Question 330044: #1, Hat sizes are determined by measuring the circumference of one's head in either inches or centimeters. Use ration and proportion to complete the following table.
Hat Size Head Circumference Head Circumference
(to nearest 1/5 inch) (to nearest centimeter)
7 1/2 23 3/5 60
7 3/8 _____ ______
#2, The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 30 mph can stop in 50 ft., how many feet will it take the same car to stop when it is traveling 20 mph?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! #1, Hat sizes are determined by measuring the circumference of one's head in either inches or centimeters. Use ratio and proportion to complete the following table.
Hat Size Head Circumference Head Circumference
(to nearest 1/5 inch) (to nearest centimeter)
7 1/2 23 3/5 60
7 3/8 _____ ______
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(x)/(7 3/8) = (23 3/5)/(7 1/2)
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(x)/(59/8) = (118/5)/(15/2)
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(x) = (59/8)*(236/75)
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x = 3481/150
x = 23 13/15 (Head Circumference to nearest 1/15 of inch
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x/(7 3/8) = 60/(7.5)
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x = (59/8)(60/7.5)
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x = 59 cm (Head circumference in centimeters)
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#2, The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r.
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d = k/r^2
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Solve for "k" using "a car traveling 30 mph can stop in 50 ft."
50 = k/30^2
50 = k/900
k = 45000
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So, equation is d = 45000/r^2
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How many feet will it take the same car
to stop when it is traveling 20 mph?
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d = 45000/20^2
d = 112.5 ft (stopping distance at 20 mph)
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Cheers,
Stan H.
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