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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2answers
75 views

Can someone help out with this geometry problem plase?

I have a pyramid $P$ that has a square pyramid and each of its 4 triangles is equilateral.I also have cuboid $C$ with height 25 and width 50, something like this: So the volume of $C$ is $25 . 50 . ...
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2answers
27 views

Define variable value - General Math

I met a little problem in one of my Math - tasks. Its quite simple: I get to cases = case 1: $(476\cdot x)+220$ case 2: $(278\cdot x)+675$ The variable x have to be a value, so case 1 and case 2 ...
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1answer
51 views

What kind of formula would I use to get all possible outcomes?

I am into a CCG, and I got a question come to mind "how many possible out comes are there for deck combinations?" The game is broken into three: Main Character (6 cards available, only one deck), ...
0
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1answer
190 views

How many number of buses that the car encounter?

A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of ...
0
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1answer
27 views

Solving the following equation

What is the easiest way to solve the following equation for g in terms of x? I seem to be going in circles, and don't know how exactly to deal with the $\pm$ symbol. Equation: $$\pm \sqrt{2}x + ...
1
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2answers
212 views

Prove that for any integer $k>1$ and any positive integer $n$, there exist $n$ consecutive odd integers whose sum is $n^k$

Found these problems in a problem book and got stuck. The book doesn't have solutions to I've come here for help. (1) Prove that for any integer $k>1$ and any positive integer $n$, there exist $n$ ...
2
votes
3answers
266 views

Where is the lost dollar?

Somebody explained me this problem, but I am not sure to understand what is wrong. ...
0
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1answer
37 views

Proof of transformations to find an approximate value

I have no idea what this questions is asking, or how to go about solving.. can someone please help? Answer:
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1answer
71 views

formula to apportion cost of transport among three people in a liftshare

I share lifts with Sed and Awk to work every day. We tally journeys owed on a spreadsheet. A week might look like this: ...
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2answers
201 views

Linear Algebra and a cube

I am currently working no a linear algebra question and do not understand how to solve it. The questions gives: ...
2
votes
2answers
78 views

Solving Abstract Problems

I'm doing this Solving Abstract Problem but I'm not sure which one it is. I mean from the Series I can see there's a pattern but in the Options I don't see images that link with the Series. Do you ...
2
votes
2answers
376 views

Question about the “master theorem” of recurrences - no “$b$” term

I'm using the master theorem to find the asymptotic run time of recurrences. For example, for a $T(n) = 4 T(n/5) + n^1$ I find that $T(n)$ is $\Theta(n^1)$, or, simply, constant time, via the set of ...
2
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0answers
73 views

Is this graph problem already solved

I would like to solve the following: Let $G=(V,E)$ be a directed graph such as $\forall (x,y) \in E, x \neq y$. Find any (all would be even better) graphs $S$ such that: $S \subset V$ $\#\{(x,y) ...
0
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1answer
164 views

Velocity and distance problem

From city A, car a sets on it's road towards city B. 9 Hours later, car b, sets from city B towards city A. The two cars met along the way. At the point of the meeting, car a, passed 240 km more than ...
0
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4answers
63 views

How can I solve these equations? [closed]

I can't figure it out, please help :S $$\begin{array}{rcl} 2x + 2xz &=& 0\\ -2y + 2yz &=& 0\\ x^2 + y^2 &=& 4 \end{array}$$ Thanks in advance!
3
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3answers
2k views

Magic Trick to Read your Mind

I am a student in High School. My math professor made a magic trick the other day in my class and he read our minds. I knew a similar trick which was based on mathematics, that's why I am asking here. ...
0
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1answer
159 views

Solving a tough system of linear equations

I have three equations and have to solve for $x, y, z$. $$ l_1l_2 + m_1m_2 + n_1n_2 = 0 $$ $$ xl_1 + ym_1 + zn_1 = 0 $$ $$ xl_2 + ym_2 + zn_2 = 0 $$ After eliminating a variable (from the last two), ...
2
votes
2answers
152 views

Show that if $z = e^{i\theta}$ is a solution to $0 = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0$, …

Show that if $z = e^{i\theta}$ is a solution to $0 = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0$ [1] where all $a_i$ are real, then $0 = a_{n-1}\sin\theta + a_{n-2}\sin2\theta + \cdots + a_0 \sin ...
0
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2answers
68 views

Define S as a set of primes such that if a, b are in S, ab+4 is in S. Show that S must be empty.

