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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18 views

how to solve these sort of problems

This problem was asked in Codeforces. This has been asked here too. The question is You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three ...
0
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0answers
14 views

Weighting with restrictions, but no clear objective function?

Here is the problem: I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$ In the traditional way, the weight of each share is ...
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1answer
31 views

could someone tell me the answer… [on hold]

A physiologist wants to test the effects of exercise and meditation on blood pressure. She devises four different exercise programs and three different meditation programs. If she wants 10 subjects ...
-4
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0answers
16 views

How to use MRUnit [on hold]

I konw that we can use MRUnit to test our mapreduce program, so I downloaded two files: "apache-mrunit-1.1.0-hadoop2-bin.tar.gz" and "apache-mrunit-1.1.0-hadoop2-src.tar.gz", but I don't know what to ...
0
votes
1answer
24 views

Orthogonal parameterization

Consider the function $$f(a,b,c,d):=\frac{\left(a^*\right)^2b^2-\left(b^*\right)^2a^2+\left(c^*\right)^2d^2-\left(d^*\right)^2c^2}{a^*a+c^*c}$$ With complex parameters $a,b,c$ and $d$ Now find any ...
1
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1answer
20 views

How to set up problem involving Poisson RV

Consider an example where customers entering a store is a Poisson random variable with $\lambda=15$. How do you find the probability that 100 or fewer people will walk into the store in any five-day ...
0
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0answers
6 views

$\frac{dy}{dx}=\sum_{k=1}^{\infty}a_k(m-k)x^{m-k-1}$ or $\frac{dy}{dx}=\sum_{k=0}^{\infty}a_k(m-k)x^{m-k-1}$

If I have $y=\sum_{k=0}^{\infty}a_kx^{m-k}$ ,then is $\frac{dy}{dx}=\sum_{k=1}^{\infty}a_k(m-k)x^{m-k-1}$ correct because ..I'm confused whether $k$ should start from $0$ or from $1$. Please ...
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0answers
22 views

Help with a matrix problem

I'm stuck with the following matrix problem: Consider $A = $$\{ X \in \mathcal{M}_2(\mathbb{C})\ \mid X = \left( \begin{array}{ccc} a & 0 \\ 0 & b \end{array} \right); a, b \in \mathbb{C}; ...
0
votes
1answer
23 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
0
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0answers
20 views

Excercise: Find the volume of the parallelepiped

Find the volume $V$ of the parallelepiped whose four adjacent vertices are the points: $A = (−2, 1, 0)$, $B = (2, 3, 2)$, $C = (1, 4, −1)$, and $D = (3, 6, 1)$. I know how to find it with three ...
0
votes
2answers
37 views

Solving an unusual equation

I need to find a real number $n$ such that $n > 1$ and: $$ \sum_{k=1}^\infty \frac{2^k}{n^k} = \frac{n-1}{n} $$ Ideally, I'd find the minimum such $n$ (if more than one exists), but really, any ...
0
votes
0answers
42 views

Finding examples before solving

So I've been solving some contest problems,and most of them require a solution in order to be solved. For example $$S_n=\left\{{n\choose n},{2n\choose n},{3n\choose n},\ldots,{n^2\choose n} \right\}$$ ...
0
votes
1answer
3 views

Discrete algebra and exponents (See body text)

Let $a,b\in\mathbb{Z}^+$. If $a \equiv b\bmod 49$, and $\gcd(a,49) = 1$. How can I find any positive integer $n > 1$, so that $b^n\equiv a\bmod 49$? I'm completely stumped by this. I've been ...
2
votes
1answer
53 views

Special feature of the function f(z) = $|i + z|^2 + az + 3$

I have to solve following problem: Find all the values of a (a is a real number) that the function f : $f(z) = |i + z|^2 + az + 3$ (z is a complex number, i is an imaginary unit) has a following ...
2
votes
1answer
43 views

Problem about problem solving

I am having some problems on how to solve a problem.When I read a chapter on say group theory or real analysis,I feel that I have grabbed the concepts quite well,but when I start solving exercises ...
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1answer
6 views

Obtaining an expression between $s'(n,r)$ and $s(n,r)$

I've a doubt in this: We're given $[x]_n=(x)(x-1)\ldots (x-(n-1))$ and $[x]^n=(x)(x+1)\ldots (x+n-1)$ . Now as we can write : $[x]_n=(x)(x-1)\ldots (x-(n-1))=a_0+a_1x+a_2x^2\ldots ...
4
votes
1answer
66 views

