Water flows from a tank of constant cross-sectional area

50 \mathrm { At } ^ { 2 }

through an orifice of constant cross-sectional area

\frac { 1 } { 4 } \mathrm { ft } ^ { 2 }

located at the bottom of the tank. Initially, the height of the water in the tank was

20 \mathrm { ft }

, and

t

sec later it was given by the equation

2 \sqrt { h } + \frac { 1 } { 25 } t - 2 \sqrt { 20 } = 0 \quad 0 \leq t \leq 50 \sqrt { 20 }

How fast was the height of the water decreasing when its height was

2 \mathrm { ft }

?
$Water flows from a tank of constant cross-sectional area 50 \mathrm { At } ^ { 2 } through an orifice of constant cross-sectional area \frac { 1 } { 4 } \mathrm { ft } ^ { 2 } located at the bottom of the tank. Initially, the height of the water in the tank was 20 \mathrm { ft } , and t sec later it was given by the equation 2 \sqrt { h } + \frac { 1 } { 25 } t - 2 \sqrt { 20 } = 0 \quad 0 \leq t \leq 50 \sqrt { 20 } How fast was the height of the water decreasing when its height was 2 \mathrm { ft } ? A) \quad 100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec } B) 100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec } C) \frac { 2 } { 25 } \mathrm { ft } / \mathrm { sec } D) \frac { \sqrt { 2 } } { 25 } \mathrm { ft } / \mathrm { sec }$

A)

\quad 100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec }

100 \sqrt { 5 } - 50 \sqrt { 2 } \mathrm { ft } / \mathrm { sec }

\frac { 2 } { 25 } \mathrm { ft } / \mathrm { sec }

\frac { \sqrt { 2 } } { 25 } \mathrm { ft } / \mathrm { sec }

Find f′f ^ { \prime }f′ In Terms Of g′g ^ { \prime }g′

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Find $f ^ { \prime }$ In Terms Of $g ^ { \prime }$

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