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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A non-equality and an inequality involving $y$ and $y_0$ from Spivak Calculus 4th ed.

It's Problem 22. from Chapter 1. I'm given: $y_0 \neq 0$ $|y - y_0| < \frac{|y_0|}{2}$ $|y - y_0| < \frac{\epsilon|y_0|^2}{2}$ and I must use them to prove that: $y \neq 0$ $|\frac{1}{y} - \frac{1}{y_0}| < \epsilon$ I haven't really ever done proof…
darkradeon
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Can we find the numbers for which the minimum of the net result is maximum?

A and B play a game.A selects one number from the set {1,2,..,9} at first and supplies it to B.B puts a plus or minus sign before the number(this act is visible to A).The process is repeated twice such that B can place a minus sign before a number…
Eisen
  • 2,434
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Distance Rate Time of 2 mice

Mouse A and Mouse B are separated by a distance of 1.62 meters underground. They decide to meet by digging all the way through. Mouse A will double his speed every day, that is, he starts to dig 2cm the first day, 4cm the second day, and so on.…
David
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equation with series

Hello to everybody I have a problem because I can't solve this equation: $$960 - \frac{84.60}{(1+x)^{\frac1{12}}} - \frac{84.60}{(1+x)^{\frac2{12}}} - \cdots - \frac{84.60}{(1+x)^{\frac{11}{12}}} - \frac{84.60}{(1+x)^{\frac{12}{12}}} = 0$$ I haven't…
Owl
  • 25
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Distance Rate Time problem

One morning, Ryan remembered lending a friend a bicycle. After breakfast, Ryan walked over to the friend’s house at 3 miles per hour, and rode the bike back home at 7 miles per hour, using the same route both ways. The round trip took 1.75 hours.…
user94805
  • 19
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Solving Euler's identity

When I first saw the Euler's identity $$e^{\theta i}=\cos(\theta)+i\sin(\theta)$$ I realized $$x=e^{\frac{πx}{2}}$$ must have a complex solution $x=i$. However, although I know the solution, I'm unable to find the way that leads to it. By some…
Blob Organic
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11 people learn 11 languages.

11 people will learn 11 languages. The teacher can teach two people two languages in each lesson. What is the minimum number of lessons required for 11 people to learn all 11 languages? (one person can learn the same language several times) My…
deepblue
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Solve for c , $y = x + c \big( \frac{mx}{c} + s \big)^a$

I get this equation $y = x + c \big( \frac{mx}{c} + s \big)^a$ how can I get the $c$ or $m$ ? I try with $\ln$ $\ln\big(\frac{y-x}{c}\big) = a \ln \big( \frac{mx}{c} + s\big)$ and now ?
juanpablo
  • 153
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Problems dependent on a parameter whose value makes every variation a new safari.

I am looking for problems dependent on a parameter whose value makes every variation a new safari. A good example of this would be the equation $x^n + y^n = z^n$ for integers $n, x, y, z$ with $xyz \ne 0.$ The case $n = 0$ has no solutions because…
Display name
  • 5,144
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how to solve $\sqrt{2x+5}+\sqrt{5x+6}=\sqrt{12x+25}$

Again a root problem.. $\sqrt{2x+5}+\sqrt{5x+6}=\sqrt{12x+25}$ Isn't there any standardized way to solve root problems..Can u plz help by giving some tips and stategies for root problems??
maths lover
  • 3,344
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Finding a vector maximising and minimising the inner product on two others vectors

I'm tying to solve a simple linear algebra problem. Let us assume that I have a vector space of dimension $R^N$. In that space I know two vectors $u$ and $v$. I want to find a vector $w$ that maximizes the inner product with $u$ but which minimizes…
Michaël Cretignier
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Solving expression

I have been struggling to show that for the following equation, where $\psi \in (0,1)$ and $S\in \{2,3,\dots\}$ $$\ln\left(\frac{1}{1-\sqrt{\psi}}\right) + \ln\left[\left(1 - \frac{\sqrt{\psi}}{S}\right)^{S}\right] - \psi = 0$$ is such that the…
danny dan
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Find the least next N-digit number with the same sum of digits.

Given a number of N-digits A, I want to find the next least N-digit number B having the same sum of digits as A, if such a number exists. The original number A can start with a 0. For ex: A-> 111 then B-> 120, A->09999 B-> 18999, A->999 then B->…
Siva Bathula
  • 123
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Exponential equation with a negative exponent

From the first sight, this equation: $\exp(-2at)=-\exp(-2bt)$ has no solution. However, Worfram Mathematica clams, it exists. I am wondering, what is the most common to solve it: perhaps, Taylor expansion? Minus in from of the second exponent…
anastasiiia
  • 131
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Finding the Remainder of $f(x)=(x-1)^2(x+2)Q(x)+R(x)$

So I'm a high school student and I'm stuck on a question. Please help. $f(x)=(x-1)^2Q(x)+3x+1$ $f(x)=(x+2)Q(x)+4$ $f(x)=(x-1)^2(x+2)Q(x)+R(x)$ My first approach was Making $R(x)=ax^2+bx+c$, I soon found out that there are only two equations not…
Lucas Kim
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