Question 5 (10 points)  A tank contains 150 liters of fluid…

Question 5 (10 points)  A tank contains 150 liters of fluid in which 10 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 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 1 (10 points)  Compute the Wronskian of the set. Al…

Question 1 (10 points)  Compute the Wronskian of the set. All steps must be shown. Then use your answer to justify whether the given set of functions is linearly independent or not.  A detailed explanation must be provided.  A value to the first part and a yes or no response to the second part is insufficient.

Question 2 (10 points) Two-part question. The parts are dist…

Question 2 (10 points) Two-part question. The parts are distinct.  Please read each question part and answer accordingly. a. Determine whether the statement is true or false.  If it is true, explain why.  If it is false, explain why or give an example that disproves the statement.  Note: An answer that simply states “True” or “False” will earn ZERO credit.  An appropriate justification must be provided as part of the solution response.  If

Question 6 (10 points)  A 16-pound object stretches a spring…

Question 6 (10 points)  A 16-pound object stretches a spring 8/9 feet by itself. There is no damping and no external forces acting on the system.  The spring is initially displaced by 6 inches upward from its equilibrium position and given a velocity of 1 ft/sec downward.  Find the displacement at any time t.