Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 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 x₁ (0) (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. = = A 100 gal x₂(0) = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).) Explain why this relationship makes intuitive sense. O Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt enters and leaves the system at the same rate. O Since the system is closed, salt leaves the system at a constant rate. O Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 25 min. (Round your answer to one decimal place.) x₂(25) =
Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 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 x₁ (0) (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. = = A 100 gal x₂(0) = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).) Explain why this relationship makes intuitive sense. O Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt enters and leaves the system at the same rate. O Since the system is closed, salt leaves the system at a constant rate. O Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 25 min. (Round your answer to one decimal place.) x₂(25) =
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter44: Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality
Section: Chapter Questions
Problem 108A: The feed of a drill is the depth of material that the drill penetrates in one revolution. The total...
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