?Water is flowing at a constant rate into a spherical tank. Let \(V(t)\) be the volume

Chapter 15, Problem 86

(choose chapter or problem)

Water is flowing at a constant rate into a spherical tank. Let \(V(t)\) be the volume of water in the tank and \(H(t)\) be the height of the water in the tank at time \(t\).

(a) What are the meanings of \(V^{\prime}(t)\) and \(H^{\prime}(t)\)? Are these derivatives positive, negative, or zero?

(b) Is \(V^{\prime \prime}(t)\) positive, negative, or zero? Explain.

(c) Let \(t_{1}, t_{2}, \text { and } t_{3}\) be the times when the tank is one-quarter full, half full, and three-quarters full, respectively. Are each of the values \(H^{\prime \prime}\left(t_{1}\right), H^{\prime \prime}\left(t_{2}\right), \text { and } H^{\prime \prime}\left(t_{3}\right)\) positive, negative, or zero? Why?

Equation Transcription:

Text Transcription:

V(t)

H(t)

t

V^prime(t)

H^prime(t)

V^prime prime(t)

t_1, t_2, t_3

H^prime prime (t_1), H^prime prime (t_2), H^prime prime (t_3)