Two tanks, each holding 100 L of liquid, are interconnected by pipes with liquid flowing from tank A into tank B at a rate of 12 L/min and from tank B into tank A at 3 L/min, as shown in the figure. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 9 L/min, and the solution flows out of tank B at 9 L/min. If, initially, tank A contains 2.6 kg of salt and tank B contains no salt (only water), determine the mass of salt in each tank at time t20. Graph on the same axes the two quantities x₁ (t) and x₂ (t), where x₁ (t) is the mass of salt in tank A and x₂ (t) is the mass in tank B. Click the icon to view the figure of the tanks. Xx What are the equations for the mass of salt in each tank at time t≥ 0? x₁ (t) = X₂ (t) = Tanks 9 L/min Pure water A x₁ (t) 100 L x₁ (0)=2.6 kg Print 12 L/min ← 3 L/min B x2 (t) 100 L X₂ (0)=0 kg Done 9 L/min Q

Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1 contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank also initially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows out from tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated in the figure are each 5 gal/min. Tank 1, capacity = 300 gal. Volume of brine =100 gal. x(t) = amount of salt (Ibs.) Tank 2, capacity = 300 gal. Volume of brine = 200 gal. y(t) = amount of salt (lbs.) (a) Write a system of differential equations that describes the amount of salt, r(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables a and y in writing your answers below. Do not use x(t) and y(t). da dt fip dt (b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t. z(t) y(t) (c) Determine the…

Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt in 100 gal of brine and tank 2 contains y(t) pounds of salt in 200 gal of brine. The brine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine in tank 2 flows out at 20 gal/min. The salt concentrations in the two tanks are x/100 pounds per gallon and y/200 pounds per gallon, respectively. The rates of change must satisfy the system of differential equations below. If the initial (t = 0) concentration in each brine tank is 0.5 lb/gal, solve the system for the amounts x(t) and y(t) of salt in the two tanks at time t. Click on the icon to view the figure. X 20x'= -6x + y 20y' = 6x-3y Figure x(t) = (Do not round until the final answer. Then round to the nearest hundredth as nee y(t) = (Do not round until the final answer. Then round to the nearest hundredth…