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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27 views

Velocity time and length problem [on hold]

A person walks from his house to the park and back in $2.5$ hours. On his way to the park, he walked at a rate of $6$ km/h, then on his way back he walked at a rate of $4$ km/h. Find the distance ...
-1
votes
2answers
57 views

Probability problem

I created this problem based on the following probability riddle here. You're a king, and you were given two groups of people, and a certain information about them. First group has 2 people. One of ...
1
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0answers
54 views

Multiple choice excercise with more than one answer correct

Q. Consider the function $$F(z)=\int_{1}^{2} \frac {1}{(x-z)^2}dx, {\text {Im}(z) \gt 0}$$ Then there is a meromorphic function function $G(z)$ on $\Bbb C$ that agrees with $F(z)$ when ${\text {Im}(...
-1
votes
0answers
33 views

Bayesian posterior probability [closed]

Let's say that you are in a casino and you have played on 3 different slot machines following this flow: Slot machine A, play 10 times, win 2 times for a total of 2$ Slot machine B, play 100 times, ...
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1answer
28 views

solving equation using square root

I have a question here... Usually, for $x^2 = 4$ $x=\sqrt{4}$ $x=±2$ But if the question is like this : $y^2 = (x+2)(x+2)$ $y^2 = (x+2)^2$ If I want to find $y$ in term of $x$,I will put square root ...
1
vote
1answer
53 views

Differential equation, Solution is a Bessel fucntion

this is my first post here. I knocked my head on a differential equation yesterday, this one: $$ \frac{12 \nu}{x^2} \frac{S(x)''}{S(x)} = -\lambda^2 $$ Where $nu$ is a constant. The book says the ...
3
votes
0answers
67 views

Does this equation have no solutions?

The question is this : The source from where I got this question was devoid of any answers to it, so I came here, this is how I proceeded : LHS : $((((({(x)^x})^{2x})^{3x})^{....x^2})^2 = (((((x)^...
2
votes
1answer
28 views

Fox and Gemstone problem. Weighing stones to compare bags.

There is a problem called Fox and Gemstone at topcoder: https://community.topcoder.com/stat?c=problem_statement&pm=14296 Basically, you have the ability to weigh individual gemstones against ...
0
votes
1answer
45 views

Minimizing a strictly convex function with inequality constraint

So we've been learning about the Kuhn Tucker conditions in my non-linear optimization course and I've been having trouble with this problem: QUestion: description here Question: a strictly convex ...
0
votes
1answer
65 views

Find the Smallest Value

Find the smallest value of $$a + \frac {1}{(a-b)b} $$ where a>b>0 I found this question in AM-GM inequality problems but I am stuck at this
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votes
1answer
30 views

find the number of tuples of positive integers [closed]

find the number of tuples (a,b,c,d) of positive integers \begin{array}{l} {a^3} = {b^2}\\ {c^3} = {d^2}\\ c - a = 64 \end{array} answer should be one of 0 , 1 , 2 , 4
0
votes
2answers
68 views

proving no real roots exist

Prove that $x^8-x^7+x^2-x+15$ has no real roots. I did it by first assuming it has real roots and then applying Descartes rule of signs. We find that if there are any real roots, they all must be ...
0
votes
1answer
29 views

number theory problem finding triplets [closed]

Find number of triplets of positive integers satisfying $2^a-5^b\cdot 7^c=1$ Given options are $0 , 1 , 2$ or infinite.
0
votes
1answer
46 views

How to find the area shared by 4 quadrants inside a square?

I was to find the blue area in this question : As described about how it's a square with 4 quadrants of same radius intertwined with each other, now to find the blue part area I thought about ...
-1
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0answers
31 views

How to study for open book exams?

I hope it's ok to ask about exams here? If not please tell me. This year was the first time I had open book exams, varying from three to six hours long. The six hour ones go fine because I have time ...
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votes
2answers
52 views

Find the solution without “common sense” assumption [closed]

Is it possible to solve the following problem without make a "common sense" assumption? In the year 1887, one person's age was exactly the sum of the digits of his birth's year. What was the person'...
3
votes
2answers
63 views

Homeomorphism from $S^1\backslash(0,1)$ to $\mathbb{R}$

I am trying to derive a bijection between $S^1\backslash{(0,1)}$ and the real line, but I am stuck on using the most obvious way Let the top point of the circle be $(0,1)$, and the blue line hits ...
1
vote
0answers
68 views

Polynomial taking irrationals to irrationals

Problem: Find all polynomials from $\mathbb{R}\to \mathbb{R}$ $f$ with integer coefficients taking irrationals to irrationals. My attempt: It is clear that the problem statement is equivalent to ...
0
votes
2answers
107 views

