box is independent of time! Then again, in an infinite square well the potential doesn't depend on time, so TDSE is reduced to TISE?
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Middle school math teachers will be using a curricular resource, CPM Core Connections Courses 1-3, to teach your student the grade-level Idaho Content Standards for Mathematics. Your middle school student will have their own physical copy of the textbook and access to an electronic textbook (e-book) to use in both the classroom and home this year.
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Math Homework Done for You!. Math Projects in Middle School. If you are a student of the middle school, you will definitely have a math project. We know how annoying projects may be, especially on math that is why doahomework.com offers help in this sphere.
Transitioning into a middle school math class is difficult, but getting personalized help can make a difference. Especially with the new Common Core math standards, more students need extra help. Whether you’re having trouble understanding word problems or can’t keep the systems of equations straight, you can ace your next 7th or 8th grade math test by getting personalized help from our.
Middle School Math Content. Below you can link to hundreds of middle school-level math worksheets throughout our website. Absolute Value. These worksheets and printable activities will help students to learn about the absolute value of numbers. Includes identifying values.
MIDDLE SCHOOL MATH MAN. ENGAGING MATH RESOURCES FOR THE MIDDLE SCHOOL CLASSROOM. Blog. Head over to my blog and stock up on creative ideas that will help engage your students and make math fun! Everything from creating a dry erase table for your classroom to tracking homework data in math class, and everything in between!
YES! Now is the time to redefine your true self using Slader’s free GO Math: Middle School Grade 7 answers. Shed the societal and cultural narratives holding you back and let free step-by-step GO Math: Middle School Grade 7 textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life.
Middle school math builds upon elementary math’s foundation and focuses on explaining why mathematical rules work so that children learn and understand the rules, not just memorize them. We also help students understand their homework as part of each session and prepare them for school tests, as well as standardized tests such as high school entrance exams.
The Utah Middle School Math Project. A University of Utah Partnership Project for 7th and 8th Grade Math. Skip to content.. Albert R. Lyman Middle School, Monticello High School, San Juan High School,. daily class activities and matching homework sets, an overview of the chapter.
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Holt Middle School Mathematics Homework Help from MathHelp.com. Over 1000 online math lessons aligned to the Holt textbooks and featuring a personal math teacher inside every lesson!
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141216175.53/warc/CC-MAIN-20201130130840-20201130160840-00087.warc.gz
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CC-MAIN-2020-50
| 4,749 | 16 |
https://slideplayer.com/slide/3369323/
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math
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Presentation on theme: "Base Units of the SI System Quantity Base Unit Abbreviation Second s"— Presentation transcript:
1 Base Units of the SI System Quantity Base Unit Abbreviation Second s Quantity Base Unit AbbreviationSecondsTimemLengthMeterMasskgKilogramA kilogram is about 2.2 pounds.
2 ü Volume cm3 (solids) or ml (liquids) Derived Units:_______________________________ of base unitsCombinationü Volume cm3 (solids) or ml (liquids)The derived unit for volume is the cubic meter, which is represented by a cube whose sides are all one meter in length.For measurements that you are likely to make, the more useful derived unit for volume is the cubic centimeter (cm3).
3 The cubic centimeter works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes.The metric unit for volume equal to one cubic decimeter is a liter (L).
4 ü Density g/cm3 (solids) or g/ml (liquids) Derived Units:ü Density g/cm3 (solids) or g/ml (liquids)Density is a ratio that compares the mass of an object to its volume.You can calculate density using this equation:
5 0ºC 100ºC Celsius Scale: Water Freezes ________ Temperature ScaleA kelvin (K) is the SI base unit of temperature.Celsius Scale:Water Freezes ________Water Boils: __________0ºC100ºCKelvin Scale:(add 273 to ºCelsius)Water Freezes_______Water Boils:________273K373K
7 Scientific NotationHandling numbers:The diameter of the sun is 1,392,000 kmThe density of the sun’s lower atmosphere is g/cm3in a gram of Hydrogen there are 602,214,000,000,000,000,000,000 atomsdistance between particles in a salt crystal is cmadd = ?Would it be easy to make a mistake?
