1. a boy is flying a kite at a height 150 feet. if the kite moves horizontally away from the boy at a rate of 20 feet per second, how fast is the string being let out when the kite is 250 feet from him?
let x = kite's horizontal distance
y = kite's vertical distance
z = kite's straight line distance
dx/dt = 20 ft/s
since y = a constant 150 ft, dy/dt = 0
the question is asking for dz/dt when z = 250 ft.
set up the relationship between the variables using Pythagoras, take the derivative w/r to time, then evaluate dz/dt.