Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁ (t) and x₂(t) of salt in tanks A and B, respectively, at time t. mixture 4 gal/min This system is described by the system of equations dx1 1 25*1 +502 dt dx2 dt dx1 dt dx2 dt = = 23×1-323/35/²/2 with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 4 pounds of salt per gallon is pumped into tank A? = pure water 3 gal/min = mixture 1 gal/min mixture 3 gal/min

Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁ (t) and x₂(t) of salt in tanks A and B, respectively, at time t. mixture 4 gal/min This system is described by the system of equations dx1 1 25*1 +502 dt dx2 dt dx1 dt dx2 dt = = 23×1-323/35/²/2 with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 4 pounds of salt per gallon is pumped into tank A? = pure water 3 gal/min = mixture 1 gal/min mixture 3 gal/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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