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# Exam 2 Answers - Math 150A Exam 2 Answers 1 The city of St...

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Math 150A – Exam 2 - Answers 1. The city of St. Leibniz lies at the intersection of two highways: one running North-South, the other running East-West. At noon, Kimi starts 4 mi. East of St. Leibniz walking West at a constant rate of 4 mi./hr. At the same time, Filipe starts 6 mi. South of St. Leibniz walking North at a constant rate of 4 mi./hr. At 3:00 that afternoon, how fast is the distance between them changing? (Hint: Draw a picture showing their locations and velocities at 3:00.) (10 points) At 3:00 Kimi has walked 12 miles West, so he’s 12 – 4 = 8 miles West of the city. Filipe has walked 12 miles North, so he’s 12 – 6 = 6 miles North of the city. 2 2 2 y x z + = dt dy y dt dx x dt dz z 2 2 2 + = 112 ) 4 )( 6 ( 2 ) 4 )( 8 ( 2 ) 10 ( 2 = + = dt dz 6 . 5 20 112 = = dt dz The distance is changing at 5.6 mph. x = 8 miles y = 6 miles z = (8 2 + 6 2 ) 1/2 = 10 miles

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2. Considering Kimi and Filipe from problem #1, at what time is the distance between them a minimum? What is that minimum distance? (Hints: 1. Put St. Leibniz at (0, 0) and write the pedestrians’ coordinates as a function of t . 2. Minimize the square of the distance.) (10 points) Kimi’s position at time t is (4 – 4 t , 0); Filipe’s position at time t is (0, -6 + 4 t ).
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Exam 2 Answers - Math 150A Exam 2 Answers 1 The city of St...

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