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Question 536040: towers of suspension bridge are 500 feet apart and extend 100 feet above the road surface. The main cables between the towers reach to within 10 feet of the road at the center of the bridge, and there are vertical supporting cables every 10 feet. Find the lengths of those supporting cables at 50 foot intervals.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! towers of suspension bridge are 500 feet apart and extend 100 feet above the road surface. The main cables between the towers reach to within 10 feet of the road at the center of the bridge, and there are vertical supporting cables every 10 feet. Find the lengths of those supporting cables at 50 foot intervals.
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Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex.
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With, origin at (0,0), place the vertex of the parabola representing the bridge at (0,10), which represents the main cables reaching within 10 ft of the road at the center.
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This places the top of the towers 250 ft from either side of the center and 100 ft above the road which are coordinates of (250,100) for one side and (-250,100) for the other side.
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Equation:
Solving for A using coordinates from one of the sides(250,100)
y=A(x-h)^2+k
100=A(250-0)^2+10
90=A(250)^2
A=90/(250)^2
A=0.00144
Equation:
y=0.00144(x^2)+10
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Main cable above the road 50 ft from center=0.00144*50^2=3.6 ft
Length of supporting cable above the road 50 ft from center=90-3.6=86.4 ft
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Main cable above the road 150 ft from center=0.00144*150^2=32.4 ft
Length of supporting cable above the road 150 ft from center=90-32.4=57.6 ft
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Main cable above the road 200 ft from center=0.00144*200^2=57.6 ft
Length of supporting cable above the road 200 ft from center=90-57.6=32.4 ft
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