The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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Relation between sub-tangent and sub-normal of $y^2 = (x+a)^3$

If the relation between sub-tangent and sub-tangent at any point on the curve $y^2 = (x+a)^3$ is $p(SN)=q(ST)$ then find the value of $p$ and $q$ where $SN$ is sub-normal and $ST$ is sub-tangent ...
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Factorial of a matrix: what could be the use of it?

Recently on this site, the question was raised how we might define the factorial operation $\mathsf{A}!$ on a square matrix $\mathsf{A}$. The answer, perhaps unsurprisingly, involves the Gamma ...
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Why does this mass equation not work in this calculus application problem?

This is a homework problem which I have already solved, but I want to know why my first approach did not work. I have already asked my professor this question, but he did not explain it very well. ...
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Resources to understand real world usage of linear algebra

I've learned linear algebra basics at university and really liked it, so I decided to learn it more deeply. Secondly, I want to work in computer science and I think linear algebra knowledge could be ...
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1answer
44 views

What use does a Cauchy principal value and divergent summation have?

Through some questionable methods, there lies an answer to the following integral. $$\int_{-a}^a\frac{dx}x=0$$ You may question its soundness at first glance since: ...
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Large sparse binary matrices with little row overlap

How can I construct sparse binary matrices $A : M \times N$, with ~ $N p$ ones in each row, so that rows don't overlap much, i.e. the maximum $\qquad \text{size} (\ A \text{ row } i \ \cap\ A ...
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1answer
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A partial derivative problem related with elasticity of substitution in Advanced Micro

Exe 3.8 Sorry, it is a problem that appears in Jehle and Reny Advanced Microeconomic Theory (3rd ed) exercise 3.8. But I think it's a partial derivative question. Letting $f_i(\mathbf{x})=\partial ...
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1answer
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$a_{A,B}=a_{A,E}+a_{E,B}$ - Relative acceleration

When two balls $A,B$ are moving under gravity , Find acceleration of $A$ relative to $B$ (That is $a_{A,B}$) a) Both $A$ and $B$ are moving down ! b) $A$ moves upwards and $B$ moves downwards (above ...
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Matrix identification

Is there any name for a square, symmetric matrix, created in the following format: $$M_{i,j} = \left\{\begin{matrix} i + j & i \neq j\\ 0 & i = j \end{matrix}\right.$$ where $i, j$ start ...
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Applications of Prüfer sequence

Reading a book about a graph theory I found out about Prüfer's sequences which converts a labeled tree of $n$ vertices into an array of $n-2$ numbers. I was actually pretty surprised by this and was ...
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Is there anything significant about the cross-quarter days, in terms of a sinusoid?

As the Earth goes around the sun, the length of the day changes, and certain cultures have celebrations or observances centered around these changes, illustrated in this graph. The red dots, the ...
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Applied Mathematics: Two particles of mass $m$ moving smoothly along the $x$-axis connected by a spring?

Two particles of mass $m$ can move smoothly along the $x$-axis and are connected by a spring of natural length $l$ and spring constant $k$. Here are the questions and my proposed answers. I'm stuck ...
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1answer
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What can we do with Propositional Logic?

I've studied a bit of propositional logic and first order logic, I know that propositional logic is sound and complete ($\Gamma \vdash \gamma$ if and only if $\Gamma \vDash \gamma$), I know what ...
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4answers
204 views

How to explain “why study prime numbers” to 5th Graders?

I tend to teach 5th graders math ever so often just so they can be "friendly" with math in a playful manner, instead of being afraid. However, one question that I constantly struggle with is this: ...
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Chess knight move in 8x8 chessboard

I've recently shown some interests in chess, and I wonder if there is a solution for the following problem: In a 8x8 chessboard, labeling the cells with numbers from 1 to 8, is there any way to find ...
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2answers
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How to use the properties of the logarithmic function

I'm coding the game asteroids. I want to make a levels manager who can create a infinity number of level increasing in difficulty. My levels have as parameters : The number of asteroids on the ...
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1answer
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Is there a term in mathematics for Metcalfe's Law?

