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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Is it possible to solve for $3$ or more unknowns with only $1$ equation

Example: $$x+3y+7z=221$$ or $$2x+5y+z+9i=383$$
tucker19
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Then the number of solutions of $| x^ 2 − [ x ] | = 1$ is?

Let $[ x ]$ denote the greatest integer less than or equal to $x$ for any real number $x$ . Then the number of solutions of $$| x^ 2 − [ x ] | = 1$$ is? A. 0 B. 1 C. 2 D. 3 By trial and error i got only $+\sqrt{2}$ as the…
onelessproblem
  • 383
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Let $a, b, c ∈ R$, $a^{2}+b^{2}+c^{2}=1$and $A = ab + bc + ca$. Then $A$:

Let $a, b, c ∈ R$, $a^{2}+b^{2}+c^{2}=1$and $A = ab + bc + ca$. Then $A$: (A) $-\tfrac{1}{2}< A < 1 $ (B).$ −1 < A < 1$ (C) $-\tfrac{1}{2}< A \leq 1 $ (D) $-\tfrac{1}{2}\leq A \leq 1 $ $$\left ( a+b+c \right )^{2}= \left ( \left ( a+b \right…
AskMSellen
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Solve $\frac{4^{2x}+4^x+1}{2^{2x}+2^x+1}=13$ for $x$

Solve $$\frac{4^{2x}+4^x+1}{2^{2x}+2^x+1}=13$$ for $x$ Any help is appreciated. I'm entering a challenge and can't reach the solution.
Nour
  • 896
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What is a common value and how to find it?

I have googled this term and did not find anything useful. This term is used multiple times in this problem explanation from the recent AMC. For example, I do not understand how the common value of $x+2$ and $3$ is $3$ and of $x+2$ and $y-4$ is…
shurup
  • 251
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Shorter proof for this?

if $G = T + N$ and $T = N * t$, where $t$ is a $\%$, find $T$ if the only given values are $G$ and $t$. I already has a formula but it needs to compute for $N$ first which is lengthy, is there a shorter formula without computing for $N$…
John Isaiah Carmona
  • 113
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Finding the highest possible product from the make up of a number

The Question This question is a maths challenge and well to explain it better I will use an example. I have a number, say $20$ I can write this as $10 + 10$ (this is a make up of the number) Now I multiply the two numbers to get $100 = 10 * 10$ The…
Max
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solving the equation to find variables.

I have an equation $M = P\left(\frac{J}{\left(1-\left(1+J\right)^{-N}\right)}\right)$ I am trying to solve it to find J but I am stuck at $\frac{P}{M} = \frac{\left(1 + J\right)^N - 1}{J(1+J)^N}$ can you please help me? Thanks!
studentMathSoftware
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Algebra: Finding rate

Here Is The Problem. Julia drove from her home to her aunt's house in 3 hours and 30 minutes. The distance between the houses is 175 miles. Knowing that distance = rate X time, find that car's average speed. Answer d = 175 mph t = 3 1/2, then 175…
Bossman759
  • 79
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Grade 10, waiting for the train.

At Berracan station, northbound trains arrive every three minutes starting at noon and finishing at midnight while southbound trains arrive every five minutes starting at noon and finishing at midnight. Each day, I walk to Berracan Station at a…
User171200
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Text problem with workers

I'm having an entrance examination in two days and I'm having problems with this math problem here. A group of workers works on two jobs in two days. The second job is 2 times smaller in volume than the first one. The first day till midday the…
Gigaxel
  • 207
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How often does theorem equivalence take place?

I remember reading once that it was found that two math theorems were essentially equivalent to each other, how often does this occur? ex. In two dimensions the divergence theorem is said to be equivalent to Green's theorem.
user344278
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Choosing pairs of numbers with distinct bounded sum

Stumbled across this problem in the list of examples for high school math exam, paraphrasing a little: What is the maximum number of pairs with integers from 1 to 22 you can choose, with each pair having a distinct sum that would not exceed…
swish
  • 850
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Can you factorial a power?

I know this may be a straight forward question, but I looked around on google for about 20 minutes to find nothing. I am currently a year 8 student and came across a problem where I have to find the highest number using the four following numbers:…
Syzcai
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Is there another way to solve this equation?

My problem is Solve the equation $$2 \left(\sqrt{x^3-7 x^2+17x-14}+\sqrt{x^4-7 x^3+23x^2-37 x+28}\right)=4x^2-17 x+25.$$ And my solve. We have $$\sqrt{x^3-7 x^2+17x-14}= \sqrt{(x-2) \left(x^2-5 x+7\right)}\leqslant \dfrac{(x-2) + (x^2-5 x+7)}{2}=…
minthao_2011
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