Consider the large mixing tanks shown in FIGURE 10.Z.5. Suppose that both tanks A and B

Chapter 10, Problem 15

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Consider the large mixing tanks shown in FIGURE 10.Z.5. Suppose that both tanks A and B initially contain a 100 gallons of brine. Liquid is pumped in and out of the tanks as indica in the figure; the mixture pumped between and out of the tanks is assumed to be well-stirred. (a) Construct a mathematical model in the form of a linear sys of first-order differential equations for the number of poundsx1(t) andx2(t} of salt in tanks A andB, respectively, at time t. Write the system in matrix form. [Hint: See Section 2.9 and 38, Chapter 2 in Review.] (b) Use the eigenvalue method of this section to solve the linear system in part (a} subject to x1(0) = 20, .Ti(O) = 5. (c) Use a graphing utility or CAS to plot the graphs of x1(t) and.Ti(t} in the same coordinate plane. (d) Suppose the system of mixing tanks is to be twued off when the number of pounds of salt in tank B e.quals that in tank A. Use a root finding application of a CAS or calculat.or t.o approximate that time. mixture

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