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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Continuous Compound

You own an antique that is currently worth 1500, and whose value increases linearly at a rate of 175 per year. If the prevailing interest rate remains constant at 5%, per year compounded continuously, ...
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1answer
29 views

LN word problem

measurement of a child's ability to learn is given by the function $$L(t)=\frac{ln(t+1)}{t+1}$$ where t is the child's age in years, for $0 ≤ t ≤ 5$ At what age does a child have the greatest ...
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Is there a polynomial $p$ such that it is bijective and $ p: \mathbb{Q}^n \rightarrow \mathbb{Q}$ for $ n>1$ ??

Let us define a polynomial $p$ defined as follow $$p: \mathbb{Q}^n \rightarrow \mathbb{Q}.$$ I acrossed this question in mind. Is there a polynomial $p$ such that it is bijective and $p: ...
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1answer
40 views

Finding the Zeros

A word problem gives this cost equation and asks to find the x where the average cost is minimized, to do so, I need to solve for average cost and derive it and then set it to zero and solve; $c(x) = ...
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1answer
58 views

How and why do rumors/gossip spread? [on hold]

I should clarify what I mean by gossip (this is taken from wiki): Idle talk or rumor, especially about the personal or private affairs of others. That seems accurate enough, though alternative ...
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1answer
26 views

Can anyone answer this with the steps of Assumption > Given > Formula > Solution?

The height in feet of a bottle rocket is given by the function $h(t)=160-16t^2$, where $t$ is the time in seconds. How long will it take for the rocket to return to the ground? What is the height of ...
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2answers
79 views

What application/deeper meaning do countable and uncountable infinities have? [on hold]

Georg Cantor proved that there are two different infinities but what application does this proof have? Is this result used in some other more useful theorem?
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3answers
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Modelling interest with differential equations (Interpretation)

I am having trouble interpreting the meaning of this differential equation model for interest on an account. The problem is as follows: Assume you have a bank account that grows at an annual ...
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0answers
18 views

Ranking event winners with a portion of total participants.

This may not be the place for this question, but its the one place I know where I'll get solid mathematical answers: I'm looking for a system that ranks event winners, but it can't require everyone ...
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0answers
31 views

Fourier series & Fourier transformation [closed]

Tell me where we use Fourier series & transform in real life? Please mention an example problem which helps me to understand easily about Fourier series &Fourier transformation?
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1answer
43 views

Current applications of the central limit theorem for binomial distributions

The central limit theorem in the binomal distribution case, also known as the De Moivre–Laplace theorem was historically used to approximate the binomal distribution with the normal distribution. I ...
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2answers
48 views

Physical applications of Chebyshev's equation.

As reported by Wikipedia, Chebyshev's equation is the second order linear differential equation $$(1-x^2) {d^2 y \over d x^2} - x {d y \over d x} + p^2 y = 0 $$ where $p$ is a real constant. Has ...
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1answer
25 views

How do I calculate the gravitational force exerted by a thin ring of uniform mass M?

I'm working on a problem and can't seem to get it. Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ...
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4answers
56 views

The Significance of Linear Approximation

I want to know what makes linear approximation so important (or useful). What I am aware of in my current state of limited understanding is that linear approximation is one of the applications of a ...
1
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1answer
29 views

Probability distribution of the number of heterozygous sites

We'll consider a stretch of DNA on a chromosome and we'll be looking at specific sites that are at certain distances on from the others. The distance between any two sites is express in centiMorgan ...
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2answers
54 views

Why do left and right switch when direction is reversed? [closed]

If I make a left turn during a trip, it becomes a right turn on my way back. Why is this?
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2answers
414 views

Can any function represent something in the real world?

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
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2answers
63 views

Can car traffic be managed by mathematical formula? [closed]

How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula? ...
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10answers
684 views

What are the most prominent uses of transfinite induction outside of set theory?

What are the most prominent uses of transfinite induction in fields of mathematics other than set theory? (Was it used in Cantor's investigations of trigonometric series?)
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2answers
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The roots of $x^4+4x^3+5x^2+2x+2=0$ one root being $-1+i$ are [closed]

The roots of $x^4+4x^3+5x^2+2x+2=0$, one root being $-1+i$ are what? please solve this problem, i need the process of solution
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1answer
37 views

What are some Applications of Hermitian Positive Definite matrices?

I am learning about Hermitian positive definite matrices and the way that they can be decomposed with Cholesky decomposition. I have learned that these matrices deserve special attention for how often ...
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4answers
180 views

Applications of algebraic topology?

Terribly sorry if this has been asked, but I'm not about to search 382 pages of technical questions in the field. I am trying to develop a very basic understanding of what algebraic topology is ...
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0answers
23 views

Can I adjust linear growth of a a subpopulation to a linear decay of the general population?

I need to estimate the amount of CF patients in Poland in the next four years. I have: estimations of the Polish population for the future years a CF patients' register for the last couple of years ...
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1answer
58 views

Does measurability really matter?

I am studying applied math and I currently got stuck on proving that a function, which emerges in a model is measurable (Borel functon), so we can integrate it. I know, that there are examples of ...
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0answers
40 views

Optimisation Problem for Pipe Nesting

I work in a company where we are supposed to produce and send pipes using trucks to buyers. Pipes of smaller diameter can be nested inside pipes of larger diameter while sending to minimize number of ...
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2answers
74 views

Imaginary $\cos^{-1}$ value significance?

