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Quiz7-3_29 - Name You have fteen minutes to complete the...

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Name: You have fifteen minutes to complete the quiz. If anything seems unclear, please ask. 1. Pacman consists of the space above the region pictured, and below the upper hemisphere center (0 , 0 , 0) and radius 1, together with the corre- sponding space below the xy -plane and above the lower hemisphere. Find the volume of Pacman. (4 points) 2. Set up integrals of a general function f ( x, y ) over the regions pictured. Use whichever of Cartesian and polar coordinates gives a simpler integral. (3 points) 3. The floor of a box, modeled by [0 , 2] × [ - 1 , 1] is heated, with the heat coming in at the left hand edge. The position of a mouse is governed by the probability density function m ( x, y ) = (2 - x ) / 4 if 0 x 2 and - 1 y 1 0 otherwise . Find the probability the mouse is in the left-hand (warmer) half of the box. (3 points) 1
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Solutions If you have any questions and / or think you’ve spotted a mistake / typo, please get in touch with me. 1. The formula for the hemisphere given in polar coordinates is
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