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
2
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2 answers

Solve: $2^{256} = 95^x$ ... what is $x$?

I expect the result to be around $40$, but I do not know how to get there? Not necessary to read: I'm doing this because I'm wondering how many (printable!) characters I need for a password strength of $256$ bit. $256$ bit is $2^{256}$…
Robert
  • 123
2
votes
1 answer

asymptotics of a solution for equation

I want to solve the equation $$\frac{x^{17/6}}{a^{17/6}} - \frac{x^2}{a} -1 = 0$$ where I assume $a \gg1$ and $x$ is the unknown. How do I compute the dependence of $x$ on $a$ as $a \rightarrow \infty$.
Descartes
  • 21
2
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1 answer

Find all pairs of integers (a,b), such that $a² + ab - b = 2018$

'Find all pairs of integers $(a,b)$ such that $a² + ab - b = 2018$' The way I have approached this is by considering each variables parity and then letting it be expressed as that parity with a different expression. For example, through casework,…
Okeh
  • 83
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2
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3 answers

At what speed should it be traveling if the driver aims to arrive at Town B at 2.00 pm?

A car will travel from Town A to Town B. If it travels at a constant speed of 60 km/h, it will arrive at 3.00 pm. If travels at a constant speed of 80kh/h, it will arrive at 1.00 pm. At what speed should it be traveling if the driver aims to arrive…
Peaceyou
  • 85
2
votes
1 answer

What is the greatest amount of postage you would not be able to pay...

What is the greatest amount of postage you would not be able to pay using only a combination of seven cent and seventeen cent stamps? I have done a similar problem and got it correct but I am just wondering if there are other ways to do this.…
NGPP1
  • 317
2
votes
2 answers

How to solve this trigonometric equation?

I want to solve the equation $$(3-\cos 4x)(\sin x - \cos x)=2.$$ I solve by putting $t = \sin x - \cos x$, but I can not find all solutions.
minthao_2011
  • 1,885
2
votes
1 answer

Fox and Gemstone problem. Weighing stones to compare bags.

There is a problem called Fox and Gemstone at topcoder: https://community.topcoder.com/stat?c=problem_statement&pm=14296 Basically, you have the ability to weigh individual gemstones against each other, but not whole bags of them. You must then…
HappyEngineer
  • 175
2
votes
4 answers

How long would it take Mustafa to do the job alone?

Murat and Mustafa can do a job together in fifteen days. After they have worked together for five days, Mustafa leaves the job. Murat completes the job in sixteen days. How long would it take Mustafa to do the job alone? The answer is 40…
semicolumn
  • 49
2
votes
2 answers

Problem involving counting about marbles

Five red cards and four blue cards are blaced in a bag, five cards are selected blind from the bag, what is the probablity that they are all red?
Lama
  • 43
2
votes
2 answers

Sultan's law involving outnumbering

A Sultan wanted to increase the number of women in his country, as compared to the number of men, so that men could have larger harems. (Sorry ladies!) To accomplish this, he proposed the following law: As soon as a mother gave birth to her first…
Justin
  • 1,225
2
votes
1 answer

Need Help Building An Equation to Find an Angle for Zeroing on a Rifle Scope

My name is Michael, and I am trying to create a small video game. I am only in high school, so my math skills lack which is why I am here to find help from nice people! I am trying to find an equation for an angle a rifle should shoot at to…
Michael
  • 23
2
votes
4 answers

Solving equations with $x^x$ on any given side

How would you solve such an equation if it's infeasible to just start trying different $x$ values? Example: $$x^x = 6.$$
moonman239
  • 553
2
votes
2 answers

Solve for a variable in the power when the base are two different values

I would like to solve for $C$ $$7^C \times 2^{n-C-1} \le \frac{2^n}{100}$$ Real questions. The different base is really throwing me off. I got up to $$7^C 2^{-C} \le \frac{1}{50} $$
chibro2
  • 1,447
1
vote
1 answer

Obtaining an expression between $s'(n,r)$ and $s(n,r)$

I've a doubt in this: We're given $[x]_n=(x)(x-1)\ldots (x-(n-1))$ and $[x]^n=(x)(x+1)\ldots (x+n-1)$ . Now as we can write : $[x]_n=(x)(x-1)\ldots (x-(n-1))=a_0+a_1x+a_2x^2\ldots +a_nx^n$. Here the coefficient of $x^r$ in expansion…
spectraa
  • 1,775
1
vote
2 answers

Show that Mandelbrot set is contained within the closed disc of r=2

Show that the Mandelbrot set is contained within the closed disc of radius 2 around the origin. How do I show this?
Nick B
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