Question 1183793
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The towers of a suspension bridge are 800 m apart and are 180 m high. 
The cable between the towers hangs in the shape of parabola, which at its lowest 
just touches the road. How high above the road is the cable 300 m away from the center?  
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<pre>
Place the origin of the coordinate system at the bridge level, half way between the towers.


Write the parabola equation in vertex form  y = ax^2  (in this form the cable touches the road at the origin of the coordinate system).


You are given that  y = 180 meters at x = 400 meters.

So you substitute these values into the parabola equation


    180 = a*400^2.


From the equation, you find  a = {{{180/400^2}}} = 0.001125.


Thus your parabola is  y = 0.001125*x^2.


Now, to answer the problem question, you substitute  x= 300  into the last equation


    y = 0.001125*300^2 = 101.25 meters.      <U>ANSWER</U>
</pre>

Solved and explained.