Aug 28, 2014
Equations for the Family
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Equations for the Family
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Equations for the Family
Nuts and Bolts
The distance a bolt protrudes past the edge of a nut is a linear function of the number of revolutions through which the bolt is turned.
The slope is the distance covered per revolution (in cm per turn).
The y-intercept is the opposite of the "length" of the nut.
The x-intercept is the number of turns required to make the bolt just flush with the other end of the nut.
Suppose the nut is 1 cm long and the bolt travels .4 cm per turn.
Snowblower Business
The profit you make after buying a snowblower and paying for a business license is a linear function of the number of jobs you get. The slope is the average amount you charge per job. The y-intercept is the starting profit deficit from the buying the blower and the license. The x-intercept is the number of jobs to break even. Suppose the blower and license are $750 and you charge $45 per job.
Sharpening Pencils
The change in the length of a pencil being sharpened is a linear function of and the number of revolutions the shaving mechanism has undergone.
The slope is the length of pencil shredded away per crank. The y-intercept is the pencil's original length,
The original length could be about 18 cm, shredding away at .1 cm per crank.
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Gas and Cigarettes
Someone pulls into a gas station to buy a carton of cigarettes and to fill his tank. The price paid is a linear function of the number of gallons he buys. The slope is the price of a gallon of gas. The y-intercept is the cost of the carton of cigarettes.
A carton of cigarettes could be $48, and a gallon of gas could be $3.26 or so.