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1. Consider the following figure below that shows two brine tanks r galmin fresh water Tank 1 ank...
1. Consider the following figure below that shows two brine tanks r gal/min fresh water Tank 1 an...
1. Consider the following figure below that shows two brine tanks r gal/min fresh water Tank 1 anks 2 containing V and V gallons of brine respectively. Fresh water flows into tank 1, while mixed brine flows from tank 1 into tank 2. Let x,() denote the amount (in pounds) of salt in tank i at time for i-1,2. If each flow rate is r gallons per minute, then a simple account of salt concentration yields the first-order system where...
Consider two brine tanks connected as shown in figure I below. Tank 1 contains xit) pounds...
Consider two brine tanks connected as shown in figure I below. Tank 1 contains xit) pounds of salt in 100 wal of brine and tank 2 contains vit) pounds of salt in 200 gal of brine. The brine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated in figure 1. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine in tank 2...
(1 point) Math 216 Homework webHW3, Problem 4 Consider the cascade of two tanks of brine shown in the figure below, wit...
(1 point) Math 216 Homework webHW3, Problem 4 Consider the cascade of two tanks of brine shown in the figure below, with V-105 gallons and V2-209 gallons being the volumes of brine in the two tanks. Each tank also initially contains 52 lb of salt. The three flow rates indicated in the figure are each 5.1 gal/min, with pure water flowing into tank (Click on the picture to see a larger version.) (a) Find the amount x(t) of salt in...
Consider two brine tanks. Tank Ti is filled with 30 gal pure water, and tank T2...
Consider two brine tanks. Tank Ti is filled with 30 gal pure water, and tank T2 with 10 gal water containing 4 lb salt. • Ti is filled with 3 gal/min water containing 3 lb/gal salt. • 11 gal/min well-mixed solution flows out of Tj into T2 • 8 gal/min well-mixed solution flows out of T2 into Ti. • Finally, 3 gal/min well-mixed solution is leaving T2. Let yi(t) be the amount of salt (in lb) in tank Ti after...
Consider the closed tank system, consisting of three brine tanks. Tank 1 has volume 20 gallons,...
Consider the closed tank system, consisting of three brine tanks. Tank 1 has volume 20 gallons, Tank 2 has volume 10 gallons, and Tank 3 has volume 20 gallons. Brine flows from Tank 1 to Tank 2, from Tank 2 to Tank 3, and from Tank 3 back to Tank 1 at the rate of 20 gallons per minute. a) Letting x1(t), x2(t), x3(t) be the amount of salt in each tank at time t, what is the first order...
5. (30 points) Initially, two large tanks A and B each hold 50 gallons of brine. The well-mixed l...
5. (30 points) Initially, two large tanks A and B each hold 50 gallons of brine. The well-mixed liquid is pumped between the tanks as shown below. Use the information on the figure to construct a mathematical model for the number of pounds of salt x, (t) and x2(t) at time t in the tanks A and B pure water 3 gal/min mixture I gal/min 50 gal mixture mixture 4 gal/min 3 gal/min Solve the system subject to the initial...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1 initially contains 30 gallons (gal) of water and 55 ounces (oz) of salt, and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min, and the well-stirred solution flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Additionally, water containing 3...
Consider two brine tanks connected as shown in the figure. The brine solution is pumped from tank 1 into tank 2 at a...
Consider two brine tanks connected as shown in the figure. The
brine solution is pumped from tank 1 into tank 2 at a rate of 10
L/min10 L/min, and from tank 2 into tank 1 at a rate of 10 L/min10
L/min. Suppose there are 50 L50 L of brine in tank 1 and 25 L25 L
of brine in tank 2. Let xx be the amount of salt, in kilograms, in
tank 1 after tt minutes have elapsed, and...
L c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations b...
l c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations below where ki = for i= 1. 2. The volumes are V,-50 (gal) and v2-25 (gal). First solve for x1(t) and x2(t) assuming that r#20 (gai in). x1(0): 25(b), and x2(0)-Ο Then find the maximum amount of salt ever in tank 2 Finally, construct a figure showing the graphs of x,(t) and x2t) dx1 dx2
l c The amounts x1 (t)...
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which...
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which 150 lbs of salt is dissolved. A salt solution consisting of 0.5×(1 + e^(-0.02t)) lb. of salt per gallon (where t is time in unit of minute) is flowing into the tank at a rate of 10 gal./min and the mixed solution is drained from tank at the same rate. Find the amount of the salt in the tank after 1 hour. (10 points)...
1. Consider the following figure below that shows two brine tanks r gal/min fresh water Tank 1 anks 2 containing V and V gallons of brine respectively. Fresh water flows into tank 1, while mixed brine flows from tank 1 into tank 2. Let x,() denote the amount (in pounds) of salt in tank i at time for i-1,2. If each flow rate is r gallons per minute, then a simple account of salt concentration yields the first-order system where...
Consider two brine tanks connected as shown in figure I below. Tank 1 contains xit) pounds of salt in 100 wal of brine and tank 2 contains vit) pounds of salt in 200 gal of brine. The brine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated in figure 1. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine in tank 2...
(1 point) Math 216 Homework webHW3, Problem 4 Consider the cascade of two tanks of brine shown in the figure below, with V-105 gallons and V2-209 gallons being the volumes of brine in the two tanks. Each tank also initially contains 52 lb of salt. The three flow rates indicated in the figure are each 5.1 gal/min, with pure water flowing into tank (Click on the picture to see a larger version.) (a) Find the amount x(t) of salt in...
Consider two brine tanks. Tank Ti is filled with 30 gal pure water, and tank T2 with 10 gal water containing 4 lb salt. • Ti is filled with 3 gal/min water containing 3 lb/gal salt. • 11 gal/min well-mixed solution flows out of Tj into T2 • 8 gal/min well-mixed solution flows out of T2 into Ti. • Finally, 3 gal/min well-mixed solution is leaving T2. Let yi(t) be the amount of salt (in lb) in tank Ti after...
5. (30 points) Initially, two large tanks A and B each hold 50 gallons of brine. The well-mixed liquid is pumped between the tanks as shown below. Use the information on the figure to construct a mathematical model for the number of pounds of salt x, (t) and x2(t) at time t in the tanks A and B pure water 3 gal/min mixture I gal/min 50 gal mixture mixture 4 gal/min 3 gal/min Solve the system subject to the initial...
Each of the tanks shown in Figure 3.2.9 contains a brine solution. Assume that Tank 1 initially contains 30 gallons (gal) of water and 55 ounces (oz) of salt, and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min, and the well-stirred solution flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Additionally, water containing 3...
Consider two brine tanks connected as shown in the figure. The
brine solution is pumped from tank 1 into tank 2 at a rate of 10
L/min10 L/min, and from tank 2 into tank 1 at a rate of 10 L/min10
L/min. Suppose there are 50 L50 L of brine in tank 1 and 25 L25 L
of brine in tank 2. Let xx be the amount of salt, in kilograms, in
tank 1 after tt minutes have elapsed, and...
l c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations below where ki = for i= 1. 2. The volumes are V,-50 (gal) and v2-25 (gal). First solve for x1(t) and x2(t) assuming that r#20 (gai in). x1(0): 25(b), and x2(0)-Ο Then find the maximum amount of salt ever in tank 2 Finally, construct a figure showing the graphs of x,(t) and x2t) dx1 dx2
l c The amounts x1 (t)...
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