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Question 995545: A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation, taking the lowest point as the origin.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation, taking the lowest point as the origin.
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Sketch the figure on an x/y coordinate system.
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Place the lowest point at (0,0)
The top of the posts will be at (-5,10) and (5,10)
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Procedure::
Form:: ax^2 + bx + c = y
Using (-5,10) you get: 25a - 5b = 10
Using (5,10) you get: 25a + 5b = 10
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50a = 20
a = 2/5
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Solve for "b"::
25a + 5b = 10
25a + 2 = 10
25a = 8
a = 8/25
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Equation:
y = (8/25)x^2 + (2/5)x
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Cheers,
Stan H.
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