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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How many number of buses that the car encounter?

A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km.…
Android developer
  • 235
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Solving the following equation

What is the easiest way to solve the following equation for g in terms of x? I seem to be going in circles, and don't know how exactly to deal with the $\pm$ symbol. Equation: $$\pm \sqrt{2}x + \ln(2\sqrt{6}+1)=…
user85362
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At Great Value Expression

Hi, How can I find the greatest value of $2k\sqrt{(r-k)(r+k))}$ with parameter $r$ such that $(r>k)$?
Andi
  • 13
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How to solve an equation involving the exponential and the logarithm

The equation $\log_3(\sqrt{x+1}+1)=(3^{x+1}-1)^2\,$ has two solutions, but I can't solve the equation.
user117872
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How to solve this nonstandard equation?

How to solve the equation $$\mathrm{e}^x + (x^3-x)\cdot \ln(x^2+x+2) - \mathrm{e}^{\sqrt[3]{x}}=0?$$ I tried. We have $x=1$ is a root of the equation. If $x>1$, $x > \sqrt[3]{x}$, therefore $\mathrm{e}^x>\mathrm{e}^{\sqrt[3]{x}}$ and $x^3 >x$,…
minthao_2011
  • 1,885
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Help understand Schwarz Inequality soqlution from Spivak's Calculus

I'm given this inequality from Spivak's Calculus book: And I need to do this: Here is the answer from the answer book: I am completely unsure what to do.I have $x_1, x_2, y_1, y_2$ in the inequality, but just $x$ and $y$ in the $(b)$…
darkradeon
  • 297
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I reach a half-dead end when trying to find the minimum possible value of an equation

I have the equation $x^2 + 4xy + 5y^2 - 4x - 6y +7$ and I'm supposed to transform it to look like this: $[x + 2(y - 1)]^2 + (y + 1)^2 + 2$ First I transformed it into: $x^2 + 4x(y - 1) + 5y^2 - 6y + 7$ and then completed the square for $x$: $[x +…
darkradeon
  • 297
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Extraneous solutions to simple equations

I had an interesting thought during my procrastination: is it legal to take an equation, say $3 = a * b * c$ and do the following: $3 = abc$ $0 = abc - 3$ $0 / a = bc - 3/a$ $0 / b = c - 3/a/b$ $0 / c = -3/a/b/c$ $0 = -3/a/b/c$ But…
kettlecrab
  • 417
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delivery performance

I need to calculate average speed of a driver as a performance indicator. I have the total miles driven and the total hours they took. Simple division of mi/hr is the speed. But I want to factor in the number of stops they're going. How can I…
Mike
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1 answer

Same attribution depending on salary

there's a house hold that consists of a husband and a wife, the husband earns $1500$ and the wife earns $2000$ and their rent is $2000$, what's the calculation to determine what percentage of their salary should be given depending on what they earn;…
joseagaleanoc
  • 103
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Can we add a valid value for an unknown variable in an equation by multiplying both sides of the equation by the same number/equation?

I have two related questions. I was solving some problems on the matter of (Let's call it "rule X"): $a^n - b^n = (a - b)(a^{n - 1} + a^{n - 2}b \space + ... + \space ab^{n - 2} + b^{n - 1})$ And at some point I encountered this equation, where…
curioushuman
  • 445
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Scaling something back to 1

I'm currently working in an modeling program and scaled something down to 85%. I would like to use another scale to transform it to back to its original size, however is proving more difficult than I thought. Simply reversing the scale does not…
Gigazelle
  • 65
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1 answer

Problem solving strategy to determine who wins a game?

Consider a game on a chess board with a single counter in the top right corner. You can only move this counter to a square that is adjacent. There are two competitors and the aim of the game is to get the counter to the bottom left corner. The…
James Chadwick
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Average commute time

Roads in town looks like this: Where $t=45$ means the path takes 45 minutes, and $t=\frac{N}{100}$ means the path takes as many minutes as the number of drivers who chose that path divided by $100$. For example, if $200$ drivers go from home to B,…
Parth Gor
  • 33
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How many positive and even factors does $2013!$ have?

How many positive and even factors does $2013!$ have? So I know that $2013 = 2\times1006 + 1$ So, does that mean $2013!$ has $1006$ even factors?
Commander Shepard
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