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Question 1073023: In a suspension bridge, two large cables are connected to two towers swing down in curves that are parabolas. Each tower rises 80 feet above the roadway, and the towers are 300 feet apart. At the center of the bridge, the two curved cables are 5 feet above the roadway. There are vertical cables that connect the roadway to these curved cables. The vertical cables are placed 15 feet apart. Vertical cables are not necessary at either of the towers. Suppose this bridge was damaged during a wind storm. Your job is to order new vertical cables to replace the ones between the two towers on the bridge.
1-Write the equation of the parabola in standard form.
(please show steps, so I can understand)
Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Each cable forms a parabola that curves upward
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Let the leftmost tower be located at the origin of our graph, then
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x coordinate of the parabola's vertex is 150 and the y coordinate is 5
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the vertex form of the parabola is
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1) y = a(x-150)^2 + 5
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we also know that the point (0, 80) is on the parabola
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using equation 1 and the point (0, 80) we have
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80 = 22500a +5
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22500a = 75
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a = 75 / 22500 = 0.003
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y = 0.003(x-150)^2 + 5
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y = 0.003(x^2 -300x +22500) + 5
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standard form of the parabola is
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y = 0.003x^2 -0.9x +72.5
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to determine cable lengths evaluate the standard form for
values of y for x = 15, 30, 45, ,,, 150
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Note be sure to order 4 of each length since each parabola has 2 of each length
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Answer by Alan3354(69443)  (Show Source):
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