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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14 views

Showing complex transformations in a fluid way

It says it all in the title: I need to show how simple complex transformations (translations and dilations, or even both) affect shapes on the complex plane in a "fluid" way – that is, creating some ...
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0answers
16 views

Minimal and maximal problem

Cuboid with contlstant volume $V$ its base is a rectangle length $nX$, width $X$ The whole area of cuboid is $A$ and $A$ was minimal area Prove with differentiation that $A^3n=54 V^2(1+n)^2$
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3answers
35 views

Mathematics for Guidance, navigation and control

I'm finishing my math degree this week and have been looking for some subject to practice and study on my own while I'm doing some work as a programmer. I'm interested in getting my master's later but ...
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1answer
33 views

Where i am going wrong in finding normal to curve?

The question is Find the perpendicular distance between the normal to the curve $$x=a\cos t+at\sin t, y=a\sin t-at\cos t$$ and the origin. Equation is given in parameterized form. My attempt ...
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1answer
134 views

Which numbers are necessary?

The Greeks were initially convinced that all numbers were rational until upon pain of contradiction were forced to accept that $\sqrt{2}$ was irrational and needed to be included in our number system ...
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31 views

Math / Physics - Curcular motion [closed]

What is the maximum speed a car can turn a 50m radius corner if the corner is banked at 15 degrees and has a coefficient of friction of 0.3?
2
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1answer
44 views

What practical purpose — or application — do directrices serve?

In Calculus II (and briefly in Trigonometry, if I remember correctly) the concept of a directrix began poking its head around conic sections. While covering parabolas, ellipses, and hyperbolas, the ...
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1answer
41 views

Applications of the wave equation

I've recently started to take interest in PDEs and how to solve them, and I'm wondering a bit about real life applications of the wave equation. So far I haven't found anything about practical ...
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32 views

mathematical terms with fractions and variables - usage in daily life?

what usage do algebraic fractions (monomial or polynomial) have in our life? Are there specific professions that deal with them now and then? Where exactly in technology do they have their very own ...
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0answers
29 views

Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... $$u_{t}=u_{tt}+2(t+1)+x(1-x) , ...
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0answers
18 views

Applications of Integration - Work Done by a Variable Force

Question states: "A 20-foot chain weighting 5 pounds per foot is lying coiled on the ground. How much work is required to raise one end of the chain to a height of 20 feet so that it is fully ...
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0answers
13 views

application of integration in graphics

Is Integration used in animation/computer graphics? If yes, then how it is used. A couple of example would be great . Thanks
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1answer
48 views

Area bounded by$ y^2=x^2(1-x^2)$

Find the area bounded by $y^2=x^2(1-x^2)$? I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
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1answer
35 views

Find the volume obtained by totating the area formed by $y=x$ and $y=\sqrt{x}$ about $y=1$

The questions asks us to find the volume of solid formed when the area between $y=x$ and $y=\sqrt{x}$ is rotated about the line $y=1$. I understand that a cone is formed. Now, to find the volume, I ...
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3answers
30 views

Practical examples of tank mixing problems?

In calculus and differential equations, a standard example of word problems are mixing problems, with some number of tanks, and brine often being an output of the system. With one tank, I can imagine ...
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1answer
28 views

Unique solution for circuits in Linear Algebra

A standard application of Linear Algebra is circuits and Kirchhoff's Laws. Does anyone know of a proof of uniqueness of a solution of a system given by these laws? There are many, many examples, but ...
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0answers
27 views

Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a ...
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1answer
89 views

What's the real life purpose of Knuth arrows?

I recently read about Knuth's Arrows. Didn't even know those operations existed. My questions is: Do they have real-life applications? Most of the times a mathematical development follows a real-life ...
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1answer
9 views

Adding two functions represented by a table of values with a different step size?

Let $f(t)$ be some numerically obtained $T$-periodic function represented by a table of values over one period or a set of points $(t, y)$ with a time step $\Delta t.$ Now let's change the ...
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2answers
37 views

The shortest total length of wire that can be used with a weight.

