The power p that can be obtained from a windmill is directly

The power p that can be obtained from a windmill is directly proportionl to the cube of the wind speed s.
(a) Write an equation that expresses this variation.
(b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is lowing at 20 mi/h.
(c) How much power will this windmill produce if the wind speed increases to 30mi/h?

Solution

The power p that can be obtained from a windmill is directly proportionl to the cube of the wind speed s.
(a) Write an equation that expresses this variation.
p(s) = ks^3
----------------------------
(b) Find the constant of proportionality for a windmill that produces 96 watts of power when the wind is lowing at 20 mi/h.
96 = k*20^3
k = 96/20^3
k = 0.012
Therefore the equation is p(s) = 0.012s^3
-------------------------------------------------
(c) How much power will this windmill produce if the wind speed increases to 30mi/h?
P(30) = 0.012*30^3
P(30) = 324 watts