document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481494>Question 481494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A semielliptic archway has a height of 20 feet and a width of 50 feet, can a truck 14 feet high and 10 feet wide drive under the archway without going into the other lane? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329969 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=329969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A semielliptic archway has a height of 20 feet and a width of 50 feet, can a truck 14 feet high and 10 feet wide drive under the archway without going into the other lane?<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Draw an ellipse with a horizontal major axis of the standard form: <BR>\n" );
document.write( "(x-h)^2/a^2+(y-k)^2/b^2=1<BR>\n" );
document.write( "Place the center of this ellipse at the origin (0,0).<BR>\n" );
document.write( "The equation now becomes: x^2/a^2+y^2/b^2=1<BR>\n" );
document.write( "The given width of the semielliptic archway of 50 feet represents the major axis=2a<BR>\n" );
document.write( "a=25<BR>\n" );
document.write( "a^2=625<BR>\n" );
document.write( "The given height of the semielliptic archway of 20 feet represents half of the major axis=b<BR>\n" );
document.write( "b=20<BR>\n" );
document.write( "b^2=400<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of the ellipse:<BR>\n" );
document.write( "x^2/625+y^2/400=1<BR>\n" );
document.write( "The top half of this ellipse represents the semielliptic archway.<BR>\n" );
document.write( ",..<BR>\n" );
document.write( "Determine whether a truck 14 feet high and 10 feet wide can drive under the archway without going into the other lane?<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Plug y=14 ft (height of truck) into the equation and solve for x (allowable width of archway).<BR>\n" );
document.write( "x^2/625+14^2/400=1<BR>\n" );
document.write( "x^2/625+196/400=1<BR>\n" );
document.write( "x^2=(1-196/400)*625=318.75<BR>\n" );
document.write( "Taking the positive sqrt because using upper half of ellipse<BR>\n" );
document.write( "x=&#8730;318.75=17.85 ft<BR>\n" );
document.write( "This means that at the height clearance of 14 ft, there is more than 17 ft of road width allowed for the 10 ft wide truck. <BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "So, the archway can easily accommodate the 14 ft high and 10 ft wide truck. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );