Question

Q2) an oil refinery, a storage tank contains 2000 gal of gasoline that initially has 100 lb of an additive dissolved in it. In preparation for winter weather, gasoline is pumped into the tank at a rate of 40 gal/min. The well-mixed solution is pumped out at a rate of 40 gal/min. How much of the additive is in the tank 20 min after the pumping process begins? Q3) a) Find the total deferential equation (dw) for the function w=x’y+zy where x=cos(t)+sin(t), y=r + cost and z=rts-sin’t? b) Use the chine rule to to find the derivative w=x'y+y'z where x=cos’t-sin't, y=2cost*sint and zet? Q4) The radius of the base and the height of a right circular cone at given instant (to) are ro=30 cm and ho=40 cm. if his increasing at rate of 2 cm per sec and volume is increasing at rate of 1500 cm/sec per sec. find the rates of change of in r?

need solution 25 minute

Answer 1

2000 gal. 2000 Volume of gasoline in the tank = Initial amount of additive = 100 pounds. Gasoline pumbed into the tank = 40gal/min. additive added into the tank = o galfani bound/min let amount of additive after t minute Act) concentration of additive after tminute =A additive remored from the tank = 400 A bound (minute 2000 A bound [minute The rate of amount of additive change in the tank Act) CA - Ao S d = osat at In (A) - 2 otto initial condition Aco) = 100 In (100) = c = ln (100) ln (A) - Sat + Incino ln (A)-In (100) = - sot -tlso it so en (A) 100 100. e-tlso Act) After 20 minute Ac20) -2150 e -0.44 A (20) = 100 100. e = 67.032 pounds. After 20 minutes amount of additive in the tank 67.032 pounds.