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Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water. Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min, of which some flows back into Tank Y at a rate of 4 litres/min, while the remainder leaves the system. (a) Draw a diagram that depicts the flow process described above. Let Qx(t1) and Qy(1), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Qx and Qy that model the flow process. (b) Is the system of differential equations homogeneous? Justify your answer. (c) Use the Laplace transform to find the amount of salt in each tank at ume r. (d) After 10 minutes, Tank X develops a leak and additional mixtures leaves out the tank at 0.05 litre/min. Rework the system with differential equations in part (a) for t2 10. (You are not required to solve the system).

Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water. Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min, of which some flows back into Tank Y at a rate of 4 litres/min, while the remainder leaves the system. (a) Draw a diagram that depicts the flow process described above. Let Qx(t1) and Qy(1), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Qx and Qy that model the flow process. (b) Is the system of differential equations homogeneous? Justify your answer. (c) Use the Laplace transform to find the amount of salt in each tank at ume r. (d) After 10 minutes, Tank X develops a leak and additional mixtures leaves out the tank at 0.05 litre/min. Rework the system with differential equations in part (a) for t2 10. (You are not required to solve the system).

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water. Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min, of which some flows back into Tank Y at a rate of 4 litres/min, while the remainder leaves the system. (a) Draw a diagram that depicts the flow process described above. Let Qx(t) and Qy(1), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Qx and Qy that model the flow process. (b) Is the system of differential equations homogeneous? Justify your answer. (c) Use the Laplace transform to find the amount of salt in each tank at ume r. (d) After 10 minutes, Tank X develops a leak and additional mixtures leaves out the tank at 0.05 litre/min. Rework the system with differential equations in part (a) for t> 10. (You are not required to solve the system).
Transcribed Image Text:Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water. Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min, of which some flows back into Tank Y at a rate of 4 litres/min, while the remainder leaves the system. (a) Draw a diagram that depicts the flow process described above. Let Qx(t) and Qy(1), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Qx and Qy that model the flow process. (b) Is the system of differential equations homogeneous? Justify your answer. (c) Use the Laplace transform to find the amount of salt in each tank at ume r. (d) After 10 minutes, Tank X develops a leak and additional mixtures leaves out the tank at 0.05 litre/min. Rework the system with differential equations in part (a) for t> 10. (You are not required to solve the system).
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