a. Explanation Given: The volume of the tank is 2,000-L, the initial concentration of the sugar solution is 40 g/L but the sugar solution with a concentration is 10 g/L and the rate of flow into the tank is 10 L/min. Result used: The differential stirred tank reaction is m ′ ( t ) = − R V m ( t ) + C i R with initial value m ( 0 ) = m 0 . Calculation: The differential equation of the stirred tank reaction is m ′ ( t ) = − R V m ( t ) + C i R with V = 2000 -L, R = 10 and C i = 10 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: 9780321965165

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

Publisher: PEARSON

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Chapter D1.5, Problem 25E

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 24E

Chapter D1.5, Problem 26E

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A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg

A tank initially holds 10 gal of fresh water. At 1= 0, a brine solution containing lb of salt per gallon is poured into the tank at a rate of 2 gal/min, while the well-stirred mixture leaves the tank at the same rate. Find (a) the amount and (b) the concentration of salt in the tank at any time t. 7.65.

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Chapter D1 Solutions

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 in a stirred tank.