document.write( "Question 1182285: Additional picnic pyramids are being constructed in the northeast corner of the park. Bridges are being built across the small stream to allow people to access the structures. \r
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\n" ); document.write( "\n" ); document.write( "The design of one bridge includes a parabolic arch, a horizontal handrail and vertical rods. The parabolic arch is defined by the equation, \r
\n" ); document.write( "\n" ); document.write( "y = - 0.1875x2 + 0.5625x + 0.328125\r
\n" ); document.write( "\n" ); document.write( "where x is the horizontal distance from one end of the bridge in metres and y is the height of the arch in metres.
\n" ); document.write( "The arch spans the stream and is anchored to the land 0.5 m beyond the edge of the stream on each side. \r
\n" ); document.write( "\n" ); document.write( "Determine the height of the handrail above the bridge surface.
\n" ); document.write( "Determine the width of the stream.
\n" ); document.write( "What is the height of the arch at the edge of the stream? Round to 2 decimal places. \r
\n" ); document.write( "\n" ); document.write( "Picture of bridge: https://ibb.co/31Td44H
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Algebra.Com's Answer #812479 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "First find the roots of the polynomial from the quadratic equation\r\n" );
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document.write( "        -0.1875x2 + 0.5625x + 0.328125 = 0\r\n" );
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document.write( "    It is EQUIVALENT to\r\n" );
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document.write( "        x^2 - 3x - 1.75 = 0\r\n" );
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document.write( "    The roots are\r\n" );
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document.write( "         =  =  = .\r\n" );
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document.write( "         =  = -0.5;    =  = 3.5.\r\n" );
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document.write( "So, the arch is anchored at   = -0.5  and   = 3.5.\r\n" );
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document.write( "The stream is between  x= 0  and  x= 3,\r\n" );
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document.write( "The width of the stream is  3 - 0 = 3 meters.\r\n" );
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document.write( "The arch has maximum height exactly half the way between the roots at x= 1.5.\r\n" );
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document.write( "The height of the arch is the value of the polynomial at x= 1.5\r\n" );
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document.write( "     = -0.1875*1.5^2 + 0.5625*1.5 + 0.328125 = 0.75 m.\r\n" );
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