document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119014>Question 1119014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An entrance to a castle is in the form of parablolic arch 6m across at the base and 3m high in the center. What is the length of a beam across the entrance, parallel to the base and 2m above it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734460 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n entrance to a castle is in the form of parablolic arch 6m across at the base and 3m high in the center.<BR>\n" );
document.write( " What is the length of a beam across the entrance, parallel to the base and 2m above it.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y, (c=0)<BR>\n" );
document.write( "the parabola begins at origin 0,0 and ends at 6,0; max is 3,3<BR>\n" );
document.write( "write an equation for each <BR>\n" );
document.write( "3,3<BR>\n" );
document.write( "9a + 3b = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "6,0<BR>\n" );
document.write( "36a + 6b = 0<BR>\n" );
document.write( "multiply the first equation by 2, subtract from the above equation<BR>\n" );
document.write( "36a + 6b = 0<BR>\n" );
document.write( "18a + 6b = 6<BR>\n" );
document.write( "---------------subtracting eliminates b, find a<BR>\n" );
document.write( "18a = -6<BR>\n" );
document.write( "a = -6/18<BR>\n" );
document.write( "a = -.3333<BR>\n" );
document.write( "find b using the first equation<BR>\n" );
document.write( "9(-.333) + 3b = 3<BR>\n" );
document.write( "-3 + 3b = 3<BR>\n" );
document.write( "3b = 3 + 3<BR>\n" );
document.write( "b = 6/3<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( " Graph the equation y = .33x^2 + 2x, green shows when y = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+8%2C+-2%2C+5%2C+-.333x%5E2%2B2x%2C+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+8%2C+-2%2C+5%2C+-.333x%5E2%2B2x%2C+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"What is the length of a beam across the entrance, parallel to the base and 2m above it.\"<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "-.33x^2 + 2x = 2<BR>\n" );
document.write( "-.33x^2 + 2x - 2 = 0<BR>\n" );
document.write( "solve for x using the quadratic formula, a=-.33, b=2, c=-2<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "x = 1.268<BR>\n" );
document.write( "x = 4.732<BR>\n" );
document.write( "Find the length of the beam<BR>\n" );
document.write( "4.732 - 1.268 = 3.464 meters, length of a beam 2 m above the base<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );