document.write( "Question 1199364: The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the bridge at the center. how high is the cable 10 feet from the end of the bridge? \n" ); document.write( "

Algebra.Com's Answer #833221 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high.
\n" ); document.write( "If the cable is 10 feet above the floor of the bridge at the center, how high is the cable 10 feet from the end of the bridge?
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document.write( "If we place the origin of the coordinate system at the bridge level midpoint between the two towers, \r\n" );
document.write( "we have the vertex of the parabola at the point (0,10).\r\n" );
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document.write( "So, we write an equation of the parabola in vertex form\r\n" );
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document.write( "    y = ax^2 + 10.\r\n" );
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document.write( "Coefficient \"a\" is unknown.  It is the only unknown in this problem now.\r\n" );
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document.write( "To find it, we use the condition at the endpoint: y= 40 at x= 120/2 = 60.  It gives\r\n" );
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document.write( "    40 = a*60^2 + 10\r\n" );
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document.write( "    40 - 10 = a*3600\r\n" );
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document.write( "       30   = 3600a\r\n" );
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document.write( "        a   =  = .\r\n" );
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document.write( "Thus the parabola is  y = .    \r\n" );
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document.write( "Having this equation ready, we substitute x = 50 ft into the equation \r\n" );
document.write( "and find the height of the cable at the point x= 50, which is 10 feet from the end of the bridge\r\n" );
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document.write( "    y =  = 30.833 ft   (rounded).    ANSWER\r\n" );
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