# Tagged Questions

This tag is in the process of being removed; please do not add this tag to new questions. Rather, use tags that describe the subject of your question, like [calculus], [algebra-precalculus], etc. For more information, see meta: http://meta.math.stackexchange.com/questions/16425.

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### Positive and négative Parts

we denote by $u^+=\max(u,0)$ and $u^-=\max(-u,0)$ the positive and the negative parts of $u$ we have that $u=u^+-u^-$ my question is : what is $u'$ using $u^+$ and $u^-$ ? and what is ...
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### What is the probability that A will win…

Two players are rolling two dices, if they get 6 Player A wins, if they get 7, player B wins, else they rolling the two dices again... What is the probability that A will win? I'd like to get any ...
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### Least squares approximation: Legendre polynomial

Find the best quadratic least squares approximation to $f(x)=e^x$ on $[-1,1]$ with respect to the inner product $\langle f(x),g(x) \rangle = \displaystyle\int_{-1}^1 f(x)g(x)dx$. I cannot figure out ...
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### Calculate length of radial intersecting a rectangle

In a rectangle like below, I need to calculate the length of any radial, from the center of the rectangle to where it intersects with the edge of the rectangle. Further, the angle of the radial is ...
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### Linear algebra proof

Let $W$ be a subspace of $\mathbb{R}^n$. Let $\vec{v}_1 ,\vec{v}_2 \in \mathbb{R}^n$. Suppose that $\vec{p}_1$ is the projection of $\vec{v}_1$ onto $W$ and $\vec{p}_2$ is the projection of ...
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### Orthogonality question

Been stuck on this one: If $\vec{x}$ is orthogonal to $\vec{u}$ and $\vec{v}$ then $\vec{x}$ is orthogonal to $\vec{u}-\vec{v}$. Any hints?
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### True/ False differential equation

Are the statements in Problems 46-54 true or false? If $F(x)$ is an antiderivative of $f(x)$, then $y=F(x)$ is a solution to the differential equation $\frac{dy}{dx}=f(x)$. If $y=F(x)$ is a solution ...
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### How to find the value of $c$ using the mean value theorem?

So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ I have $f(x)=e^{\frac{-x}{2}}$ over the interal [0,12]. Using the mean value theorem I ...
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### How Can I figure out when cosine = $\frac{2}{\pi}$?

So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ So I am trying to find $c$ for $f(x)=\sin x$ over the interval $[0,\frac{\pi}{2}]$. So using the Mean Value ...
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### What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ [closed]

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ How to calculate this without calculator?
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### Combination of quadratic and arithmetic series

Problem: Calculate $\dfrac{1^2+2^2+3^2+4^2+\cdots+23333330^2}{1+2+3+4+\cdots+23333330}$. Attempt: I know the denominator is arithmetic series and equals ...
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### Deducing an optimal gambling strategy (using martingales).

Apologies in advance for the length, I tried being precise. Suppose a game where in each turn you can gamble a certain amount of money on the result of a fair coin toss. If the coin comes out tails ...
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### Proving 7n+5 is never a cubic number?

This is from a question that starts with: An arithmetic progression of integers an is one in which $a_n=a_0+nd$, where $a_0$ and $d$ are integers and n takes successive values $0, 1, 2, \cdots$ Prove ...
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### How to find the third vertex of an isosceles triangle given 2 points.

This is the full problem: The points $A(5,1)$ and $B(-3,6)$ represent one of the equal sides of an isosceles triangle. Determine one of the possible points that would represent the third vertex of the ...
Im taking an introduction to logarithms. Of course a short review of exponentiation is inherent for a clear understanding of logarithms. I was asked to find, for example, $27^x = 3$. (without the use ...