document.write( "Question 1190859: The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high. If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola using midpoint of the bridge as the origin. (Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly along the horizontal.) \n" ); document.write( "

Algebra.Com's Answer #822606 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high.
\n" ); document.write( "If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola
\n" ); document.write( "using midpoint of the bridge as the origin.
\n" ); document.write( "(Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly
\n" ); document.write( "along the horizontal.)
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document.write( "If we place the origin of the coordinate system at the bridge length midpoint, we have the vertex of the parabola\r\n" );
document.write( "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.  To find it, we use the condition at the endpoint: y= 40 at x= 120/2 = 60.\r\n" );
document.write( "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 = .      ANSWER\r\n" );
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