My educational guess: Most likely Condensation, due to the fact that the in order for precipitation to happen (condensation must occur in short amount of time). Please know this is an educational guess and it may be wrong, you are risking your answer. And if you got it wrong because of me, I’m terribly sorry. God bless you and I hope this helped.
One is the integral of e^x times cos x.
Use integration by parts.
15 is A, 22+X=8
I don't have time to solve the rest RN but will come back later
If we write y=f(x)=(x-h)²+k, then y-k=(x-h)². This is vertex form where the vertex is (h,k)=(3,3) so h and k are both 3. We can see this if we put x=3 in the shifted function. This is a minimum point for the function because for every other x f(x) is greater then 3. The minimum point is the vertex.