Suppose a weight is to be held $10 ft$ below a horizontal line $AB$ by a wire in the shape of a $Y$. If the points $A$ and $B$ are $8 ft$ apart, what is the shortest total length of wire that can ...
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0answers
12 views

Gini Index vs. Revenue for 124,587,000 people and $61,129,151,690,805.40 base

I have a question, given that the gini index is geometrically the ratio between the area enclosed by even income distribution in the United States and actual income distribution, and the area between ...
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3answers
99 views

Why does the Elo rating system work?

The Elo rating system is used to rank players in games such as chess. I can find plenty of explanations online of how to compute someone's Elo rating, how to actually crunch the numbers in practice, ...
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0answers
35 views

What are useful mappings (operators) in image reconstruction

I'd like to ask the technician mates to provide some information regarding mappings and image reconstruction operators. Please, if possible, provide some articles and helpful discussions about useful ...
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2answers
36 views

Probability of survival for system

Consider a system with three identical components and their fault rate is exponentially distributed with $\lambda > 0$. The system needs all three components to function (series system). If you ...
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0answers
32 views

Book recomendation for studying applied Differential Geometry and Topology

What are some good books(or notes in the internet) for (self)studying applied topology and applied differential geometry?
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1answer
33 views

Tropical geometry: practical applications?

In 1960, E. Wigner published a paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Theoretical mathematical structures pave the way to further advances and ...
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1answer
41 views

Fourier Analysis and its applications [duplicate]

My question has two parts: $1)$ Could anyone explain in simple terms what a Fourier Transform is? $2)$ What are some of the applications of Fourier Analysis in the field of high school mathematics? ...
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0answers
20 views

Applications of Khatri-Rao matrices

I'm interested in what applications there are for Khatri-Rao matrices, and in particular for solving linear systems of equations involving Khatri-Rao matrices. A Khatri-Rao matrix is a block matrix ...
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1answer
42 views

Constant Force Pendulum (undamped)

How does one sketch the derivation of the equation of motion for a planar pendulum of length l and mass m in constant gravity g, subject to a constant torque force F (directed along the tangent to the ...
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0answers
28 views

What are examples of multi-valued mappings in the real world? [closed]

I would like to know about some examples of multi-valued mappings in the real world. Like for example, a function that relates the set of signals emitted by bats and the echo received from nearby ...
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1answer
15 views

Show that if $Q'$ is any point on the line of action of $F$, then $PQ × F$ = $PQ'× F$

If a force $F$ is applied to an object at a point $Q$, then the line through $Q$ parallel to $F$ is called the line of action of the force. We defined the vector moment of $F$ about a point $P$ to be ...
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1answer
47 views

Why do at least half of all random orderings generate a binary space partition of size $n+4n\ln n$ in the random binary space partition algorithm?

Let $S$ be a finite ordered set of non-intersecting finite line segments in the plane. Let's randomly shuffle the elements of $S$ such that each possible permutation of those elements has equal ...
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1answer
28 views

applications of (topological and algebraic) commutative diagrams in organic synthesis

In algebraic topology, there are a lot of commutative diagrams and commutative diagrams up to homotopy. Different ways of compositions of maps in a commutative diagram are equal or homotopy ...
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2answers
57 views

Find the work. Application to physics

A trough in a shape of a semicircular cylinder , is filled with water whose mass density is 1000 $kg/m^3$ . Suppose the water was initially filled to a depth of 3 m. Set up an integral for the work ...
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0answers
27 views

In search of a College Leve Pre Algebra Applications Textbook

I am looking for a textbook at the college level that mainly focuses on applying algebra to situations. I want students to know how to set up the equations, not just solve them.
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13 views

Applications of $\{ e^{i\lambda_n t}\}_{n\in\mathbb Z}$ for $\lambda_n\in\mathbb C$.

