Question
Asked Dec 24, 2019
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The middle span of the Golden Gate Bridge in San Francisco is supported by cables from two towers 4200 ft apart. The tops of the towers are 500 ft above the roadway. Assuming that the cables are parabolic and are at road level halfway between the towers, find the height of the cables 1000 ft from the center of the bridge. Round to the nearest foot.

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Expert Answer

Step 1

Given:

The middle span of the Golden Gate Bridge in San Francisco is supported by cables from two towers 4200 ft apart. The tops of the towers are 500 ft above the roadway. If the cables are parabolic and are at road level halfway between the towers, find the height of the cables 1000 ft from the center of the bridge. Round to the nearest foot.

Step 2

Let the roadway at the halfway mark from the two towers being the origin (0,0).

so, there are three point that will be on the parabola (-2100,500), (0,0) and (2100,500).

From below figure we can clearly see this:

 

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(-2100,500) (2100,500) 500 ft. 500 ft. (0,0) -1000 ft.- -2100 ft. -2100 ft.-

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Step 3

Now the vertex form equati...

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y = a(x- h) +k Since vertex is at the origin Therefore, y = a(x-0)° +0 y = ax

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Math

Algebra