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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1
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1answer
21 views

How to express combined discrete-continuous RVs in one pdf?

Let's say we have a random variable $X$ that behaves in two different ways where $X\sim$Bernoulli(1/3) AND $X\sim U(0,1)$. $X$ follows the Bernoulli distribution 25% of the time and the uniform ...
0
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0answers
8 views

Are there tools for presentation and vizualization of deduction?

I read that Kalish and Montague introduced a natural deduction method (http://en.wikipedia.org/wiki/Donald_Kalish), which can be easily implemented in software. Any other tools who can help a logician ...
0
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0answers
18 views

Solve equation with simplex method

I have equation below and I'm newbie to this method. Can you help me with tutorial or maybe with steps to solve this equation? I know I can use simplex tables, but I don't know a good explanation of ...
0
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1answer
18 views

$5$ General Planes make how many CLOSED SPACES?

Actual problem is How many spaces $5$planes divide a space into? and by some analogy and proof, I found that $5$planes divides a space into $26$spaces. in fact, I considered first "How ...
1
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1answer
33 views

straightforward calculus problem

Find the arc length of the graph of $\displaystyle \large x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$. Hint: Use symmetry with respect to the line $y=x$. Let $y=x$ intersect at $a$. So, $\displaystyle ...
-4
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1answer
37 views

equation solver online

can you tell me please if is there an online or software tool that will solve equations like $-8sin3x + 5cos3x = 4.3$ for $0< x <360$? that I will just type equations like the above and it will ...
0
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0answers
48 views

inclusion-exclusion principle help

Five people are seated around a circular table with five identical seats. Each person wishes to move to a different seat than their current one. By applying the inclusion-exclusion principle, find the ...
1
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2answers
49 views

Finding supremum in $S=\{q\in\Bbb Q:q<x\}$ [closed]

Let $x$ be in $\Bbb R$ and $S=\{q\in\Bbb Q:q<x\}$. Prove $x=\sup S$. Don't understand how to approach this or solve this.
2
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4answers
140 views

If $\omega + 1 = \omega$, find $\omega$ ($\omega \not= - \infty$ or $\infty$)

If $\omega + 1 = \omega$, find $\omega$ ($\omega \not= - \infty$ or $\infty$). It does not have to be a real number. My teacher gave us this question just to play around with, and my first ...
1
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1answer
26 views

Finding the square roots of a complex number.

Express $z=4\sqrt2(1+i)$ in modulus/argument form. Hence find the two square roots of $z$ and mark their representations on an Argand Diagram. So far I've worked out the mod/arg form of the ...
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0answers
25 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
16 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 ...
0
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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
25 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 ...
2
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0answers
11 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 ...
0
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0answers
24 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
37 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
25 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 ...
1
vote
2answers
45 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
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0answers
46 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
7 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
54 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
51 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 ...
1
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1answer
7 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 ...
5
votes
1answer
69 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 ...
4
votes
1answer
139 views

The no. of ways dividing a polygon with $n+1$ sides into triangular regions…

Please if any one can help me explaining this concept, I can't proceed further due to this.... Let $h(n)$ denote the no. of ways dividing a convex polygon region with $(n+1)$ sides into ...
2
votes
2answers
83 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 = ...
1
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2answers
51 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
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2answers
130 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
84 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 ...
7
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4answers
237 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 ...
0
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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
37 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 ...
0
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2answers
26 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?
0
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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 ...
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0answers
20 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
vote
1answer
28 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 ...
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3answers
192 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
63 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
79 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
25 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 ...
0
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2answers
39 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
75 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
26 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, ...
0
votes
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
130 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 ...
2
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0answers
57 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 ...