Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

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1answer
25 views

What area can this question be categorized into?

In a game of 12 players that lasts for exactly 75 minutes there are 6 reserves who alternate equally with starting players. It means that all players, including reserves, are in the game for exactly ...
2
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1answer
34 views

Need Help Building An Equation to Find an Angle for Zeroing on a Rifle Scope

My name is Michael, and I am trying to create a small video game. I am only in high school, so my math skills lack which is why I am here to find help from nice people! I am trying to find an ...
1
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1answer
43 views

Determinant of a matrix with binomial coefficients.

Let $n \in\mathbb{N}$ and $A=(a_{ij})$ where \begin{equation}a_{ij}=\binom{i+j}{i}\end{equation} for $0\leq i,j \leq n$. Show that $A$ has an inverse and that every element of $A^{-1}$ is an integer. ...
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0answers
31 views

Is there a better way to determine the function in the integrand?

I need to find $U(z)$ given that $\Delta\ll 1$. $$\int_{-\Delta/2}^{\Delta/2} U(z) \, dz = C$$ $C$ and $\Delta$ are constants. Since $\Delta$ is small I am just using $$ U(z) = C / \Delta\,.$$ It ...
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0answers
11 views

Correct distribution for cell visibility in 3D grid

I have 3D grid of cells. Each cell can be in two states: visible, not visible. The camera is positioned on the side and looks at the grid. Random variable X is defined as a number of visible cells in ...
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2answers
56 views

How to solve this integral and have arccos(…) as a result?

$$\int {\sqrt{\csc^{2}x -1}} \, d(\cos^2x)$$ I need to solve this integral in order to arrive to a solution that looks like $x= \arccos(...)$ The main substitution is already done, I don't know how ...
0
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1answer
53 views

A question from Hoffman's linear Algebra

the question is on Section 1.4 exercise 7, it says: find all solutions of $$2x_1 - 3x_2 - 7x_3 + 5x_4 + 2x_5 = -2$$ $$x_1 - 2x_2 - 4x_3 + 3x_4 + x_5 = -2$$ $$2x_1 - 4x_3 + 2x_4 + x_5 = 3$$ ...
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0answers
14 views

Steady state of advection diffusion

I am looking for the non trivial solution to the advection diffusion equation: \begin{equation} \frac{\partial}{\partial x}\left(D_x \frac{\partial c}{\partial x} - uc\right) ...
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3answers
174 views

How to solve this inequality, with the hypothesis more complicated than the conclusion?

Given $x,y,z \in \mathbb{R}$ and $x,y,z>2,$ I want to show that if, $$\frac{1}{x^2-4}+\frac{1}{y^2-4}+\frac{1}{z^2-4} = \frac{1}{7}$$ then, $$\frac{1}{x+2} + \frac{1}{y+2} + \frac{1}{z+2} \leq ...
7
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2answers
172 views

USSR Exam problem

I obtained this problem from here. A car starts from point $A$ towards $B$ at the same time as a motorcycle starts from $B$ to $A$ (but with a lesser speed). At the moment they meet, a second ...
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0answers
17 views

Weak Law of Large Numbers and Central Limiting Theorem problem

From past experience, a teacher knows that the result of an exam is a random variable, with average $75$ and standard deviation $8$. How many students must take the exam to guarantee, with a ...
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vote
4answers
32 views

Simple mod problem

It’s kind of a silly question but I can't find a simple way for finding the value of variable $d$ . $(5*d) \mod 8 = 1$ I normally just do this recursively by saying $d=d+1$ until I get the right ...
1
vote
1answer
18 views

Matrix representation in exponential form

So having worked out beforehand that $Λ(v) = \begin{pmatrix} γ&0&\frac{-γv}{c}\\ 0&1&0\\\frac{-γv}{c}&0&γ\end{pmatrix}$ where $Λ(v) ∈ SO(2,1)$ is a matrix representation of a ...
0
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1answer
89 views

How do pupils solve 2nd degree equations in Germany? (different from Spain)

I'm from Spain and in Spain the undergraduate pupils learn to solve a 2nd degree (i.e. quadratic) equation using the formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ but years ago I had a colleague who did ...
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2answers
31 views

Under what conditions would the function $\prod_{i=1}^{n}{\frac{r_i}{r_i - 1}}$ be decreasing with respect to $n$?

