Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 90 pounds of salt are dissolved in the solution in tank A and 60 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 100 gal B 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 ✗₁ (t) and x2(t) at time t in tanks A and B, respectively. dx1 dt dx2 dt x1(0) ×2(0): = || = Ibs = lbs (b) Find a relationship between the variables ✗₁ (t) and x2(t) that holds at time t. (Write an equation using X1 for ×₁(t) and ×2 for x2(t).) Explain why this relationship makes intuitive sense. 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 enters the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt leaves the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 20 min. (Round your answer to one decimal place.) x2(20) = Ibs
Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 90 pounds of salt are dissolved in the solution in tank A and 60 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 100 gal B 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 ✗₁ (t) and x2(t) at time t in tanks A and B, respectively. dx1 dt dx2 dt x1(0) ×2(0): = || = Ibs = lbs (b) Find a relationship between the variables ✗₁ (t) and x2(t) that holds at time t. (Write an equation using X1 for ×₁(t) and ×2 for x2(t).) Explain why this relationship makes intuitive sense. 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 enters the system at a constant rate. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt leaves the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 20 min. (Round your answer to one decimal place.) x2(20) = Ibs
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 90 pounds of salt are dissolved in the solution in tank A and 60 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
100 gal
B
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 ✗₁ (t) and x2(t) at time t in tanks A and B, respectively.
dx1
dt
dx2
dt
x1(0)
×2(0):
=
||
=
Ibs
=
lbs
(b) Find a relationship between the variables ✗₁ (t) and x2(t) that holds at time t. (Write an equation using X1 for
×₁(t) and
×2
for x2(t).)
Explain why this relationship makes intuitive sense.
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 enters the system at a constant rate.
Since the system is closed, no salt enters or leaves the system.
Since the system is closed, salt leaves the system at a constant rate.
Use this relationship to help find the amount of salt in tank B at t = 20 min. (Round your answer to one decimal place.)
x2(20) =
Ibs
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