College Algebra & Trigonometry, 2018a

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4.9. OPTIMIZATION 249 The distance between the two ships is measured along the diagonal. Because this creates a right triangle, we can use the Pythagorean Theorem to represent the distance between the ships. Buoy 10 miles 12 mph Ship #1 10 miles d Ship #2 7 mph In this case the legs of the right triangle begin as 10 miles, but they get shorter as the ships travel closer to the buoy. For Ship #1, the distance decreases by 12 miles every hour - this means that the first ship will pass the buoy in less than one hour. The distance between Ship #1 and the buoy can be represented as (10−12t), where t is the number of hours spent traveling. Similarly, the distance between Ship #2 and the buoy can be represented as (10 − 7t). So, using the Pythagorean Theorem, we can represent the distance between the ships at any given time as: d 2 =(10− 7t) 2 +(10− 12t) 2 or d = √ (10 − 7t) 2 +(10− 12t) 2
250 CHAPTER 4. FUNCTIONS The graph of this distance function looks like this: 8 6 4 2 (0.98, 3.6) −1 1 2 3 4 The minimum point on the distance graph indicates the time at which the ships are closest together. After traveling for 0.98 hours, the ships will be about 3.6 miles apart. They will then start moving farther apart.
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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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College Algebra & Trigonometry, 2018a

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