Define $S$ as a set of primes such that $(a \in S) \land (b \in S) \implies (ab + 4) \in S$ [$a$ and $b$ can be the same number]. Show that $S$ must be empty. A hint is given ... "work modulo 7." ...
2
votes
2answers
48 views

Searching for an explicit functional form

Let $f:\mathbb N \to \mathbb R$ be a strictly decreasing function. Suppose $$\frac{f(x)}{f(x+1)}=2^x,\qquad \forall x\in\mathbb N.$$ Is it possible to find an explicit functional form of $f$? Any hint ...
2
votes
1answer
45 views

Simplify $y^\top x -\log(\sum_i e^{x_i})$

Simplify $\sup_x y^\top x -\log(\sum_i e^{x_i})$ The first order conditions yield $y_i=\frac{e^{x_i}}{\sum_i e^{x_i}}$. How do I eliminate $x_i$ from the equation? I know the answer to be $\sum ...
2
votes
3answers
95 views

Separating $3n$ points on the plane by a line

I am trying to solve a problem in geometry (a contest-type question), and I wondering if the following result is true. (If it is true, then it makes life much easier!) Suppose there are $3n$ ...
1
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1answer
48 views

General solution of a second order PDE

I have the second order PDE $t^5u_{xx}-tu_{tt}+2u_t=0$ and need to find it's general solution. My problem is that since it's a second order PDE the method for first order quasi-linear PDE doesn't seem ...
5
votes
1answer
81 views

An integration question.

An help in the following problem: Let $f:[-1,1] \longrightarrow \mathbb{R}$ a $C^1$ function, i.e., continuously differentiable. Suppose that we have $$\int_{-1}^{1} f(x)\;dx = \pi ...
10
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1answer
191 views

Inequality $\frac{a + \sqrt{ab} + \sqrt[3]{abc}}{3} \leq \sqrt[3]{a \cdot \frac{a+b}{2} \cdot \frac{a+b+c}{3}}.$

Someone can to help me with a hint in the following problem: Show that for any $a,b,c>0$, $$\frac{a + \sqrt{ab} + \sqrt[3]{abc}}{3} \leq \sqrt[3]{a \cdot \frac{a+b}{2} \cdot ...
5
votes
0answers
107 views

Different ways of operating an infinite continued fraction

Given the continued fraction below, $$ \cfrac{1}{\cfrac{1}{\cfrac{1}{\cdots}+\cfrac{1}{\cdots}}+\cfrac{1}{\cfrac{1}{\cdots}+\cfrac{1}{\cdots}}} $$ I wanted to know to which number it converged, so I ...
3
votes
1answer
51 views

How many (linear) order types are there on a set of n elements?

Given number $n$ variables $a_1, a_2, \dots, a_n$. How many way can we place $>$, $=$ between them ? For example, for $n = 3$ (Let's call $a_1 = x, a_2=y, a_3=z$ for convenient). There are 13 way: ...
0
votes
1answer
37 views

At Great Value Expression

Hi, How can I find the greatest value of $2k\sqrt{(r-k)(r+k))}$ with parameter $r$ such that $(r>k)$?
0
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1answer
71 views

Distance Question

Two trains set out of two cities, A and B, simultaneously; One from A and one from B. Until the meeting one train has passed $108$ km more than the other. Later, one of the trains arrived at it's ...
0
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1answer
95 views

Stuck solving an equation using the floor operator.

I am not entirely familiar with the equation ninja'ing involving the floor operators. Here is my problem. I need to solve for $x$. Everything is an integer, including $x$: $$ a - 1 = \lfloor {\frac{x ...
0
votes
4answers
51 views

Solve for $x$ when a maximum over $x$ and a constant is involved

This may be a simple question, but I'm not sure how to find the algebraic solution for a problem like: $ax=b+\max(cx,d)$ where $a,b,c$, and $d$ are known. Wolfram-Alpha is not able to give me a ...
1
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3answers
94 views

There exists an integer with alternating digits $1$ and $2$ which is divisible by $2013$

Could someone give me hints in how to solve the following (rather interesting) problem? Prove that there exists an integer consisting of an alternance of $1$s and $2$s with as many $1$s as $2$s ...
5
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3answers
120 views

Prove that any two numbers of the form $2^{2^n}+1$ are coprime to one another.

