DRAINING a t ank A tank has a constant cross-sectional area of 50 ft 2 and an orifice of constant cross-sectional area of 1 2 ft 2 located at the bottom of the tank (see the accompanying figure). If the tank is filled with water to a height of h ft and allowed to drain, then the height of the water decreases at a rate (in feet per second) that is described by the equation dh dt = − 1 25 ( 20 − t 50 ) ( 0 ≤ t ≤ 50 20 ) Find an expression for the height of the water at any time t (in seconds) if its height initially is 20 ft.
DRAINING a t ank A tank has a constant cross-sectional area of 50 ft 2 and an orifice of constant cross-sectional area of 1 2 ft 2 located at the bottom of the tank (see the accompanying figure). If the tank is filled with water to a height of h ft and allowed to drain, then the height of the water decreases at a rate (in feet per second) that is described by the equation dh dt = − 1 25 ( 20 − t 50 ) ( 0 ≤ t ≤ 50 20 ) Find an expression for the height of the water at any time t (in seconds) if its height initially is 20 ft.
Solution Summary: The author explains how the expression for the height of the water at any time t is h=20+t25left.
DRAINING a tank A tank has a constant cross-sectional area of 50 ft2 and an orifice of constant cross-sectional area of
1
2
ft2 located at the bottom of the tank (see the accompanying figure).
If the tank is filled with water to a height of h ft and allowed to drain, then the height of the water decreases at a rate (in feet per second) that is described by the equation
dh
dt
=
−
1
25
(
20
−
t
50
)
(
0
≤
t
≤
50
20
)
Find an expression for the height of the water at any time t (in seconds) if its height initially is 20 ft.
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