document.write( "Question 1100845: a parabolic opening of a tunnel is 32m wide measured from side to side along the ground.At the points that are 4m from each side, the tunnel entrence is 6m high\r
\n" ); document.write( "\n" ); document.write( "find the maximum height to the tunnel to 1 decimal place \n" ); document.write( "

Algebra.Com's Answer #715371 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Put the origin of the coordinate system at the highest point of the arch, the axis \"y\" directed vertically up.\r\n" );
document.write( "\r\n" );
document.write( "so the the origin of the coordinate system will be THE VERTEX of the parabola.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You have y = ax^2 as the equation of the parabola with the negative unknown coefficient \"a\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation for \"a\" is\r\n" );
document.write( "\r\n" );
document.write( "y(12) - y(16) =  -  = 6,     (1)\r\n" );
document.write( "\r\n" );
document.write( "saying that  at the distance of 12 = 16-4 meters from the side the height of the tunnel is 6 meters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then  a =  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence and finally, the equation of the parabola is\r\n" );
document.write( "\r\n" );
document.write( "y =  \r\n" );
document.write( "\r\n" );
document.write( "in this coordinate system.   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The maximal height of the tunnel is   = 13.7 meters.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );