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Questions tagged [applications]

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.)

2
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3answers
26 views

Finding numerical values to an equation describing a hyperplane or a plane (any software suggestion?)

The following equation $$0.27a+0.1b+0.13c=70$$ can admit many solution. Is there any software/methods I can use so that I can have a large list of all the possible numerical solutions to this equation?...
-1
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0answers
15 views

Using statistics in petroleum engineering [closed]

How can engineers use mathematical statistics to determine relationship between number of wells and oil, gas and water production?
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0answers
11 views

Using the law of conservation of Energy for a collision under gravity.(applied maths)

One end of a light elastic string of natural length l passing through a small smooth ring of mass m is attached to a point O of a ceiling. A particle P of mass M attached to the other end of the ...
1
vote
2answers
45 views

What are some practical usages of computing volume in $n$ dimensions?

I am not sure if this is really a mathematical problem, but I know how to find volume of say a sphere in n dimensions, but after coming to realize how to do this, i just don't get what would be the ...
-1
votes
0answers
24 views

Applied probability

Can anyone provide me a real life situation where the following probability is used or any application of it : $$\mathbb{P}[X+\theta Y<r \mid \theta X+Y<r],$$ where, $X$ and $Y$ are iid random ...
1
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0answers
9 views

Finding the optimum parameters for volumetric swept 3D display application utilizing planetary gear system

Imagine a planetary gear system as below: There are two curved screens attached to a shaft of the planet (little purple gear). The curves are logarithmic spirals. So they are rotating with the ...
1
vote
1answer
45 views

What would be the explicit formula of a “dictionary” function / relation?

What would be the explicit formula of a " dictionary" function / relation that would put in the "dictionary order" all the words of a natural language ( having an alphabet)? I think that one of the ...
1
vote
0answers
20 views

What are the use cases of the Dirichlet energy in computer vision?

I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What are specific ...
4
votes
2answers
238 views

Real-world applications of fields, rings and groups in linear algebra.

Real-world applications of fields, rings and groups in linear algebra. A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
0
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0answers
31 views

Physical interpretation of Dirichlet energy for a membrane.

In the following model of a membrane with a mass particle in it, why does the integral represents the elastic energy of the system? Let $\Omega$ be an open connected region (the membrane) in $\Re^2$, ...
0
votes
1answer
66 views

Where is the usefulness of Fourier Transform I was promised? [closed]

Before I started my PDE course I heard about Fourier Transform and how useful it is (waves, heat problem, etc) but I recently finished it and all we did is solve some PDE problems where we had to ...
2
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0answers
33 views

Real world application of finding all simple paths on a graph

I am currently designing a general purpose graph database. Recently I have started to consider supporting the "find all simple paths between two nodes" operation on the graph. However while there are ...
0
votes
2answers
25 views

Norml, Application of derivatives

If $x+4y =14$ is normal to the curve $y^2=αx^3 - β$ at $(2,3)$, then the value of $α+β$ is? I equated the slope of the normal with the value of $-dx/dy$ and found $α=2$, how do I find $β$?
0
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1answer
43 views

Examples of applying Dirichlet's approximation.

I've seen many examples of Dirichlet's approximation being proven , or other questions regarding to the theory of the approximation on this site and others but I would like to see a concrete example ...
0
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0answers
36 views

Integral transform with reciprocal complex exponential functions?

I tried answering a question that ended up with an expression $$\mathcal F\left\{e^{\left(\frac{2\pi j} {t}\right)}\right\}$$ Now this function we know from famous identity is $$e^{ai} = \cos(a)+i\...
1
vote
1answer
50 views

Find the interval in which $f(x)$ increases and decreases.

Let $f(x) = 2x^3 -9x^2 + 12 x + 6$ so $f'(x) = 6x^2-18x + 12 = 6 (x-1)(x-2)$ I need the intervals in which $f(x)$ strictly increases, $f'(x)>0$ when $x <1$ and $x>2$ and thus $f(x)$ ...
0
votes
0answers
26 views

Exponential equation with top and bottom limits?