What is the size of the angle $\angle AMC$? [duplicate]

Suppose we have a triangle $\triangle ABC$ where the size of two angles are given: $\angle B=15^\circ$ and $\angle C=30^\circ$. We draw the median $AM$, so now what is the size of angle $\angle AMC$? ...
2
votes
3answers
71 views

Let $f$ be a differentiable function defined for all real $x$, where $f(x)\ge 0$ for all $x\in[0,a]$

Let $f$ to be a differentiable function defined for all real $x$, where $f(x)\ge 0$ for all $x\in[0,a]$.If $$\int_0^a f(x)\,dx = a, $$ then $$2\int_0^{5a}\left(f\left( \frac x 5 \right) + 3 \right)\,...
0
votes
1answer
36 views

Topology: What is a quick way to check whether a subset $D$ is dense in $(X, \mathcal{T})$?

Def $1$: Let $(X, \mathcal{T})$ be a topological space, then $D \subseteq X$ is dense if $\overline {D} = X$ Def $2$: $x \in \overline D$ iff for all $U \in \mathcal{T}, x \in U \implies D \cap U \...
0
votes
1answer
69 views

Simplifying $(m^3)^4(2x^3)^7(m^2)^5(3x)^2$

I am having trouble with simplifying the following algebraic expression: $$(m^3)^4(2x^3)^7(m^2)^5(3x)^2$$ I have been able to do the exponents and all the other equations I needed to simplify but ...
0
votes
1answer
15 views

How to find the seeding number for acheiving the minimum cost?

Consider there are n integers. I have to pick one Random integer 'R' and i have to subtract 'R' with each element of the 'N' integers. Result has to be added. Result that i will achieve should be the ...
2
votes
1answer
114 views

Please help me solve this $x(\sqrt{2x+5}+\sqrt[3]{7x+13}) = 3x+6$

Wolfram Alpha shows that the answer is $x=2\,$ and $x=-2\,$ but what would be the best way of simplifying this equation ? It has been many years since I was in school , and I just cannot wrap my head ...
1
vote
2answers
44 views

How do you deduce the integer whose multiplicative inverse decimal has a digit sequence or repetend length of 3 digits?

A positive integer's, n, reciprocal, $\frac{1}{n}$, in which the decimal's repetend has a length of three digits which starts at the decimal mark. e.g. 0.037037... of the integer, 27 ,reciprocal $\...
0
votes
1answer
19 views

Two people running up and down escalators

Couldn't really figure out a good title for this post, I am sorry. But here's the problem: PREMISE: Two people, A and B, are running, with speed u, up and down separate escalators with length L. ...
3
votes
1answer
90 views

Divide a 2D polygon with N vertices into triangles draw in a 3D space

I'm developing a C++ software and I have a problem with a polygon with N vertices. I have a set of N vertices unordered. This vertices describe an polygon. I'm developing a planetarium and I want ...
1
vote
1answer
40 views

Models of Comprehension Schema

Let $M_\alpha$ for $\alpha\in ON$ be transitive sets and let $M=\bigcup_{\alpha\in ON}M_\alpha$. Suppose that (i) for every $\alpha<\beta$, we have $M_\alpha\in M_\beta$ and (ii) for every limit $\...
1
vote
1answer
57 views

How to predict the incidents of synchronization for multiple oscillations.

EDIT: I changed the title of this question and made this edit based on a conversation with a friend. While I am dealing with mechanical cams the plain fact is that what I have is an oscillation in ...
2
votes
0answers
34 views

How often does theorem equivalence take place?

I remember reading once that it was found that two math theorems were essentially equivalent to each other, how often does this occur? ex. In two dimensions the divergence theorem is said to be ...
1
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2answers
93 views

How does one solve this kind of equation: $3^x=x+3$

How does one solve this kind of equation: $$3^x=x+3$$ I tried playing around with logs but it didn't get me anywhere. I plotted the two functions $f(x)=3^x$ and $g(x)=x+3$ on a graph to estimate the ...
1
vote
1answer
15 views

Choosing pairs of numbers with distinct bounded sum

Stumbled across this problem in the list of examples for high school math exam, paraphrasing a little: ...
0
votes
1answer
18 views

Finding the set of values for k of a modulus function.

