8. A tank initially contains 500 L of pure water. Two streams of brine enter the tank: one with a salt concentration of 0.3 kg/L at a raté of 6 L/min, and one with a salt concentration of 0.7 kg/L at a rate of 4 L/min. The solution is kept thoroughly mixed and drains out of the tank at a rate of 10 L/min. (a) Set up a differential equation that models this situation, where y(t) is the amount of salt in the tank after t minutes. (b) Solve this differential equation to find y(t), the amount of salt in the tank after t minutes.
8. A tank initially contains 500 L of pure water. Two streams of brine enter the tank: one with a salt concentration of 0.3 kg/L at a raté of 6 L/min, and one with a salt concentration of 0.7 kg/L at a rate of 4 L/min. The solution is kept thoroughly mixed and drains out of the tank at a rate of 10 L/min. (a) Set up a differential equation that models this situation, where y(t) is the amount of salt in the tank after t minutes. (b) Solve this differential equation to find y(t), the amount of salt in the tank after t minutes.
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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a and b if you don't mind please
Transcribed Image Text:8. A tank initially contains 500 L of pure water. Two streams of brine enter the tank: one with a salt concentration
of 0.3 kg/L at a rate of 6 L/min, and one with a salt concentration of 0.7 kg/L at a rate of 4 L/min. The
solution is kept thoroughly mixed and drains out of the tank at a rate of 10 L/min.
(a) Set up a differential equation that models this situation, where y(t) is the amount of salt in the tank after
t minutes.
(b) Solve this differential equation to find y(t), the amount of salt in the tank after t minutes.
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