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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How to solve an irrational equation?

I want to solve this equation $$2 (x-2) \sqrt{5-x^2}+(x+1)\sqrt{5+x^2} = 7 x-5.$$ I tried The given equation equavalent to $$2 (x-2) (\sqrt{5-x^2}-2)+(x+1)(\sqrt{5+x^2}- 3)=0$$ or $$(x-2)(x+1)\left [\dfrac{x+2}{\sqrt{5+x^2} + 3} -…
minthao_2011
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Clock Problem, Number of Chimes

An old fashioned clock chimes as many times as the number of hours it is when it hits a new hour. For example, the clock ticks two times when the clock reads two or the clock ticks 12 times when the clock reads 12. Additionally, it ticks exactly one…
algebra1
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A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two will appear?

The "at least" confuses me. But I am assuming one head will appear. Making P(first head) = 1. Correct answer: 3/7 I start with the formula: P(A and B) = P(A) • P(B|A) Fitting the conditions into this formula, P(A) = 1, P(A and B) I interpret as…
most venerable sir
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Is there an exact answer to this equation?

$$\frac{1}{x} +\ln(x)\ln(\ln x)=1$$ The solution to this equation is approximately $x \sim 5.13425\ldots$ but is there an exact answer?
Rob
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Problem leading simple equations

A sum of Rs. 8.85 is made up of 124 coins which are either 10 paisa coins or 5 paisa coins ; how many coins are there each Note : Rs. 1 = 100 paisas
user245542
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Simplifying $\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$

Simplifying $$\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$$ When I try, the numerator cancels out to $0$, yet the answer sheet says $(25-a)^2/10000$. Where am I going wrong & how is getting $10 000$ there even…
Christabel
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How to calculate perimeter using the area and the perimeter of a smaller area

I have having trouble understanding how to break this problem apart. I have an $ L$ shape with a rectangle in it. The smaller rectangle has a side of $5 m$ and a side of $7 m$, the $L$ shape has an area of $6.25m^2$ I can work out the total area…
Ashley Hughes
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Fitting the closest coefficients in a system of millions of simultaneous equations?

I don't really know the correct terminology to describe this, but let's say we have many values of $(x_n, y_n, z_n)$. Also let's say that our description of 'many' means that $i$ ranges from $1$ to some number in the order of millions. I would like…
Genghis Smith
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Surface Area and Volume relationship

I know that the $SA = 6s^2$ and that the volume is equal to the base $x$ the $side = s^3$. However, I'm not sure how to approach this though.
Hamza
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How does one find the change?

I tried using ratios but I failed. I need to subtract one to get the correct answer. I remember finding the change before, but I've forgotten how to. Any hints?
Hamza
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Solve $16x^{-3}=-2$

Solve $16x^{-3}=-2$. My working: \begin{align} 16x^{-3}&=-2\\ \frac{1}{16x^{3}}&=-2\\ \frac{16x^3}{16x^3}&=-32x^3\\ 1&=-32x^{3}\\ -32x^{3}&=1\\ -32x&=\sqrt[3]{1}\\ -32x&=1\\ x&=\frac{-1}{32} \end{align} Is this right? What have I done wrong?
Thomas Winkworth
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Four golfers in a square in two teams of two - who tees off second given that one person is diagonal from another?

I am not sure if I am interpreting the question correctly per se. I drew a picture in which Clark was diagonal from Diana. So, that means Chris could either face Clark OR Diana. If Chris is facing Clark, then Chris tees off first and Diana tees off…
Joe
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Is there a method or algorithm to solve "in what base is the equation true" questions?

I have been given some exercises in which I'm given some equation that doesn't hold in base ten, and I need to figure out in which base the equation does hold. For example: $\sqrt{41} = 5$ which I guessed by trial and error and concluded base…
Alex Terreaux
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List of N items, randomly putting them in order, showing the procedure ends.

On a bookshelf, there are N tomes of the encyclopedia in random order. Every hour, a librarian takes a tome which is not in place and puts it in its place, and we must show this process will stop eventually. I managed to solve this question assuming…
sagooz
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Problem Solving - Ways to add 6 even, positive, non-zero integers to get 26

I believe I have gotten all of the ways now - thanks for the hints below Yun, Andre Nicolas, and Gerry Myerson. If anyone could confirm my answer (I feel there should be more possibilities, but for the numbers to be increasing left-right, I have…
Joe
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