A rocket is launched from a tower. The height of the rocket, y in feet, 15 related to the time after launch, x in seconds, by the given equation. Using
this equation, find the maximum height reached by the rocket, to the nearest
tenth of a foot.
y = –16x2 + 228x + 71

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0

Ethan is proving that the slope between any two points on a straight line is the same. he has already proved that triangles 1 and 2 are similar. drag statements and reasons to complete the proof.

Which of the following exponentially equations is equivalent to the logarithmic equation below?