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Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. mixture 3 gal/min 100ga 100 gal mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively. dt X1(0) - Ibs x2(0) - Ibs (b) Find a relationship between the variables x1(t) and x2(t) that holds at time t. (Write an equation using x1 for x1(t) and x2 for x2(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Use this relationship to help find the amount of salt in tank B at t = 35 min. (Round your answer to one decimal place.) *2(35) - Ibs

Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. mixture 3 gal/min 100ga 100 gal mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively. dt X1(0) - Ibs x2(0) - Ibs (b) Find a relationship between the variables x1(t) and x2(t) that holds at time t. (Write an equation using x1 for x1(t) and x2 for x2(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Use this relationship to help find the amount of salt in tank B at t = 35 min. (Round your answer to one decimal place.) *2(35) - Ibs

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. mixture 3 gal/min A B 100 gal 100 gal mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively. dx 1 dt dx2 dt X1(0) = Ibs x2(0) Ibs (b) Find a relationship between the variables x1(t) and x2(t) that holds at time t. (Write an equation using ×1 for x1(t) and x2 for x2(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Use this relationship to help find the amount of salt in tank B att = 35 min. (Round your answer to one decimal place.) X2(35) = Ibs
Transcribed Image Text:Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. mixture 3 gal/min A B 100 gal 100 gal mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively. dx 1 dt dx2 dt X1(0) = Ibs x2(0) Ibs (b) Find a relationship between the variables x1(t) and x2(t) that holds at time t. (Write an equation using ×1 for x1(t) and x2 for x2(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Use this relationship to help find the amount of salt in tank B att = 35 min. (Round your answer to one decimal place.) X2(35) = Ibs
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