Metcalfe's Law states that the value of a network is proportionate to the square of the number of users. This comes from the idea that there are $N*(N-1)/2$ pairs in a network of size $N$. Does this ...
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45 views

What is the exact role of the integrals in a PID Controller?

I am trying to understand the function of a PID Controller. It returns a value, which is the sum of three components. The proportional, derivative and integral components. I am having issues grasping ...
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3answers
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Applications of Multivariable Calculus

As part of the final for my Multivariable Calculus class, I am to create a project wherein I find an application of some multivariable calculus subject (up to and including Green's Theorem), and ...
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1answer
41 views

Applied Mathematics: Spherical Polar Coordinates and Newton's Second Law

I've been attempting this question but can't seem to find a solution. Question: A particle of mass $m$ moves under the influence of a force which, in spherical polar coordinates, only acts in the ...
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Numerical solution of the stationary Navier-Stokes equations

Let $d\le 3$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. I'm considering an incompressible Newtonian fluid with uniform density $\rho_0$ and viscosity $\nu$. In this case, the stationary ...
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1answer
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Locus Equation $f(r) = \frac{-h^2}{r^3}$?

For the Locus equation $$\frac{\mathrm{d^2}u }{\mathrm{d} \theta^2} + u = - \frac{1}{h^2u^2}f\left(\frac{1}{u} \right )$$ How do I find the solution for $f(r)= \frac{-h^2}{r^3}$ and sketch the ...
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1answer
36 views

Optimization problem, finding the dimensions of the container of least cost.

A closed rectangular container with a square base is to have a volume of $2000$ cubic centimeters. It costs twice as much per square centimeter for the top and bottom as it does for ...
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What are the applications of functional analysis?

I recently had a course on functional analysis. I was thinking of studying the mathematical applications of functional analysis. I came to know it had some applications on calculus of variations. I am ...
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51 views

Fixed Points of Polynomial (Application of Mean Value and Intermediate Value Theorems)

The question is: A number $a$ is called a fixed point of a function $f$ if $f(a)=a$. Consider the function $f(x)=x^{87}+4x+2, x\in\Bbb R.$ (a) Use the Mean Value Theorem to show that $f(x)$ ...
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Uses of vector spaces over $\mathbb Q$

I know of two applications of vector spaces over $\mathbb Q$ to problems posed by people not specifically interested in vector spaces over $\mathbb Q$: Hilbert's third problem; and The Buckingham pi ...
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Is there any way to find out how many intervals greater than x exist in a list of values?

I'm not a professional mathematics, but I have a problem of applied mathematics. Beforehand, I apologize for not using more technical terms. I hope I can be as clear as possible: Given the following ...
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1answer
22 views

Natural applications of the Sum-to-Product formulas

The Sum-to-Product formulas are formulas used to express sums and differences of $\sin$ and $\cos$, for example $$\cos(p)+\cos(q)=2\cos(\frac{p+q}{2})\cos(\frac{p-q}{2})$$ Are there any good, ...
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What is the purpose of K-Theory?

I have recognized that there is a theory called K-Theory in mathematics is used also for applications in mathematical physics. There is existing algebraic K-Theory and topological K-Theory. Are ...
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39 views

Importance and Applications of Cuban Primes

Are there any applications of cuban primes, or are they only considered to be within the realm of pure mathematics? Is there anything significant about them specifically? Would more research into ...
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Calculating the years needed to double energy in the system

Using the following information: The EROI of corn ethanol is 1.3:1 Gross system energy per unit out = $EROI / [EROI-1]$ This means for each extra unit of energy produced, 4.33 units of energy were ...
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How large rectangles fit on canvas

I have images whose side ratios are known, and the number of images is known. I have canvas ...
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21 views

Word problem based on differentiation - a right circular cone.

