a. Explanation Given: The volume of the tank is 1500-L,the concentration of the salt solution is 20g/L and the rate of flow into the tank is 3L/min. Result used: The differential stirred tank reaction is m ′ ( t ) = − R V m ( t ) + C i R with its initial value m ( 0 ) = m 0 . Calculation: The differential equation for the stirred tank reaction is m ′ ( t ) = − R V m ( t ) + C i R with V = 1500 -L, R = 3 and C i = 20 b . To determine To solve: The initial value problem of the given function and graph its solution.

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter D1.5, Problem 24E

To determine

To find: The initial value problem for mass of the substance.

To determine

To solve: The initial value problem of the given function and graph its solution.

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Chapter D1.5, Problem 23E

Chapter D1.5, Problem 25E

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3b. Find the concentration of the syrup in the tank at time t.

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1. A tank initially holds 80 gal of a brine solution containing Ib of salt per gallon. At t = 0, another brine solution containing 1 Ib of salt per gallon is poured into the tank at the rate of 4 gal/min while the well stirred mixture leaves the tank at the rate of 8 gal/min. a. Find the amount of salt in the tank at any time t. b. Determine when the tank will be empty. c. Determine when the tank will hold 40 gal of solution. d. Find the amount of salt in the tank when the tank contains exactly 40 gal of solution. e. Determine when the tank will contain the most salt.

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Calculus: Early Transcendentals (2nd Edition)

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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The initial value problem for mass of the substance.

Solution Summary: The author explains the initial value problem for mass of the substance, and the differential equation for the stirred tank reaction.