When I was bored in AP Psych last year, I jokingly asked myself if there was a cosine inverse of $2$. Curious about it, I tried calculating it as follows: $$ \begin{align*} \cos (x) &= 2 \\ \sin ...
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1answer
41 views

What languages does Zipf's law not hold for?

Despite reading on a book of mine that all languages of all times obeyed Zipf's law, the english Wikipedia article only says most. Is it correct? If so, is a counterexample known?
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Why we should study “sub-energy” function and what are its applications in mathematics?

I read some papers in optimization and I found this term "Sub-energy function" that is a new mathematical term to me. Aside from "its a large area in mathematics," why we should study it? What's its ...
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2answers
99 views

What's interesting in latus rectum?

I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical ...
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24 views

How to find an optimal solution for a missing player in a double-elimination tournament

Say that you have a double elimination tournament consisting of four teams with 2 players. Each of those teams of partners could be: (A,B), (C,D), (E,F), and (G,H), where A is B's partner, C is D's ...
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1answer
27 views

Finding $f-$invariant subspaces

How could you know, given a linear application $f:\mathbb R^n\to\mathbb R^n$, the $f-$invariant subspaces of arbitrary dimension? For example, let $f:\mathbb R^4\to\mathbb R^4$ with associated matrix: ...
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186 views

Physical meaning of linear ODE $xy''+2y' + \lambda^2 x y = 0$

As reported by Wikipedia - Sinc function, $y(x)=\lambda \operatorname{sinc}(\lambda x)$ is a solution of the linear ordinary differential equation $$x \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} + ...
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Research into the application of Jacobi matrices

The general real infinte hermitian Jacobi matrix is written in the form $$ \textbf{$J$}:= \ \left( \begin{array}{cccccc} b_1 & a_1 & 0 & \cdots & 0 & \cdots \\ a_1 & b_2 & ...
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Which argument in KL Divergence minimization?

The KL divergence $D_{KL}(p||q) = p^T\ln(\frac{p}{q})$ is not a distance measure because first of all it is not symmetric. In applications, one usually has a prior distribution, say $y$, and wants ...
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1answer
111 views

Why more than 3 dimensions in linear algebra?

This might seem a silly question, but I was wondering why mathematicians came out with more than 3 dimensions when studying vector spaces, matrices, etc. I cannot visualise more than 3 dimensions, so ...
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3answers
107 views

Puzzle: leaning a ladder at $45^\circ$ to a wall using only yourself

This question was asked to my friend in an interview. You are provided a ladder and are led to a wall. The ladder must be kept against the wall making an angle of $45^\circ$ with the floor. You are ...
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1answer
43 views

differential equation - rectilinear movement of a boat using propulsion

I have a problem in my differential equation book that I can't solve because it gives me data that I can't seem to fit in the equation that the book gives me. This is something that I just don't get. ...
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1answer
35 views

Non-STEM applications of Calculus? [closed]

I was talking with a friend, who is a liberal arts major, about the everyday applications of math. We agreed about how Algebra directly applied to the average person's life, but the only examples of ...
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1answer
39 views

Why is my phase correlation not equal to the real correlation?

If I understand the correlation theorem correctly, it states: $ f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\}, $ also called a phase correlation. Above ...
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A good book about theoretical ecology (Quantitative analysis of movement)

I would like to ask if anyone knows a good book to start studying animal patterns of movement. I am interested in exploring different approaches, in particular models in stochastic settings. I have ...
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0answers
26 views

[Levenberg-Marquardt]What is the link between positive-definiteness and well-conditioning?

Working on optimization problems through neural networks, I use the Levenberg-Marquardt algorithm. I have read this assertion that I do not understand : A positive definite diagonal matrix is ...
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0answers
24 views

Application of Bernstein's theorem

There is a theorem due to Bernstein related to analytic functions : If $f : ]0,1[ \to \mathbb{R}$ is an absolutely monotonous function (that is a $\mathcal{C}^\infty$ function such that for ...
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1answer
35 views

Mixture of mixtures.

I am formulating this problem for work, so it is important that I get it right. As of right now I am only considering the case where the number of chemicals is equal to the number of pre-made ...
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1answer
29 views

Mixing chemicals in ratios

I am trying to figure out a mixing problem and I'm stuck because it seems to have two levels. I'm going to write a simpler form here of the problem I am working on. Say that we have 60 pounds of a ...
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0answers
18 views

How to choose assymetry for KL divergence?

I have two 2D probability distributions of eye movements of two different images. Suppose I call the first distribution of Image 1: $P$, and the second distribution of image 2: $Q$. Since ...
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0answers
34 views

Math-a-magic: How to force all participants onto same color squares of checker board?

Setup Setup 3x3 checker board. X O X O X O X O X Rules Audience picks a random square on the board for their point of origin. [not sure if this ...
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2answers
88 views

Calculus - Finding the Linear Equation which equals area

I am really stuck on this question... I think it involves finding integration but am struggling to understand the concepts involved. I have attempted the equation $y=70$ through trial and error, ...
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0answers
38 views

Examples and applications of homogeneus models in model theory.

Does anyone know any specific examples or applications of homogeneus models, to model theory or any other branch? For example, an application would be that prime models are isomorphic in a countable ...
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0answers
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Fourier coefficients for pattern analysis

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
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19 views

Deriving the inverse of RGB to HSV transformation

Today we had the conversion from RGB to HSV coordinates and vice versa in a multimedia systems exam. And I was puzzled between the conversion. RGB and HSV are of course the color spaces. The ...