Often, continuity is derived as a "special case" of the limit of a function, which is defined as: Let D be a subset of R. The function $f:D \rightarrow R$...

I am having some troubles with a question that subtracts powers. Solve for unknown: $$3^{x+4} - 5(3^x) = 684$$ I have a hunch that I should apply factoriz...

I can't seem to figure this problem out, there doesn't seem to be enough information. Find the standard equation of the parabola that has a vert...

What are some applications of abstract algebra in computer science an undergraduate could begin exploring after a first course? Gallian's text goes i...

Given that P(A and B)=0.1 and P(A and B')=0.4 find P(A or B') if A and B are independent. The ans is 0.9 Please tell me the rule you use in the ...

I have been asked to determine whether- $h : \mathbb{N} \rightarrow \mathbb{N}$ defined by $h(x) = x^3$ is injective, surjective or bijective. And why?

Given $X \sim \text{NBin}(n,p)$, I've seen two different calculations for $\mathbb{E} (X)$: \begin{align*} &1. \mathbb{E} (X) = \frac{n}{p}, \qua...

All of the theorems I have found in my textbook and on the internet just state the converse; is it true both ways?

This may appear a dumb question, but I was thinking about this in a deeper way. If we are concerning about the set of real numbers, and hence we are in $\...

If $p^3+p=q^2+q$ where $p$ and $q$ are prime numbers, Find all the solutions (p, q) I tried to solve this exercise using that: $p^2 = -1(\text{mod} \, q)$...