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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.)

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Real life applications of a circle? (Conics)

for my Math 2U assignment, we have to discuss real life applications of different conic sections. However, apart from the wheel, I cannot find or think of any other real life applications of the ...
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0answers
42 views

Has the rigour of real analysis shown some unexpected truths about real life that would have otherwise not be discovered?

It is a common question, "what is the use of real analysis", and the answer is usually "it adds rigour to our mathematical tools and machinery to make sure that they work without just saying they do". ...
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1answer
44 views

Is gaussian elimination “used”?

According to the book Linear algebra and its applications by Strang, "(The) good method is Gaussian Elimination. This is the algorithm that is constantly used to solve large systems of equations". Is ...
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1answer
44 views

Mathematics of war references

I have an upcoming talk in on data science. Now a ways such topics have been hijacked by talks on the use of machine learning. Deviating from the trend, I want to focus of core advancement of ...
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25 views

“Gaps in the Mats” problem

Problem Background* The mat at your karate dojo composed of 160 square interlocking foam tiles. Along each edge of each tile, there are has five "teeth" (10cm long) and five spaces-for-teeth (again ...
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What is considered to be a Heap’s law?

I’m not sure if this is more physics question than mathematics but anyways. Something is usually said to follow Heap’s law if it is given as a function $V(n)=K n^b$, where $b$ and $K$ are constants (...
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1answer
28 views

How to convert an instantaneous mortality rate to a weekly mortality rate

I want to convert an instantaneous mortality rate that is reported per year (actual value = $0.58y^{-1}$) into a weekly mortality rate. This answer gives the formula as $j=(1+i)^{1/12}-1$ where $j$ ...
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1answer
59 views

Were the wagers in the June 3, 2019 Final Jeopardy! round rationale?

The long-running U.S. television program Jeopardy! is a trivia question-and-answer (or answer-and-question) game show, involving three players competing to be the fastest to correctly answer questions,...
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2answers
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searching for function composed of s(x) + x with reasonably efficient inverse

To model my data, i need a function that resembles $f(x) = s(x) + x$ with $f : \mathbb{R} \rightarrow \mathbb{R}$, where $s(x)$ is a sigmoid-like function with co-domain $(0,1)$. So if we look at the ...
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17answers
7k views

What is a simple, physical situation where complex numbers emerge naturally? [duplicate]

I'm trying to teach middle schoolers about the emergence of complex numbers and I want to motivate this organically. By this, I mean some sort of real world problem that people were trying to solve ...
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1answer
50 views

Real life application of Cyclic group [closed]

The encryption in Caesar cipher given by: $E_k(P)\equiv P+k\,(\mathrm{mod}\,26)$, where $P$ is the plain text and $k$ is the shift key. and The decryption in Caesar cipher given by: $D_k(C)\equiv C-k\...
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1answer
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Areas of Applied Combinatorics

I love combinatorics, but do not really want to do pure math exclusively. I like the format of pure math (that is the theorem-proof-theorem-proof format), but would also like what to do research that ...
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2answers
108 views

Partial Differentiation of an equation using implicit differentiation confusion

I wanted to ask a question about implicit differentiation in partial differentiation. When I was at school, I remember partial differentiation as something like this: When you have a function ...
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3answers
27 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?...
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0answers
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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 ...
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2answers
49 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 ...
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0answers
10 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 ...
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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 ...
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1answer
35 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 ...
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2answers
257 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 ...
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0answers
32 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 $\Re^2$, ...
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1answer
70 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 ...
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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 ...
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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 $β$?
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1answer
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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 ...
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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\...
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1answer
51 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 $f(x)$ ...
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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 ...
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2answers
62 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 ...
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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 ...
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0answers
27 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 ...
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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, ...
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0answers
13 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 ...
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1answer
61 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 ...
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1answer
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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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1answer
63 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 ...
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72 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 ...
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1answer
43 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 ...
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1answer
133 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 ...
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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 ...
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77 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?
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1answer
52 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 [...
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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 ...
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8answers
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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/...
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1answer
48 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
413 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 ...
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1answer
36 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)^...
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0answers
63 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 ...
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1answer
37 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 ...