Consider the double mixing problem depicted in Figure 1.7.6. (a) Show that...

Consider the double mixing problem depicted in Figure 1.7.6.

(a) Show that the following are differential equationsfor A₁(t) and A₂(t):

where V₁ and V₂ are constants.

(b) Let r₁ = 6 L/min, r₂ = 4 L/min, r₃ = 3 L/min, and c₁ = 0.5 g/L. If the first tank initially holds 40 L of water in which 4 grams of chemical is dissolved, whereas the second tank initially contains 20 g of chemical dissolved in 20 L of water, determine the amount of chemical in the second tank after 10 min.