# Thread: Rates of change

1. ## Rates of change

A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

_________ ft/min
(b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.
_________ ft^3/min

2. Originally Posted by tradar
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

_________ ft/min
(b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.
_________ ft^3/min

Have a look here: http://www.mathhelpforum.com/math-he...-calculus.html

3. That helped for the first part...THANKS!

how do I relate that to the second part?

4. Originally Posted by tradar
That helped for the first part...THANKS!

how do I relate that to the second part?
I assume that you found out:

$\dfrac{dV}{dt} = 12h\cdot \dfrac{dh}{dt}$

With question a) you plug in the values for $\dfrac{dV}{dt}$ and h and calculate $\dfrac{dh}{dt}$

while with b) you plug in the values for $\dfrac{dh}{dt}$ and h and calculate $\dfrac{dV}{dt}$