document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124230>Question 1124230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds.\r<BR>\n" );
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document.write( "Below is the table: \r<BR>\n" );
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document.write( "x, seconds after the ball is thrown.  y, ball's height, infeet, above the ground<BR>\n" );
document.write( "1	                                                               339<BR>\n" );
document.write( "3	                                                               321<BR>\n" );
document.write( "4	                                                               264\r<BR>\n" );
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document.write( "Find the quadratic function y= ax2 + bx + c whose graph passes through the given points.\r<BR>\n" );
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document.write( "Y=<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740573 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=740573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Below is the table: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >- {seconds after the ball is thrown)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >-(ball's height, infeet, above the ground)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >                              |<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%09 ALIGN=MIDDLE  ALT=\"1%09\"   DISABLED_style= \"max-width:90%; height:auto;\" >                                                          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339 ALIGN=MIDDLE  ALT=\"339\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >	                                                             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321 ALIGN=MIDDLE  ALT=\"321\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%09 ALIGN=MIDDLE  ALT=\"4%09\"   DISABLED_style= \"max-width:90%; height:auto;\" >                                                          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+264 ALIGN=MIDDLE  ALT=\"+264\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > whose graph passes through the given points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >...plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=339 ALIGN=MIDDLE  ALT=\"y=339\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+a%2A1%5E2+%2B+b%2A1+%2B+c ALIGN=MIDDLE  ALT=\"339=+a%2A1%5E2+%2B+b%2A1+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+a+%2B+b+%2B+c ALIGN=MIDDLE  ALT=\"339=+a+%2B+b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >...plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=321 ALIGN=MIDDLE  ALT=\"y=321\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321=+a%2A3%5E2+%2B+b%2A3+%2B+c ALIGN=MIDDLE  ALT=\"321=+a%2A3%5E2+%2B+b%2A3+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321=+9a+%2B+3b+%2B+c ALIGN=MIDDLE  ALT=\"321=+9a+%2B+3b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >...plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=264 ALIGN=MIDDLE  ALT=\"y=264\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264=+a%2A4%5E2+%2B+b%2A4+%2B+c ALIGN=MIDDLE  ALT=\"264=+a%2A4%5E2+%2B+b%2A4+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264=+16a+%2B+4b+%2B+c ALIGN=MIDDLE  ALT=\"264=+16a+%2B+4b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3\r<BR>\n" );
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document.write( "------------------------------solve the system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+a+%2B+b+%2B+c ALIGN=MIDDLE  ALT=\"339=+a+%2B+b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321=+9a+%2B+3b+%2B+c ALIGN=MIDDLE  ALT=\"321=+9a+%2B+3b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.2<BR>\n" );
document.write( "-----------------------------------------subtract eq2 from eq1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339-321=+a-9a+%2B+b-3b+%2B+c-c ALIGN=MIDDLE  ALT=\"339-321=+a-9a+%2B+b-3b+%2B+c-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=+-8a+-2b+ ALIGN=MIDDLE  ALT=\"18=+-8a+-2b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a=++-2b-18+ ALIGN=MIDDLE  ALT=\"8a=++-2b-18+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-2b%2F8-18%2F8+ ALIGN=MIDDLE  ALT=\"a=++-2b%2F8-18%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-b%2F4-9%2F4+ ALIGN=MIDDLE  ALT=\"a=++-b%2F4-9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............eq.1a\r<BR>\n" );
document.write( "\n" );
document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264=+16a+%2B+4b+%2B+c ALIGN=MIDDLE  ALT=\"264=+16a+%2B+4b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321=+9a+%2B+3b+%2B+c ALIGN=MIDDLE  ALT=\"321=+9a+%2B+3b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.2<BR>\n" );
document.write( "-----------------------------------------------subtract eq.2 rom eq.3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=264-321=+16a-9a+%2B+4b-3b+%2B+c-c ALIGN=MIDDLE  ALT=\"264-321=+16a-9a+%2B+4b-3b+%2B+c-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-57=+7a+%2B+b ALIGN=MIDDLE  ALT=\"-57=+7a+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-57-b=+7a+ ALIGN=MIDDLE  ALT=\"-57-b=+7a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-57%2F7-b%2F7+ ALIGN=MIDDLE  ALT=\"a=-57%2F7-b%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............eq.1b\r<BR>\n" );
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document.write( "from eq.1a and eq.1b we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F4-9%2F4=+-57%2F7-b%2F7 ALIGN=MIDDLE  ALT=\"+-b%2F4-9%2F4=+-57%2F7-b%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >............solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b-9%29%2F4=+%28-57-b%29%2F7 ALIGN=MIDDLE  ALT=\"+%28-b-9%29%2F4=+%28-57-b%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28-b-9%29=+4%28-57-b%29 ALIGN=MIDDLE  ALT=\"7%28-b-9%29=+4%28-57-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7b-63=+-228-4b ALIGN=MIDDLE  ALT=\"-7b-63=+-228-4b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=228-63=+7b-4b ALIGN=MIDDLE  ALT=\"228-63=+7b-4b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165=+3b ALIGN=MIDDLE  ALT=\"165=+3b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=165%2F3 ALIGN=MIDDLE  ALT=\"+b=165%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+b=+55%29 ALIGN=MIDDLE  ALT=\"highlight%28+b=+55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "go back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-b%2F4-9%2F4+ ALIGN=MIDDLE  ALT=\"a=++-b%2F4-9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............eq.1a, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-%2855%29%2F4-9%2F4+ ALIGN=MIDDLE  ALT=\"a=++-%2855%29%2F4-9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-%2855%2B9%29%2F4+ ALIGN=MIDDLE  ALT=\"a=++-%2855%2B9%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=++-64%2F4+ ALIGN=MIDDLE  ALT=\"a=++-64%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=++-16%29+ ALIGN=MIDDLE  ALT=\"highlight%28a=++-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+a+%2B+b+%2B+c ALIGN=MIDDLE  ALT=\"339=+a+%2B+b+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+-16+%2B55+%2B+c ALIGN=MIDDLE  ALT=\"339=+-16+%2B55+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=339=+39%2B+c ALIGN=MIDDLE  ALT=\"339=+39%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=339-39 ALIGN=MIDDLE  ALT=\"c=339-39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=300%29 ALIGN=MIDDLE  ALT=\"highlight%28c=300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then, your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=+-16x%5E2+%2B55x+%2B+300+%29 ALIGN=MIDDLE  ALT=\"highlight%28y=+-16x%5E2+%2B55x+%2B+300+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );