Question 109725: My daughters math problems are making me crazy, hope you can help me so I can help her.
Speed on a hill problem: The maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. Suppose that the car can go a maximum of 63 mph up a 2 degree hill, and a max of 105 mph down a 5 degree hill. (going downhill can be thought of as going up a hill at -5 degrees).
a) Write a particular equation expressing max speed in terms of steepness.
b) How fast could you go down a 7 degree hill?
c) If your top speed is 83 mph, how steep is the hill? Is it up or down?
d) What does the speed-intercept equal, and what does it represent?
e) What does the steepness-intercept equal and what does it reprsent?
f) Sketch and label the graph using a reasonable domain.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. Suppose that the car can go a maximum of 63 mph up a 2 degree hill, and a max of 105 mph down a 5 degree hill. (going downhill can be thought of as going up a hill at -5 degrees).
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You have two points: (2,63) and (-5,105)
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a) Write a particular equation expressing max speed in terms of steepness.
slope = [105-63]/[-5-2] = 42/-7 = -6
63 = -6*2+b
b = 63+12
b = +75
EQUATION:
speed = -6(steepness)+75
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b) How fast could you go down a 7 degree hill?
speed = -6(-7)+75
speed = 42+75 = 117
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c) If your top speed is 83 mph, how steep is the hill? Is it up or down?
83 = -6(steepness)+75
8 = -6(steepness)
steepness = -4/3
It's negative so it's down
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d) What does the speed-intercept equal, and what does it represent?
When the steepness is zero the maximum speed = 75 mph
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e) What does the steepness-slope equal and what does it reprsent?
When steepness increases one-degree max speed decreases by 6 mph
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f) Sketch and label the graph using a reasonable domain.
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Cheers,
Stan H.
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