document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117289>Question 117289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello unfortunatly I can't figure out this word problem and i REALLY need help!\r<BR>\n" );
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document.write( "A Pythagorean fractal tree starts at Stage 1 with a square of side length 1m. At every consecutive stage, an isoceles right triangle and two squares are attached to the last square(s) drawn. Determine the total area at the 10th stage and the 100th stage. Determine the general term and make conclusions. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85354 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=85354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I found only this for you:\r<BR>\n" );
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document.write( "Iteration <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the construction adds <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > squares of size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F2%29sqrt%282%29%29%5E2n ALIGN=MIDDLE  ALT=\"%28%281%2F2%29sqrt%282%29%29%5E2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a total area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Thus the area of the tree might seem to grow without bound in the limit<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+-%3Einfinity ALIGN=MIDDLE  ALT=\"n+-%3Einfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "However, some of the squares overlap starting at the order <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > iteration, and the tree actually has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=finite ALIGN=MIDDLE  ALT=\"finite\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+area ALIGN=MIDDLE  ALT=\"+area\"   DISABLED_style= \"max-width:90%; height:auto;\" > because it fits inside a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A4 ALIGN=MIDDLE  ALT=\"6%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > box.<BR>\n" );
document.write( "It can be shown easily that the area <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Pythagoras+ ALIGN=MIDDLE  ALT=\"Pythagoras+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tree ALIGN=MIDDLE  ALT=\"tree\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be in the range \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%3C+A+%3C18 ALIGN=MIDDLE  ALT=\"5+%3C+A+%3C18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which can be narrowed down further with extra effort. \r<BR>\n" );
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document.write( "Little seems to be known about the actual value of <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" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10%281%2F2%2Asqrt%282%29%29%5E20=1 ALIGN=MIDDLE  ALT=\"2%5E10%281%2F2%2Asqrt%282%29%29%5E20=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10%28.5%2A1.4142%29%29%5E20=1 ALIGN=MIDDLE  ALT=\"2%5E10%28.5%2A1.4142%29%29%5E20=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10%28.707%29%29%5E20=1 ALIGN=MIDDLE  ALT=\"2%5E10%28.707%29%29%5E20=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024%28.707%29%5E20=1 ALIGN=MIDDLE  ALT=\"1024%28.707%29%5E20=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024%28.000976%29=1 ALIGN=MIDDLE  ALT=\"1024%28.000976%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=1 ALIGN=MIDDLE  ALT=\"1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=100 ALIGN=MIDDLE  ALT=\"n=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E100%281%2F2%2Asqrt%282%29%29%5E200=1 ALIGN=MIDDLE  ALT=\"2%5E100%281%2F2%2Asqrt%282%29%29%5E200=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E100%28.5%2A1.4142%29%29%5E200=1 ALIGN=MIDDLE  ALT=\"2%5E100%28.5%2A1.4142%29%29%5E200=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E100%28.707%29%29%5E200=1 ALIGN=MIDDLE  ALT=\"2%5E100%28.707%29%29%5E200=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2676%2A10%5E30%2A1.046%2A10%5E-31=1 ALIGN=MIDDLE  ALT=\"1.2676%2A10%5E30%2A1.046%2A10%5E-31=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.3%2A10%5E30%2A1%2F%281.046%2A10%5E31%29=1 ALIGN=MIDDLE  ALT=\"1.3%2A10%5E30%2A1%2F%281.046%2A10%5E31%29=1\"   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=1.3%281%2F%281.046%2A10%29%29=1 ALIGN=MIDDLE  ALT=\"1.3%281%2F%281.046%2A10%29%29=1\"   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=1.3%2A.9+=1 ALIGN=MIDDLE  ALT=\"1.3%2A.9+=1\"   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=1.17=1 ALIGN=MIDDLE  ALT=\"1.17=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.17 ALIGN=MIDDLE  ALT=\"1.17\"   DISABLED_style= \"max-width:90%; height:auto;\" > could be rounded to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope it will help. </SPAN>\n" );
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