2. a A 2000 liter tank contains 500 Liters of water with a salt concentration of 10 g/L Water with a salt concentration of 50 g/L is flowing into the tank at the rate of 80L/min. The fluid mixes right away and is pumped out at the rate of 40 L/min . Let y(t) represent the quantity of salt in the tank at time t. For example, before you pump salt water into the tank, the initial amount of salt is 10 g/L times 500 Liters = 5000 grams. dy the rate at which the salt amount in the tank changes is dt = ( 40y gr/L Explain 5000 y+40t, Hint: think about rate in - rate out to get the net rate. Solve for y(t)
2. a A 2000 liter tank contains 500 Liters of water with a salt concentration of 10 g/L Water with a salt concentration of 50 g/L is flowing into the tank at the rate of 80L/min. The fluid mixes right away and is pumped out at the rate of 40 L/min . Let y(t) represent the quantity of salt in the tank at time t. For example, before you pump salt water into the tank, the initial amount of salt is 10 g/L times 500 Liters = 5000 grams. dy the rate at which the salt amount in the tank changes is dt = ( 40y gr/L Explain 5000 y+40t, Hint: think about rate in - rate out to get the net rate. Solve for y(t)
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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2. a A 2000 liter tank contains 500 Liters of water with a salt concentration of 10 g/L
Water with a salt concentration of 50 g/L is flowing into the tank at the rate of 80L/min.
The fluid mixes right away and is pumped out at the rate of 40 L/min .
Let y(t) represent the quantity of salt in the tank at time t. For example, before you pump salt water
into the tank, the initial amount of salt is 10 g/L times 500 Liters = 5000 grams.
dy
40y
Explain why the rate at which the salt amount in the tank changes is
dt
(5000
y+40t) gr/L
Hint: think about rate in - rate out to get the net rate .
Solve for y(t)
b. What is the salt concentration when the tank starts to overflow ?
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