MATH 222 Quiz: MATH 222 UW Madison Quiz4 ans

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turquoisegnu128

31 Jan 2019

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Problem 2 (15 points): mixture problem: a 200-gal tank is half full of distilled water. Since at the beginning, the 200-gal tank is half full, the time to ll this tank is: Let m(t) denote the mass of concentrate in the tank at time t. then we have: m(t + 1) m(t) = {5 0. 5 3 m(t) V (t) is the density of the concentrate at time t. and v (t) = 100 + 2t as we got above. where m(t) We solve this rst-order linear di erential equation by integrating factor:u(t) = e e. Then we have: ln(100+2t) = (100 + 2t) Use unitial condition: m(0) = 0, we have: 0 = 50 + c. Method 2: use (t) as variable. m(t) = 50 + t + 50000(100 + 2t) . Let"s use min as the unit of time. At time t, the volume is:v (t) = 100 + 2t.

Related Questions

Mixture In Exercises 35-38, consider a tank that at time contains gallons of a solution of which, by weight, pounds is soluble concentrate. Another solution containing pounds of the concentrate per gallon is running into the tank at the rate of gallons per minute. The solution in the tank is kept well stirred and is withdrawn at the rate of gallons per minute.

A 200-gallon tank is half full of distilled water. Starting, at time , a solution containing 0.5 pound of concentrate per gallon is admitted to the tank at a rate of 5 gallons per minute, and the well-stirred mixture is withdrawn at a rate of 3 gallons per minute.