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Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallon ber minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons ber minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, (t) and y(t), of salt in tanks A and B, respectively, at time t are. Select the correct answer for x(t), (t), and the initial conditions. You should select three answer choices.

Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallon ber minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons ber minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, (t) and y(t), of salt in tanks A and B, respectively, at time t are. Select the correct answer for x(t), (t), and the initial conditions. You should select three answer choices.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, x(t) and y(t), of salt in tanks A and B, respectively, at time t are . Select the correct answer for x(t), y(t), and the initial conditions. You should select three answer choices. x(0) = 5, y(0) = 20 O x(0) = 20, y(0) = 5 %3! dx/dt = 2 - x/40 + y/15 dx/dt = 4 - 3x/40 + y/15 dy/dt = 3x/40 - y/5 %3D dx/dt = 2 - 3x/40 + y/15 O dy/dt = x/40 - y/5 dy/dt = x/40 - y/3
Transcribed Image Text:Tank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains 30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentration of 0.5 pounds of salt per gallon of water is pumped into Tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallons per minute, and the solution from tank B is also pumped out the of the system at the rate of 4 gallons per minute. The correct differential equations with initials conditions for the amounts, x(t) and y(t), of salt in tanks A and B, respectively, at time t are . Select the correct answer for x(t), y(t), and the initial conditions. You should select three answer choices. x(0) = 5, y(0) = 20 O x(0) = 20, y(0) = 5 %3! dx/dt = 2 - x/40 + y/15 dx/dt = 4 - 3x/40 + y/15 dy/dt = 3x/40 - y/5 %3D dx/dt = 2 - 3x/40 + y/15 O dy/dt = x/40 - y/5 dy/dt = x/40 - y/3
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