Alright, I will need some assistance for two problems that I face. Thanks in advance.
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 1.9 foot deep?
(b) If the water is rising at a rate of inch per minute when h = 2.5, determine the rate at which water is being pumped into the trough.
Honestly I'm not sure how to do this one at all, I need an explanation.
All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the volume changing when each edge is 3 centimeter(s)?
-I set dV/dt as 6 cm/s
-We must find dx/dt when x=3cm
The eq. is V=x^3
So dV/dt = 3x^2 (dr/dt)
so I solved for dr/dt, dr/dt = dV/dt*1/3x^2. Then I plugged in 3 for x, but this wasn't correct, where did I go wrong? Thanks a lot guys, much appreciated.