Velvet Star Monitor

Dodecahedron volume

How can I derive the volume of a regular dodecahedron? A. P. Kiselev's Stereometry suggests that we cut it into a cube and congruent "tent-like" soli...

What is a projective plane? How is it different from an affine plane?

I came across the definition in the book titled Elliptic Curves by Anthony W Knapp, couldn't understand it so looked online, which just confused me m...

Evaluating an infinite series using partial fractions...

I am having trouble evaluating an infinite series that uses partial fractions. The problem is as follows: $$ \sum_{n = 1}^{\infty}{1 \over n\left(n + 1\ri...

Implementing a matrix that describes the word problem

A rental car company has three locations in Lexington. One at the airport, one downtown, and one on Nicholasville road. 95% of cars rented at the airport ...

Inequality . finding the maximum value.

Let $k$ be a real number such that the inequality, $\sqrt{x-1}+\sqrt{4-x}>k$ has a solution. What is the maximum value of $k$.

If $0

Finding the derivative of an inverse function.

Let $f(x) = (-x^2)/(x^2+1)$. If g(x) is the inverse function of f(x) and f(1)=-1/2, what us g'(-1/2)? Can someone explain how to do the above problem...

Simple explanation of Dijkstra's Algorithm?

Can anyone provide a simple explanation of Dijkstra's Algorithm? My text, discrete mathematics with applications by Susanna Epp provides a very compl...

How to use LU decomposition to solve Ax = b

Using LU Decomposition how can I solve for vector $x$ in the system $Ax = b$, given $A$ and $b$. For simplicities sake where $A$ is a 3x3 matrix and $b$ i...

What makes a difference if the ruler is marked?

The classical straightedge and compass construction problems, i.e. squaring the circle, devising a trisecting algorithm for a generic angle, doubling the ...