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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Not able to solve $({\frac{1}{2}})^p + ({\frac{1}{3}})^p + ({\frac{1}{7}})^p - 1 = 0.$

I'm not able to solve $$({\frac{1}{2}})^p + ({\frac{1}{3}})^p + ({\frac{1}{7}})^p - 1 = 0.$$ If you put values of $p$ (like $\frac{1}{2}$ or 2) back in the equation it doesn't satisfy! So please check your values also. What I found is: If $p = 1$…
Arnab Dutta
  • 597
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Improving Problem Solving Skills

After recently getting into math and math problem solving, I took the AMC 10 (my first AMC exam) and got a rather low score. I want to improve my problem-solving skills and perhaps double-degree in the future (music performance + math). I am…
user913112
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Find the domain of $f(x)$ $=$ $\sqrt{1 + ln(1- x)}$

My solution Since the argument of ln must be greater than zero: $1 - x > 0$ $ - x > -1$ $ x < 1 $ Then, because $f(x)$ must be a real number, we have: $1 + ln(1-x) \ge 0$ $ln(1-x) \ge -1$ For the next result I used the follwing property: $e^{ln…
Nameless
  • 415
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Write 1000 using three 13s

The brother of a classmate, who is in elementary school, got the following homework, but he can't figure it out. So his brother shared it to see if someone in his class could help out with it: "Write the number 1000 with 3 numbers 13". Only the…
freethinker36
  • 232
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$|f''(x)|\leq M$ implies $|f(c)-f(a)-(c-a)\frac{f(b)-f(a)}{b-a}|\leq \frac{1}{8} M(b-a)^2$

I am stuck with this problem. $f : [a,b] \to \mathbb R$ is double differentiable on $[a,b]$ and suppose $|f''(x)|\leq M ~ \forall x \in [a,b]$. Let $c \in (a,b)$. Then $|f(c)-f(a)-(c-a)\frac{f(b)-f(a)}{b-a}|\leq \frac{1}{8} M(b-a)^2$ I can prove…
user732848
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What strategy would you use to make your mathematics sound in this question?

The domain of $f(x)$ is $\mathbb{R}$. For all $x \in \mathbb{R}$, $f(x+1)=2f(x)$. For $x \in (0,1]$, $f(x)=x(x-1)$. Find the least value of $k$ so that $f(x) \geq -\frac{3}{4}$ for all $x \in (-\infty, k]$. I tried manipulating first $f(x+1)=2f(x)$,…
Billy Claxtone
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What formula could I use to find out how many paperclips my factories could produce?

I'm playing Universal Paperclips and I'm near the end of the game. I currently have 2.3 quadrillion factories. Each factory un-upgraded can produce 100 billion clips per second. The first upgrade increases each factory's performance by 100x. The…
Himitsu_no_Yami
  • 63
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Problem solving : calculate the maximum profit

A small company produces flower groups for Christmas. They have access to two sorts of flowers “hyacinter” and “Christmas stars”. For flower group A it’s needed 5 hyacinter and 2 Christmas stars and for group B it’s needed 3 hyacinter and 4…
Pedro Alvarès
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How do you solve $r=\operatorname{ceil}\left(\frac{l+r\cdot t}{c}\right)$ for $r$?

As I was creating a function for printing monospaced text to a limited-length console with a certain level of indentation, I found a difficult equation to solve without programming around it: $r=\operatorname{ceil}\left(\frac{l+r\cdot t}{c}\right)$.…
Zach K
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How do I solve: tan(a + ...) - tan(a + ...) = tan(a + ...) - tan(a + ...)

How would I go about solving this equation for $ \alpha $? $$ \tan (\alpha + \Theta _1) - \tan (\alpha + \Theta _0) = \tan (\alpha + \Theta _0) - \tan (\alpha + \Theta _2) $$ Is there a way to calculate $\alpha$ directly or do I have to…
GRASBOCK
  • 123
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If $U = f(y+αx) + f(y-αx)$, with $f$ differentiable, show that when $x=0$, then $Ux = 0$.

Can anyone help me with the following execrise? If $U(x,y) = f(y+αx) + f(y-αx)$, with $f$ differentiable, show that when $x=0$, then $U_x(0,y) = 0$.
Dhmhgr13
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solve an equation with a given value

I'm trying to solve the following equation for the value of t, but either my computer is too slow or the function is too sophisticated. The cell bar on the right side is just black and the program doesn't solve it. The equation is:…
Elijah Shepherd
  • 111
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How to arrive from $x^2y^2－x^2－y^2－6xy＋4$ to $(xy＋x＋y－2）(xy－x－y－2）$?

How do we arrive from $x^2y^2－x^2－y^2－6xy＋4$ to $(xy＋x＋y－2）(xy－x－y－2）$ ? According to my book these two are equal, but I can't understand how to transform one to another.
brilliant
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(Business Math) Compound Interest Problem Solving

John invested his money in a time deposit that pays $0.5\%$ compound interest in a year. How much will his money be after $5$ years? How much interest will he gain? Given: Rate ($r$): $0.5\%$ or $0.005$ Time ($t$): $5$ years Principal Amount…
AnotherStudent
  • 21
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How do I simplify integrating factor?

I have obtained following integrating factor from ODE ($y^{\prime} + a(x) = g(x)$): $ e^{\,A(x)} \:\:=\:\ e^{- \ln |\cos(x)|+c}$ where $ e^{\,A(x)}$ is integrating factor and $A(x) = \int a(x)\,\mathrm{d}x$. $e^{- \ln |\cos(x)|+c}$ should equal to…
Josh E.
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