Explanation Given information: In the following figure, Tank 1 is filled with V 1 litres of water containing blue dye at an initial concentration of c 0 g/L. water flows into the tank at a rate of R L/min, is mixed instantaneously with the dye solution, and flows out through the bottom at the same rate R. Let c 1 ( t ) be the dye concentration in the tank at time t. Let g 1 ( t ) be the number of grams of dye in the tank at time t. Then g 1 ( t ) = V 1 c 1 ( t ) g ′ 1 ( t ) = V 1 c ′ 1 ( t ) Now, g ' 1 ( t ) = grams of dye in − grams of dye out = 0 − g ( t ) V 1 ⋅ < To determine (b) To solve: c 1 ( t ) with V 1 = 300 L , R = 50 , c 0 = 10 g / L .

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Differential Equations

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Chapter 9.5, Problem 43E

To determine

(a)

To explain:

The reason for c1(t) satisfies the differential equation dc1dt=−RV1c1.

To determine

(b)

To solve:

c1(t) with V1=300L,R=50,c0=10g/L.

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Chapter 9.5, Problem 42E

Chapter 9.5, Problem 44E

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Calculus: Early Transcendentals

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E

Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - Prob. 53E Ch. 9.1 - Prob. 54E Ch. 9.1 - Prob. 55E Ch. 9.1 - Prob. 56E Ch. 9.1 - 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(a) To explain: The reason for c 1 ( t ) satisfies the differential equation d c 1 d t = − R V 1 c 1 .

Solution Summary: The author explains that the reason for c_1(t) satisfies the differential equation.

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(a)

To explain:

The reason for c1(t) satisfies the differential equation dc1dt=−RV1c1.

(b)

To solve:

c1(t) with V1=300L,R=50,c0=10g/L.

Want to see the full answer?

Chapter 9 Solutions

(a) To explain: The reason for c 1 ( t ) satisfies the differential equation d c 1 d t = − R V 1 c 1 .

Solution Summary: The author explains that the reason for c_1(t) satisfies the differential equation.

Concept explainers

Videos

(a) To explain: The reason for c1(t) satisfies the differential equation dc1dt=−RV1c1.

(b) To solve: c1(t) with V1=300L,R=50,c0=10g/L.

Want to see the full answer?

Chapter 9 Solutions

(a)

To explain:

The reason for c1(t) satisfies the differential equation dc1dt=−RV1c1.

(b)

To solve:

c1(t) with V1=300L,R=50,c0=10g/L.