"Find the set of values of k for which |(x-4)(x+2)| = k has four solutions." EDIT: Ok so I thought I'd start with setting the modulus function equal to k and -k to get the two set of results. Doing ...
1
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0answers
48 views

Euclidean algorithm: THE GAME OF EUCLID

In his book "Elementary Number Theory:A Problem Solving Approach" (Euclidean algorithm/Derived Sets/ first chapter page:17,19) Joe Roberts describes a number: $$\tau=\frac{1+\sqrt{5}}{2}$$ further he ...
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0answers
44 views

Numerically solve an equation using Python

How could I (numerically) solve this equation for $\alpha$ given $x_i$ (these are known) ? $\sum_{i=1}^N\frac{1}{x_i-\alpha} = \frac{2N}{\sum_{i=1}^{N}(x_i-\alpha)^2}\sum_{i=1}^{N}{(x_i-\alpha)}$ In ...
1
vote
2answers
75 views

Why we not check conditions while solving questions?

Note:Down ward problem is just an example to express my question(I know the both solution of problem are insufficient but the first solution is in my 10+2 book and second one is mine which is ...
2
votes
3answers
58 views

Find two fractions such that their sum added to their product equals $1$

This is a very interesting word problem that I came across in an old textbook of mine. So I managed to make a formula redefining the question, but other than that, the textbook gave no hints really ...
0
votes
3answers
67 views

When Ben added $2$ of $4$ together repeatedly, he got $4$ consecutive numbers. Show that either $3$ or $1$ of his $4$ numbers were even

Ben had $4$ numbers: $a, b, c,$ and $d$. $a+c=e$ $a+d=f$ $b+c=g$ $b+d=h$ $e,f,g,h$ are consecutive. Prove that either $1$ or $3$ of $a,b,c,d$ were even
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1answer
40 views

What are the $5$ different combinations of $4$ numbers that can add to $8, 9, 10$ or $11$? [duplicate]

There are $5$ combinations of $4$ numbers from $1-9$. If you write these on two coins, so there are $2$ numbers on each coin. Then you flip the coin. The sum of the two numbers add to $8,9,10,$ or $11....
0
votes
1answer
22 views

How many different ways can you order a binary code (only 1s and 0s) if there is 5 of one and 6 of the other?

If you have 6 0's and 5 1's, like in binary, how many different ways can you order them? Also, there is a popup saying that the question appears subjective. Is it?
3
votes
2answers
89 views

How can the policeman catch the gangster?

I try to solve the following problem (Moscow Mathematical Olympiad, 1978) There is a town with six streets: four sides of a square and two its middle lines. Policeman tries to catch a gangster. If ...
0
votes
1answer
25 views

Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through -6.

Given $f(x)=x^2-4x+3$, find the points on the curve $y=f(x)$ where the tangent to the curve passes through $(0,-6)$. State the equations of the tangents at these points. Hi everyone, I tried to find ...
1
vote
0answers
54 views

Sum of correlated random variables and the Law of Large Numbers?

Suppose I have a random variable $X$ which can take values on the set $\mathcal{X}=\{1,2,\dots,m\}$ and $X$ is drawn according to the given probability mass function $\mathbf{p}=\{p_1,p_2,\dots,p_m\}$...
3
votes
1answer
35 views

Using the Weak Law of Large Numbers for a product or random variables?

I need to calculate the average of the following quantity: \begin{equation} S_n=\prod_{i=1}^nS(X_i) \tag{1} \label{eq:1} \end{equation} with $S(X_i):=o_{X_i}b_{X_i}$, where each $X_i\in \mathcal{X}=\...
0
votes
1answer
57 views

What are some efficient ways to go about a problem where you cannot exceed the other by 2?

I need an efficient way to go about this problem, for practice for my problem solving test. This is not a part of the actual test. This is the type of question that I am struggling with There are two ...
0
votes
1answer
14 views

Is there a analytic algorithm to solve for a partially specified constant present in function & its derivative with the rate of change at an x value?

I have a Calculus problem that I am not entirely happy with how I solved it. Given the following information: $$y = x^{k} + x^{k-2}$$ $$(k \in \mathbb{N}) \wedge (k \mod{2} \neq 0) \wedge (k > 1)...
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0answers
43 views

partition of $\mathbb{Z}$ into finitely many translation

Few days ago, a friend of mine gave me this problem : Let $X \subset \mathbb{Z}$ and suppose that $a_1, a_2, \cdots, a_n$ are integers such that $X+a_1, \cdots, X+a_n$ is a partition of $\...
1
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0answers
44 views

Solving for y in $4+x^3+y^3-3xy = 0$

I was trying to solve for $y$ in this equation: $4+x^3+y^3-3xy = 0$. I put it into WolframAlpha and it gave me an complicated answer. It appears like it used the cubic formula, except when I tried to ...
2
votes
0answers
17 views

How do I describe an XYZ velocity in a written sentence?

I'm creating a voice interface for Amazon Echo, providing status information regarding the International Space Station (ISS). I'm attempting to express the XYZ velocity of ISS. Speed inquiry example ...