(30 Points) Suppose there are two tanks, each initially containing 100 gallons of salt water, connected...

Transcribed Image Text:

(30 Points) Suppose there are two tanks, each initially containing 100 gallons of salt water, connected to a series of pipes as shown at right. Initially, the amount of salt in the first tank is 20 pounds, while that in the second tank is 5 pounds. Pure Water Mixture 2 gal/min 1 gal/min T, T2 At some point, a mechanism is started whereby fluid – some pure water, some salt water – is pumped in and out of the tanks as indicated. We assume that the mixtures pumped between and out of the tanks is at all times instantaneously well-stirred. Use the above information and Mixture Mixture Mixture 1 gal/min 2 gal/min 1 gal/min accompanying diagram to answer Parts (a) and (b) below. Note: The entire problem, including all answers and all associated work supporting those answers, must be based upon and demonstrate the deriving of solutions by means of matrices and vectors only. Any divergence will result in no credit, regardless of any creativity you may show in the process. a) (10 Points) Construct a system of linear first order differential equations modeling the rates at which the quantities of salt in each tank is changing. Your answer must be compete in all aspects. (30 Points) Suppose there are two tanks, each initially containing 100 gallons of salt water, connected to a series of pipes as shown at right. Initially, the amount of salt in the first tank is 20 pounds, while that in the second tank is 5 pounds. Pure Water Mixture 2 gal/min 1 gal/min T, T2 At some point, a mechanism is started whereby fluid – some pure water, some salt water – is pumped in and out of the tanks as indicated. We assume that the mixtures pumped between and out of the tanks is at all times instantaneously well-stirred. Use the above information and Mixture Mixture Mixture 1 gal/min 2 gal/min 1 gal/min accompanying diagram to answer Parts (a) and (b) below. Note: The entire problem, including all answers and all associated work supporting those answers, must be based upon and demonstrate the deriving of solutions by means of matrices and vectors only. Any divergence will result in no credit, regardless of any creativity you may show in the process. a) (10 Points) Construct a system of linear first order differential equations modeling the rates at which the quantities of salt in each tank is changing. Your answer must be compete in all aspects.