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Q1. Each of the two tanks contains 200 gal of water, in which initially 100 lb (Tank T₁ )and 200 lb (Tank T₂)of fertilizer are dissolved. The inflow, circulation, and outflow are shown in Figur1. The mixture is kept uniform by stirring. Find the fertilizer contents y₁ (t) in T₁ and y2 (t) in T₂. 12 gal/min (Pure water) 4 gal/min 16 gal/min 12 gal/min

Q1. Each of the two tanks contains 200 gal of water, in which initially 100 lb (Tank T₁ )and 200 lb (Tank T₂)of fertilizer are dissolved. The inflow, circulation, and outflow are shown in Figur1. The mixture is kept uniform by stirring. Find the fertilizer contents y₁ (t) in T₁ and y2 (t) in T₂. 12 gal/min (Pure water) 4 gal/min 16 gal/min 12 gal/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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**Q1.** Each of the two tanks contains 200 gallons of water, in which initially 100 lb (Tank \(T_1\)) and 200 lb (Tank \(T_2\)) of fertilizer are dissolved. The inflow, circulation, and outflow are shown in Figure 1. The mixture is kept uniform by stirring. Find the fertilizer contents \(y_1(t)\) in \(T_1\) and \(y_2(t)\) in \(T_2\). ### Diagram Explanation: - **Tank \(T_1\):** Initially contains 100 lb of fertilizer. - **Tank \(T_2\):** Initially contains 200 lb of fertilizer. - **Flow Rates:** - Pure water flows into \(T_1\) at 12 gallons per minute. - Solution flows from \(T_1\) to \(T_2\) at 4 gallons per minute. - Solution flows from \(T_2\) to \(T_1\) at 16 gallons per minute. - Outflow from \(T_2\) is 12 gallons per minute.
Transcribed Image Text:**Q1.** Each of the two tanks contains 200 gallons of water, in which initially 100 lb (Tank \(T_1\)) and 200 lb (Tank \(T_2\)) of fertilizer are dissolved. The inflow, circulation, and outflow are shown in Figure 1. The mixture is kept uniform by stirring. Find the fertilizer contents \(y_1(t)\) in \(T_1\) and \(y_2(t)\) in \(T_2\). ### Diagram Explanation: - **Tank \(T_1\):** Initially contains 100 lb of fertilizer. - **Tank \(T_2\):** Initially contains 200 lb of fertilizer. - **Flow Rates:** - Pure water flows into \(T_1\) at 12 gallons per minute. - Solution flows from \(T_1\) to \(T_2\) at 4 gallons per minute. - Solution flows from \(T_2\) to \(T_1\) at 16 gallons per minute. - Outflow from \(T_2\) is 12 gallons per minute.
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