Problem #6: A large tank contains 100 litres of water in which 25 grams of salt is dissolved. Brine containing 10 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 #6(a): (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after 7 minutes. Which of the following is a differential equation for x(1)? (A) = (E) (1) dt dx R dr dx = 8-x(t) (B) = =8- Enter your answer as a symbolic function of t, as in these examples 80-x(1) (F)-8 =8- 80 5x(t) 100+3r 5 x(t) 100 + 8t 8 x(1) 100+ 3r (C) dx = 40-x(1) (D) dt (G) = 80 dt dx 8x(t) (H) 100+ 3r = 40- 4 5 x(t) 100+ St = 40 - 8x(t) 100+ Sr
Problem #6: A large tank contains 100 litres of water in which 25 grams of salt is dissolved. Brine containing 10 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 #6(a): (a) Find an expression for the amount of water in the tank after t minutes. (b) Let x(t) be the amount of salt in the tank after 7 minutes. Which of the following is a differential equation for x(1)? (A) = (E) (1) dt dx R dr dx = 8-x(t) (B) = =8- Enter your answer as a symbolic function of t, as in these examples 80-x(1) (F)-8 =8- 80 5x(t) 100+3r 5 x(t) 100 + 8t 8 x(1) 100+ 3r (C) dx = 40-x(1) (D) dt (G) = 80 dt dx 8x(t) (H) 100+ 3r = 40- 4 5 x(t) 100+ St = 40 - 8x(t) 100+ Sr
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem #6: A large tank contains 100 litres of water in which 25 grams of salt is dissolved. Brine containing 10 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 #6(a):
(a) Find an expression for the amount of water in the tank after t minutes.
(b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation for
x(t)?
(A)
(E)
=
= 8-x(1) (B)
= 80-x(t) (F)
dx
(1) = 80
Problem 6(b): Select
5x(t)
100+ 3t
dr
Enter your answer as a symbolic
function of t, as in these
examples
=8-
dx
= 8
5 x(t)
100+ St
8x(t)
100+ 3t
(C)dx=40-x(1) (D)
dt
(G) = 80
8x(1)
100+ 3r
dx 40
(H)
dx
dt
4
5.x(t)
100 + St
= 40 -
8.x(1)
100 + St
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