(a) Reread of Exercises 3.3. In that problem you were asked to show that the system of

Chapter 4, Problem 27

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(a) Reread of Exercises 3.3. In that problem you were asked to show that the system of differential equations is a model for the amounts of salt in the connected mixing tanks A, B, and C shown in Figure 3.3.7. Solve the system subject to x1(0) 15, x2(t) 10, x3(t) 5. dx3 dt 2 75 x2 1 25 x3 dx2 dt 1 50 x1 2 75 x2 dx1 dt 1 50 x1 (b) Use a CAS to graph x1(t), x2(t), and x3(t) in the same coordinate plane (as in Figure 4.9.1) on the interval [0, 200]. (c) Because only pure water is pumped into Tank A, it stands to reason that the salt will eventually be flushed out of all three tanks. Use a root-findin application of a CAS to determine the time when the amount of salt in each tank is less than or equal to 0.5 pound. When will the amounts of salt x1(t), x2(t), and x3(t) be simultaneously less than or equal to 0.5 pound? NONL