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Unformatted text preview: APPM 2350 Summer 2006 Exam 2 July 12, 2006 1 INSTRUCTIONS: Computers, calculators, books, notes, frying monkeys, etc. are not permitted. Some (possibly) useful formulae are attached. Write your name, your instructor’s name, and the color of your exam sheet on the front of your bluebook. Work all problems. Start each problem on a new page . Show your work clearly and box your final answer. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. The porosity of the soil in a circular field, x 2 + y 2 ≤ 1, is given by p ( x,y ) = 4 x 2 + 2 y 2 − 2 y . Find the locations in the field where water will drain the fastest and slowest ( i.e. the absolute maximum and minimum porosity). 2. A goldsmith wants to make a gold brooch in the shape given in polar coordinates by r ≤ 1 − sin( θ ). The density of gold she is going to use on this brooch design is given by δ ( x,y ) = 2 + 3 radicalbig x 2 + y 2 . Sketch the shape of the brooch and determine the total amount of gold she will need to use. Hints: 1) the area of this shape is 3 π 2 ; 2) sin 2 ( a ) = 1 2 (1 − cos(2 a ))....
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