No. of integral solutions of $x_1+x_2+x_3+x_4=20.$

I've to solve a no. of questions of this type but don't get how to do it: Determine the no. of integral solutions of $x_1+x_2+x_3+x_4=20.$ given the constraint that $$1\leq x_1\leq ...
-3
votes
1answer
24 views

Compound Interest [closed]

Suppose you are solving a problem involving compound interest. How do you know whether to determine the amount or present value of a given sum of money? Hope you can answer my question, thanks in ...
2
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2answers
82 views

Difficulty understanding the solutions to $x'' = -\omega^2 x$

For some reasons involving physics, I'm supposed to consider the equation $x'' = -\omega^2 x$. Normally, I would say the solutions are of the form $x = A \cos(\omega t + \phi)$. But when $\omega = ...
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2answers
45 views

Damped simple harmonic oscillator, phase space

I want to calculate and draw the phase space trajectory of this damped harmonic oscillator: $$\ddot{x}+\gamma\,\dot{x}+\omega^2x=0$$ for the two cases $\gamma=2\omega$ and $\gamma=\omega$. I'm ...
4
votes
2answers
115 views

I have used Cauchy and Jensen. It is not helping me very much. Advice on solving this problem.

Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$ \frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $$ for each ...
1
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2answers
71 views

How to teach Critical Thinking

I am currently tutoring a few students in an entry level physics course and had some trouble recently when it comes to helping them with problem solving. The students I am helping don't have many ...
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4answers
199 views

100 sequential parking spaces

In my high school's math club today, we explored but did not solve this interesting problem: 100 autonomous robotic vehicles enter a warehouse in arbitrary order to park. Inside the warehouse, there ...
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1answer
71 views

How can I find x and z if: $\sqrt{(x-20)^{2} + (5-30)^{2} + (z-40)^{2}} = 100$ and $x \sqrt\frac{1}{6} + 5\sqrt\frac{1}{3} + z \sqrt\frac12= 0$?

How can I find x and z if: $\sqrt{((x-20)^{2} + (5-30)^{2} + (z-40)^{2})} = 100$ and $\left(x\times \sqrt\frac{1}{6} + 5\times \sqrt\frac{1}{3} + z\times \sqrt\frac{1}{2}\right) = 0$ ?
1
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4answers
34 views

How can one isolate x in a formula of the form:$ (x-20)^{2} = -(y-40)^{2} - 525$?

I am trying to isolate x in the equation $$(x-20)^{2} = -(y-40)^{2} - 525.$$ How can I do it?
1
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0answers
30 views

no. of regions a plane is divided into by $n$ lines in general position

My notes state the Counting process for knowing no. of regions a plane is divided into by $n$ lines in general position := Let $h_1(n)=$ No. of parts a line is divided by $n$ distinct ...
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2answers
25 views

Show that Mandelbrot set is contained within the closed disc of r=2 [closed]

Show that the Mandelbrot set is contained within the closed disc of radius 2 around the origin. How do I show this?
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3answers
35 views

How to solve $\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$

I have a problem with solving following equation: $$\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$$ (where $a$, $b$ are real numbers and $i$ is an imaginary unit) I tried to simplify its left side ...
0
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0answers
16 views

Bounded/Unbounded sets. [Mandelbrot set]

This is the last question from my assignment. For Part a I have: $z_{n+1}=z_n^2+c$ $\Rightarrow c =z_{n+1}-z_n^2$ $\Rightarrow |c|=|z_{n+1}-z_n^2|=|z_{n+1}-z_n^2||-1|=|z_n^2-z_{n+1}|$ ...
1
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1answer
25 views

Understanding $\Delta(\vert f \vert ^p)$ when $f$ is holomorphic, $p>0.$

Let $\Delta$ denote the Laplacian. I am trying to prove that if $f=u+iv$ is holomorphic on an open set $U\subset \mathbb{C}$ and $f$ is nonvanishing, then $$\Delta (\vert f\vert^p)=p^2\vert ...
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0answers
25 views

Solving N for HN=0, Given H is a special type of skew symmetric (n x n, n is a odd number) matrix.

Solving $N\ \mathrm{for}\ H \times N =0$, given $H$ is a special type of skew symmetric matrix $(n \times n, n\ \mathrm{is\ an\ odd\ number}\ n=2k+1)$, 0 on diagonal and 1, -1 in off-diagonal ...
3
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3answers
181 views

How does one spot an error in a math proof?

