408CF09assign6 - $30,000 per kilometer to lay wire under...

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M408C Fall 2009 Assignment 6 Due Thursday, October 15 You should have read and understood sections 4.7, 4.9, and 5.1 before completing this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. A poster is to contain 50 square inches of printed matter with margins of 4 inches each at the top and bottom and 2 inches on each side. Find the dimensions of such a poster with smallest possible total area. 2. A power line is needed to connect a power station on the shore of a river to an island 4 kilometers downstream and 1 kilometer offshore. Find the minimum cost for such a line given that it costs $50,000 per kilometer to lay wire under water and
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Unformatted text preview: $30,000 per kilometer to lay wire under ground. 3. Find the function f from the information given: f 00 = 2 x-3, f (2) =-1, and f (0) = 3. 4. A motorcyclist is traveling at a constant speed of 60 miles per hour when he sees a jackknifed tractor trailer blocking the road. His brakes impart to the motorcycle a constant negative acceleration of 20 feet per second per second. If he is 200 feet feet from the tractor when he applies the brakes, will he be able to avoid a collision? If so, how far from the trailer will he be when he comes to a stop? If not, at what speed will he hit the trailer? (Warning: Pay attention to the units.) 5. An object moving in a straight line has velocity function v ( t ) = 25-( t-5) 2 , for 0 ≤ t ≤ 5, where velocity is measured in ft/sec and time in seconds. Using subintervals of 1 seconds each, find upper and lower approximations of the distance traveled by the object....
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