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Question 53000: In planning for a new item, a manufactuer 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
Driving down a mountain, Tom finds that he has descended 1800 ft 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 tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! x=100 items [Identify the independent variable (x)]
y=10,000 [Identify the dependent variable (y) that changes depending upon (x)]
Coordinate points (100; 10,000)
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x=300 items [Identify the independent variable (x)]
y=$22,000 [Identify the dependent variable (y) that changes depending upon (x)]
Coordinate points (300; 22,000)
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Slope = m = (y2-y1)/(x2-x1) [Formula for the slope of a line]
m=(y2-y1)/(x2-x1)
m=(22,000-10,000)/(300-100) [Plug-in the values]
m=60
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y=mx+b [Slope-intercept form of a line]
22,000=(60)(300)+b
22,000=18000+b
b=4000
y=60x+4000
C(x)=60x+4000
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Driving down a mountain, Tom finds that he has descended 1800 ft 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.
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Slope = m = rise/run=-1800/3.25=-553.85
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