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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-3
votes
0answers
24 views

A travelling salesman problem

There is a salesman who is travelling to a country and needs to visit every town there. It is possible to travel to any two towns either by boat or by cart. The same type of travel is available in ...
7
votes
3answers
288 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
27 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
30 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
0answers
18 views

Need help with a mathematical program formulation about air

I have to create a mathematical model regarding air. Air flows through multiple rooms, and in each room something happens to one or multiple properties of the air (heated, cooled down, moisture ...
0
votes
2answers
15 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
31 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
14 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
11 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
28 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 ...
0
votes
1answer
27 views

Understanding percentages [closed]

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
52 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
24 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
30 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
38 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 ...
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
74 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
8 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
49 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
9 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
116 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
35 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
68 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
108 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
43 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? ...
0
votes
3answers
35 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
52 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
121 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
865 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
104 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
40 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
20 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
37 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
39 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
446 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
471 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. $$ 9x^2+12x=-4 $$