A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min = How much salt is in the tank when t = 0? y(0) = How much salt (in kg) is in the tank after t minutes? y = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min = How much salt is in the tank when t = 0? y(0) = How much salt (in kg) is in the tank after t minutes? y = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
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:A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per
liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min.
Let y(t) be the amount of salt (in kg) in the tank after t minutes.
(a) Find the rate of change of amount of salt in the tank after t minutes.
dy
dt
kg
min
How much salt is in the tank when t = 0?
y(0)
How much salt (in kg) is in the tank after t minutes?
y =
=
kg
(b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.)
y(50) =
kg
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