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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0
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1answer
25 views

Understanding percentages [on hold]

If I have $733.00$ dollars and my rent is $30\%$ of that, how much money are they taking? In dollars, my understanding of of how to use percentage is very limited so I need help solving this problem. ...
-1
votes
1answer
49 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. ...
0
votes
1answer
21 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
28 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?
-1
votes
0answers
12 views

Seeking feedback for my math site: climbingahead.com [on hold]

I built out a math site for kids at climbingahead.com It's like a daily dose of quick math exercises. Would love to hear what folks think about it. thx
-3
votes
3answers
40 views

A carpenter used 1/9 of a box of nails… [on hold]

A carpenter used 1/9 of a box of nails while working on a birdhouse and was able to finish 1/6 of it. At this rate how many boxes will he need to finish the entire birdhouse? I am having problems ...
2
votes
6answers
36 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
50 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 ...
-1
votes
0answers
19 views

reference for unsolved problems in ETCS [closed]

I am looking for unsolved problems in the theory of "elementary theory of category of sets" are there references for (foundational) problems in the category of sets as foundation?
0
votes
0answers
16 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 ...
-2
votes
0answers
17 views

Present Values for a house loan

If I have a loan of $449,100$ with an interest rate of $5.48\%$ and I have an increase in repayment per month every $3$ years for $30$ years by $200$, and the starting repayment per month is $2544.3$, ...
0
votes
2answers
65 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
37 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
7 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 ...
3
votes
0answers
48 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
37 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
8 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
103 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
58 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 ...
2
votes
1answer
34 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
58 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
105 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
42 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
27 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? ...
1
vote
3answers
31 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
51 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
67 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
120 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
843 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
103 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
38 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
63 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
19 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 ...
2
votes
2answers
36 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 3 and ...
0
votes
1answer
38 views

how many hexagons can be found in the graph?

At first sight I thought that this question requires considering different cases, but I find it difficult to convince myself as to how to start this question. Could someone please give me some ...
1
vote
1answer
26 views

Solving natural log equations

The equation $\ln(|y+1|)= x-2$ where you solve for $y$, I am just unsure of how the absolute value plays into this. I am assuming that I would convert to exponential form to get $|y+1|=e^{x-2}$ and ...
5
votes
3answers
444 views

Problem Solving Positive Integers

This is a very interesting word problem that I came across in an old textbook of mine. So I know the maximum value of the HCF has to be a factor of $540$ and mayhaps the Euclidean Algorithm, but other ...
1
vote
2answers
26 views

A question on inequality and differentiation of logarithms

Show by differentiating that $\ln x$ is a concave function of $x$. Deduce that if $p,q,x,y$ are positive real numbers with ${1\over p}+{1\over q}=1$, then $$xy \lt {x^p\over p}+{y^q\over q}$$ I ...
12
votes
2answers
469 views

Show divisibility by 7

I was stuck at this question: Suppose $a^2+b^2=c^2$ for $a,b,c \in \mathbb Z$, and neither $a$ nor $b$ is a multiple of 7. Show that $a^2-b^2$ is a multiple of 7 I tried to write $b^2$ as ...
0
votes
1answer
27 views

How to show the average x-coordinates of four collinear points on the curve is a constant?

Show that if four distinct points of the curve $y=2x^4+7x^3+3x-5$ are collinear then their average x-coordinate is some constant k. Find k. Shall I use vector to calculate their x-coordinate, or ...
-7
votes
3answers
60 views

Algebra 2 Help??!… [closed]

use the discriminant to find the number and kind of solutions for the following equation. $$ 9x^2+12x=-4 $$
2
votes
1answer
63 views

Quartic equation or Sextic equation? And how to solve it?

In this arxiv paper (p. 11, eq. (3.2)) the authors claim that equation (3.2) is ... a quartic equation [...] which can be solved explicitly. The equation in question is \begin{equation} ...
0
votes
1answer
76 views

Showing that an oscillator has its amplitude reduced after completing half-cycle

Consider a mass $m$ at position $x(t)$ on a rough horizontal table attached to the origin by a spring with constant $k$ (restoring force $-kx$) and with a dry friction force $f$ $$\begin{cases} ...
0
votes
4answers
56 views

Lawn mowing problem solving

Kate can mow the lawn in 45 minutes. Kate's sister takes twice as long to mow the same lawn. If they both have a mower and mow the lawn together, how many minutes will it take them? I know the answer ...
3
votes
3answers
53 views

Which is greater as $n$ gets larger, $f(n)=2^{2^{2^n}}$ or $g(n)=100^{100^n}$?

It is the first time I met such a question: Which is greater as $n$ gets larger, $f(n)=2^{2^{2^n}}$ or $g(n)=100^{100^n}$? Intuitively I think $f(n)$ would gradually become larger as $n$ gets ...
0
votes
2answers
52 views

A tricky diophantine equation with factorials

I am being unable to solve this diophantine equation. Does anyone have any suggestions. Let $n$ and $m$ both be non-negative integers. Find all solutions to $$n(nm - 2)! = (n!)^m$$ How would one ...
2
votes
2answers
71 views

Show that $1+(x_1x_2…x_n)^{\frac{1}{n}} \leq [(1+x_1)(1+x_2)…(1+x_n)]^{\frac{1}{n}}$

Show that $1+(x_1x_2...x_n)^{\frac{1}{n}} \leq [(1+x_1)(1+x_2)...(1+x_n)]^{\frac{1}{n}}, \forall x_i \geq 0, i = 1,2,3...,n$ So, I have to make this function something like this: ...
8
votes
4answers
379 views

How To Develop A Higher Mathematical Aptitude? [closed]

First off I must say I'm pretty blown away by the vast majority of the people in this forum. I do aspire to reach the knowledge of mathematics as shown on the site, but honestly it's a little daunting ...