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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6 views

Probabilities of each waitlist person

Coming from this, $10$ Applicants for a exclusive club membership. I found that you can use total probability to consider existing and old members leaving/returning as members in the club, ended up ...
1
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1answer
837 views

How to calculate per unit costs for multiple items

I had a supplier give me a quote last week that seems very strange, can someone help me out? The quote is for IT hardware, but for simplicity (and anonymity) I'll use apples and oranges: ...
0
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1answer
7 views

Mpg to l/100km conversion problem?

We have two vehicles A: old truck that does 17 mpg (13.84 l/100km) B: old car that does 47 mpg (5.00 l/100km) We are looking to replace one of these vehicles with a new one (of the same ...
0
votes
1answer
30 views

Let $S=[0,1) \cup [2,3]$ and $f:S \to \Bbb R$ be a strictly increasing map such that $f(S)$ is connected. Which of the following statements is true?

$f$ has exactly one discontinuity. $f$ has exactly two discontinuities. $f$ has infinitely many discontinuities. $f$ is continuous. I know theorems related to connectedness and ...
3
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4answers
70 views

How to find unknowns $w_1,w_2,w_3$ that satisfy $t=w_1f_1 + w_2f_2 + w_3f_3$?

For any $i \in \{1,2,3\}$, let: $w_i \in [0,1]$ is an unknown number such that $\sum_{i \in \{1,2,3\}} w_i = 1$. $t$ is a known number in $[0,1]$. Suppose that $t = 0.8$. $f_i$ is also a known ...
0
votes
1answer
12 views

Finding the rate at which the space diagonal of a cube is decreasing

This is the context of the question: I'm assuming by the space diagonal (although I'm not sure) to be the area of the right-angled traingle created by the diagonal. Let this space be $V$, then we ...
2
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1answer
54 views

If $y'+y=|x|$ and $y(-1)=0$, what is $y(1)$?

If $y'+y=|x|$ and $y(-1)=0$, what is $y(1)$? I calculated the integrating factor to be $e^x$. Then $e^x y'+ e^x y=e^x |x|$ hence $\frac {d(e^x y)}{dx}=e^x |x|$ hence $d(e^x y)=e^x|x|dx $ ...
2
votes
1answer
38 views

solve $54 x + 16 y = 2400$ for integer values of x,y

How to get integer values for x and y that satisfy: $$54 x + 16 y = 2400$$ Someone told me that I can do it using Euclid-Wallis algorithm, but I don't understand it so, if there isn't any else ...
0
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0answers
46 views

Reference request for a very particular problem solving skill

I want to start with an apology for a very verbose description of my question but if there is a way to cut it down, please let know and I will do so right away. I have been trying to get better at ...
2
votes
1answer
65 views

Proof that there are no solutions this equation. (3 variables, Square root and Sine) [on hold]

Hypothesis: There do not exist three different positive integers $a,b,c$ such that $$ -\sqrt{ab}\cdot \sin(p \cdot (a-b))+\sqrt{ac}\cdot \sin(p \cdot (a-c)) -\sqrt{bc}\cdot \sin(p \cdot (b-c)) =0 $$ ...
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0answers
34 views

Books or website about solving IMO problems

Hey I want to solve IMO problems like the problem in the image below, but I cannot solve the problem or any of the problems in the IMO, so do you guys have some good website or books that teach how to ...
0
votes
1answer
357 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
0
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0answers
22 views

Parameterization which is closed under addition

Suppose $\beta_1(t)$ and $\beta_2(t)$ are two parametric curves defined on $[0,1]$. Let $\beta_1^*(t)$ and $\beta_2^*(t)$ are two re-parametrized of the above curves. Now, I looking for a ...
4
votes
5answers
64 views

Why is the solution to $\sqrt{6-5x}=x$ only $x=1$ and not $x=-6$? [duplicate]

I solved the equation $\sqrt{6-5x}=x$ as follows: $$(\sqrt{6-5x})^2=x^2$$ $$6-5x=x^2$$ $$0=x^2+5x-6=(x+6)(x-1)$$ $$x=-6 \quad \text{or} \quad x=1$$ If I plug in $x=-6$ into the original equation, I ...
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2answers
2k views

Find a thousand natural numbers such that their sum equals their product

The question is to find a thousand natural numbers such that their sum equals their product. Here's my approach : I worked on this question for lesser cases : \begin{align*} &2 \times 2 = 2 + ...
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2answers
36 views

I need some help with Geometry. Is this a correct answer to this problem?

