Two Very Large Tanks A And B Are Each Partially Filled With 100 Gallons Of Brine Initially 110 Pounds Of Salt Are Diss 1 (111.23 KiB) Viewed 28 times
Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 110 pounds of salt are dissolved in the solution in tank A and 40 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. dx₁ dt dx2 dt mixture 3 gal/min 00 A 100 gal 100 gal (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively. 3x9 100-t mixture 2 gal/min 2x1 + 100+ t X₁ (0) = 110 2x1 100+ t 3x2 100-t B lbs
x₂(0) 40 = lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using X₁ x₁ + x₂ = 150 Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. O Since the system is closed, salt leaves the system at a constant rate. O Since the system is closed, no salt enters or leaves the system. O Since the system is closed, salt enters and leaves the system at the same rate. O Since the system is closed, salt is not exchanged between the two tanks. Solve the initial value problem of the amount of salt in tank B at time t. x₂(t) = for x₁ (t) and Use this relationship to help find the amount of salt in tank B at t = 30 min. (Round your answer to one decimal place.) x₂(30) = X lbs x2 for x₂(t).)
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