So I'm coding a interactive sliding bar that changes based on the value that is given. Currently the interaction between the value given and the bar is static and I would like to make it flow with the ...
0
votes
2answers
60 views

A calculus problem from high school textbook

A man 150 cm tall, walks away from a source of light situated at the top of a pole 5 m high at the rate of 0.7 m/s. Find the rate at which: his shadow is lengthening the tip of his shadow is moving ...
0
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0answers
13 views

Bayesian Network vs MultiVariate Analysis vs Induction

I work with JS programmer on the logic for a web app. We have factors that influence a composition of a set. Envision rows in Excel that tell a set to have 5 members or 10, etc. Each row has certain ...
0
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0answers
25 views

Need to create a formula for points distribution in the game

There is the following data for a simple game: 3 players General points pool - 30000 Each player has a force. Initial force value - 100 During the game force indicator is changing. Min value of force ...
1
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0answers
18 views

Calculate weighted percentages to incorporate discounts

I apologize if I have titled this question incorrectly. I am selling products online. Customers can purchase the products plain, or they can purchase it with one of two logo design applications, ...
1
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0answers
9 views

Heaps' Law equation derivation

I'm actually not sure if this question is allowed on this community since it's more of a linguistics question than it is a mathematics question. I've searched extensively on the Web and have failed to ...
0
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1answer
58 views

Proving uniqueness of solution to 1-D Wave equation without energy conservation

We have a homogeneous string of length L fastened at its ends, performing small transverse motion in a vertical plane. The tension in the string is assumed sufficiently large for gravitational forces ...
-1
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1answer
36 views

how to show that (F∘T) = (T∘ F) [closed]

We have E a vector space , T and F two endomorphisms of E such as i) F got dim(E) eigenvalues of multiplicity 1 ii) each eigenvector of F is also an eigenvector of T And we have to show that (F∘...
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vote
1answer
62 views

What is application of following exercise?

I had done following excercise. Consider the function $f:X\to Y$ where Y is compact Hausdorff space. Then $f$ is continuous if and only if the graph of $f$, $$G_f=\{(x,f(x)) \mid x\in X\},$$ is ...
2
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0answers
69 views

Practical applications of semidefinite programming

I am looking for practical applications of semidefinite- programming. So far, I found that the low-rank matrix completion problem (recomendendattion matrices) can be expressed as a semidefinite ...
0
votes
1answer
41 views

Given $a_0, a_1,…,a_n$ are the real numbers satisfying

Given $a_0, a_1, .., a_n$ are the real numbers satisfying $$\dfrac {a_0}{n+1} + \dfrac {a_1}{n} +......+\dfrac {a_{n-1}}{2}+a_n=0$$ then prove that there exists at least one real root of the equation ...
3
votes
1answer
121 views

Using Rolle's theorem to show $e^x=1+x$ has only one real root

Applying Rolle's Theorem, prove that the given equation has only one root: $$e^x=1+x$$ By inspection, we can say that $x=0$ is one root of the equation. But how can we use Rolle's theorem to prove ...
0
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0answers
17 views

Impact of individual parts to the whole when measuring yearly performance

Suppose I have a scenario where I want to compare the performances of two different time periods, but I want to break down exactly what caused the difference in performance. I have performance of ...
1
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0answers
69 views

What are the practical uses of Fermat's Last Theorem? [closed]

Given the wide attention it has received from the math community, what are the practical uses of Fermat's Last Theorem?
0
votes
1answer
51 views

calculus applied to fields in physics

Having trouble with the maths in this question, I realise this is a physics question so I apologise if this isn't allowed, but some mathematicians might be able to solve it well. I asked this in the ...
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0answers
10 views

Swaying string, a question regarding the derivation of formula

In my textbook, with $S=|\mathbf{S}|$, from the picture below, they derive $\int_{x}^{x+h}\rho_lu_{tt}''d\lambda=S(x+h)\sin(\alpha(x+h))- S(x)\sin(\alpha(x))+\int_{x}^{x+h}Fd\lambda$, where $F$ is [...
1
vote
1answer
26 views

Which logistic equation is better for solving this question?