8 Easier to use scientific notation Scientific notation expresses numbers as a multiple of two factors: a number between 1 and10; and ten raised to a power, or exponent.M x 10nM = between 1 & 10n = integer (1, 2, 3...)
9 The exponent tells you how many times the first factor must be multiplied by ten. When numbers larger than 1 are expressed in scientific notation, the power of ten is positive.When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative.
10 Change the following data into scientific notation. The diameter of the Sun is km.The density of the Sun’s lower atmosphereis g/cm3.
11 Move the decimal point to produce a factor between 1 and 10 Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction.
12 Try a few!1. 6.3x x103 =?2. (8.0x104) (5.0x102) =?x1079.0x105x10-85.0x109
14 Dimensional analysis is a method of problem-solving that focuses on the units used to describe matter.For example, if you want to convert a temperature in degrees Celsius to a temperature in Kelvin, you focus on the relationship between the units in the two temperature scales.
15 A conversion factor is a ratio of equivalent values used to express the same quantity in different units.
16 A conversion factor is always equal to 1. Because a quantity does not change when it is multiplied or divided by 1, conversion factors change the units of a quantity without changing its value.
17 Dimensional Analysis (aka Factor label) 1. Rulesdecide what info is givenDetermine what info you wantSet up a plan, use conversion (bridge)cancel units that are the same in the numerator and denominatorsolvecheck to make sure answer makes sense
18 a. How many meters in a one hundred yard dash? 1inch = 2.54 cm Examplesa. How many meters in a one hundred yard dash? 1inch = 2.54 cm=3ft1yd12 in1 ft2.54 cm1 in1 m100 cm91.4m100 ydsXXXX? m
19 Who Won? J. Faklaris = = 23.5 feet X X 100cm 1m 1 inch 2.54 cm X 1 ft12 inWho Won?J. Faklaris == 23.5 feet
20 b. How many kg in a 4 ounce McDonald's hamburger? 1kg = 1000g 16 ounces = 1 pound 1 pound = 454 grams
21 c. If Shaq is 7'2" tall how many millimeters tall is he. 1 inch = 2 c. If Shaq is 7'2" tall how many millimeters tall is he? 1 inch = 2.54 cm
23 e. A computer switch switches 60 times in a microsecond, how many times does it switch in a minute? microsecond = 1 sec
24 f. How many milliliters in a 12 fl oz can of soda. 1000ml = 1L 1L = 1 f. How many milliliters in a 12 fl oz can of soda? 1000ml = 1L 1L = 1.06 quarts 4 quarts = 1 gal1gal = 128 fluid oz.
25 How Reliable are Measurements? How Reliable are Measurements?Accuracy & PrecisionWhen scientists make measurements, they evaluate both the accuracy and the precision of the measurements.Accuracy refers to how close a measured value is to an accepted value.Precision refers to how close a series of measurements are to one another.
26 An archery target illustrates the difference between accuracy and precision.
27 An archery target illustrates the difference between accuracy and precision.
28 How Reliable are Measurements? Percent Error How Reliable are Measurements? Percent Errorpercent error:percent error = |observed value - true value | x 100true value
29 Often, precision is limited by the available tools. F. Significant Figures (sig figs)margin of error?Include all known values, plus one estimated valueOften, precision is limited by the available tools.Scientists indicate the precision of measurements by the number of digits they report.A value of 2.40 g is more precise than a value of 2.4 g.
30 The digits that are reported are called significant figures. Significant Figures (sig figs)The digits that are reported are called significant figures.Significant figures include all known digits plus one estimated digit.
