document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970979>Question 970979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The opening of a cave 20 feet wide is in the shape of a semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?\r<BR>\n" );
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document.write( "Pls Help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593607 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The opening of a cave 20 feet wide is in the shape of a semi ellipse. <BR>\n" );
document.write( "If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "A semi-ellipse opening 20' wide and 15' high at the centre.<BR>\n" );
document.write( "Find height of opening at 5' from centre.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "We have an ellipse centred at origin, with <BR>\n" );
document.write( "a = semi-x-axis = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F2 ALIGN=MIDDLE  ALT=\"20%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10'<BR>\n" );
document.write( "b = semi-y-xaxis = 15'<BR>\n" );
document.write( " <BR>\n" );
document.write( "The standard equation of an ellipse is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Fa%29%5E2%2B%28y%2Fb%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x%2Fa%29%5E2%2B%28y%2Fb%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting a and b,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F10%29%5E2%2B%28y%2F15%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x%2F10%29%5E2%2B%28y%2F15%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "At 5' from centre, x=5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F10%29%5E2%2B%28y%2F15%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%285%2F10%29%5E2%2B%28y%2F15%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2F15%29%5E2+=+1-%285%2F10%29%5E2+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28y%2F15%29%5E2+=+1-%285%2F10%29%5E2+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15+%28sqrt%283%2F4%29%29+=+12.99 ALIGN=MIDDLE  ALT=\"y=15+%28sqrt%283%2F4%29%29+=+12.99\"   DISABLED_style= \"max-width:90%; height:auto;\" >' approximately<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "The height of the cave opening at 5' from the centre is approximately 12.99' </SPAN>\n" );
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