A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration025 (kg/L) (b) Set up an initial value problem for the quantity y, in kg, of salt in the tank at time t minutes. - (ko/min) - 50 (kg) (0) (c) Solve the initial value problem in part (b). y(t) -

A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration025 (kg/L) (b) Set up an initial value problem for the quantity y, in kg, of salt in the tank at time t minutes. - (ko/min) - 50 (kg) (0) (c) Solve the initial value problem in part (b). 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

A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt per liter enters a
tank at the rate 8 L/min. The solution
mixed and drains from the tank at the same rate.
(a) What is the concentration of our solution in the tank initially?
concentration025 (kg/L)
(b) Set up an initial value problem for the quantity y, in kg, of salt in the tank at time t minutes.
(kg/min)
(0)
50 (kg)
di
(c) Solve the initial value problem in part (b).
y(1)
(d) Find the amount of salt in the tank after 1.5 hours.
amount 9 kg)
(e) Find the concentration of salt in the solution in the tank as time approaches infinity.
concentration .0125 (kg/)

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