document.write( "Question 1100161: Suspension Bridge. \r
\n" ); document.write( "\n" ); document.write( "If one parabolic segment of a suspension bridge is 400 feet and if the cables at the vertex are suspended 10 feet above the bridge, whereas the height of the cables 200 feet from the vertex reaches 50 feet, find the equation of the parabolic path of the suspension cables.\r
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Algebra.Com's Answer #714683 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "If one parabolic segment of a suspension bridge is 400 feet and if the cables at the vertex are suspended 10 feet above the bridge,
\n" ); document.write( "whereas the height of the cables 200 feet from the vertex reaches 50 feet, find the equation of the parabolic path of the suspension cables.\r
\n" ); document.write( "\n" ); document.write( "Enter the equation in standard form.\r
\n" ); document.write( "\n" ); document.write( "The equation of the parabolic path of the suspension cables is what?
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document.write( "Place the origin of the coordinate system at the bridge level, under the vertex of the cable. \r\n" );
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document.write( "     (The term \"vertex\" is used in the condition, assuming that you know its meaning.\r\n" );
document.write( "      If not, then the vertex is the point where the cable is CLOSEST to the bridge: where the cable is at the minimal level).\r\n" );
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document.write( "In this coordinate system, the cable is a parabola  y = ax^2 + b,\r\n" );
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document.write( "where b is exactly the elevation of the lowest point of the cable over the bridge, and \"a\" is an unknown coefficient.\r\n" );
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document.write( "From the condition, you have b = 10 ft, obviously.  So,  y = ax^2 + 10.\r\n" );
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document.write( "All you need to do is to find the coefficient \"a\".\r\n" );
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document.write( "For it, use the condition that at the distance 200 ft from the vetex (along the bridge, naturally) the height of the cable is 50 ft:\r\n" );
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document.write( " 50 = a*200^2 + 10.\r\n" );
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document.write( "From this equation  a =  =  = 0.001.\r\n" );
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document.write( "Thus the equation of the parabola is  y = 0.001*x^2 + 10,\r\n" );
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document.write( "where x is the distance along the bridge from the vertex position.\r\n" );
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document.write( "That's all.  The problem is solved.\r\n" );
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