Two very large tanks A and 8 are each partially filled with 100 gallons of brine....

 

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Two very large tanks A and 8 are each partially filled with 100 gallons of brine. Initially, 115 pounds of salt are dissolved in the solution in tank A and 35 pounds of salt are dissolved in the solution in tank 8, 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 100 gal 100 gal mixture 2 galmin (a) Uso the information given in the figure to construct a mathematical model for the number of pounds of salt x, (t) and x,() at time tin tanks A and 8, respectively. dt dt (0) *(0) - Ibs (b) Find a relationship between the varlables x,() andtn that holds at time t. (Write an equation using x, for x, () and x, for x(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t 40 min. (Round your answer to one decimal place.) X(40) - Ibs Two very large tanks A and 8 are each partially filled with 100 gallons of brine. Initially, 115 pounds of salt are dissolved in the solution in tank A and 35 pounds of salt are dissolved in the solution in tank 8, 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 100 gal 100 gal mixture 2 galmin (a) Uso the information given in the figure to construct a mathematical model for the number of pounds of salt x, (t) and x,() at time tin tanks A and 8, respectively. dt dt (0) *(0) - Ibs (b) Find a relationship between the varlables x,() andtn that holds at time t. (Write an equation using x, for x, () and x, for x(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t 40 min. (Round your answer to one decimal place.) X(40) - Ibs

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Solution B are ea ch Very large tanks A and TWo a partial... View the full answer