A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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![A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate
5 L/min.
(a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes:
dy
dt
=(kg/min) y(0) = k
kg.
(b) Solve the initial value problem in part (a)
y(t)
=0kg.
=
(c) Find the amount of salt in the tank after 4 hours.
amount = (kg)
(d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =
=(kg/L)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2133c9-e1e5-4d56-9c72-044227328930%2F1fd51fba-54ba-4eba-ae79-0fa40e0cdbab%2F76jpyyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate
5 L/min.
(a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes:
dy
dt
=(kg/min) y(0) = k
kg.
(b) Solve the initial value problem in part (a)
y(t)
=0kg.
=
(c) Find the amount of salt in the tank after 4 hours.
amount = (kg)
(d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =
=(kg/L)
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