# MATH 116 2008 Midterm 2 Version B Solutions -...

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Calculus II Midterm 2June, 200821. (3 marks each; total 9 marks)Answer each question in the space provided. YouMUST show your work.a)Ifkis a nonzero constant andtky=is a solution of the differential equation226ytdtdy=, findkb)Given the parametric equationsttx2sincos2+=andtty2cossin2+=finddxdywhen0=t3.,.c)Find the approximate value of the solution to the initial value problem22008-B-Solutions
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Calculus II Midterm 2June, 200832. (5 marks)The vertical face of a dam across a river has the shape of aV(seeillustration below) 5m across the top and 8m deep at the center.What is the force that theriver exerts on the dam?Here, the water surface is at the top of the dam.Note:diagramis not to scale.2008-B-Solutions<.<,\05.-~twe~-JZf..1-;:'\{)'\i\cx-\vl"'\')"'-'::,1D~i"Clhl~):os-w---'"\."(-j'tl"-'j')=W<0..<--\~lq''''l';'\Dl~0-~)6j'1.-Gn"Sl~~-\~)b@~\"\1'Slty'-;'--\l~l')-l~""t. \1:5l'1.~}:::;'5n\.,\.,\,.Itl'NG2>
Calculus II Midterm 2June, 20084

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