Exam2_2 10 - hamburgers the restaurant will sell if it...

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Taylor, Douglas – Exam 2 – Due: Oct 31 2007, 1:00 am – Inst: JEGilbert 10 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 diFerentiation, 2 x dx dt + 2 y dy dt = 0 . In this case dy dt = - x y dx dt . But again by Pythagoras, if x = 12, then y = 9. Thus, if the foot of the ladder is moving away from the wall at a speed of dx dt = 6 ft/sec , and x = 12, then the velocity of the top of the ladder is given by dy dt = - 4 3 dx dt . Consequently, the speed the top of the ladder is falling is speed = 8 ft/sec . keywords: speed, ladder, related rates 020 (part 1 of 1) 10 points After spending $ x in advertising per day, a McDonalds restaurant ±nds that it sells N hamburgers where N = 1400 + 240 x - 5 x 2 . Estimate using diFerentials how many more
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Unformatted text preview: hamburgers the restaurant will sell if it in-creases its daily spending on advertising from $17 to $17 . 50. 1. 36 more hamburgers 2. 35 more hamburgers correct 3. 37 more hamburgers 4. 33 more hamburgers 5. 34 more hamburgers Explanation: After diFerentiation, N ( x ) = 240-10 x. If x is increased by $ x , then the approximate increase, N , in N will thus be given by N N ( x ) x = (240-10 x ) x. When x = 17 and x = . 5, therefore, the McDonalds restaurant can expect to sell approximately 35 more hamburgers. keywords: spending, marginal spending, dif-ferential...
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