Consider the cascade of two tanks of brine shown in the figure below, with V =...

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Consider the cascade of two tanks of brine shown in the figure below, with V₁ = 110 gallons and V₂ = 194 gallons being the volumes of brine in the two tanks. Each tank also initially contains 47 lb of dissolved salt. The three flow rates indicated in the figure are each 5.6 gal/min, with pure water flowing into tank 1. Solve for y(t) using the function x(t) found in part (a). y(t) = (a) Find the amount x(1) of salt in tank 1 at time t. x(t) = (b) Suppose that y(t), the amount of salt in tank 2 at time t, is given by the differential equation dy 5.6x dt 110 (c) Finally, find the maximum amount of salt ever in tank 2. Maximum amount of salt= lbs. 55 P Nowe (Click on the picture to see a larger version.) = 5.6y 194 Consider the cascade of two tanks of brine shown in the figure below, with V₁ = 110 gallons and V₂ = 194 gallons being the volumes of brine in the two tanks. Each tank also initially contains 47 lb of dissolved salt. The three flow rates indicated in the figure are each 5.6 gal/min, with pure water flowing into tank 1. Solve for y(t) using the function x(t) found in part (a). y(t) = (a) Find the amount x(1) of salt in tank 1 at time t. x(t) = (b) Suppose that y(t), the amount of salt in tank 2 at time t, is given by the differential equation dy 5.6x dt 110 (c) Finally, find the maximum amount of salt ever in tank 2. Maximum amount of salt= lbs. 55 P Nowe (Click on the picture to see a larger version.) = 5.6y 194

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To find the amount of salt in tank 1 at time t we need to first find the rate of change of salt in t... View the full answer