The radius of a sphere is increasing at a constant rate of 7 feet per second. At the instant when the volume of the sphere is 274274 cubic feet, what is the rate of change of the volume? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V= 3 4 πr 3 . Round your answer to three decimal places.

You are a clerk at convenience store. a customer owes 11.69 for a bag of potatoes chips. she gives you a five dollar bill. how much change should the customer receive?

Solve 2^x=32 and rewrite this equation in a logarithmic form

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