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 #814271 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "The towers of a suspension bridge are 800 m apart and are 180 m high.
\n" ); document.write( "The cable between the towers hangs in the shape of parabola, which at its lowest
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document.write( "Place the origin of the coordinate system at the bridge level, half way between the towers.\r\n" );
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document.write( "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).\r\n" );
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document.write( "You are given that  y = 180 meters at x = 400 meters.\r\n" );
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document.write( "So you substitute these values into the parabola equation\r\n" );
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document.write( "    180 = a*400^2.\r\n" );
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document.write( "From the equation, you find  a =  = 0.001125.\r\n" );
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document.write( "Thus your parabola is  y = 0.001125*x^2.\r\n" );
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document.write( "Now, to answer the problem question, you substitute  x= 300  into the last equation\r\n" );
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document.write( "    y = 0.001125*300^2 = 101.25 meters.      ANSWER\r\n" );
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