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Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a 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.

Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a 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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 8E
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Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a 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. =10-7x+ dz dt dy dt 6 = 25+y-x-18y r(0) = , y(0) = X
Transcribed Image Text:Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a 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. =10-7x+ dz dt dy dt 6 = 25+y-x-18y r(0) = , y(0) = X
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