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.

learn more… | top users | synonyms

0
votes
0answers
19 views

What does equally likely imply in this case?

Suppose I have: $30$ red balls ($10$ of which are wooden; $20$ are plastic), $20$ blue balls ($5$ of which are wooden; $15$ are plastic), and $50$ white balls ($25$ are wooden $and$ 25 are ...
5
votes
1answer
174 views

How to solve this system of exponential equations?

Solve the following system of equations ($x,y \in \Bbb R$): $$\begin{cases} 3^{x+3y-2} + 6\cdot 3^{y^2+4x-2} &=5^{5y-3x} + 2\cdot 3^{y^2-2y+1}\\ 1+2\sqrt{x+y-1} &=3\sqrt[3]{3y-2x}. ...
2
votes
1answer
38 views

Diophantine-like equations

So I was solving a problem and encountered a specific system of equations that I don't know if a solutions exists for it or not. $$\begin{align} 4ny&=d^2-a^2\\ -4nx+4ny&=d^2-b^2\\ ...
-1
votes
1answer
60 views

Solution of $x+\log(x)=c$ [duplicate]

how to solve the following equation? $x+\log(x)=n+c$,where $c$ is constant, and $n$ is positive number and allow to be infinity. Intuitively, if let $n \to \infty$, the approximate solution will be ...
0
votes
1answer
34 views

Cartesian Product with two experiments and two boxes filled with balls

So this is a homework question and I'm looking for guidance if I have done the question correctly. Box 1 contains 1000 bulbs of which 10% are defective. Box 2 contains 2000 bulbs of which 5% are ...
3
votes
2answers
83 views

Expected Value for the tries taken to complete this game

Suppose I have a Checkerboard of length l and breadth b. Two people, A and B decide to play a game. The rules of the game are as follows: -A is blindfolded -B arranged the checkerboard as follows: ...
0
votes
3answers
72 views

10 year old homework ABCDE +BCDE =

Kids maths homework - ABCDE + BCDE + CDE ______ 74915 We're told A = 7. I don't even know how to go about working this out. Help?!
0
votes
1answer
145 views

Finding the solution set for all unit vectors orthogonal to a given vector $\vec{v}=\langle{3,4,0}\rangle$.

My question will be very similar to this question. However, I found either the solutions didn't answer all of my questions, or were overall too confusing to do so. Say I set $a$ and $b$ to be real ...
0
votes
2answers
27 views

Solution set of a linear system with three equations and three unknowns with at least two distinct solutions.

Proposition: If $(x_0, y_0, z_0)$ and $(x_1, y_1, z_1)$ are two distinct solutions of a linear system with three equations and three unknowns then $t(x_1-x_0, y_1-y_0, z_1-z_0)$ is also a ...
3
votes
1answer
37 views

Unknown notation used in matrix proof.

I have been given the following task (by my professor, with no mentionable context): Prove that $\displaystyle \left[ \begin{array}{rr} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{array} ...
1
vote
2answers
45 views

Determining values of a coefficient for which a system is and isn't consistent.

Given the system : \begin{array}{ccccrcc} x & + & 2y & + & z & = & 3 \\ x & + & 3y & - & z & = & 1 \\ x & + & 2y & + & (a^2-8)z & = ...
14
votes
3answers
537 views

Succinct Proof: All Pentagons Are Star Shaped

Question: What is a succinct proof that all pentagons are star shaped? In case the term star shaped (or star convex) is unfamiliar or forgotten: Definition Reminder: A subset $X$ of ...
0
votes
1answer
30 views

Need one example solving trigonometry.

Calculate $\sin \beta, \tan \beta, \cot \beta, \cos(2\beta)$ if $\cos \beta = {5 \over 13}$ and $\beta \in (0^{\circ},90^{\circ})$. I'm a student and I forgot how to solve it correctly...I need just ...
0
votes
2answers
46 views

Finding the d value that will keep all coefficients at a minimum in a Cubic

I have a particular scenario. In this scenario, we have the standard cubic equation, ax^3 + bx^2 + cx + d = y as well as 3 points that are graphed, as can be ...
0
votes
2answers
19 views

confused on to leave in centimeters or convert to cubic centimeters

The volume $V$ of the cylinder is $65\pi \mathrm{cm}^3$. The height of the cylinder is $5$ centimeters. Use the formula $V = Bh$ to find the area of the base of the cylinder.
-1
votes
2answers
48 views

Basic Math Question for Health Care

This is super basic, but I have not been in school for YEARS. I am a bit dusty. Any-who, Its a common word problem, and as follows: A licensed practical nurse gives 1800 milligrams of penicillin over ...
0
votes
1answer
18 views

Show that this construction preserves connectedness

Let $G_1$ and $G_2$ be $k$-connected graphs and let $v_1\in V(G_1)$ and $v_2\in V(G_2)$ be such that $\deg v_1=\deg v_2=k$. Form a new graph, $H$, by putting an $M$-matching of size $k$---conneect ...
0
votes
0answers
17 views