So I was given a question about spread of disease: A virus is spreading through a city of 50,000 people who take no precautions. The virus was brought to the town by 100 people and it was found ...
4
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8answers
965 views

Practical application of matrices and determinants

I have learned recently about matrices and determinants and also about the geometrical interpretations, i.e, how the matrix is used for linear transformations and how determinants tell us about area/...
1
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1answer
46 views

Equations or areas where $(AA^T)^x$ or $(A^TA)^x$ are used as applications

Let $A$ be square or rectangular and $x\in \mathbb{R}$. Can you point me to equations/areas out there where $(AA^T)^x$ or $(A^TA)^x$ or their eigenvalues are used as applications? e.g. we find them in ...
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6answers
384 views

Importance of differentiation [duplicate]

I have just started learning about differentiation. I know that differentiation is about finding the slopes of curves of functions and etc. I have many saying that differential and integral calculus ...
1
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1answer
35 views

Find a homeomorphism

Let $X=A\cup B \cup C$ where $A=\{(x,y) :(x+2)^2 +y^2 =1\}$ and $B=\{x^2+y^2 \leq 1\}$ and $C=\{(x,y) :(x-2)^2 +y^2 =1\}$. Find a homeomorphism between the quotient space $X/B$ and $E=\{(x,y) :(x-1)^...
2
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0answers
58 views

real world applications of direct sums

I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was ...
0
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1answer
36 views

Surface area of a sphere over a disc

What's the surface area of the sphere $x^2 + y^2 + z^2 = 1$ over the disc $(x-1/2)^2 + y^2 \le 1/4$ ? I've tried something, but I don't think it's right, as it's not a "nice answer" So here is what ...
8
votes
3answers
159 views

Applications of “finite mathematics” to physics

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias. When I think of applications of maths outside of itself, I ...
0
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0answers
25 views

How is it possible a ruled surface to be composed of straight lines?

And a double ruled surface is composed of two groups of straight lines. This is what gives to this shape its exceptional resistance to buckling How is it possible a curved surface to be composed of ...
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0answers
25 views

Probability of stripes being distinguishable given probability density functions for each luminance

I have an image with seven stripes on it (or three stripes on a dark background), and the goal is to estimate the probability of whether they are distinguishable from one another. If the values of ...
1
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1answer
18 views

Disagreeing methods for computing pregnancy probabilities

Something that I would have thought to be dead simple nearly drove me crazy! Let's say we make a small study of women who have similar factors for becoming pregnant. Let's say the study runs for two ...
1
vote
1answer
31 views

Are there applications of equivalent matrices?

Similar to the definition here, matrices $A$, $B$ $\in \mathbb{C}^{m\times n}$ are said to be equivalent if there exist some invertible $m\times m$ matrix $P$ and some invertible $n\times n$ matrix $Q$...
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1answer
16 views

Differentiated - Rates of change

A triangle $ABC$ is made out of an elastic piece of string. Vertices A and B are being pulled apart so that the length of the base $AB$ is increasing at of $3 \ cm \ s^{-1}$ and the height $h$ is ...
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0answers
36 views

“Work done” my a muscle during weight-lifting

I'm looking for a simplistic way to describe the "work" done by muscles during compound weightlifting movements. Perhaps not work in the precise physics sense, but an overall idea of how much the ...
1
vote
1answer
30 views

Purpose of rotation of a Function or Graph

You are able to rotate any function by an arbitrary angle around the origin using the formula, $$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, ...
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0answers
21 views

Area transformation

I have two rows of different types A and B. Every row is of the size 1$\times$N, where every element can be either 1 or -1. If we consider a single row of type A={-1,1,1,1,-1,1,-1,...} of size 1$\...
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0answers
14 views

R²/Plane Subset Equation With Plane Homothetic Transformation

Let's consider $H_k∶\ \left\{\begin{matrix}\mathbb{R}^2\rightarrow\mathbb{R}^2\\(x,y)\longmapsto(kx,ky)\\\end{matrix}\right.\ $. It is an homothetic transformation of $\mathbb{R}^2$ of center $(0,0)$...
0
votes
2answers
55 views

Find if the function $\frac{(1-2xy)}{(x^2 +y^2)}$ has a max or min value for $(x,y)=/=(0,0)$

Does the function $\frac{1-2xy}{x^2 +y^2}$ have a max or min value for $(x,y)=/=0$? What I've tried so far is to take the the partial derivatives: $$\frac{\partial f}{\partial x} = \frac{2(-x+x^2*y ...