I have the following question: Suppose $$f(x) = \left\{\begin{array}{cc}x^2 & \text{if }x\leq 2 \\ mx+b& \text{if }x>2\end{array}\right.$$ If $...

Can you please explain what the difference between an integral curve and the solution of a differential equation is? My book gives an example that $$\frac...

How can I show that $ALL_{DFA}$ is in P ? $ALL_{DFA} = \{ \langle A \rangle \mid A \text{ is a DFA and } L(A) = \Sigma^* \}$

I have having an issue identifying the inner function of this function: $$f(g(x))=\frac{1}{\sqrt{x+1}}$$ I "need" to take the derivative of it; ...

Question. If $A$ is a $4 \times 6$ matrix with rank $3$, then the reduced row echelon form of A has (1) at least one zero row. (2) at least one zero colum...

Let $K$ be a circle with center $B$ and $A,C,D$ points on the circle. Further let $\overline{BE}$ be the perpendicular bisector of $\overline{AC}$. Then i...

Water evaporates from an open bowl of unspecified shape at a rate proportional to the area ofthe water surface; that is, $$\frac{dV}{dt} = -cA(h)$$ where ...

Given that X and Y are random variables show that: $$E[E[X \mid Y]] = E[X]$$ I was thinking that I could use the definition of expected value (the summati...

This problem is dedicated to Leon the professional. This question came to my mind when I was contemplating on the numbers 1-20 arranged interestingly arou...

I am on the hypothesis testing for two populations unit. I need some intuitive explanation as to why this formula is used. My statistics professor put thi...