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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Searching for an explicit functional form

Let $f:\mathbb N \to \mathbb R$ be a strictly decreasing function. Suppose $$\frac{f(x)}{f(x+1)}=2^x,\qquad \forall x\in\mathbb N.$$ Is it possible to find an explicit functional form of $f$? Any hint at finding a solution is appreciated.
Herr K.
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solve for m by rewriting the equation (transposition)

In the following equation how would I rewrite the equation to solve for $m$? $$z=\frac{-4m-8+\sqrt{(4m+8)^2+4(4(mx+y-4m-4))}}{8}$$ when $x=66$ and $y=22$ and $z=10$
DeveloperChris
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The Generalized Jug Problem - a different question

“If you have a five-liter and a three-liter bottle and plenty of water, how can you get four liters of water in the five-liter bottle?” We (all) know this problem, and its natural generalization, “Given a p-liter and q-liter jug what amounts…
Fabio Carello
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Analytical methods to solve a cubic equation

I'm having trouble solving this cubic equation: $x^3 - 7x^2 -27x+64=0$ I was able to prove that it has no rational roots, and by graphing the cubic function, I found that its 3 roots are all real, being irrational. Is there any analytical method of…
Train Heartnet
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How do I know if a theorem has been proposed and proved

I'm trying to write a paper where the proof requires some theorems. I can prove these theorems myself, but I don't know if they have already been proved, and if so I only need to quote them. Is there any alternative to reading more papers? Or…
槿铃兔
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How do I determine whether our idea is novel?

Mathematics talent runs in my family, but although I enjoy learning about things in mathematics and biostatistics, I am a biochemist by training. So I read a blog post by a mathematician, and started thinking, and writing, and consulting with my…
Michael Roberts
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Can you hand calculate an unknown exponent above 0 and below 1 easily?

Can you hand calculate an unknown exponent? I was recently calculating something and entered $\log 6.7$ in my calculator only to quickly feel frustrated that I did not even know how to begin to calculate by hand the number. Is there a method to hand…
CodeCamper
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Equation to find how many cubes can be used to create a bigger cube

I think I was able to solve the following problem without algebra but I would love to know if there is an equation for this problem: Twenty-seven unit cubes are coloured completely blue or completely yellow. All twenty-seven unit cubes are…
dagda1
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How to solve a system of equations

I have this system of equations: 3x²+7y²=55 and 2x²+7xy=60 Is there a method of solving [x,y] without using x²=t, y²=z?
Ofir Orpaz Elman
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Represent RPG Increasing Formula

I am having trouble with the following math problem. There is a variable "xp" that starts at 0. At xp of 0, the level is 1. At xp 500, the level is 2; at xp 1250 the level is 3; at xp 2250 the level is 4, and so on. 0 xp (lvl1) + 500 xp (lvl2) + 750…
Abdulla
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Hotel room number problem

There is a building containing N number of hotel rooms. All of these hotel rooms have a unique hotel room number. There is an employee in charge of looking after each hotel room. One day, the employees are curious to find out the room numbers of all…
liam casey
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Tips for solving equations for a variable

I am trying to solve the following equation for $V_{12}$: $$\sqrt{\frac{1+\frac{V_{1}}{c}}{1-\frac{V_{1}}{c}}}\sqrt{\frac{1+\frac{V_{12}}{c}}{1-\frac{V_{12}}{c}}}=\sqrt{\frac{1+\frac{V_{2}}{c}}{1-\frac{V_{2}}{c}}}$$ (this is not really relevant, but…
jng224
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How to solve for t in the equation mentioned below?

Equation: $(25+e^{4t})(2e^{2t}) - \frac{3}{2}(4e^{4t}) = 0$ I'm having some problems solving for t. These are the steps I attempt to take: $50e^{2t} + 2e^{6t} - 6e^{4t} = 0$ $50 + 2e^{4t} - 6e^{2t} = 0$ $2e^{4t} - 6e^{2t} = -50$ $e^{4t} - 3e^{2t}…
Amai
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What is the solution to this equation: $e^x+2x=0$

I cant find any program that actually solves this type of equations and I cant find anything helpful about this type. What is the name of these equations and how do I solve this one? Thanks.
Antonis
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Word problem - Problem Solving

My kid is practicing word problem. I have an issue with the question which i m unable to produce any solution. Would be appreciated if any solution is provided. QUESTION: In the village there were four different types of animals: pigs, sheep,…
Muhammad Umair Shafique
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