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a5 - Jonathan Kim Assignment A5 MATH141 Winter 2008 You may...

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Jonathan Kim Assignment A5 MATH141, Winter 2008 You may attempt each problem a maximum of 5 times. Please remember that, while WeBWorK can usually check only the correctness of your answers, your responsibility in this course is to be able to justify your answers to problems of all these types, and others. The assignment is due Monday, March 24, 2008, at 11:30 PM. 1. (1 pt) For each set of Cartesian coordinates x y , match the equivalent set of Polar coordinates r θ . 1. ( -2.3 , 7.6 ) 2. ( 1.3 , 1.7 ) 3. ( -2 , 8.6 ) 4. ( 2 , 9.2 ) A. 7 9404 1 8647 B. 8 8295 1 7993 C. 2 1401 0 9179 D. 9 4149 1 3567 Correct Answers: A C B D 2. (1 pt) Consider the parametric curve given by the equations x t t 2 4 t 26 y t t 2 4 t 28 How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=8 ? Correct Answers: 56.5685424949238 3. (1 pt) Find the length of the parametrized curve given by x t 0 t 3 6 t 2 12 t y t 1 t 3 3 t 2 9 t for t between 0 and 1: Hint: ds dt is a quadratic polynomial with integer coefficients. Correct Answers: 13 4. (1 pt) Determine the area of the region enclosed by the as- troid x θ 4cos 3 θ y θ 4sin 3 θ Correct Answers: 18.8495559215388 5.
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