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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What is the method of solving an equation set in which the unknowns are in denominator?

$ \frac{a_1}{x} + \frac{b_1}{y} + \frac{c_1}{z} = d_1 \\ \frac{a_2}{x} + \frac{b_2}{y} + \frac{c_2}{z} = d_2 \\ \frac{a_3}{x} + \frac{b_3}{y} + \frac{c_3}{z} = d_3 $ $ a_i, b_i, c_i, d_i $: known constants $ x, y, z $: unknown variables First of…
hkBattousai
  • 4,543
3
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7 answers

Evaluate $x+y=xy=3$ how would you evaluate $x^4+y^4$?

I know how to evaluate $x^3 +y^3$ when $x+y=xy=3$, but how would you evaluate for? $$x^4+y^4$$ Any help would be appreciated.Thanks in advance!
mathfanatic
  • 31
3
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0 answers

Sought-Given-Solution-Answers

I am a German student attending lectures delivered in English at the KTH Stockholm. There I am supposed to solve a problem sheet, using a "Sought-Given-Solution-Answer approach". I am not really into english math. Is it just meant to be…
Adrian Pfeifle
  • 131
3
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1 answer

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 $$t^4+t^3-7 t^2-5 t+16=0. \tag{2}$$ But I can't prove two equations (1) and (2)…
minhthien_2016
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1 answer

Solving the simultaneous equations $x + y - z = 12$ and $x^2 + y^2 - z^2 = 12$

I found the following question online (it was a past question on the BMO): find all positive integer solutions $x,y,z$ solving the simultaneous equations $ x + y - z = 12 \ $ and $\ x^2 + y^2 - z^2 = 12 $ . Normally these questions have a simple…
Zestylemonzi
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4 answers

Variation of a "Who is Lying" Question

While reading Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr, I came across a problem I was not sure how to solve. One of the five members of a company's board of directors…
Joe
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Sequence pattern question

I have the following question. Let $S_1$ be the sequence of positive integers $1,2,3,4,5 , \ldots$ and define sequence $S_{n+1}$ in terms of $S_n$ by adding $1$ to the integers of $S_n$ which are divisible by $n$. I need to find integers $n$ such…
user121692
  • 417
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0 answers

$\frac{dy}{dx}=\sum_{k=1}^{\infty}a_k(m-k)x^{m-k-1}$ or $\frac{dy}{dx}=\sum_{k=0}^{\infty}a_k(m-k)x^{m-k-1}$

If I have $y=\sum_{k=0}^{\infty}a_kx^{m-k}$ ,then is $\frac{dy}{dx}=\sum_{k=1}^{\infty}a_k(m-k)x^{m-k-1}$ correct because ..I'm confused whether $k$ should start from $0$ or from $1$. Please explain..
kittuu
  • 161
2
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0 answers

Trying to make a formula to find maximum driving time.

I am trying to figure out how to make a formula (that will eventually be used in excel.) to figure out, how much driving time could be done in a block of time. In this case, 24 hours. And theses are the variables: 1 Driver can drive 3 different…
eeb3
  • 21
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3 answers

Guess the right permutation game

Consider the following game (somewhat similar to Bulls and Cows): player A selects a permutation of $n$ different numbers, say $1$ to $n$. Player B then has to guess the permutation: he suggests some permutation and A has to reveal which numbers are…
malenkiy_scot
  • 517
2
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2 answers

Solve this equation. Can anybody do it?

$$x / y = a + b \log(y)$$ Above is a relation between x and y. I have x. How do I find y ? Given: a and b are constants. a is 0.710 while b is -0.014
MycrofD
  • 231
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2 answers

How to solve this equation or system of equations?

I want to solve the equation $$(5 x-4) \cdot\sqrt{2 x-3}-(4 x-5)\cdot \sqrt{3 x-2}=2.$$ I tried. Put $a = \sqrt{2 x-3}\geqslant 0$ and $b =\sqrt{3 x-2}\geqslant 0 $. Suppose $$5x-4=m(2x-3)+n(3x-2)$$ then $m=\dfrac{2}{5}$ and…
minthao_2011
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2
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1 answer

Calculate the area of this object problem

Stuck on the last questions of my homework that's due in tomorrow. Somebody help. I think it's to do with integration but i can't do it. Can anyone give me a hint?
John
  • 111
2
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2 answers

Based on census data and namm data, how many musicians are there?

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there? Any help would be appreciated...
brendan
  • 21
2
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1 answer

Pile of cards(Tournament of Towns)

I have been trying this problem for a while.But somehow, my proof(I tried an inductive approach) appears to be break down at some point.Here it is: There is a large pile of cards.On each card one of the numbers 1,2,..,n is written.It is known that…
Eisen
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