Fill valleys of waveform (flatten them, level them out)

I have waveform data and want to fill the valleys with a given maximum width. That is, I have sample values with a constant distance. The parameter "maximum width" determines the y-position of the ...
2
votes
0answers
49 views

Find the angle between asymptotes

Sketch the locus of the centres of circles which touch two fixed and unequal circles. Find the angle between the asymptotes How shall I find the locus when the size of the circles are not ...
-1
votes
1answer
53 views

How to solve for X in this equation?

$$n * x * cos(\frac{\pi}2 * \frac{x}{x+b}) + c = y$$ How would I get X on one side of the equation instead of y? Normally I work the equation forwards knowing X. The other variables are constants. ...
1
vote
1answer
61 views

What is the quickest way to find Nash equilibria in two player bimatrix game?

Suppose the cost/penalty matrix of a game is given as: $$M = \begin{bmatrix} (-5,-5) & (0,0) \\ (0,0) & (-3,-3) \end{bmatrix}$$ Then the game as two equilibria $(u_{11},u_{21})$ and ...
0
votes
3answers
161 views

Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
2
votes
6answers
42 views

Solving for $x$ in an exponential equation

Say we the following equation $$F(x) = \frac{\exp(a+bx)}{1 + \exp(a+bx)}$$ Now we set $x=0$ and we want to solve for $a$ as a function of $F_0$. So that, we have: $$F_0 = \frac{\exp(a)}{1 + ...
4
votes
3answers
60 views

Let $g_{n}$ be the no. of derangements with $n$ elements and $f_{n}$ the no. of permutations with one fixed point. Show that $|g_{n}-f_{n}|=1$

This is a problem from Loren Larson's "Problem solving through problems", 2.5.13, page 78. Let $S_{n}=${$1,2,...,n$}. A derangement of $S_{n}$ is a permutation with no fixed points. Let $g_{n}$ be ...
1
vote
1answer
35 views

How to minimise the upper boundary of this weird function?

Let $\{x\}$ denote the fractional part of $x$, which is $\{x\}=x-[x]$. Let $f_{a,b}(x)=\{x+a\}+2\{x+b\}$ and let its range be $\{m_{a,b},M_{a,b})$. Find the minimum value of $M_{a,b}$ as $a$ and ...
0
votes
0answers
22 views

Existence of an $x,U$-fan in a $k$-connected graph

Let $G$ be a $k$-connected graph. An $x,U$-fan is a set $U\subseteq V(G)$ of size $|U|\ge k$ together with a vertex $x\in V(G)\backslash U$ and a set of disjoint $x,U$-paths whose only common vertex ...
0
votes
2answers
136 views

A mathematics competition had 9 easy and 6 difficult problems

A mathematics competition had 9 easy and 6 difficult problems. Each of the participants in the competition solved 14 out of 15 problems. For each pair consisting of an easy and a difficult problem, ...
1
vote
1answer
67 views

Solve this question involving temperatures?

So I am given 2 formulas: $$ \frac{dT}{dt}=-k(T_t-T_s)$$ Where $\frac{dT}{dt}$ rate at which the object's temperature is changing $T(t)$ is the temperature of the object at time $t$ $T(s)$ is the ...
0
votes
0answers
31 views

solving homogeneous equation using r programming language

How to solve for the non trivial solution to the homogeneous system of linear equation.. I tried with solve command but it gives only trivial solutions. eigen(A)$vector[,x] gives answer only for ...
4
votes
1answer
63 views

If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value.

I am trying to solve this question, If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value. I've tried this, $$x^2-2x + z^2-2z + 2 + y^2 = 0$$ $$ ...
2
votes
0answers
42 views

Help with Definition of Limits (Finding a delta given epsilon)

The problem says: Find a $\delta$ such that $|f(x)-l| < \epsilon$ for all x satisfying $0 < |x-a| < \delta$ when $f(x) = x^4; l = a^4$. What I did so far was $|x^4-a^4| < \epsilon$ so ...
0
votes
0answers
23 views

What is the independent and dependent variables, the linear equation model, the practical meaning of the slope and vertical intercept for each?

Identify the independent and dependent variables, and the linear equation model for A and B? What is the practical meaning of the slope and vertical intercept for A and B? A. You make a down payment ...
1
vote
2answers
157 views

Determine all positive integers $n$ which have a divisor $d$ with the property that $dn+1$ is a divisor of $d^2 + n^2$

Determine all positive integers $n$ which have a divisor $d$ with the property that $dn+1$ is a divisor of $d^2 + n^2$. So i formed the equation that $$\frac{n}{d} = \frac{d^2 + n^2}{dn + 1}$$ And ...
2
votes
0answers
67 views

Is it possible to bruteforce a differential equation

Is there any method to solve differential equations which involves just a number of basic functions combined into various permutations (with various factors) which are then fed into the differential ...
3
votes
1answer
39 views

Picking out a subset of elements from a finite product of cyclic groups

Let $C_n$ be the cyclic group of order $n$, and let $G = \prod_{i=1}^n C_n = \underbrace{C_n \times C_n \times \ldots \times C_n}_{n \text{ times}}$. For $g = (g_1,g_2,\ldots, g_n) \in G$, call $g$ ...
31
votes
1answer
2k views

Is it possible to construct a sequence that ends in 1000000000?

