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Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let Vi(t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q2(t) describing the mixing process. (Show your work to get a full credit)

Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let Vi(t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q2(t) describing the mixing process. (Show your work to get a full credit)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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Q₁ (t) = Q₂ (t) = Q₁(0) = Q₂ (0) =
Transcribed Image Text:Q₁ (t) = Q₂ (t) = Q₁(0) = Q₂ (0) =
1. Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let V₁ (t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q₂(t) describing the mixing process. (Show your work to get a full credit) Tank 1 72 Tank 2 T4
Transcribed Image Text:1. Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let V₁ (t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q₂(t) describing the mixing process. (Show your work to get a full credit) Tank 1 72 Tank 2 T4
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