Determine the function?

Question

If you have a 5 ft tall cylinder full of water and it is losing water at a steady rate causing the water level to drop an inch every minute, determine a function ( call it H(t) ) that will give you the water height for any minute t.

2nd part
If you are only considering values of t for which the cylinder is not empty, what would be the domian for the function?


I have answers for both I am just not sure if they are right so i wanted to see what other people would get! THANKS

where does the .833 come from?

Answer 1

1.) H(t) = 5 - 0.08333(t)
(where t is in minutes and h(t) is in feet)
(1 inch = 0.0833 ft )

2.) Domain will be [0, 60)

Answer 2

Converting the height to inches,
H(t) = 60 - t
The domain is 0 ≤ t ≤ 60

Answer 3

V=pi*r^2*H
H= V/pi*r^2
dH/dt= 1/pi*r^2 *dV/dt and dV/dt = -1/12 *pi r^2 cubic feet/min
so
dH /dt = -1/12 and H = -1/12*t +Ho
H= -1/12 *t+5
-1/12 *t +5 >= 0 so t<= 60 min
Domain 0<=t <=60

Answer 4

H(t) = 5 - (0.833t)


0=5-0.833t
t=6.0024

Domain: {x ≥ 6.0024, x∈ℜ}