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A tank contains 70 kg of salt and 1000 L of water. Water containing 0.6 of salt enters the tank at the rate 20 min. The solution mixed and drains from the tank at the rate 4 min. A(t) is the amount of salt in the tank at time t measured in kilograms. (a) A(0)= 70 (kg) (b) A differential equation for the amount of salt in the tank is = 0. (Use t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is (d) A(t) = (kg) (250 + 4t) L 4 (e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold the solution.) concentration =

A tank contains 70 kg of salt and 1000 L of water. Water containing 0.6 of salt enters the tank at the rate 20 min. The solution mixed and drains from the tank at the rate 4 min. A(t) is the amount of salt in the tank at time t measured in kilograms. (a) A(0)= 70 (kg) (b) A differential equation for the amount of salt in the tank is = 0. (Use t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is (d) A(t) = (kg) (250 + 4t) L 4 (e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold the solution.) concentration =

Advanced Engineering Mathematics
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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Only b, d and e The Integrating Factor for part C is correct
A tank contains 70 kg of salt and 1000 L of water. Water containing 0.64 of salt enters the tank at the rate 20. The solution is mixed and drains from the tank at the rate 4 min. A(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = 70 (kg) (b) A differential equation for the amount of salt in the tank is = 0. (Use t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is (d) A(t) = (kg) (250 + 4t) L 4 (e) 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 =
Transcribed Image Text:A tank contains 70 kg of salt and 1000 L of water. Water containing 0.64 of salt enters the tank at the rate 20. The solution is mixed and drains from the tank at the rate 4 min. A(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = 70 (kg) (b) A differential equation for the amount of salt in the tank is = 0. (Use t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is (d) A(t) = (kg) (250 + 4t) L 4 (e) 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 =
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