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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Qu
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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