document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394062>Question 394062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tunnel through a mountain takes the shape of a semi-ellipse.  The tunnel is 100 feet wide and has a maximum height at its center of 30 feet.  If the clearance height for vehicles needs to be a minimum of 16 feet, how much total width do they have available? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279887 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A tunnel through a mountain takes the shape of a semi-ellipse. The tunnel is 100 feet wide and has a maximum height at its center of 30 feet. If the clearance height for vehicles needs to be a minimum of 16 feet, how much total width do they have available?\r<BR>\n" );
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document.write( "Standard form of an ellipse:\r<BR>\n" );
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document.write( "x^2/a^2+y^2/b^2=1<BR>\n" );
document.write( "assume the center of the ellipse is at (0,0) <BR>\n" );
document.write( "a=50 (major axis)<BR>\n" );
document.write( "b=30 (minor axis)\r<BR>\n" );
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document.write( "x^2/50^2+y^2/30^2=1<BR>\n" );
document.write( "x^2/2500+y^2/900=1<BR>\n" );
document.write( "900x^2+2500y^2=900*2500<BR>\n" );
document.write( "900x^2=900*2500-2500y^2<BR>\n" );
document.write( "x^2=2500-(2500/900)y^2<BR>\n" );
document.write( "x^2=2500-(25/9)y^2<BR>\n" );
document.write( "x=sqrt(2500-(25/9)y^2)\r<BR>\n" );
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document.write( "given: y=16 feet of minimum clearance required<BR>\n" );
document.write( "x=sqrt(2500-(25/9)*16^2<BR>\n" );
document.write( "=+ or- sqrt(1788.89)=+-42.30 feet<BR>\n" );
document.write( "ans: total width required = 2*42.30 =84.6 feet (at this width the height of the tunnel is 16 feet) </SPAN>\n" );
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