Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 80 pounds of salt are dissolved in the solution in tank A and 70 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. 100 gal mixture 3 gal/min mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x₂(t) and x₂(t) at time t in tanks A and B, respectively. dx dx2 *₂ (0) - x₂(0) - lbs B 100 gal lbs (b) Find a relationship between the variables x, (t) and x₂(t) that holds at time t. (Write an equation using x, for x, (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 is not exchanged between the two tanks. O 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, salt enters and leaves the system at the same 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) - lbs
Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 80 pounds of salt are dissolved in the solution in tank A and 70 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. 100 gal mixture 3 gal/min mixture 2 gal/min (a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x₂(t) and x₂(t) at time t in tanks A and B, respectively. dx dx2 *₂ (0) - x₂(0) - lbs B 100 gal lbs (b) Find a relationship between the variables x, (t) and x₂(t) that holds at time t. (Write an equation using x, for x, (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 is not exchanged between the two tanks. O 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, salt enters and leaves the system at the same 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) - lbs
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
2. please
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,