So I know that $$\frac{r}{r - 1}$$ is a decreasing function of $r$. My question is: Under what conditions would the following function be decreasing with respect to $n$? $$\displaystyle ...
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3answers
36 views

Problem leading simple equations

A sum of Rs. 8.85 is made up of 124 coins which are either 10 paisa coins or 5 paisa coins ; how many coins are there each Note : Rs. 1 = 100 paisas
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2answers
23 views

Problem leading equations

The question is : "A and B begin to play with 60$ each. If they play till A's money is double B's, what does A win?" Now i tried to solve it like they both have 60\$ each, then A got his money ...
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2answers
64 views

Defining the $L^2$ norm of a vector valued function

I am considering a collection of function of the type, $ f:[0,2\pi]\rightarrow \mathbb{R^2}$. I want to define the $L^2$ norm of the function in that space. I am defining the a norm of ...
0
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2answers
24 views

System of equations that I'm having trouble with

$a/(x+y) - b/(x-y) = 1$ $b/(x+y) + a/(x-y) = (b^2-a^2)/2ab$ The answer to the values of $x$ and $y$ are given as $x=a-b, y=a+b$. How is that achieved?
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0answers
23 views

General and sufficient condition of independence

I'm having troubles with this proof: Let $\{Z_i\}_{i\in\mathbb{Z}}$ be i.i.d. random variables with zero mean and unit standard deviation. For $(a_0, a_1, ..., a_r)$ a sequence of $r$ real numbers ...
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1answer
69 views

$\mathbb{A}^2\setminus (0,0)$ is not affine

I want to prove that $X = \mathbb{A}^2\setminus (0,0)$ is not affine. My attempt: If $\Bbbk[X] = \Bbbk[x,y]$ then $X$ is not affine since $(x,y) \subset \Bbbk[x,y]$ is a proper ideal, but $V(x,y) \cap ...
4
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1answer
47 views

Inverse Fourier transform of $\frac{1-e^{-2\pi ift}}{2\pi if}$

I would like to calculate the inverse Fourier transform of the following $$H(f) = \frac{1-e^{-2\pi i f t}}{2\pi i f}$$ Can anyone tell me and explain to me how to do that? I don't want just an ...
2
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0answers
44 views

Reference request - Problem book by subject

I'm looking for good problem textbooks for self-study. I know only of two of this sort: "Introduction to Measure Theory" by Terry Tao, and "Problems in Algebraic Number Theory" by Esmonde and Murty. ...
1
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1answer
66 views

Strange sum of random variables

So guys, I'm having this hard proof to solve in probability. I don't really know how to tackle it! Hope that someone can help. Let $\{Z_i\}_{i\in\mathbb{Z}}$ be i.i.d. random variables with zero mean ...
3
votes
3answers
95 views

What is the value of $a^4+b^4+c^4$?

Consider $a,b,c$ such that $a+b+c =1, a^2+b^2+c^2=2$ and $a^3+b^3+c^3=3$. Find the value of $a^4+b^4+c^4$, if possible. Trial: I observe that \begin{align} a^4+b^4+c^4 ...
1
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1answer
14 views

Solving a matrix for color manipulation

I'm making an application that deals with color transforms. The idea is that if you give it an RGB color and apply a color matrix transform it outputs another color. In this case I'm giving the color ...
1
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2answers
49 views

Can I use eigenvalues to find the inverse of a vector?

I have two 1D matrices (say dimension 1xn) called A and B. Multiplying these: A . B = M. Where M is a scalar. Knowing B and M, can I find A? One cannot take the inverse of a vector, but is it ...
3
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4answers
400 views

SAT Maths Question About Fractions

Whilst revising, a problem caught my eye and I cannot seem to find an answer. I am usually bad at these types of questions. On a certain Russian-American committee, $\frac23$ of members are men, ...
1
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1answer
55 views

Kill the creeps with minimum cost

Oz plays popular ARTS Dota 2. Invoker is one of the favourite Oz's heroes. Oz's skills are not perfect yet, so he uses only two spells - SunStrike and Tornado. Each of these spells takes some mana ...
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2answers
156 views

Proving $\sqrt{2}(a+b+c) \geq \sqrt{1+a^2} + \sqrt{1+b^2} + \sqrt{1+c^2}$

I've been going through some of my notes when I found the following inequality for $a,b,c>0$ and $abc=1$: $$ \begin{equation*} \sqrt{2}(a+b+c) \geq \sqrt{1+a^2} + \sqrt{1+b^2} + \sqrt{1+c^2} ...
2
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5answers
225 views

Help With SAT Maths Problem (Percentages and Numbers)

I usually solve SAT questions easily and fast, but this one got me thinking for several minutes and I cannot seem to find an answer. Here it is: In 1995, Diana read $10$ English and $7$ French ...
16
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2answers
169 views

$xf(y)+yf(x)\leq 1$ for all $x,y\in[0,1]$ implies $\int_0^1 f(x) \,dx\leq\frac{\pi}{4}$

I want to show that if $f\colon [0,1]\to\mathbb{R}$ is continuous and $xf(y)+yf(x)\leq 1$ for all $x,y\in[0,1]$ then we have the following inequality: $$\int_0^1 f(x) \, dx\leq\frac{\pi}{4}.$$ The ...
0
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0answers
29 views

