How do you simplify this equation: $\dbinom{n}{k}-\dbinom{n-1}{k-1}-\dbinom{n-2}{k-1}$ I simplified it to this: $\dfrac{n!}{k!(n-k)!}-\dfrac{(n-1)!}{(k-1)...

Find the bounded solution of Laplace's equation in the region $\Omega=\{(r,\theta):r>1,0<\theta<\pi\}$ subject to the boundary conditions $u...

I was able to determine a resultant vector based on the sum of two vectors and told to express them in vector units. Here is my answer that was correct: $...

What is the largest 2-digit prime factor of the integer $\dbinom{200}{100}$?

I typed in $\tan 90^{\circ}$ in Google and it gave $1.6331779\mathrm{E}16$. How did it come to this answer? Limits? Some magic?

I want to evaluate the following integral: $$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}^3}\mathrm{d}x$$ If I do it with the substitution $x=R\tan(\varphi)$ I...

I am trying to understand an example from my textbook. Let's say $Z = X + Y$, where $X$ and $Y$ are independent uniform random variables with range $...

This inquiry has recently come to me in my study of trigonometry and the unit circle. It was said right from the very start that counterclockwise rotation...

Given $$A=\begin{pmatrix} 5 & 6 & 6-x & 8 \\ 2 & 2-x & 2 & 8 \\ 6 & 6 & 2 & 8 \\ 2 & 3 & 6 & 7 \end{pmatri...

Hello everyone we have exams tomorrow and i am practising vectors and i wanted some help here. Finding the area of the parallelogram spanned by vectors &l...