The height of a right circular cone increases by $k\%$, its semi vertical angle remaining constant. Assuming $k$ to be small what is the approximate percentage increase in (i) total surface area (ii) ...
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1answer
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Find maximum depth of water, given height,$h=1.8\sin[2\pi{t-4.00\over12.4}]+3.1$

At a seaport, the depth of the water $h$ metres at a time $t$ hours during a certain day is given by this formula; $$h=1.8\sin[2\pi{t-4.00\over12.4}]+3.1$$ What is the maximum depth of the water? ...
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Clash of Clans. What's the total time to train?

all about clash of clans game. I have total of 6 barracks. Two of them produces one barbarian each every 20 seconds, the another two barracks produces one archer each every 25 seconds, and the last ...
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About Codd's theorem

I was learning about databases and I have developed a rough idea that the design of databases has got quite a lot to do with mathematics. The most common and probably advanced form of databases are ...
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2answers
85 views

When do we use Tensor?

I'm carious to see applications of tensor product. Is there any set of things that if they happen or we encounter them then we use tensor product, tensor algebra, ...? I will be happy if it be ...
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221 views

Physical interpretation of the Lebesgue integral

Is there a physical interpretation of the Lebesgue measure and an associated experiment that shows that it is the 'right' measure to use to model various phenomena in the physical world? I'm asking ...
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Statistics application problem - estimate number of items by weight

An experiment was conducted by weighting 20 sets of items with known quantity and the weight of items in each trail were obtained. We also know the weight of each item is supposed to be $W$ kg ...
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1answer
31 views

Practical use of order of rotational Symmetry.

Has anyone know what is the use of finding the order of the rotational symmetry of a figure? A student of mine ask that question from me. I search it but could not find any. Plz help. ...
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23 views

What practical applications do SDEs and SPDEs have?

I will study from the probability thory to its application to stochastic differential equations with my friend. Of cource I'm looking forward to study them but would be a littel discouraging because I ...
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How to plan a ride by several buses?

Given a source location and a destination location, and an acceptable range of departure times, or an acceptable range of arrival times, and a schedule of available bus routes (e.g. ...
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What kind of mathematics do I need to solve for a sequence of operations to get from one state to another?

I'm trying to solve a certain type of engineering problem, but I don't know what kind of math would apply to solving this problem. I'm not asking to solve the problem for me, but I am having trouble ...
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1answer
71 views

Applications of Whitney's Approximation Theorem

I am reading the book Introduction to Smooth Manifolds by John Lee. In his book he proves a theorem called the Whitney's Approximation theorem which essentially states that any continuous map can be ...
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1answer
50 views

Probability of getting into at least one university given grades and scores

A number of websites offer tools which estimate odds of being accepted to universities given grades and standardized test scores, based on applicant data. The question of calculating odds of getting ...
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Rotating sphere

I want to rotate a ball by placing it on rotating cylinders. I want these cylinders to touch all points on the ball. (I am attempting to sand a ball) Is there a way to determine how many cylinders I ...
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1answer
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How to resample translated grid to ensure consistent interpolation?

I have a grid of values, sampled at certain locations. I'd like to translate grid by some offset and resample it. The questions is: what should be the resampling and interpolation formulas such that ...
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Applications of iterated sinusoidal functions?

When I teach freshman calculus, I assign artificial exercises for practice such as differentiating $\exp\cos x$, $\exp\exp x$, $\sin\cos x$, etc. Iterated exponentials like do have real-world ...
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What are the steps to write a control function?

I have a system defined like this: $$\delta\delta x(t) = \rho(t) \cos(\alpha(t)) \\ \delta\delta y(t) = -g + \rho(t) \sin(\alpha(t))$$ I need to write a control function to calculate $\rho(t)$ and ...
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Economics Application of Rates of Change

The Consumer Price Index ($CPI$) is a statistical estimate of the change of prices of goods and services bought for consumption. It is generally calculated by collecting the prices of a sample of ...