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quiz8_sol - MATH 174 Quiz 8 Tuesday April 12 ~ Name W...

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Unformatted text preview: MATH 174 Quiz 8 Tuesday April 12 ~ Name: W. Section: PID: Solve the problem systematically and neatly and show all your work. (2pts) 1. Find the spherical coordinates (p, gt, 6) and the cylindrical coordinates (7", 6, z) for the point (:13,y,z) = (1,1, 1) in rectangular coordinates. Z. yaxtl‘flry L 3 Y= J; 589: lexI—tyle 21‘ % J. woes) ”’5 000947, 2; Poor}; :3 Dal-{fwd :5 d): Ont-,4“: X I J3; KX'PWSZQDS B 008‘ 9““? :ijg— ” z - - L (4pts) 2. Evaluate F> 6' LI” by applying the transformation u=x—y,v=2x+y L>K' and integrating over an appropriate region in the uv—plane. 92/; g E E E E E E E g E g E E g (4pts) 3. Find the center of mass of a solid of constant density bounded below by the paraboloid z = x2 + 312 and above by the plane 2 = 4. v L “ ALP ijzyg 320M): 0271-» I: 32:0455 yea/ram « $745 ~ Mxy “—8. 3 : M 1" j 50 ”(L/‘4 WV % MS MS (0) D) f) ...
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