In the given problem, if the height function were given byh(t) = (4.2 - 0.14t)2, at what time would the tank be empty? What doesyour answer say about the domain of this solution? EXAMPLE 7 Flow from a tank Imagine a large cylindrical tank with cross-sectionalarea A. The bottom of the tank has a circular drain with cross-sectional area a. Assumethe tank is initially filled with water to a height (in meters) of h(0) = H (Figure 9.7).According to Torricelli's law, the height of the water t seconds after the drain is openedis described by the differential equationh'(t) = -kVh, where t = 0, k =Aand g = 9.8 m/s is the acceleration due to gravity.a. According to the differential equation, is h an increasing or decreasing function of t,for t 2 0?b. Verify by substitution that the solution of the initial value problem isA() = ( Vĩ - )".c. Graph the solution for H = 1.44 m, A = 1 m², and a0.05 m?.с.d. After how many seconds is the tank in part (c) empty?

Given: The height function was given by h(t) = (4.2 - 0.14t)2.

Answered: EXAMPLE 7 Flow from a tank Imagine a…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In the given problem, if the height function were given by
h(t) = (4.2 - 0.14t)², at what time would the tank be empty? What does
your answer say about the domain of this solution?

EXAMPLE 7 Flow from a tank Imagine a large cylindrical tank with cross-sectional
area A. The bottom of the tank has a circular drain with cross-sectional area a. Assume
the tank is initially filled with water to a height (in meters) of h(0) = H (Figure 9.7).
According to Torricelli's law, the height of the water t seconds after the drain is opened
is described by the differential equation
h'(t) = -kVh, where t = 0, k =
A
and g = 9.8 m/s is the acceleration due to gravity.
a. According to the differential equation, is h an increasing or decreasing function of t,
for t 2 0?
b. Verify by substitution that the solution of the initial value problem is
A() = ( Vĩ - )".
c. Graph the solution for H = 1.44 m, A = 1 m², and a
0.05 m?.
с.
d. After how many seconds is the tank in part (c) empty?

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