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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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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 .
And, the content leaves the tank at rate = 10 .
Initially tank contains 10 kg of salt in 100 liter of water then f(0)=10
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