I have 2 questions about how to find the characteristic polynomial of some graphs. If G is a simple cycle with n vertices and n edges, $C_n$, I need to fi...

In calculating the Sharpe Ratio: $S = (\frac{\bar r_p - r_f}{\sigma_p})$ Where: $\bar r_p$ = Portfolio return (See below) $r_f$ = Risk free rate = 0.03 (f...

I have to find the parametric functions that represent the curve: $$\left(\frac{x - x_0}a\right)^2 + \left(\frac{y - y_0}b\right)^2 = 1$$ The notes simpli...

So, a basic word problem has gone viral on FaceBook quite a few times now and many people remain convinced of their own incorrect answers. Suppose a man w...

Hi i have these two problems that are part of a practice set i am doing for exams, i can't seem to get around them. If you can answer any of them tha...

Inspired by this question, the finite difference solution for the PDE of $$u_t = \kappa u_{xx}$$ with initial/boundary conditions of $$ u(x,0) = 0\\ u(0,t...

I need a formula (preferably something I can write with JavaScript, so simple arithmetic) that will map my value that is between 0.5 and 1, to a new value...

I was thinking about the rule where $\space\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$ and why it worked, and I found this question: Rule for multiplying ...

Show that if a graph $G$ of order $n$ is triangle-free, then $$n \ge \delta(G) + \Delta(G).$$ What I have tried so far is as follows. I wish to show $n &g...

I have the question "Write down the equation of the line passing through the origin and perpendicular to y = 2X + 3". I know that the equation of a line i...