Homework Help!!

Question

The height of a triangle is increasing at a rate of  centimeters/minute while the area of the triangle is increasing at a rate of  square centimeters per minute. At what rate is the base of the triangle changing when the height is  centimeters and the area is  square centimeters?

Answer 1

dh/dt = + 1.5 , dA/dt = + 4.5. , h = 9 , A = 80 so b = 160 / 9.

A = 1/2 bh

dA/dt = 1/2(h·db/dt + b·dh/dt)

4.5 = 1/2 (9db/dt + 80/3)

9 = 9db/dt + 80/3

-53/3 = 9 db/dt

db/dt = - 53 / 27 cm/min