Velvet Star Monitor

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Is Wolfram Alpha linear independence wrong or am I missing something?

Maybe it's because you can't ask those questions to wolfram & I should use a matrix instead but when imputting linear independence {$t$, $t^...

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Triangle inscribed inside a circle: prove that $abc = 4 \times area \times R$

The solution to Putnam 2000 A5 uses this formula, for which the following proof is given: (source: https://mks.mff.cuni.cz/kalva/putnam/psoln/psol005.html...

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Solving $3x - 40 \cdot 2 = x + 5$

What did I do wrong? Start problem got rid of the 2 on the left side by reversing the multiplication simplified - got rid of the two on the left side and ...

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Why can't three unit regular triangles cover a unit square?

A square with edge length $1$ has area $1$. An equilateral triangle with edge length $1$ has area $\sqrt{3}/4 \approx 0.433$. So three such triangles have...

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Function has vertical tangent or vertical cusp?

Determine whether or not the graph of the function has a vertical tangent or vertical cusp at the indicated point c. $f(x) = (x+2)^7/3$ $c=-2$ I took the ...

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Implicit differentiation word problem involving the surface area of a cylinder

The radius, $r$, of the base of a circular cylinder increases by 2 feet per second while the height, $h$, decreases by 1 foot per second. How fast is the ...

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Difference between collinear vectors and parallel vectors? [closed]

I can't understand the difference between the two. The definitions are as written in textbook: Parallel vectors are vectors which have same or parall...

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conventional notation for magnitude and vector

Suppose as an example I have the magnitude of an electric $\left \| \vec{E} \right \|=\frac{\lambda}{2\epsilon s\pi}$ This is the equivalent to $\vec{E}=\...

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Any example of strongly convex functions whose gradients are Lipschitz continuous in $\mathbb{R}^N$

Let $f:\mathbb{R}^N\to\mathbb{R}$ be strongly convex and its gradient is Lipschitz continuous, i.e., for some $l>0$ and $L>0$ we have $$f(y)\geq f(x...

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Concrete example of the Lie derivative of a one-form

Let $\alpha$ be a one-form and $X$ a vector field. For example take: \begin{align*} \alpha &= y^2 dx + x^2 dy\\ &\\ X &= \frac{\partial}{\part...

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