Problem #2: A large tank contains 50 litres of water in which 25 grams of salt is dissolved. Brine containing 12 grams of salt per litre is pumped into the tank at a rate of 8 litres per minute. The well mixed solution is pumped out of the tank at a rate of 5 litres per minute. Problem #2(a): (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(1) be the amount of salt in the tank after 7 minutes. Which of the following is a differential equation for x(t)? (A) (E) (1) Problem #2(b): dx = 96- 8.x(t) 50+ 3t = 8 (B) = 8 - x(t) (F) - 5.x(t) 50 + 8t dx dt = 96- = 40 - 5 x(t) 50 + 3t 8 x(t) 50 +8t (C) (G) dx = 40-x(1) (D) = 8- dt = 40 - x(t) 8.x(t) 50+ 3t 50+8t (H)=96 - 2x(1)
Problem #2: A large tank contains 50 litres of water in which 25 grams of salt is dissolved. Brine containing 12 grams of salt per litre is pumped into the tank at a rate of 8 litres per minute. The well mixed solution is pumped out of the tank at a rate of 5 litres per minute. Problem #2(a): (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(1) be the amount of salt in the tank after 7 minutes. Which of the following is a differential equation for x(t)? (A) (E) (1) Problem #2(b): dx = 96- 8.x(t) 50+ 3t = 8 (B) = 8 - x(t) (F) - 5.x(t) 50 + 8t dx dt = 96- = 40 - 5 x(t) 50 + 3t 8 x(t) 50 +8t (C) (G) dx = 40-x(1) (D) = 8- dt = 40 - x(t) 8.x(t) 50+ 3t 50+8t (H)=96 - 2x(1)
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:Problem #2: A large tank contains 50 litres of water in which 25 grams of salt is dissolved. Brine containing 12 grams of salt
per litre is pumped into the tank at a rate of 8 litres per minute. The well mixed solution is pumped out of the tank
at a rate of 5 litres per minute.
Problem #2(a):
(a) Find an expression for the amount of water in the tank after t minutes.
(b) Let x(1) be the amount of salt in the tank after 7 minutes. Which of the following is a differential equation for
x(t)?
(A)
(E)
(1)
Problem #2(b):
dx
= 96-
8.x(t)
50+ 3t
= 8
(B)
= 8 - x(t) (F) -
5.x(t)
50 + 8t
dx
= 96-
dt
= 40 -
5 x(t)
50 + 3t
(C) = 40-x(1) (D) = 8-
dx
dt
8 x(t)
50 +8t (G)
= 40 - x(t)
8.x(t)
50+ 3t
50+8t (H)=96 - 2x(1)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 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,
