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A tank initially contains a solution of 5 pounds of salt in 40 gallons of water. Water with 3/5 pound of salt per gallon is added to the tank at 8 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q' (t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t)= =

A tank initially contains a solution of 5 pounds of salt in 40 gallons of water. Water with 3/5 pound of salt per gallon is added to the tank at 8 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q' (t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t)= =

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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Subject:- Advance Mathematic 

A tank initially contains a solution of 5 pounds of salt in 40 gallons of water. Water with 3/5 pound of salt per gallon is added to the tank at 8 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t)= = t→∞o
Transcribed Image Text:A tank initially contains a solution of 5 pounds of salt in 40 gallons of water. Water with 3/5 pound of salt per gallon is added to the tank at 8 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t)= = t→∞o
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