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 #734480 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "One way to set this up to make the calculations as simple as possible is to put the center of the arch at (0,3); then the bases of the arch are at (-3,0) and (3,0).<br><BR>\n" );
document.write( "With the vertex of the parabola at (0,3), the equation of the parabola is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2B3 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "for some constant a.<br><BR>\n" );
document.write( "To find the value of a, use either of the other known point on the parabola:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a%283%5E2%29%2B3 ALIGN=MIDDLE  ALT=\"0+=+a%283%5E2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+9a%2B3 ALIGN=MIDDLE  ALT=\"0+=+9a%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a+=+-3 ALIGN=MIDDLE  ALT=\"9a+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-1%2F3 ALIGN=MIDDLE  ALT=\"a+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F3%29x%5E2%2B3 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F3%29x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the length of the beam, set y=2 and solve for x.  The length of the beam will be the difference between the two x values.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+%28-1%2F3%29x%5E2%2B3 ALIGN=MIDDLE  ALT=\"2+=+%28-1%2F3%29x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+=+%28-1%2F3%29x%5E2 ALIGN=MIDDLE  ALT=\"-1+=+%28-1%2F3%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+3 ALIGN=MIDDLE  ALT=\"x%5E2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The length of the beam in meters is the difference between sqrt(3) and -sqrt(3), which is 2*sqrt(3), or 3.464 to 3 decimal places. </SPAN>\n" );
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