Question

Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 95 pounds of salt are dissolved in the solution in tank A and 55 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 A B 100 gal 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 $x_1(t)$ and $x_2(t)$ at time $t$ in tanks A and B, respectively. $frac{dx_1}{dt} = $frac{dx_2}{dt} = x_1(0) = lbs x_2(0) = lbs (b) Find a relationship between the variables $x_1(t)$ and $x_2(t)$ that holds at time $t$. (Write an equation using $x_1$ for $x_1(t)$ and $x_2$ for $x_2(t)$.) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. 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. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Use this relationship to help find the amount of salt in tank B at $t = 30$ min. (Round your answer to one decimal place.) x_2(30) = lbs

          Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 95 pounds of salt are dissolved in the solution in tank A and 55 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
A
B
100 gal
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 $x_1(t)$ and $x_2(t)$ at time $t$ in tanks A and B, respectively.
$frac{dx_1}{dt} = 
$frac{dx_2}{dt} = 
x_1(0) = 
 lbs
x_2(0) = 
 lbs
(b) Find a relationship between the variables $x_1(t)$ and $x_2(t)$ that holds at time $t$. (Write an equation using $x_1$ for $x_1(t)$ and $x_2$ for $x_2(t)$.)
Explain why this relationship makes intuitive sense.
Since the system is closed, salt enters the system at a constant rate.
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.
Since the system is closed, salt leaves the system at a constant rate.
Since the system is closed, no salt enters or leaves the system.
Use this relationship to help find the amount of salt in tank B at $t = 30$ min. (Round your answer to one decimal place.)
x_2(30) = 
 lbs

$Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 95 pounds of salt are dissolved in the solution in tank A and 55 pounds of salt are dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the figure below. mixture 3 gal/min A B 100 gal 100 gal mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t in tanks A and B, respectively. fracdx1dt =fracdx2dt = x1(0) = lbs x2(0) = lbs (b) Find a relationship between the variables x1(t) and x2(t) that holds at time t. (Write an equation using x1 for x1(t) and x2 for x2(t).) Explain why this relationship makes intuitive sense. Since the system is closed, salt enters the system at a constant rate. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Use this relationship to help find the amount of salt in tank B at t = 30 min. (Round your answer to one decimal place.) x2(30) = lbs$

Added by Kimberly R.

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