Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50 grams of salt in 40 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B. Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks. dx 8 3 dt 40 dy 50 * - y+ 28 8 dt x(0) = 60 o , y(0) = | 50
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50 grams of salt in 40 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B. Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks. dx 8 3 dt 40 dy 50 * - y+ 28 8 dt x(0) = 60 o , y(0) = | 50
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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Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50 grams of salt in 40 liters of water.
A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting xx represent the grams of salt in Tank A, and yy represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
dxdtdxdt = −850x+340y+5Correct
dydtdydt = 850x−12y+28Incorrect
x(0)x(0) = Correct, y(0)y(0) = Correct
A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting xx represent the grams of salt in Tank A, and yy represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
dxdtdxdt = −850x+340y+5Correct
dydtdydt = 850x−12y+28Incorrect
x(0)x(0) = Correct, y(0)y(0) = Correct
Submit QuestionQuestion 1
Transcribed Image Text:Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50
grams of salt in 40 liters of water.
A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank
B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank
A. An additional 12 L/min drains from Tank B.
Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the
system of differential equations for these two tanks.
dx
8
3
50 *+ 10 Y+ 5
40
dt
dy
50 * - zy+28
8
dt
x(0) = 60
o , y(0) = | 50
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