31 Non-zero measurements are always significant (7.23 has three sig figs) Rules for significant figuresNon-zero measurements are always significant(7.23 has three sig figs)2. Zeros between non-zero numbers are always significant(60.5 g = 3)
32 3. zeros that act as place holders are not significant Rules for significant figures3. zeros that act as place holders are not significantex:. 3 cm = 0.03 m _____ sig fig4. All final zeros to the right of the decimal place and arise as a part of a measurement are significantex: _____ sig fig1Place holder4
33 6.00x102 = _____ sig fig 6.0x102 = ______ sig fig 3 ex: 600? use scientific notation6.00x102 = _____ sig fig6.0x102 = ______ sig fig6 x102 = ______ sig fig1321
34 6. counting numbers and defined constants have an infinite number of sig figs ex: 1000ml = 1L _____ sig figex: H2 = 2 atoms = all significantinfinite
35 7. At times the answer to a calculation contains more figures than are significantex: sig fig = 3.62sig fig = __________sig fig = __________sig fig = __________sig fig = __________sig fig = __________Rounding:If less than 5, drop it and all figures to the right.If it is more than 5, increase the number to be rounded by oneIf it is 5 and followed by any digit, round upIf it is 5 and not followed by any digit, look at the figure to be roundedEven #, drop 5 and figures that followOdd #, round up7.56220.127.116.118.10
36 7. The result of an addition or subtraction should be reported to the same number of decimal places as that of the term with the least number of decimal places.ex:5.6?=1649.1
37 8. The answer to a multiplication or division problem is rounded off to the same number of sig fig as is possessed by the least precise term used in the calculation.ex: x =?= 36
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057504.60/warc/CC-MAIN-20210924050055-20210924080055-00358.warc.gz
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CC-MAIN-2021-39
| 7,257 | 35 |
https://bumpercarfilms.com/qa/question-which-type-of-speed-is-found-by-looking-at-a-speedometer.html
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math
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- Can Google maps show speed?
- Does speedometer measure speed or velocity?
- How does speedometer measure speed?
- Can an object have zero velocity and nonzero acceleration?
- What does a speedometer and odometer indicate?
- Do speedometers show true speed?
- What is the difference between a speedometer and odometer?
- What is the most accurate speedometer app?
- What are the 4 types of speed?
- What does the speedometer of a car read?
- What is difference between speed and velocity?
- How fast are we going?
Can Google maps show speed?
The speedometer feature is available on Android phones.
Google also has speed limit indicators and speed camera alerts, so make sure you’re checking those, too.
Google rolled out the speedometer in Maps to all Android users — so if you use Google Maps on your iPhone, you won’t see it yet..
Does speedometer measure speed or velocity?
Speedometers do not measure velocity. Velocity indicates how fast something is changing position. It is a “vector quantity,” which means it involves two measurements. Both an object’s speed and its direction are included in velocity.
How does speedometer measure speed?
Mechanical speedometers measure the speed of a car by being linked mechanically with the gearbox output shaft . Since this shaft lies ‘downstream’ of the gear box, the speed with which it rotates is independent of gear changes and so gives a true measure of the road speed.
Can an object have zero velocity and nonzero acceleration?
Yes. Anytime the velocity is constant, the acceleration is zero. For example, a car traveling at a constant 90 km/h in a straight line has nonzero velocity and zero acceleration. … Its acceleration will change in magnitude and direction as the elevator starts and stops.
What does a speedometer and odometer indicate?
Speedometer, instrument that indicates the speed of a vehicle, usually combined with a device known as an odometer that records the distance traveled.
Do speedometers show true speed?
“The accuracy of the speedometer in most vehicles, including Volkswagens, is generally within a few percentage points of actual speed,” Tetzlaff says. “Odometer readings are designed to be quite accurate.”
What is the difference between a speedometer and odometer?
The odometer is the device which is used to measure the distance travelled. The distance travelled by vehicle between any two points can be known by the odometer. The speedometer is the device which can tell us the instantaneous speed of any vehicle.
What is the most accurate speedometer app?
Still, some may want to use these for something. Here are the best speedometer apps for Android….You may unsubscribe at any time.GPS Speedometer and Odometer.DigiHUD Speedometer.Drag Racer Car Performance.SpeedView.Ulysse Speedometer.Nov 15, 2020
What are the 4 types of speed?
There are four types of speed and they are:Uniform speed.Variable speed.Average speed.Instantaneous speed.Nov 10, 2020
What does the speedometer of a car read?
