Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt in 100 gal of brine and tank 2 contains y(t) pounds of salt in 200 gal of brine. Thebrine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine intank 2 flows out at 20 gal/min. The salt concentrations in the two tanks are x/100 pounds per gallon and y/200 pounds per gallon, respectively. The rates of change must satisfy the systemof differential equations below. If the initial (t = 0) concentration in each brine tank is 0.5 lb/gal, solve the system for the amounts x(t) and y(t) of salt in the two tanks at time t.Click on the icon to view the figure.X20x'= -6x + y20y' = 6x-3yFigurex(t) =(Do not round until the final answer. Then round to the nearest hundredth as neey(t) =(Do not round until the final answer. Then round to the nearest hundredth as nee20 gal/minFresh waterx(1) lb100 galTank 110 gal/min→30 gal/miny(t) lb200 galTank 220 gal/minPrintDone

Answered: Image /qna-images/answer/87a98162-b5b3-484b-a424-75bb8b040455.jpg

Answered: Consider two brine tanks connected as…

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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Two well-mixed tanks are interconnected. Tank A contains 60 grams of salt in 40 liters of water, and Tank B contains 70 grams of salt in 20 liters of water. A briny solution with concentration 2 gram/L flows into Tank A at a rate of 7 L/min, while a solution with concentration 3 grams/L flows into Tank B at a rate of 5 L/min. The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B. Letting x1 represent the grams of salt in Tank A, and x2 represent the grams of salt in Tank B, set up the IVP for amount of salt in these two tanks. x2 x1(0) = ' 23(0) =
Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows from lake A into lake B, and from lake B into lake C, both inflows and outflows at the same rate of 525 km2/year. Suppose that at time t=0 (years), the pollutant concentration of lake B, caused by past industrial pollution that has now been ordered to cease, is five times that of lake A. If the outflow from lake B to lake C is perfectly mixed lake water, how long will it take to reduce the pollution concentration in lake B to twice that of lake A? (Choose all correct answers) OA More than five years. OB Less than eight years. OC Less than six years. D D. More than 11 years.
4. 3m 6 m 12 m bh 2 в. ( V - Bh V- UL V= %3D B. B.
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The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules when y = 18 m/sec, what is K when y = 10 m/sec.
Ex. 1: Water is flowing through an inclined pipeline of diameter 20 cm & 40 cm at section A & B respectively. Section A & B are located at height of 2 m & 2.5 m respectively from ground level. The discharge through pipe is 30 1/s. If the pressure at A is 20 kPa, find the pressure at point B.
Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows from lake A into lake B, and from lake B into lake C, both inflows and outflows at the same rate of 525 km3/year. Suppose that at time t=0 (years), the pollutant concentration of lake B, caused by past industrial pollution that has now been ordered to cease, is five times that of lake A. If the outflow from lake B to lake C is perfectly mixed lake water, how long will it take to reduce the pollution concentration in lake B to twice that of lake A? Choose all correct answers. B Approximately 6.3 years. Approximately 4.4 years. Approximately 5 years. Approximately 8.3 years. Approximately 7 years.
My cat Pythagoras has purchased and installed in my back yard a large barrel with a 400-gallon capacity. It is initially half full of clean water. But he has three hoses feeding this barrel, each with a rate of flow of 2 gal./min. of water. Two provide the barrel with clean water, but the third contains a concentration of 2 g/gal. of liquid calculus text books. My other cat, Jolie, has decided to sabotage this process by puncturing a hole toward the bottom of this barrel that allows 4 gal./min. to leak. If we assume that there is a benevolent feline deity that blissfully stirs this barrel with a rather large spoon, then write a differential equation that mathematically models the rate at which the amount of liquid calculus text books changes in the barrel (at least up to the time it fills). Thereafter, solve this differential equation.
A student is concerned with the amount of air pollution students are exposed to in the school's parking lot after school. The student conducts an investigation to compare the quantity of particulate matter released from the diesel-powered buses, natural gas-powered buses, and the large and small cars as they idle waiting to pick up students. To make measurements, a small piece of white fabric is used to collect particulate matter from the tailpipe of each vehicle as it idles for five minutes. Each piece of fabric is then analyzed to measure the amount of particulate matter it collected. (i) Identify the independent variable in the investigation. (j) Identify one variable that was not mentioned in the description that could affect the results of the investigation. (k) Describe a realistic alternate sampling method to collect particulate matter from the vehicles in the investigation. (1) The student wants to ensure that the results are reliable. Explain how the student could modify the…
2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?
1. Suppose that a commercial truck has an efficiency of 120 – 2v m(v) miles/gallon going at speed of v miles/hour. The driver's rate is 15 dollars/hr, and gas is $3.50/gal- lon. a. Find the cost C(v) per mile to travel at speed v mph. b. Find the cheapest driving speed.
the beam supports a roof that weighs 250 pounds per foot and supports a concentrated load of 1,200 pounds at the overhanging end. Determine the support reactions at A and B.

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