I hope this is not a dumb question but I truly would like to know: How do you know when a proof breaks down and when an error has occurred?
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0answers
59 views

Terence Tao's problem solution

Suppose you are trying to get from one end $A$ of a terminal to the other end $B$. (For simplicity, assume the terminal is a one-dimensional line segment.) Some portions of the terminal have moving ...
5
votes
1answer
72 views

When is the next palindrome?

Okay, this is more just for fun than anything else. I'm driving in my car today, (true story) and my odometer is about to hit $81,818$. So, being a math nerd and all, I immediately see the pattern ...
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0answers
24 views

Mathematical Rube Goldberg problem

Is there a book or website that has mathematical rube goldberg-style puzzles? In other words, puzzles that require you to compute something, then compute something based on that, and then iterate for ...
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2answers
35 views

Second Order Partial Differentiation

I don't have a clue on how to start this question. I have a feeling I will need to use the Clairaut's theorem: $f_xy=f_yx$ Can anyone advise?
1
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2answers
71 views

How to Think Better

I just took a quiz and am dumbfounded by my lack of insight. Consider what kind of idiot I'd have to be to do the following: Point A = (8,-15) and point B = (-8,15). P is the locus of points (x,y) ...
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0answers
58 views

Finishing a problem using equalities

This is my problem: Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$\frac{a^{n+2}}{a^n + (n-1)\,b^n} + \frac{b^{n+2}}{b^n + (n-1)\,c^n} + \frac{c^{n+2}}{c^n + ...
1
vote
1answer
24 views

Train distances leaving at certain times

A train leaves Boston to Fort Lauderdale traveling at $125$ mph. An hour later, another train leaves Fort Lauderdale traveling to Boston at a rate of $140$ mph. When the two trains meet each other, ...
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1answer
31 views

Number of Chess Moves that a piece is lost

Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you ...
4
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2answers
128 views

finding the difference of perfect squares

Find the difference between the smallest perfect square larger than one million and the largest perfect square smaller than one million. I did not want to use a calculator for this question. I ...
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0answers
56 views

Least sum of power of distances

Let $n$ points in a $3$-dimensional space. Find the point $X$ that minimizes the sum of distances $\|A_1X\|^q+ \|A_2X\|^q + ... +\|A_nX\|^q $ (where $q \in \mathbb{Q}$). Are there any general ...
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0answers
21 views

Criticise work with simple graphs & problem solving

So I'm studying graph theory at the moment and would like some constructive criticism or thoughts on my method. The problem can be formulated as follows. I'm looking for someone to verify my answer as ...
3
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1answer
56 views

Application of the Green-Tao theorem

I am currently trying to find some good exercises in analytic number theory, suitable for undergraduates. I have mentioned the Green-Tao theorem for arithmetic progressions of primes but I am ...
1
vote
1answer
28 views

Derivative Functions [closed]

Consider $f(x)= ax^2 + bx$ where $a$ and $b$ are real numbers. If $f(1)=-1$ and $f'(-1)=-7$, find the values of $a$ and $b$? I genuinely do not understand how to do it! Please help
2
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1answer
24 views

Distinct elements in the Union and Intersection of A and B

Take a set $x$ with $10$ distinct elements. Rule: Everytime you have two subsets, $A$ and $B,$ you also have $A\cup B$ and $A \cap B.$ What is the maximum number of subsets you can have such ...
3
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1answer
58 views

How do I solve $x=\log^e{(x+1)}$ analytically?

How do I solve the following, analytically? $$x=\log^e{(x+1)}$$ It looks like it should be simple, but whether I take the $e$th root of each side or take the $\log$ of each side (ending up with a ...
1
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0answers
31 views

How to solve this Ricatti-like ODE

I have been trying to solve the following ODE \begin{equation*} \dfrac{d\pi}{dx}x=c_1+\pi(x) c_2 + \pi(x)^2(c_3-x), \end{equation*} where, for every $i=1,2,3$, $c_i$ is a constant real value. ...
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2answers
27 views

Lottery problem - Chance of 4 out of 5 balls matching?

In a lottery, an urn contains 40 balls that are numbered 1, 2, ..., 40. Each week, 5 balls are drawn from the urn without replacement. To enter, one chooses 5 numbers. Anyone who correctly predicts ...
4
votes
2answers
170 views

Least sum of distances

Problem: Let $A, B, C, D$ be points in a $3$-dimensional space. Find the point $X$ that minimizes the sum of the distances $AX+ BX + CX + DX$. Context: During a course, I was assigned a ...