A cistern in the form of an inverted circular cone is being filled with water at the rate of 80 liters per minute. If the cistern is 7 meters deep, and the radius of its opening is 4 meters, find the rate at which the water level is rising in the cistern 40 minutes after the filling process began. Round any intermediate calculations, if needed, to no
less than six decimal places, and round your final answer to three decimal places. (Hint: 1 m = 1000 L.)

In the 30-60-90 triangle below side s has a length of and side r has a length

3. a sum of $2700 is to be given in the form of 63 prizes. if the prize is of either $100 or $25, find the number of prizes of each type.

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