MATH 253 2010 Midterm 2 Version D Solutions - 2010-D-Solutions Calculus II Midterm 2 March 2010 2 1(3 marks each total 12 marks Answer each question in

MATH 253 2010 Midterm 2 Version D Solutions -...

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Calculus II Midterm 2 March, 2010 2 1. (3 marks each; total 12 marks) Answer each question in the space provided. You MUST show your work. a)Given the parametric equations tx25+=, 1962++=ttyfind dxdyevaluated at the point (7, 16). b)Consider a 60 L tank filled with water, initially containing 0.03 kg of salt per litre. Water containing 0.1 kg/L of salt flows into the tank at the rate of 5 L/min. If the salt-water solution in the tank is thoroughly mixed and flows out from the tank at a rate of 5 L/min, then set upthe differential equation describing the rate of change of salt (call it A) in kg in the tank as a function of time (call it t) in minutes, and state the corresponding initial condition. You do NOT have to solve the equation. c)Ifuvwwvwuwvuf53cos),,(42++=, find vd) For what nonzero values of kdoes the function ktBktAycossin+=satisfy the differential equation 04=+yy? State all possible values. f

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