Velvet Star Monitor

updates

Finding the shortest distance between two lines

I know how to find the distance between a point and a line, not between two lines. Find the shortest distance between the lines $(-1,1,4) + t(1,1,-1)$ and...

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Taking derivatives of Trig Functions

So I have the equation $\frac{d}{dx}[\cos(2x)-3\sin(x)-1]$ What I did was simplify $\cos(2x)$ to $1-2\sin^2(x)$ by applying the double angle formula. Here...

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Proof by Induction for a recursive sequence and a formula

So I have a homework assignment that has brought me great strain over the past 2 days. No video or online example have been able to help me with this issu...

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Concept of using limits to find horizontal asymptotes.

$$y=\dfrac{(\sin x)^3}{x^2}$$ My professor explained how to do this problem by using limits. I am a little confused as to why he used limits because in th...

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Finding $\sin \theta$ and $\cos \theta$ while vector is given.

If v = 2i -3j, then find $\sin \theta$ and $ \cos \theta$? Solution manual says: Can someone expound on what solution manual said, I am having hard time u...

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How to reverse formula $S = \frac{n(n+1)}{2}$ [closed]

I'm using this formula $S = \frac{n(n+1)}{2}$ to calculate sum of numbers from 1 to $n$. But, I want to recover $n$ value. If I have $S$ value. Is it...

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Are the letter choices in algebra meaningful?

p= F−E(S) / k I saw someone post a math problem like the one above. I wonder why they used those letters, if they have a particular meaning or if they cou...

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Express roots in polynomials of equation $x^3+x^2-2x-1=0$

If $\alpha$ is a root of equation $x^3+x^2-2x-1=0$, then find the other two roots in polynomials of $\alpha$, with rational coefficients. I've seen s...

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updates

Product of inner products

Is product of innerproduct again a inner product of two vectors? For example - Is $ (< u,v >)(< x,y >) = < m,n > $? And if yes is m and ...

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updates

Archimedean Principle

Prove the Archimedean principle for $\mathbb{Q}$, the set of rational numbers. I know the proof for real numbers If not, then the nonempty set $S = \{nx \...

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