Explanation Use the given values of R i n = 20 1 + t g a l / min and R o u t = 5 g a l / min to determine the value of d V d t which is then integrated to obtain the equation and hence the particular solution Given: Water flows into a tank at the variable rate of R i n = 20 1 + t g a l / min and out at the constant rate R o u t = 5 g a l / min . V ( t ) is the volume of water in the tank at time t . Calculation: Use the given values of R i n = 20 1 + t g a l / min and R o u t = 5 g a l / min to determine the rate of change of volume of water to be equal to d V d t = R To determine (b) The maximum value of V To determine (c) To plot V ( t ) and estimate the time t at which the tank will be empty.

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 10.5, Problem 37E

To determine

(a)

To set up a differential equation for $V (t)$ and solve it with the initial condition $V (0) = 100$

To determine

(b)

The maximum value of $V$

To determine

(c)

To plot $V (t)$ and estimate the time $t$ at which the tank will be empty.

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Chapter 10.5, Problem 36E

Chapter 10.5, Problem 38E

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Chapter 10 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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(a) To set up a differential equation for V ( t ) and solve it with the initial condition V ( 0 ) = 100

Solution Summary: The author explains how to set up a differential equation for V and solve it with the initial condition V ( 0 ) = 100.

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(a)

To set up a differential equation for $V (t)$ and solve it with the initial condition $V (0) = 100$

(b)

The maximum value of $V$

(c)

To plot $V (t)$ and estimate the time $t$ at which the tank will be empty.

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Chapter 10 Solutions

(a) To set up a differential equation for V ( t ) and solve it with the initial condition V ( 0 ) = 100

Solution Summary: The author explains how to set up a differential equation for V and solve it with the initial condition V ( 0 ) = 100.

Concept explainers

Videos

(a) To set up a differential equation for V(t) and solve it with the initial condition V(0)=100

(b) The maximum value of V

(c) To plot V(t) and estimate the time t at which the tank will be empty.

Want to see the full answer?

Chapter 10 Solutions

(a)

To set up a differential equation for $V (t)$ and solve it with the initial condition $V (0) = 100$

(b)

The maximum value of $V$

(c)

To plot $V (t)$ and estimate the time $t$ at which the tank will be empty.