What is the reciprocal of $(-1/2)^k$? The answer is meant to be $2^{-k}$ as if you flip something upside down the power becomes negative. However, I am no...

The professor of the topology course stated the theorem, without proof, as: Seifert-van Kampen Theorem: I. Let $X=\bigcup_{i=1}^nU_i,$ where $U_i$ are ope...

So we consider a vector space V which is defined by $f(x)=ax+be^x+csin(x)$ where a, b and c are real. I was able to prove that this was in fact a vector s...

A box contains 100 balls, numbered from 1 to 100. If two balls are selected at random and at the same time from the box, what is the probability that the ...

I read the following version of the spectral theorem in Banach Algebra Techniques in Operator Theory by Douglas: I'm trying to understand why this is...

Can someone please walk me through the steps on how I can get an answer for a decimal problem involving sum and difference formulas? Thank you very much, ...

The concept of velocity is by definition the movement divided by the interval of time between initial position and final position. If $f(t)$ is the positi...

I know that fourth angles of Lambert quadrilaterals are acute in hyperbolic geometry and right in Euclidean, but why are fourth angles only able to be obt...

Anyone know a good derivation of the linear interpolation: $$\frac{y-y_0}{x-x_0}=\frac{y_1-y_0}{x_1-x_0}$$ Wikipedia gives one, which I don't underst...

I would like to know if there is a mathematical approach to finding the LCM of $(29^{17} +2 , 29^{17} -1)$? Even if we would rearrange it to a fraction of...