Good day, I have a question regarding geometry. I don't know whether my answer is correct because the answer in my book uses a totally different method for solving this particular problem. Here's ...
1
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0answers
31 views

Variation of the opaque forest problem (a.k.a farmyard problem)

I was wondering about the following variation of the opaque forest problem (see here and there for previous questions) : What is the least length set of segments that will intersect every straight ...
4
votes
2answers
56 views

The chart-problem; problem solving

In how many ways can we construct a $6\times 6$ chart with only $1$ and $-1$ such that in every row and column, the product is always positive?
3
votes
2answers
36 views

Combinatorics Question with bridges and inability to cross over each other

Several small villages are situated on the banks of a straight river. On one side, there are $20$ villages in a row, and on the other there are $15$ villages in a row. I would like to build bridges, ...
0
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0answers
39 views

How can the lagrange multipliers in a simple constrained cost minimization problem be calculated? (for binding constraints)

Is there a simple algebric way to calculate the shadow prices (lambda) of the binding constraints given below? This is a cost minimization problem dependent on the generation output. The cost of ...
7
votes
2answers
287 views

Prove Divisibility In Fibonacci Sequence Over A Prime Number

In The Fibonacci sequence which is defined as $$ F_n=F_{n-1}+F_{n-2}, $$ lets say we have the number $p$ which is an odd prime. Prove that: $F_{p-1} + F_{p+1} -1$ Is divisible by $p$. Prove that ...
3
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1answer
81 views

Which is larger, $e^\pi$ or $\pi^e$? [duplicate]

I don't know how to approach this. I tried expanding $e^{\pi}$ using the power series but that was a dead end since I didn't know what to do with it. I tried estimating if $e \log({\pi})$ was ...
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0answers
16 views

Erlang and Poisson Distribution [closed]

Erlang distribution is a series of Exponential distributions random variables having same parameter(arrival rate per unit time), now instead of taking all series of exponential distributions in Erlang ...
5
votes
1answer
44 views

What is the probability that the upturned faces of three fair dice are all of different numbers?

Three fair dice are rolled ($6$ sides). What is the probability that the upturned faces of the three dice are all of different numbers? I got that the number of possible outcomes total is $6^3$ ...
0
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0answers
69 views

Integration of the product of Hermite Polynomial and exponential function

how to proceed with these two integration.. $$\int^0_{−∞}e^{−ax2}H_{2k}(x)dx=?$$ $$\int^∞_{0}e^{−ax2}H_{2k}(x)dx=?$$ where $$H_n(x)$$ is the Hermite Polynomial (physicist's convention).
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2answers
43 views

How to solve this equation using logs

How do solve this equation for x using logarithms? $$4^x = 6^x-3$$ If it is not possible using logarithms, please provide another way. Thank you in advance
4
votes
2answers
246 views

Is there any easy way to solve two equations with three unknowns?

Is there a way to solve the below simultaneous equations? One possible solution is $a_1=20.0948$, $a_2=10.0948$, $a_3=6.3448$. The variables are actually dual variables of the binding constraints. ...
0
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2answers
52 views

Solving modulo equations with one variable

Given the following equation: $$10 = 4^x \pmod {18}$$ How can one know what are the correct values for $x$ ?
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1answer
52 views

Launching a Plaintext Attack against Affine Cipher

Update 2 Being new to the world of Stack Exchange I did not realize that there exists a site solely devoted to cryptography. In light of this, I hope someone could help me migrate this question to ...
0
votes
1answer
52 views

Why do people say that some problem is hard when they do not actually prove it?

I have read many times in different papers something like the following (I do not remember the exact words though): "The problem is nonlinear non-convex programming problem which is hard to ...
0
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1answer
34 views

PDF of negative $\cos(X)$

Let $Y = - \cos(X)$, then what will be the pdf? Please share if you have any idea. If $Y = \cos(X)$, where $X$ is uniformly distributed in the interval $(0, 2 \pi]$, then the pdf is given by ...
0
votes
1answer
19 views

Find the lenght of a rectangle between two parabolas

I'm trying to find the length of $PQ$ but the best thing I have done so far is finding that the point $T$ is $(0,4)$, as well as finding the distance between the two turning points to be $6$. Can ...
0
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0answers
24 views

What is the probability of having the second child as a boy? [duplicate]

A couple had their first child, a boy, born on Wednesday. What is the probability that the second child is also a boy ? I thought it was a simple case where the probability is just 1/2 because there ...
0
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0answers
40 views

