College Algebra & Trigonometry, 2018a

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4.9. OPTIMIZATION 247 are the dimensions of the box that minimizes the cost? What is the cost of this box? Surface Area of a cylinder = 2πr 2 +2πrh Volume of a cylinder = πr 2 h 7) A cylindrical can with a top will be made from 200 in 2 of tin. What would be the height and radius of the can of maximum volume? 8) A cylindrical can with a top will have a volume of 500 cm 3 . If the sides and bottom cost $0.002 per square cm and the top costs $0.0035 per square cm, find the dimensions of the least expensive can that will have a volume of 500 cm 3 . How much does it cost to make this can?
248 CHAPTER 4. FUNCTIONS Distance Optimization One ship is 10 miles due east of a buoy and is sailing due west, towards the buoy at 12 mph. Another ship is 10 miles due south of the same buoy and sailing due north, also towards the buoy at 7 mph. a) Write a function that represents the distance between the two ships in terms of t, the elapsed time in hours. b) Graph the function and determine the value of t when the ships are closest together. How far apart are the ships at this time? Round the value of t to the nearest 100th of an hour. Round the distance to the nearest tenth of a mile. Here is a diagram that represents the problem: Buoy 10 miles 12 mph Ship #1 10 miles Ship #2 7 mph
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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88 CHAPTER 2. POLYNOMIAL AND RATION
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College Algebra & Trigonometry, 2018a

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