document.write( "Question 1183793: 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? \n" ); document.write( "

Algebra.Com's Answer #814273 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The solution from the other tutor is a perfectly good formal solution by finding the equation of the parabola.

\n" ); document.write( "There is no need to find the equation exactly; the answer can be obtained in moments informally.

\n" ); document.write( "From the center of the bridge to each end is 400m; we want to find the height 300m from the center of the bridge.

\n" ); document.write( "Since the cable is in the shape of a parabola with its vertex at the center of the bridge, the height of the cable 3/4 of the way from the center of the bridge to each tower is the height of the tower, multiplied by (3/4)^2.

\n" ); document.write( " $\"180%28%283%2F4%29%5E2%29+=+101.25\"$

\n" ); document.write( "ANSWER: 101.25m

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