The speedometer of a car shows its instantaneous speed (as we understand it) and not the average speed. Technically, instantaneous speed is also average speed, but calculated over a very, very small time period. Speed is nothing but a ratio of distance traveled and time taken.
What is difference between speed and velocity?
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object’s movement. Put another way, speed is a scalar value, while velocity is a vector.
How fast are we going?
Thus, the surface of the earth at the equator moves at a speed of 460 meters per second–or roughly 1,000 miles per hour. As schoolchildren, we learn that the earth is moving about our sun in a very nearly circular orbit. It covers this route at a speed of nearly 30 kilometers per second, or 67,000 miles per hour.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991641.5/warc/CC-MAIN-20210511025739-20210511055739-00541.warc.gz
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CC-MAIN-2021-21
| 3,876 | 38 |
https://www.logicprep.com/blog/?category=ACT+Math
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math
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This question can be solved in multiple ways:
The standard “math” way to solve it is to recognize that the two angles on the line are supplementary and so must add up to 180 degrees. We then set up the equation (4x + 6) + 2x = 180, and solve to get that x = 29. Since the question is asking for the measure of the smaller angle, which is 2x, we then double this to get (D) 58 degrees.
Another approach to the question is to approximate the measure of the smaller angle by simply eyeballing it: it looks to be slightly more than 45 degrees. We then go to the answer choices. The figures on the ACT Math are drawn roughly to scale, so what answer choices can we eliminate? Well, (A), (B), and (C) are all far too small. We can also eliminate (E) because we know that it’s possible to set up an equation to solve for the smaller angle.
Interestingly, for this particular question, eyeballing the figure to arrive at the answer is actually faster than solving the question algebraically. In addition, eyeballing avoids a common mistake students make when solving this question algebraically. That is, many students set up the equation and correctly solve for x, finding that x = 29. They forget, though, that the question is asking for the measure of the smaller angle (which is 2x), and they choose (C). (Note: Solving this question algebraically is still great as a primary strategy and can be done very quickly if you’re comfortable with the algebra.)
While eyeballing can be helpful, it should be thought of more as an extra tool rather than as a primary problem solving-strategy. The technique is only relevant for questions with figures, and, even on such questions, it often can’t be used by itself to narrow down to one answer. However, it 1) can be the most efficient way of solving certain questions, 2) will often allow you to eliminate at least two answers on many other questions if you need to make an educated guess, and 3) provides a way to double-check your work if you solve the question using a more standard math approach. For example, in the question above, if a student decides to solve the question algebraically, he or she can then quickly glance at the figure to see whether the answer makes sense given the scale.
As a final example, consider this question, again taken from a real ACT, as featured in The Real ACT book, test 4:
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CC-MAIN-2019-13
| 2,360 | 6 |
http://www.solutioninn.com/repeat-exercise-9-assuming-that-the-population-standard-deviation-s
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math
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Question: Repeat Exercise 9 assuming that the population standard deviation s
Repeat Exercise 9 assuming that the population standard deviation s is known to be 3.8 chocolate chips. Conduct the hypothesis test using a known value of the population standard deviation σ.
Relevant QuestionsRepeat Exercise 10 assuming that the population standard deviation s is known to be 5.01 km. Conduct the hypothesis test using a known value of the population standard deviation σ. The Jefferson Valley Bank once had a separate customer waiting line at each teller window, but it now has a single waiting line that feeds the teller windows as vacancies occur. The standard deviation of customer waiting ...Repeat the preceding exercise using the pulse rates of women listed in Data Set 1 of Appendix B. For this sample, n = 40 and s = 11.6 beats per minute. Identify the null hypothesis, alternative hypothesis, test statistic, ...Data Set 21 in Appendix B includes a simple random sample of “wheat” pennies. U.S. Mint specifications now use a standard deviation of 0.0230 g for weights of pennies. Use a 0.01 significance level to test the claim that ...In the Pennsylvania Match 6 lottery, six numbers between 1 and 49 are randomly drawn. To simulate the number selection process, a TI-83/84 Plus calculator was used to randomly generate 100 numbers between 1 and 49 inclusive. ...
