Question: The power P produced by a windmill is proportional to the square of the diameter d of the windmill and to the cube of the speed v of the wind.
(a) Write a formula for P as a function of d and v.
(b) A windmill generates 100 kW of power at a certain wind speed. If a second windmill is built having twice the diameter of the original, what fraction of the original wind speed is needed by the second windmill to produce 100 kW?
(c) Sketch a contour diagram for P.