Full problem statement: Prove that any two numbers of the follwing sequence are relatively prime: $2 + 1, 2^2+1, 2^4 + 1, 2^8+1, ... 2^{2^n} + 1 $ So far I have tried to use Euclid's algorithm with ...
1
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2answers
93 views

Solving quadratic system

If $a,b,c\in \mathbb{R}$ satisfy the system $a^2+ab+b^2=9$; $b^2+bc+c^2=16$;. $c^2+ac+a^2=25$. Find $ab+ac+bc$
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votes
3answers
301 views

simplification of an complex exponential equation

There are these steps in a solutions manual I do not follow. I struggle to find any good and problem specific information about this kind of math wizardry on my own. I don't really know what to google ...
1
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1answer
140 views

$\arccos$ of an imaginary number

How can I solve a $\arccos$ of an imaginary number? like: $$\cos x = 0.9i$$ Because I can't make the $\arccos$ of a imaginary number
0
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2answers
82 views

How to solve an equation involving the exponential and the logarithm

The equation $\log_3(\sqrt{x+1}+1)=(3^{x+1}-1)^2\,$ has two solutions, but I can't solve the equation.
5
votes
3answers
193 views

How to solve for $x$ in $\sqrt[4]{x+27}+\sqrt[4]{55-x}=4$?

I'm trying to guess a method for getting the values that work on this irrational equation: $$\sqrt[4]{x+27}+\sqrt[4]{55-x}=4, x\in\mathbb C$$ After using the formula ...
1
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0answers
49 views

Reputation probabilities

Is there a probabilistic model for what one's reputation can be on MSE? I can of course obtain increments of points in +2, +5, + 10, + 15, +50, +100. Are there models for what my reputation will ...
1
vote
0answers
262 views

Solving system if equations containing trigonometric functions with Ti-Nspire

In trying to solve the following system of equation: $20000\times9.81+a\cos b=0$ $a\sin b=6.17\times20000$ Find $a$ and $b$ . It gives me something containing "n2" in bold and I don't know why? ...
0
votes
3answers
252 views

GRE Question [Word Problem]

The following is a question i got wrong on the GRE practice test. There is no explanation provided. I have actually a confusion as to what is even being asked and how they get the answer $r^{2} ...
1
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2answers
116 views

Right angle triangle simple problem

The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the other; express both the angles in degrees. So I have found the following answers : ...
1
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2answers
374 views

Number of people having shaken hands an odd number of times

This is from a book called USSR Olympiad Problem book: Every living person has shaken hands with a certain number of other persons. Prove that a count of the number of people who have shaken hands ...
2
votes
2answers
97 views

solve for m by rewriting the equation (transposition)

In the following equation how would I rewrite the equation to solve for $m$? $$z=\frac{-4m-8+\sqrt{(4m+8)^2+4(4(mx+y-4m-4))}}{8}$$ when $x=66$ and $y=22$ and $z=10$
2
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2answers
97 views

Tricky differentials problem involving continuous functions

Suppose $f$ is a continuous function on $[0, \infty )$, differentials on $(0, \infty)$, such that $f(0)=1$ and $f'(x)> \frac{1}{2\surd (x+1)} \forall x>0$. Show that $f(x)> \surd (x+1)$. ...
2
votes
2answers
236 views

Calculate the determinant of $3\times 3$ matrix with $\sin x$ and powers of $\cos x$

How to calculate the determinant of this matrix $A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}$ ...
1
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0answers
47 views

Solving a system of equations with fractional parts and a system with round parts

I have the following two systems of equations: $a = x_{11} - \{x_{11} + \frac{4 - \sqrt{2}}{7}b + \frac{4 - \sqrt{2}}{7}c + \frac{2\sqrt{2} - 1}{7}d\}$ $b = x_{12} - \{x_{12} + \frac{4 - ...
6
votes
3answers
116 views

What should I do if I don't know where to start?

Sometimes getting started on a problem seems to be the hardest part. Once you find something to sink your teeth into, everything goes smoothly. What are some good things to try when you're staring at ...
1
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3answers
58 views

Solve inverse tangents

How do I solve the following equation: $$ \tan^{-1}\frac{x}{10^6}+\tan^{-1}\frac{x}{10^7}=90^{\circ}$$ WA Step by step solution from wolframalpha is unavailable.
1
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1answer
35 views

Finding a y(x) that satisfies $ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $

I'm having problem with finding a y(x) that satisfies $$ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $$ Here is what I tried to do. $$ y(x) = \int_ \! \left(\frac{x} ...