A water trough has a semicircular cross section with a radius of 5 feet. Water starts flowing into the trough in such a way that the depth of the water is increasing at a rate of 2 inches per hour.

(a) Write a function w = f(t) relating the width w of the surface of the water to the time t, in hours. Make sure to specify the domain and compute the range.
(b) After how many hours will the surface of the water have a width of 6 feet?
(c) Write a function t =f(w) relating the time to the width of the surface of the water.
 
 
 
 

Hints:  depth of trough, y, y² = r² + x²   where x is t , time in hours
r = 5 - (1/6)t   note that the width is 2 times the radius