Consider the two interconnected tanks shown in Figure 7.1.6. Tank 1 initially contains30 gal of water and 25 oz of salt, and Tank 2 initially contains 20 gal of water and 15 ozof salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. Themixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min.Water containing 3 oz/gal of saltalso flows into Tank 2 at a rate of 1 gal/min (from the outside). The mixture drains fromTank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min,while the remainder leaves the system.(a) Let Q1(t) and Q2(t), respectively, be the amount of salt in each tank at time t. Writedown differential equations and initial conditions that model the flow process. Observethat the system of differential equations is nonhomogeneous.(b) Find the values of Q1 and Q2 for which the system is in equilibriumthat is, does notchange with time. Let QE1 and QE2 be the equilibrium values. Can you predict which tankwill approach its equilibrium state more rapidly?(c) Let x1 = Q1(t) QE1 and x2 = Q2(t) QE2 . Determine an initial value problem for x1and x2. Observe that the system of equations for x1 and x2 is homogeneous.

L3 - 4 ▯ ▯ 1 ex. Sketch the graph of y = −2s n x . 2 1 −π π −1 ex. Sketch the graph of y = |sin(x − π)|. 1 −π π −1