Question

8.2 HC 15. As shown in Figure 8.2.6 two large connected mixing tanks A and B initially contain 100 1liters of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out ofa tank is assumed to be well-stirred. (a) Construct a mathematical model in the form of a linear system 1 0 5,1 0 18. X 1 2 1 -2.8 0 of first-order differential equations for the number of kilograms (t) and x2(t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. [Hint: Review Section 3.3. 19. (a) Use computer so system in Proble Figure 8.2.2. Als (h) Use the eigenvalue method of this section to solve the linear system in part (a) subject to x (0) (b) Obtain the Car in part (a). 20, x2(0) 5 (c) Use a graphing utility x() and x2(t) in the same coordinate plane. or CAS to plot the graphs of (c) Draw the eige 20. Find phase portra each system find lines in your phas (d) Suppose the system of mixing tanks is to be turned off when the number of kilograms of salt in tank B equals that in tank A. Use a root-finding application of a CAS or calcu- lator to approximate that time. 8.2.2 Repeated Ei mixture pure water 2 L/min In Problems 21-30 f 1 L/min dx = 3x- y 21. dt dy =9x - 3y dt B (-1 3 -3 5 23. X' = dx 25. 3x-y - dt mixture mixture mixture 1 L/min 2 L/min 1 L/min dy = x + y- dt FIGURE 8.2.6 Mixing tanks in Problem 15 dz =x-yt dt 16. In Problem 27 of Exercises 4.9 you were asked to solve the .11

Its question 15 that i am stuck with.

I want to know how the model looks like and how to make it.

Answer 1

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