The towers of the golden gate bridge connecting san francisco to marin county are 1280 meters apart and rise 160 meters above th
e road. the cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers.what is the height of the cable 200 meters from a tower? round to the nearest meter.
To solve the problem you must apply the following proccedure:
1. The information given in the problem is:
- <span>The towers are 1280 meters apart and rise 160 meters above the road. - The cable between the towers has the shape of a parabola. - The cable touches the sides of the road midway between the towers.
2. Therefore, you must apply the t</span>he standard form of the equation of a parabola with vertex at the origin. The parabola opens up, so:
x^2=4py
3. First, you need to find p:
p=x^2/4y
x=640 when y=160
p=(640)^2/(4x160) p=640
4. Now you need to find y. The problem asks for the height of the cable <span>200 meters from a tower, therefore: </span> x=640-200 x=440
