document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971199>Question 971199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cross section of a 12 - foot -high cooling tower is in the form of a hyperbola. its top and bottom parts are 8 feet wide and the narrowest part is 4 feet. A man painting the tower must place a horizontal plank exactly spanning the upper 6 feet width of the cross section of the tower. At what point from the ground should the plank be placed?\r<BR>\n" );
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document.write( "Pls help me with this problem </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593756 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=593756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cross section of a 12 - foot -high cooling tower is in the form of a hyperbola. its top and bottom parts are 8 feet wide and the narrowest part is 4 feet. A man painting the tower must place a horizontal plank exactly spanning the upper 6 feet width of the cross section of the tower. At what point from the ground should the plank be placed? <BR>\n" );
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document.write( "The cooling tower can be represented by a hyperbola with horizontal transverse axis with center at the origin.<BR>\n" );
document.write( "Its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For given problem:<BR>\n" );
document.write( "a=2 (distance from center to vertices(the narrowest part)<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "solve for b^2 using coordinates (4, 6) of the point at the top right corner of the tower<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2%2F4-6%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"4%5E2%2F4-6%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F4-36%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"16%2F4-36%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "36/b^2=4-1=3<BR>\n" );
document.write( "b^2=12<BR>\n" );
document.write( "equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4-y%5E2%2F12=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4-y%5E2%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "plug in coordinates(3, y) of the point at the top right corner of the horizontal plank and solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4-y%5E2%2F12=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4-y%5E2%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2%2F4-y%5E2%2F12=1 ALIGN=MIDDLE  ALT=\"3%5E2%2F4-y%5E2%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9/4-1=y^2/12<BR>\n" );
document.write( "5/4=y^2/12<BR>\n" );
document.write( "y^2=15<BR>\n" );
document.write( "y=&#8730;15=3.87<BR>\n" );
document.write( "At what point from the ground should the plank be placed? 3.87 ft<BR>\n" );
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