Movement of birds - Acceleration, Velocity, Time and Displacement. Needed for an assignment

Hi so there are a quandary of birds sitting on a tree.There are $3$ teams observing the movement of the birds. Team $1$ observes that on their first flight the birds move a short distance across a ...
4
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3answers
163 views

Numbers with 2015

I like to build math problems; to solve the one below I should first find a certain square and use it in my solution. I would want to know if anyone can solve this problem otherwise. Thanks. ...
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0answers
30 views

A little bit more difficult problem regarding rooted plane trees

A question regarding rooted plane trees bothers me. We know that the number of rooted plane trees with $n$ nodes equals to $n-{th}$ Catalan number, that is $|Tn| = Cn$. But what is this number if we ...
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3answers
46 views

Simplifying $\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$

Simplifying $$\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$$ When I try, the numerator cancels out to $0$, yet the answer sheet says $(25-a)^2/10000$. Where am I going ...
1
vote
1answer
23 views

Fitting the closest coefficients in a system of millions of simultaneous equations?

I don't really know the correct terminology to describe this, but let's say we have many values of $(x_n, y_n, z_n)$. Also let's say that our description of 'many' means that $i$ ranges from $1$ to ...
2
votes
4answers
76 views

Solving equations with $x^x$ on any given side [duplicate]

How would you solve such an equation if it's infeasible to just start trying different $x$ values? Example: $$x^x = 6.$$
1
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4answers
37 views

Inequality for sides and height of right angle triangle

Someone recently posed the question to me for the above, is c+h or a+b greater, without originally the x and y lengths. I used this method: (mainly pythagorus) $a^2+b^2=c^2=(x+y)^2=x^2+y^2+2xy$ ...
1
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1answer
40 views

Help Obtaining Numerical Approximation of Lambert W Solution

I am studying a particular generating function $$\frac{2e^x}{e^{2x}+1+2x}$$ and I thought I would try to solve the equation $$e^{2x}+1+2x=0$$ to determine for what value of $x$ if any the function ...
3
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2answers
108 views

Solve first order nonlinear differential equations

I want to solve this nonlinear 1-st order ODE, $$\frac{1}{1+x}=(\frac{1}{x-y}-\frac{1}{y})\frac{dy}{dx}$$ I find it non-separable, and Wolfram Alpha does not give me a closed form solution, but the ...
2
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0answers
96 views

Cognitive processes involved solving IMO level problems [closed]

I am currently 16 years old and, though I'm obviously not as good as most of the people on this site, I have always been considerably better than most of my classmates in mathematics. This, of course, ...
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2answers
44 views

Finding the missing length

How do i find the ST?? What more information do I need? I used Pythagorean theorem, but I still can't find the answer.
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2answers
35 views

Traveling salesman problem (TSP): what is the Relation with number of vertices and length of the found route?

I know that there are many algorithms (exact or approximate) which implement the traveling salesman problem. I would like to know the relation between the number of the vertices (i.e., the places to ...
2
votes
1answer
143 views

Aliens to the Moon

$N$ Aliens want to reach their Moon ($D$ meters away), but they can only put on each other, making a vertical chain. Every $Alien(i)$ has an height $X(i)$ and a lenght of their arms $Y(i)$. ...
0
votes
1answer
21 views

Compute a basic Side of two rooms, given total Area and total perimeter

My Gf's professor asked her to solve this problem: Two square rooms have an area of $52m^2$. The two rooms have a perimeter of 40 meters. Given this, we need to compute the length of the side of the ...
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1answer
35 views

How long will it take for one of them or both of them?

One knight can storm a castle in 15 days. He and his partner can do it in 10 days. How long does it take the partner to storm the same castle alone? Pipe A can fill a pool in 5 hours, while pipe B ...
0
votes
1answer
103 views

The Area of shaded region in a circle

I'm having trouble solving this problem. I can't solve this. I don't know where and how to start. I don't know there is any formula for finding the area for this kind of shape, and if it did, I ...
1
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0answers
27 views

Essential singularity of c.c.(z)

According to my lecture notes, $z^*$ has an essential singularity (asterix denotes complex conjugate). However, it is not explained why nor at which point. Can anyone elaborate where the singularity ...
1
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3answers
66 views

$f(x)$ is a polynomial satisfying $2 + f(x)f(y)=f(x)+f(y)+f(xy)$, find $f(f(2)$), given $f(2)=5.$

If f(x) is a polynomial satisfying $2 + f(x)f(y)=f(x)+f(y)+f(xy)$, find $f(f(2))$, given $f(2)=5.$ ATTEMPT:- $f(f(2))=f(5)$, We can find $f(0)$,$f(1)$ and $f(1/2)$ to be $1,2$ and $5/4$ ...