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A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of water. Let S (t) be the amount of salt in the tank at any time t and S'(t) its derivative. -5S (t) (i) Use the balance law to prove that P" (t) 50 + t (ii) How much salt will there be in the tank after 30 min?

A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of water. Let S (t) be the amount of salt in the tank at any time t and S'(t) its derivative. -5S (t) (i) Use the balance law to prove that P" (t) 50 + t (ii) How much salt will there be in the tank after 30 min?

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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A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of water. Let S (t) be the amount of salt in the tank at any time t and S'(t) its derivative. -59 (t) (i) Use the balance law to prove that S"(t) 50 +t (ii) How much salt will there be in the tank after 30 min?
Transcribed Image Text:A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of water. Let S (t) be the amount of salt in the tank at any time t and S'(t) its derivative. -59 (t) (i) Use the balance law to prove that S"(t) 50 +t (ii) How much salt will there be in the tank after 30 min?
Expert Solution
Step 1

Let f(t) be the amount of salt in the tank at any time t.

Given that 

Pure water is entering in tank at rate = 12 l/min.

And, the content leaves the tank at rate = 10  l/min.

Initially tank contains 10 kg of salt in 100 liter of water then f(0)=10

 

 

 

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