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pre-calc 2.8

pre-calc 2.8 - Section 2.8 Modeling Using Variation I...

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Section 2.8 Modeling Using Variation I. Direct Variation If a variable y varies directly as (or is directly proportional to) a variable x, then we can describe the situation by kx y = , where k is a nonzero constant called the constant of variation or the constant of proportionality . EX 1: The weight, W, of an aluminum canoe varies directly as its length, L. If a 6 foot canoe weighs 75 lbs., how much does a 16 ft. canoe weigh? EX 2: The number of gallons of water, W, used when taking a shower varies directly as the time, t, in minutes, in the shower. A shower lasting 5 minutes used 30 gallons of water. How much water is used in a shower lasting 11 minutes? II. Direct Variation with Power - y varies directly as the nth power of x if there exists some nonzero constant k such that n kx y = . EX 3: The distance required to stop a car varies directly as the square of its speed. If 200 feet are required to stop a car traveling 60 miles per hour, how many feet are required to stop a car traveling 100 miles per hour?

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