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CHAPTER 11 Quadratic Applications
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1000r 20,000 1000r 20,000 5:5 r2 400 2000r 5:5r2 2200 0 5:5r2 2000r 2200 r q 2000 2000 2 4 5:5 2200
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2 5:5 p 2000 4,000,000 48,400 11 p 2000 4,048,400 2000 2012:063617 % % 365; 11 11   2000 2012:063617 is negative 11
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The plane would have averaged about 365 mph without the wind 5 Let r represent the plane s average speed without the wind The plane s average speed from Minneapolis to Atlanta (against the headwind) is r 30 The plane s average speed from Atlanta to Minneapolis (with the tailwind) is r 30 The total time in the air is 51 hours and the distance between Atlanta to Minneapolis is 900 2 900 miles The time in the air from Minneapolis to Atlanta is r 30 900 hours, and the time in the air from Atlanta to Minneapolis is r 30 hours The time in the air from Minneapolis to Atlanta plus the time in the air from Minneapolis to Atlanta is 5 1 5:5 hours The 2 900 900 5:5 The LCD is equation to solve is r 30 r 30 r 30 r 30 900 r 30 900 r 30 r 30 r 30 r 30 5:5 r 30 900 r 30 900 r 30 5:5 r 30 r 30 r 30 r 30 900r 27,000 900r 27; 000 5:5 r2 900 1800r 5:5r2 4950 0 5:5r2 1800r 4950
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CHAPTER 11 Quadratic Applications
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q 1800 1800 2 4 5:5 4950
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2 5:5 p p 1800 3;240;000 108;900 1800 3;348;900 11 11   1800 1830 1800 1830 330 is negative 11 11
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The plane s average speed without the wind was 330 mph If you need to nd the distance between two bodies traveling at right angles away from each other, you must use the Pythagorean Theorem: a2 b2 c2 in addition to D RT
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A car passes under a railway trestle at the same time a train is crossing the trestle The car is headed south at an average speed of 40 mph The train is traveling east at an average speed of 30 mph After how long will the car and train be 10 miles apart Let t represent the number of hours after the train and car pass each other (Because the rate is given in miles per hour, time must be given in hours) The distance traveled by the car after t hours is 40t and that of the train is 30t:
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a2 b2 c2 40t 2 30t 2 102
40t 2 30t 2 102 1600t2 900t2 100 2500t2 100
CHAPTER 11 Quadratic Applications
t2 100 2500 r 100 t 2500 t 10 1 50 5
After 1 of an hour (or 12 minutes) the car and train will be 10 miles 5 apart
Practice
1 A car and plane leave an airport at the same time The car travels eastward at an average speed of 45 mph The plane travels southward at an average speed of 200 mph After how long will they be 164 miles apart 2 Two joggers begin jogging from the same point One jogs south at the rate of 8 mph and the other jogs east at a rate of 6 mph When will they be ve miles apart 3 A cross-country cyclist crosses a railroad track just after a train passed The train is traveling southward at an average speed of 60 mph The cyclist is traveling westward at an average speed of 11 mph When will they be 244 miles apart 4 A motor scooter and a car left a parking lot at the same time The motor scooter traveled north at 24 mph The car traveled west at 45 mph How long did it take for the scooter and car to be 34 miles apart 5 Two cars pass each other at 4:00 at an overpass One car is headed north at an average speed of 60 mph and the other is headed east at an average speed of 50 mph At what time will the cars be 104 miles apart Give your solution to the nearest minute
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