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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Solving equation with exponentials

How to solve $ {z = x^y, x = y^z, y = z^x }$ for $ x, y $ and $ z? $ Is some sort of triple Lambert W to be introduced? Done so far: Taking logs, $$ \log z = y \log x , \log x = z \log y , \log y = x \log z ; $$ Plug the third into second and that…
Narasimham
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One hundred indistinguishable ants are dropped on a hoop of diameter 1

I have this question which I am not sure how to solve: One hundred indistinguishable ants are dropped on a hoop of diameter 1. Each ant is traveling either clockwise or counterclockwise with a constant speed of 1 meter per minute. When two ants…
user121692
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What are solutions to $2^x=x$?

Are there any solutions (real, complex , matrix etc.) to $2^x=x$? The best I can come up with is $\ln 2 = \frac{\ln x}{x}$ or $x^{\frac{1}{x}}=2$
jimjim
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How to show that $3^x+4^x=5^x$ has only one solution?

How to show that $3^x+4^x=5^x$ has only one solution? Thanks in advice.
Hakoona Matata
  • 99
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How can I solve the system of equations?

How can I solve the system of equations? $$\begin{cases} x^2 y^2+12 x y^3-18 x y-18y^4-4 y^2+27=0,&\\ x^2 y^2-3 x y^3-3 x y+5 y^2=0. \end{cases}$$ I have not any idea to solve.
minthao_2011
  • 1,885
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Is there a solution to the equation x^x^x^x^x^x^... = 2?

I have been asked the following brainteaser, is there a solution to the equation: $$ x^{x^{x^{...}}} = 2$$ (x to the power of itself an infinite number of times) I am not sure about how to approach this one.
BlueTrin
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Number of Chess Moves that a piece is lost

Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you can't avoid taking over another piece? (Assuming of…
iordanis
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Solving for x in equation for chem

In the answers to a chem problem is just gives this equation: (34.969) (x) + (36.966) (1 - x) = 35.453, and says solve for x. But I have no clue how to solve for x....
windy401
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If I end up with $10,000 because I lost 20% in 2 years...

If I end up with 10,000 after losing 20% in two years...How much did I have in the first place?
user173640
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How to solve this age problem?

I am solving the following question. Please guide me!! The ages of A and B are in the ratio of 5:7 and C and D are in the ratio of 5:7.Let sum of their ages is 150, what is the difference between the ages of A and D? My Solution: $A/B= 5/7$ , Thus…
Syeda
  • 125
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Solving an equation

I have the following equation: $x_1^3 = \hat{x}_1^3 + e_1\delta(x_1,e_1)$ I have to find the function $\delta(\cdot)$ for which this equation holds. By definition: $e_1 = \hat{x}_1 - x_1$ So I am able to write: $x_1^3 = \hat{x}_1^3 +…
Pietair
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LASSO Problem - A matrix structure!

I'm wondering if anybody knows about the structure of $A^{m\times n}$ in real big data LASSO problems. I want to ask if anybody know what is the degree of sparsity and separability(number of nonzero elements in each row) of this kind of problem in…
Amir D.
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Unsure how to solve equation

I have the problem. Solve: $x^3 - 3x^2 + 2x - 5 = 0$. I've done similar, simpler ones like this, but in this case I don't know. Can someone at least tell me what you'd even call this exact type of problem so I can google it and learn how to do this…
windy401
  • 1,211
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How many real solutions of this equation?

How many real solutions of this equation $$\sqrt{x}+\sqrt{1-x^2}=\sqrt{2-3 x-4 x^2}?$$ I posted my question at here https://mathematica.stackexchange.com/questions/51316/how-can-i-get-the-exact-real-solution-of-this-equation In my opinion, there is…
minthao_2011
  • 1,885
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How does $2N_{h-2}$ become $2^{h/2}$?

I'm reading the Lecture 6 notes from MIT OCW Introduction to Algorithms, which discusses AVL trees, and I'm confused about one of the relations below: Balance: Worst when every node differs by 1 -- let $N_h$ = min # nodes in height-h AVL…
tony19
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