A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
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
Transcribed Image Text:A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate
5 L/min.
(a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes:
dy
dt
=(kg/min) y(0) = k
kg.
(b) Solve the initial value problem in part (a)
y(t)
=0kg.
=
(c) Find the amount of salt in the tank after 4 hours.
amount = (kg)
(d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =
=(kg/L)
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 3 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,
