8. Use the Variation of Parameters method to solve: y" - 8y' + 16y= 10e** sec (x) (6 pts) 9. Consider a 1500-liter capac

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8 Use The Variation Of Parameters Method To Solve Y 8y 16y 10e Sec X 6 Pts 9 Consider A 1500 Liter Capac 1 (83.38 KiB) Viewed 35 times

8. Use the Variation of Parameters method to solve: y" - 8y' + 16y= 10e** sec (x) (6 pts) 9. Consider a 1500-liter capacity tank of drinking water that contains 1000 liters of water in which 4g of copper are dissolved. (That may not seem like much, but the maximum allowable concentration in the US is 1.3 mg/L.) Suppose that water with a copper concentration of 1 mg/L enters the tank at a rate of 5 liters per minute, is well-stirred, and the mixture leaves the tank at 5 liters per minute. (a) Set up and solve the initial value problem and then determine when (to the nearest hundredth of a minute) the copper concentration will reach 1.3 mg/L (6 pts) (b) Suppose that, actually, the pump moving the mixture out of the tank is damaged and that the mixture is leaving the tank at only 3 liters per minute. (Water is still coming in at 5 liters per minute.) Set up and solve this problem and then determine the concentration of copper in the water in the tank at the moment the tank reaches capacity. (3 pts) 10. A force of 1 Newton stretches a springmeters. A 1 kg mass is attached to the spring and is initially released from rest 1 meter below the equilibrium position. (a) Suppose the spring has a damping force equal to 4 times the instantaneous velocity and is being driven by an external force, f(t) = 13 sin(2t), write the IVP that this problem describes. (3 pts) (b) Solve the equation in part (a) to obtain the equation of motion of the mass. Use exact fractions to report. Do not use decimals. (6 pts)