Question 5 (10 points)  A tank contains 210 liters of fluid…

Question 5 (10 points)  A tank contains 210 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min, and the well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time .

Question 5 (10 points)  A tank contains 360 liters of fluid…

Question 5 (10 points)  A tank contains 360 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 6 L/min, and the well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time .

Question 6 (10 points)  A 8-pound object stretches a spring…

Question 6 (10 points)  A 8-pound object stretches a spring 3 inches by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 1 inch upward from its equilibrium position and given a velocity of 2 ft/sec downward.  Find the displacement at any time t.