Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.1 - Functions and Their Graphs - Exercises 1.1 - Page 13: 72

Answer

a. $ C(x)=180\times\sqrt {x^{2}+800^{2}}-100x+1056000$ b. The least expensive location for point Q should be less than 2000 ft

Work Step by Step

a. We know that 1 mile=5280ft, so 2 miles=10560ft. The distance between the power plant and point Q is: $ d=\sqrt {x^{2}+800^{2}}$ and the total cost is: $ C(x)=180\times\sqrt {x^{2}+800^{2}}+100\times(10560-x)=180\times\sqrt {x^{2}+800^{2}}-100x+1056000$ b. See the table below. As the cost $ C(x)$ increases across $ x=2000ft $, the least expensive location for point Q should be less than 2000 ft
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