Starting from the number $1$ we write down a sequence of numbers where the next number in the sequence is obtained from the previous one either by doubling it or rearranging its digits (not allowing ...
2
votes
2answers
121 views

Prove that every positive integer less than or equal to the square root of a is a near factor of a

In many computer languages, the division operation ignores remainders. Let's denote this by the operation $//$, so for instance $13//3 = 4$. If for some $b$, $a//b = c$ then we say that $c$ is a near ...
3
votes
1answer
190 views

Undergraduate mathematics competitions

I am a freshman (math undergraduate) here in Argentina and I am deeply interested in mathematical olympiads but I really need some advice. Right now, my problem solving skills are good but not that ...
-3
votes
2answers
52 views

How many spare tyres are needed? [closed]

I am about to start a $27,000$ km trip. I check the specifications of tyres to use to find that each is good for only $18,000$ km. What is the fewest number of spare tyres I need to take so I can ...
1
vote
2answers
75 views

The number of numbers whose digits are different and add up to 36

All the digits of a number are different, the first digit is not zero, and the sum of the digits is 36. There are N × 7! such numbers. What is the value of N? How should I approach this problem? ...
0
votes
3answers
43 views

What can you say about a number with remainder 1 and 2 when divided by 3 and 4 respectively?

I was trying to solve a problem which states: How many two-digit numbers have remainder 1 when divided by 3 and remainder 2 when divided by 4? and solved it by writing down individual numbers... ...
1
vote
3answers
67 views

Solve the system of equations $\begin{cases} xy-2y-3 &=\sqrt{y-x-1}+\sqrt{y-3x+5} \\ (1-y)\sqrt{2x-y}+2(x-1) &=(2x-y-1)\sqrt{y}. \end{cases}$

Solve the following system of equations ($x,y \in \Bbb R$): $$\begin{cases} xy-2y-3 &=\sqrt{y-x-1}+\sqrt{y-3x+5} \\ (1-y)\sqrt{2x-y}+2(x-1) &=(2x-y-1)\sqrt{y}. \end{cases}$$ I think this ...
3
votes
5answers
88 views

Solve the equation $x(\log \log k - \log x) = \log k$

I want to solve this equation by expressing $x$ in function of $k$. Is it possible? Thanks.
3
votes
4answers
187 views

If $x\cos(\theta)-\sin(\theta)=1$ then what is the value of $x^2+(1+x^2)\sin(\theta)=1$

The question given is, If $x\cos(\theta)-\sin(\theta)=1$ then find the value of $x^2+(1+x^2)\sin(\theta)$. There are four options given $1$, $-1$, $0$ and $2$. I tried using $\sin^2+\cos^2=1$. I ...
4
votes
5answers
1k views

If $x^3+y^3=72$ and $xy=8$ then find the value of $x-y$.

I recently came across a question, If $x^3+y^3=72$ and $xy=8$ then find the value of $(x-y)$. By trial and error I found that $x=4$ and $y=2$ satisfies both the conditions. But in general how ...
5
votes
0answers
112 views

Approximating $\pi$ by an expression of the form $\sqrt{\sqrt{ \cdots \sqrt{ n!! \cdots !}}}$

Here is a problem that appeared as a prize challenge in a periodical for science students, back when I was a student: Find an approximation of $\pi$ formed of the numbers $0$ through $9$, each used ...
1
vote
0answers
60 views

Minimization of a multivariate quadratic equation

I am interested in the minimum of a general multivariate quadratic equation for non-negative real numbers: $$ \begin{aligned} & \underset{x_i}{\text{minimize}} & & ...
1
vote
1answer
67 views

How to apply Euler's Formula in topology to this problem?

Prove that it is impossible to make a football out of exactly 9 squares and $m$ octagons, where $m \ge 4$. (In this context, a “football” is a convex polyhedron in which at least 3 edges meet ...
0
votes
0answers
21 views

Any way to factor, collect variable from this equation?

For a sum of quadratic solutions, is there any possible way to factor out the variable $P$ from the following real function? $QT$ is also a variable, and If it matters, $P > 0$ and all indexed ...
1
vote
2answers
117 views

How to shade one square to make the figure symmetrical about exactly one axis? [closed]

I find it hard to understand the answer, which says How to understand the answer given? Why does it say 'only line of symmetry possible is the diagonal through $1$ and $5$? What if I shade $2$ and ...