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Question 65531: (52)Business and finance. In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
(46)Technology. Driving down a mountain, Tom finds that he has descended 1800ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
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You have two points relating C and x: (100,10000) and (300,22000)
The equation you want looks like C=mx+b
m=[22000-10000]/[300-100]=12000/200=60
Using one of the point values for x and C and m=60 you can solve for "b"
10000=60(100)b
b=10000-6000=4000
EQUATION: Cost=60x+4000
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(46)Technology. Driving down a mountain, Tom finds that he has descended 1800ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
Slope = -1800 ft/3.25 mi=553.85 ft/mi
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Cheers,
Stan H.
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