Velvet Star Monitor

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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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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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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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Convert 1-5 Grading Scale to 1-100 Grading System

I am creating a formula in Excel to convert 1-5 Grading Scale to 1-100 Grading System Suppose that I have the following table: 97-100 = 1.00 94 - 96 = 1.2...

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How do Lagrange multipliers work to find the lowest value of a function subject to a constraint?

I have been using Lagrange multipliers in constrained optimization problems, but I don't see how they actually work to simultaneously satisfy the con...

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Calculating the radius of the circumscribed sphere of an arbitrary tetrahedron, edge lengths given

In two dimensional Euclidean space, it is not hard to calculate the radius of the circumscribed circle of an arbitrary triangle when all the side lengths ...

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Proving that a transformation is an isometry and find the projectivity which reperesents

Consider the transformation: $T \begin{bmatrix} x \\ y \\ \end{bmatrix} $ $\mapsto$$\frac{\sqrt{2}}{2} \begin{bmatrix} x+y-1 \\ -x+y+1 \\ \end{bmatrix} $ ...

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