Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [problem-solving]

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.

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.

4495 questions
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Help Solving Equation From A Paper

In the paper, entitled: A Closed Form Solution for the Pull-in Voltage of the Micro Bridge (Link to PDF: https://pdfs.semanticscholar.org/0d31/33707b1243f6b4e3344c4fa19b831b010b8b.pdf) ... the following equation appears: I really don't know how…
james
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3 answers

Find a bug under 6 tiles

The question seems rather simple, yet it is suprisingly difficult. There is a bug under one of six tiles and it is my job to find it. The tiles lie in a row. At night, the bug moves randomly 1 tile, so it either moves to the left or to the right.…
Alex
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How to deal with a mathematical problem if I don't know the answer?

The problem is I'm looking on shortest path between points problem and the intuition tells me that the shortest path between points happens when paths don't cross. It's a step one. Then for all sub-paths we're connecting nearest points (I didn't…
Smart Wannabe
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How can I solve this nice rational equation

I am trying solve this equation $$\dfrac{3x^2 + 4x + 5}{\sqrt{5x^2 + 4x +3}}+\dfrac{8x^2 + 9x + 10}{\sqrt{10x^2 + 9x +8}} = 5.$$ Where $x \in \mathbb{R}$. I knew that $x=-1$ is a given solution. But I can't solve it. I tried We rewrite the given…
minthao_2011
  • 1,885
4
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5 answers

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.
Dingo13
  • 435
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1 answer

A 20 × 20 × 20 cube is built of 1 × 2 × 2 bricks. Prove that one can pierce it by a needle without piercing a brick.

A 20 × 20 × 20 cube is built of 1 × 2 × 2 bricks. Prove that one can pierce it by a needle without piercing a brick. Taken from Engel's book, but no solution was given. Here's my solution: Look down one of the faces of the cube. Call the 19^2…
user1299784
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how does the word math represent a four digit number

I just don't get it had it on a test can you help me? It was a test for math olympiads this is how the question looked exactly: MATH x 4 …
lili
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No idea how to solve this equation using two exponentials

The equation I have is: $$A = B ( \exp(C x) - \exp(-Dx) )$$ How do I solve for $x$ given $A$, $B$, $C$, $D$? I have no idea how. The only idea I have is that I could express these in terms of a taylor series, but is there a better way that I do not…
sciencenewbie
  • 217
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Prove some member of the sequence $7, 77, 777, 7777, \dots$ is divisible by $2019$.

Prove that some member of the sequence $7, 77, 777, 7777, \dots$ is divisible by $2019$. So far I have figured that as $2019$ is divisible by $3$, then if one of the terms of the sequence $$ a_{n} = 7\left(\frac{10^{n}-1}{9}\right) $$ is divisible…
Kit Boothroyd
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Mathematical problems solved by (biological) evolution

The bees have solved the problem of dividing a surface into regions of equal area with the least total perimeter (honeycomb conjecture) by trial and error. Are there any other examples of solutions of mathematical problems by biological evolution,…
curious_metazoan
  • 359
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3 answers

When to sell a coin collection

Problem: A person inherits a coin collection that has a value of $2000e^{\sqrt{t}}$ m.u. (monetary unit) after $t$ years. Assume a bank interest of 7% per year. At which time $t_0$ years (if there is one) is it best to sell the coin collection and…
mf67
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Dividing planes with lines and spheres

What is the greatest number of parts a plane can be divided into using $n$ infinite straight lines? What about $n$ circles? Can you generalise this into 3-dimensional space, planes and spheres? For lines, I got $U_{n+1}=U_n+n,$ with $U_0=1.$ And for…
user61067
  • 467
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How to solve system of equations?

I want to sove the system of equations $$\begin{cases} x^3 y-y^4=7,\\ x^2 y+2 xy^2+y^3=9. \end{cases} $$ I tried divide these two equations we obtain $$\dfrac{x^3 - y^3}{(x+y)^2 } = \dfrac{7}{9}$$ From here, I don't know how to solve.
minthao_2011
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greatest common divisor is 7 and the least common multiple is 16940

How many such number-pairs are there for which the greatest common divisor is 7 and the least common multiple is 16940?
NGPP1
  • 317
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2 answers

Silly maths question about heuristics

A farmer owns $200$ kg of cucumbers that contain $99 \%$ water. After a day lying in the sun, the cucumbers only contain $98\%$ of water. How much kg does the farmer has now? How silly it may seem I don't really understand why the answer is…
Anonymous196
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