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. mixture 3 gal/min = 100 gal = mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x, (t) and x₂(t) at time t in tanks A and B, respectively. dx₁ dt dx₂ dt x₂ (0) = x₂(0) = lbs B 100 gal 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. O Since the system is closed, salt leaves the system at a constant rate. 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. 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.) *₂ (25) = lbs
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. mixture 3 gal/min = 100 gal = mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x, (t) and x₂(t) at time t in tanks A and B, respectively. dx₁ dt dx₂ dt x₂ (0) = x₂(0) = lbs B 100 gal 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. O Since the system is closed, salt leaves the system at a constant rate. 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. 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.) *₂ (25) = lbs
Chapter3: Polynomial Functions
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Transcribed Image Text: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.
mixture
3 gal/min
dx₂ =
dt
x₁ (0) =
A
100 gal
i
(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.
dx1 =
dt
x₂ (0) =
mixture
2 gal/min
lbs
lbs
B
100 gal
(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.
O Since the system is closed, salt leaves the system at a constant rate.
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.
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) =
lbs
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