Post your question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688997.70/warc/CC-MAIN-20170922145724-20170922165724-00622.warc.gz
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CC-MAIN-2017-39
| 1,395 | 4 |
https://www.shaalaa.com/question-bank-solutions/the-perimeter-triangle-144-cm-ratio-lengths-its-side-2-3-4-construct-triangle-construct-a-triangle-given-the-lengths-of-its-three-sides_77446
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math
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The perimeter of a triangle is 14.4 cm and the ratio of lengths of its side is 2 : 3 : 4. Construct the triangle.
Steps of construction:
1: A line AB = 14.4 cm is drawn.
2: Darw a ray AC making an acute angle at A in the downward direction. Then, divid it into (2 + 3 + 4) = 9 parts.
3: Join B and A9.
4: Draw a line parallel to BA9 at A2 and A5 intersecting AB at X and Y respectively..
5: With X as centre and XA as radius, draw an arc.
6: With Y as centre and YB as radius, draw an arc cutting the previous arc at Z.
7: Join XZ and YZ.
Hence, △XYZ is the required triangle.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077818.23/warc/CC-MAIN-20210414125133-20210414155133-00557.warc.gz
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CC-MAIN-2021-17
| 578 | 10 |
http://mathhelpforum.com/algebra/86891-need-help-miles-its-cost-question.html
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math
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please tell me the anwser and method of doing it thanx.
Follow Math Help Forum on Facebook and Google+
rounding off the cost per litre to nearest 10p gives 90p
rounding off the distance to nearest 100 gives 1200 miles
So answer =total fuel required * Cost per liter of fuel=
now convert the unit.
answeer is "c" (as already told to you by Bebrave)
View Tag Cloud
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123549.87/warc/CC-MAIN-20170423031203-00020-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 362 | 8 |
http://www.peltzsodding.com/diy/determining-area/
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math
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Our rolls are 2ft x 5ft or 10square foot rools. Use the formula below to determine your installation area.
Square or Rectangle areas:
lengh times width, then divide by 10
Pi (3.14) times radius squared, then divide by 10
0.5 times base, times height, then divide by 10
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100583.13/warc/CC-MAIN-20231206031946-20231206061946-00723.warc.gz
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CC-MAIN-2023-50
| 268 | 5 |
http://forums.wolfram.com/mathgroup/archive/2004/Apr/msg00062.html
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math
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Plotting a surface side-by-side
- To: mathgroup at smc.vnet.net
- Subject: [mg47324] Plotting a surface side-by-side
- From: ppga at ono.com (Jose)
- Date: Mon, 5 Apr 2004 05:23:06 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I need to plot a 3D-surface, but I need to plot it side-by-side. Also I need to color its sides in gray level. I think it is not a problem if the side is 'curved' but how to meke it if it is plane? I mean, if one has to plot an arc of Sin(x), it can be properly done by FilledPlot. But what happens if I want to draw this arc in the 3D-space. There is is 3D version of FilledPlot? At the end, I expect your aids for doing this. I am interested more in the best final result than in the easiest way to do that. Thanks in advance! Wishes!
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945459.17/warc/CC-MAIN-20180421223015-20180422003015-00629.warc.gz
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CC-MAIN-2018-17
| 774 | 7 |
https://litpick.com/review/zero-oxymoron-review-champion721
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math
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Three friends, Oxymoron, Nikias, and Aurelias are talking about mathematics. This was a long time ago, and these men did not know much about the world around them. However, it did not stop them from trying to make sense of numbers and mathematics. One day Oxymoron claims something great: that it is possible to have nothing, and therefore be at zero. However, this is a radical idea that no one at that time easily accepts, mostly because this would change mathematics forever.
Because this story was very short, it was to the point. It gave an interesting view of how things were so long ago. One of the characters is often described as fat, which is not very nice. Thankfully the rest of the story is very good. My favorite character was Oxymoron, who did not give up his beliefs even when everybody else rejected them.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400210996.32/warc/CC-MAIN-20200923113029-20200923143029-00036.warc.gz
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CC-MAIN-2020-40
| 822 | 2 |
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