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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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
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1answer
70 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
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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
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1answer
115 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 ...
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2answers
80 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 $\...
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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
98 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
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1answer
43 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
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1answer
58 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
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0answers
35 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 ...
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2answers
94 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
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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
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1answer
22 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 ...
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0answers
49 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
46 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 ...
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2answers
76 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
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3answers
60 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 ...
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3answers
69 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
42 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....
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1answer
24 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
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2answers
95 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
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2answers
27 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 ...
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0answers
56 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
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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
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1answer
58 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
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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 $\...
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0answers
45 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
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0answers
19 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 ...
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3answers
44 views

Linear Algebra | Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions

I am a college student, and this summer I am taking a 15 week course on linear algebra. I was doing my homework today, and I am not sure if my solution is correct. The problem is stated as follows: ...
1
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1answer
50 views

Can you factorial a power?

I know this may be a straight forward question, but I looked around on google for about 20 minutes to find nothing. I am currently a year 8 student and came across a problem where I have to find the ...
3
votes
1answer
70 views

How can I prove this equation has no real solution?

I have an equation $$x^2-5 x+10+(x-4) \sqrt{1+x}=0. \tag{1}$$ Now I am trying to prove this equation has no real solution. I tried. Put $t = \sqrt{1+x}$, then, I got $$t^4+t^3-7 t^2-5 t+16=0. \tag{2}...
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3answers
30 views

shortcut technique to solve algebric problem

If we multiply three consecutive numbers, we get 120. what the summation of those numbers? Is there any shortcut way of solving this problem without doing much ...
2
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1answer
37 views

Probability of selecting a jury

Does anyone know how to find the probability of selecting a jury of $12$ people ($6$ men and $6$ women) out of an initial group of $18$ people ($6$ men and $12$ women)? With my knowledge of ...
3
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0answers
60 views

What are the essential tools and proof techniques for beginning smooth manifolds and differential topology?

I am an undergraduate currently taking a first course in smooth manifolds. I feel that I understand the material intuitively. But, I'm having trouble turning my intuition into proofs. I was hoping ...
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3answers
41 views

Finding Matrix A from Eigenvalues and Eigenvectors (Diagonalization)

Question: Let $A$ be a $3 \times 3$ Matrix such that $[-3,4,1]$ is the eigenvector corresponding to eigenvalue $3$, and $[6,-3,2]$ is an eigenvector corresponding to the eigenvalue $2$. If $v$ = ...
2
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1answer
43 views

$f(x)$ is a quadratic polynomial with leading coefficient $1$, $|f(x)| \leq 8 \: \forall \: x \in [1,9]$ find $f(x)$

$f(x)$ is a polynomial of the form ($b,c$ are real numbers) $$f(x) = x^2+bx+c$$ such that $|f(x)| \leq 8 \: \forall \: x \in [1,9]$. Find all $f(x)$ satisfying the given condition. I found ...
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0answers
48 views

Minimizing the effort after toilet visit

We live together with 5 people (4 men and 1 woman) and the woman wants everyone to close the toilet after every turn (i.e. bring the seat and cover down, for smell reasons). To me this seems unfair. ...
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1answer
36 views

$f(x)=-(x-2k)^2(x-4k)-k\quad$ where $k\gt 0\quad$ [closed]

$f(x)=-(x-2k)^2(x-4k)-k\quad$ where $k\gt 0\quad$ (i) Show that the local max occurs at $\left(\frac{10k}3,\frac{32k^3}{27}-k\right)\quad$. (ii) If the local max point is to occur on the x-axis, ...
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2answers
70 views

Probability of winning a prize in a raffle (that each person can only win once)

There is a raffle coming up. 4000 tickets have been sold, and there are 10 prizes to win. I have bought 8 tickets. What are the odds I will win a prize? Note: each person can only win once. There ...
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1answer
17 views

Simultaneous equations change expression variables

I have a deceptively simple-looking problem. $$A + B = A'\\ C + D = B'\\ A + C = C'\\ B + D = D'$$ On LHS $4$ variables $A, B, C, D$ On RHS $4$ variables $A', B', C', D'$ Is it possible to ...
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2answers
56 views

Solving for an unknown symmetric matrix using an answer found by a commutator.

Suppose I have, for $A,X$ real square symmetric matrices, and $B$ skew-symmetric and real, $AX-XA=B$, with $B$ and $A$ known and $X$ unknown. What properties of $X$ need to be satisfied to find $X$ ...
5
votes
3answers
90 views

What's the best way to compute $\frac{a^4 + b^4 + c^4}{a^2 + b^2 + c^2}$

So, my teacher gave us this to compute yesterday, and I'm completly confused on how should I proceed : $$\frac{1^4 + 2012^4 +2013^4}{1^2 + 2012^2 + 2013^2}$$ I've tried several ways, but most of ...
0
votes
1answer
21 views

Right Triangle Angle problem

I know that this can be easy, but I found it a bit difficult so maybe someone can just explain or give a hint to me. I have a right triangle $ABC$ with points $D$ and $E$ on its hypotenuse so $AB=AE$ ...
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1answer
93 views

How to do complicated problem without messy mind?

I have trouble when doing complicated problem, when I look at a problem with so much information. (e.g. deal with some concrete example such as proving a 'ugly' space is homeomorphic to another 'ugly' ...
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2answers
28 views

Solving Trig Equation with Unknown Inside and Outside of Function

In my physics course, we're covering physical pendulums, and we are to essentially analyze the range of angles within the interval $\left[0, \frac{\pi}{6}\right]$ to show that $\sin\theta \approx \...
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8answers
8k views

How to debug math?

May seem strange as I'm good in programming, but I just started diving into math. ATM I'm learning combinatorics at Khan Academy, and here's an example of a question that I struggled with (that's not ...
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1answer
36 views

Three screw problem

There are three identical screws with diffrent amounts of nuts and disks on them. Here is the problem picture: How do you calculate the weight of a screw, the nuts and the disks?
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0answers
10 views

Minimizing log-likelihood function

Below is a problem I'm currently working on. I am having trouble seeing how I can obtain the wk and wko values for equation (1). I cannot see how one would solve the negative log-likelihood function ...
0
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0answers
17 views

How does one get $p=2$ from a condition that there be non-trivial linear transformations of every dimension that to any power are $p$-norm-preserving?

Verifying that (p=2) satisfies $$\forall n\in\mathbb{Z}^+.\exists A\in(\mathbb{R}^{n\times n}\setminus\{I_n\}).\forall k\in\mathbb{R}.\forall v\in\mathbb{R}^{n}.\left\|A^kv\right\|_p\!\!=\left\|v\...