Show that the integers $a$ and $b$ can be chosen such that $ ha-kb=1$ holds for any given integers $h$ and $k$

During a longer calculation I encountered a problem where I need to show that one can pick two integers $a$ and $b$ such that $ha-kb=1$. Here $h$ and $k$ are two given integers. We have to assume ...
0
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0answers
12 views

How to determine the right initial and boundary conditions of the nonlinear PDE system

The nonlinear PDE system is from a research paper in 2000. The authors solved the system by using an ordinary differential equation integrator in FortranVariable-coefficient Ordinary Differential ...
1
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1answer
24 views

Technical meaning of two alike combinatorial problems

I am confused in how to interpret two alike combinatorial problems, because to me they both look the same. These are the problems: How many ways are there to put $24$ distinguishable flags on $18$ ...
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votes
3answers
3k views

An equation about a rectangle with given perimeter

I am doing a revision calculator paper and am stuck on an algebra question. There is a picture of a rectangle. One side is $x-2,$ another side is $2x +1.$ The question is. Setup and solve an ...
1
vote
1answer
23 views

How to find a formula that is true for the given model in the First Order Logic?

I think I might get lost in the definitions. I am not sure if this is the right way to deal with models and formulas in the First Order Logic. I am not looking for the solution for this particular ...
0
votes
2answers
42 views

How many integers less than 2015 are multiples of 2 or 3 (or both)?

Here is what I did. To find all the multiples of 2 that is less than 2015 all we need to do is divide by 2. The same can be done for multiples of 3 that is less than 2015: 2015 / 2 = 1007 ...
41
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14answers
4k views

Examples of famous problems resolved easily

Have there been examples of seemingly long standing hard problems, answered quite easily possibly with tools existing at the time the problems were made? More modern examples would be nice. An example ...
0
votes
2answers
28 views

Basic probability exercise

Consider the problem of selecting two candidates from a group of five persons for a job. Knowing that the candidates differ in their degree of readiness (1 is the best prepared, 2 is less ...
0
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2answers
28 views

Calculate number of sides of cylinder so each side is a certain width

I'm working on a video-game and as part of the level, I need to create one half of the room curved. For the cylinder, all sides should be of width 450cm, and the cylinder will have radius of 1475cm, ...
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3answers
2k views

Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?

I understand "transform methods" as recipes, but beyond this they are a big mystery to me. There are two aspects of them I find bewildering. One is the sheer number of them. Is there a unified ...
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1answer
45 views

Balkan Olympiad in Mathematics 2001 [closed]

Where can I find the solutions of the problems from the Balkan Olympiad in Mathematics 2001, Belgrade?
0
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1answer
41 views

Finding the least number of dots to add into a 10x10 grid

I have a 10x10 grid where are some dots. What is the least number of dots that I need to add in order to have 3 dots in every row and column have odd number of dots in every row and column have ...
0
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5answers
49 views

380 is what percent less than 600?

I'm New to percentages and this sum is confusing me a bit. If the question was " 380 is what percent of 600" , I would have converted it to an equation as follows.. 380 = ?% × 600 'n then I could ...
0
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2answers
49 views

How to find the maximum of this function $\dfrac{(1+x+y)^2}{(1+x)(1+y)}$?

The function with two variables is defined as follows: $$f(x,y)=\dfrac{(1+x+y)^2}{(1+x)(1+y)},$$ for all $0<x_{min}\leqslant x\leqslant x_{max}<\infty$ and for all $0<y_{min}\leqslant ...
2
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0answers
26 views

expectation half-normal distribution or expectation Truncated Normal Distribution [duplicate]

I want to calculate integrals $$ \begin{split} \int_0^\infty x \exp\{ ax-b x^2\} dx &= \int_0^\infty x\exp\{-b(x^2-\frac{a}{b}x)\}dx\\ &= ...
1
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4answers
70 views

how to find $t$ from $2t^2-0.01t^4=100$?

how to find $t$, from $2t^2-0.01t^4=100$? I was guessing may be I can take $t^2$ common but if it is so so why cannot we take $t$ common in other cases? I mean, for example: $t^2+4t=-4$ why can we ...
0
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0answers
47 views

How to simplify a problem with two variables?

I am trying to solve this problem. Let $\Delta$ be a positive number. I would like to find the values of $x$ and $y$ such that: $$ \left(1+\dfrac{x}{1+y}\right)\cdot\left(1+\dfrac{y}{1+x}\right) ...