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Two very large tanks A and B are each partially tilled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 15 pounds of solt are dissolved in the solution in tank B. The system is closed in that the well stirred liquid is pumped only between the tanks, as shown in the tigure below. mixture 3 gal/min B 100 gal 100 gal mixture 2 gal/min (a) LUsc the Information glven In the lgure to construct a mathematical model for the number of paunds of salt x, (t) and xit) at time t in tanles A and H, respoctively. Ibs x (0) - Ibs (b) Tind a relationship between the variables x,() and x2() that holds at time t. (Write an cquation using x, for x.() and x, for x.) Lxplein why this relationship makes Intuitive sense. Since the system Is claned, salt enters the system at a canstant rate. Since the system is closed, salt Icaves the system at a constant rate. Since the system Is clased, salt Is not exchanged betwoen the twa tanks. Since the system is closed, salt enters and leeves the system at the same rate. O Since the system is clased, no salt cnters or loaves the system. Sulve Lhe inilisal value preblem uf Lhe umuunt vi sell inn lunk B el Lime L.

Two very large tanks A and B are each partially tilled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 15 pounds of solt are dissolved in the solution in tank B. The system is closed in that the well stirred liquid is pumped only between the tanks, as shown in the tigure below. mixture 3 gal/min B 100 gal 100 gal mixture 2 gal/min (a) LUsc the Information glven In the lgure to construct a mathematical model for the number of paunds of salt x, (t) and xit) at time t in tanles A and H, respoctively. Ibs x (0) - Ibs (b) Tind a relationship between the variables x,() and x2() that holds at time t. (Write an cquation using x, for x.() and x, for x.) Lxplein why this relationship makes Intuitive sense. Since the system Is claned, salt enters the system at a canstant rate. Since the system is closed, salt Icaves the system at a constant rate. Since the system Is clased, salt Is not exchanged betwoen the twa tanks. Since the system is closed, salt enters and leeves the system at the same rate. O Since the system is clased, no salt cnters or loaves the system. Sulve Lhe inilisal value preblem uf Lhe umuunt vi sell inn lunk B el Lime L.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 36E
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Two very large tanks A and B are each partially tilled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 15 pounds of solt are dissolved in the solution in tank B. The system is closed in that the well stirred liquid is pumped only between the tanks, as shown in the tigure below. mixture 3 gal/min B 100 gal 100 gal mixture 2 gal/min (a) LUsc the Information glven In the lgure to construct a mathematical model for the number of paunds of salt x, (t) and xit) at time t in tanles A and H, respoctively. Ibs x (0) - Ibs (b) Tind a relationship between the variables x,() and x) that holds et time t. (Write an ecuation using x, for x () and x, for x.) Lxplein why this relationship makes Intuitive sense. Since the system in claned, salt enters the system at a canstant rata. Since the system is closed, salt Iceves the system at a constant rate. Since the system Is clased, salt Is not exchanged betwoen the twa tanks. Since the system is closed, salt enters and leeves the system at the same rate. O Since the system is clased, no salt cnters or loaves the system. Sulve Lhe inilisl value preblem uf Lhe umuunl of sell in lunk 8 al Lime L. Use this relationship to help rind the amount of salt in tank 8 at !- 20 min. Round your answer to one decimal place.) *3(20) = [ Ibs
Transcribed Image Text:Two very large tanks A and B are each partially tilled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 15 pounds of solt are dissolved in the solution in tank B. The system is closed in that the well stirred liquid is pumped only between the tanks, as shown in the tigure below. mixture 3 gal/min B 100 gal 100 gal mixture 2 gal/min (a) LUsc the Information glven In the lgure to construct a mathematical model for the number of paunds of salt x, (t) and xit) at time t in tanles A and H, respoctively. Ibs x (0) - Ibs (b) Tind a relationship between the variables x,() and x) that holds et time t. (Write an ecuation using x, for x () and x, for x.) Lxplein why this relationship makes Intuitive sense. Since the system in claned, salt enters the system at a canstant rata. Since the system is closed, salt Iceves the system at a constant rate. Since the system Is clased, salt Is not exchanged betwoen the twa tanks. Since the system is closed, salt enters and leeves the system at the same rate. O Since the system is clased, no salt cnters or loaves the system. Sulve Lhe inilisl value preblem uf Lhe umuunl of sell in lunk 8 al Lime L. Use this relationship to help rind the amount of salt in tank 8 at !- 20 min. Round your answer to one decimal place.) *3(20) = [ Ibs
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