The system $\{ e^{i\lambda_n t}\}_{n\in\mathbb Z}$ is a Riesz basis for $L^2(-\pi,\pi)$, for $\lambda_n\in\mathbb R$ and under Kadec's condition; see: M.I. Kadec, The exact value of the ...
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1answer
21 views

How to develop an algorithm to prioritize set members based on various criteria

I tried looking for responses and Google. It has been a while since I used math to any capacity and the lack of application is only surpassed by my inability to articulate the concepts. That's my ...
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1answer
28 views

Yet Another Question Concerning Conditional Probability v. Intersection of Events

I know that this is a common problem for students, and evidently I'm no exception; but I simply cannot wrap my head around the difference between when we desire the probability of an intersection of ...
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4answers
110 views

What are some applications of Chebotarev Density Theorem?

Let $L/K$ be a Galois extension of number fields and let $\mathcal{C}$ be a conjugacy class in $Gal(L/K)$. Let $\mathbb{P}(K)$ be the set of all prime ideals in $K$ and let ...
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2answers
77 views

How applicable is Goldbach's conjecture to real world scenarios? [closed]

In what scenarios is Goldbach's conjecture, that all even numbers greater than 4 are the sum of two prime numbers; a natural conjecture to research?
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0answers
18 views

Consider a fluid with velocity $\mathbf{q}=(x,y,z^2)$. Is this fluid incompressible at $z=-1$?

I have answered the question but I'm wondering about the case where $z=-1$. Incompressible $\implies \space \nabla \cdot \mathbf{q}=0$ $\therefore $ we have $2+2z=0 \implies$ that the fluid is ...
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1answer
46 views

If $f(x)$ is continuous on $[a,b]$ and differentiable on $(a,b)$ then $(\frac{f'(c)}{3c^2}) = (\frac{f(b)-f(a)}{b^3 -a^3})$ where$c ∈ (a,b)$.

If $f(x)$ is continuous on $[a,b]$ and differentiable in $(a,b)$, then $(\frac{f'(c)}{3c^2}) = (\frac{f(b)-f(a)}{b^3 -a^3})$ for some $c ∈ (a,b)$. I have tried in this manner: Let us assume ...
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2answers
74 views

UnFlattening a 1/2 Triaxial Ellipsoid: Reconstructing a Squashed Tortoise

BACKSTORY: I have a flat tortoise. I need to figure out its original dimensions. I'm a paleontologist, and the site I'm working at has produced a [Hespertestudo crassiscutata], a giant tortoise ...
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0answers
19 views

The 1,1 coordinate of a Leslie matrix

I'm reading about Leslie matrices and I think I get the main idea. In the matrix, for instance, $$ \left( \begin{matrix} .2 & 1.1 & .5 \\ .9 & 0 & 0 \\ 0 & .7 & 0 ...
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1answer
57 views

How can I curve a test grade knowing only the average and the highest score?

I am trying to get a raw score for my test grade, but I don't know anything about the distribution of test grades; all the information I have is the average and the highest score (and of course my own ...
0
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1answer
52 views

applications of Multivariate Calculus in computer science

I am currently studying Multivariate Calculus (Larson and Edwards book). I want to do a project in computer science to see some nice applications of things I am learning. Any specific source of ...
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2answers
30 views

Exploiting symmetry to prove results

Given a real number number $n$, find a partition whose product is least / max. I.e: $n=a_1+a_2+a_3+ \cdots+a_m$ (Here $m$ is a variable as well) What can the maximum/minimum value of $a_1a_2a_3\cdots ...
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1answer
46 views

is this natural probability, statistics, or fraud

I think I may have uncovered a corrupt box draw practice in greyhound racing. Can someone please help me find the truth using math? It is rumored that one trainer is being given preferential box ...
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2answers
91 views

Interesting real life applications of elementary mathematics

If you teach mathematics to future highschool teachers, you often feel that they are bored because what they learn at university does not have much to do with what they will have to teach in school, ...
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1answer
54 views

Work problem - chain hanging on the ground

I am a bit tripped up on the following work problem -- A 30 ft long chain is hanging from one end on a hook, 25 feet above the ground; naturally, this means 5 feet of the hook are on the ground ...