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Question 1185203: Hi, I hope you are doing fine. Can you help me?
A skateboard ramp is deigned to have a parabolic cross section. If the ends of the ramp should be 20 feet apart, derived the equation of its cross section using any height of your choice. What is the height of the ramp 5 feet from its center?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A skateboard ramp is deigned to have a parabolic cross section. If the ends of the ramp should be 20 feet apart, derived the equation of its cross section using any height of your choice. What is the height of the ramp 5 feet from its center?
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For a parabola centered on the y-axis, y-int = (0,h), and with x-intercepts of -10 and +10:
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Parabolas have the form y = ax^2 + bx + c
At x = 0, c = h
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At x = -10:
y = a*100 - 10b + h
At x = +10:
y = a*100 + 10b + h
----------------------------------- Subtract
- 20b = 0
b = 0
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Add them
200a + 2h = 0
a = -h/100
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---> y = -hx^2/100 + h
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5 feet from the center:
y = -h/4 + h ---> 3h/4
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