Cylindrical Tank Draining
Hi! I'm new here, and studying for a test. I was wondering if someone can help me out.
3.) When the valve at the bottom of a cylindrical tank is opened, the rate at which the level of liquid in the tank drops is proportional to the square root of the depth of the liquid. Thus, if y(t) is the liquid's depth at time "t" minutes after the valve is opened, water drains from the tank according to the differential equation dy/dt = -k √y for some positive constant k that depends on the size of the drain.
a) Suppose that y(0) = 9 and y(20) = 4. Find an equation for y(t).
I'm assuming you have to seperate the variables and integrate.
√y dy = -k dt
But I'm not exactly sure how the first bits of information fit in. Some help, please?
b)At what time is the water level dropping at a rate of .1 feet per minute?
Help here, as well.
Thanks a bunch. I appreciate it.