Exam2_3 3 - ◦ F and places on a table in his dining room...

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Version 208 – Exam 2 – Radin – (58305) 3 the ladder is 9 feet away from the base of the wall? 1. speed = 4 ft/sec 2. speed = 15 4 ft/sec correct 3. speed = 9 2 ft/sec 4. speed = 17 4 ft/sec 5. speed = 7 2 ft/sec Explanation: Let y be the height of the ladder when the foot of the ladder is x feet from the base of the wall as shown in Fgure x ft. 15 ft. We have to express dy/dt in terms of x, y and dx/dt . But by Pythagoras’ theorem, x 2 + y 2 = 225 , so by implicit di±erentiation, 2 x dx dt + 2 y dy dt = 0 . In this case dy dt = x y dx dt . But again by Pythagoras, if x = 9, then y = 12. Thus, if the foot of the ladder is moving away from the wall at a speed of dx dt = 5 ft/sec , and x = 9, then the velocity of the top of the ladder is given by dy dt = 3 4 dx dt . Consequently, the speed the top of the ladder is falling is speed = 15 4 ft/sec . 007 10.0 points Richard removes a turkey from the oven after it reaches a temperature of 186
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Unformatted text preview: ◦ F and places on a table in his dining room where the temperature is 80 ◦ F . After 10 minutes the temperature of the turkey is 166 ◦ F , while after 20 minutes it is 160 ◦ F . Use linear ap-proximation to predict the temperature of the turkey after half an hour. 1. temp ≈ 153 ◦ F 2. temp ≈ 152 ◦ F 3. temp ≈ 155 ◦ F 4. temp ≈ 151 ◦ F 5. temp ≈ 154 ◦ F correct Explanation: If T ( t ) is the temperature of the turkey after t minutes, then the given data tell us that T (0) = 186 , T (10) = 166 , T (20) = 160 , while the fact that the room temperature is 80 ◦ F means that T ( t ) gets closer to 80 ◦ F as t increases. Now by linear approximation T ( t ) ≈ T (20) + T ′ (20)( t − 20) , ( t > 20) ,...
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