document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022931>Question 1022931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fable about the tortoise an the hare? what? lol (math)?<BR>\n" );
document.write( "hello this is a math question that confused me from the first line. I do need help. \r<BR>\n" );
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document.write( "Sorry if its a little long. \r<BR>\n" );
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document.write( "You may have heard the fable about the tortoise and the hare. Suppose the tortise and he hare are running a 2000 m race. the tortoise proceeds very slow, never changing its speed. <BR>\n" );
document.write( "The hare runs very quickly at the start. \r<BR>\n" );
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document.write( "The tortoise travels 20m every minute. The hare travels 1000m in the 1st minute but, in each minute, after that, it travels only half of the remaining distance. (in the 2nd minute, the hare travels half of the remaining 1000 m and so on) \r<BR>\n" );
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document.write( "a) write the series for the distance the tortoise travels for the first few minutes of each race, where Sn represents the total distance traveled after n minutes. <BR>\n" );
document.write( "Each term of the series will represent the distance the tortoise travels in that minute. \r<BR>\n" );
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document.write( "(what?? so confused lol) \r<BR>\n" );
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document.write( "b) write the series for the distance the hare travels for the first few minutes of the race, where Sn represents the total distance traveled after n minutes. Each term of the series represents the distance the hare travels in that minute. \r<BR>\n" );
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document.write( "so I guess they want me to do one for the Tortoise and one for the Hare. \r<BR>\n" );
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document.write( "then finally \r<BR>\n" );
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document.write( "c) Analyze an compare the two series. include information such as Sn for both the tortoise and the hare and your conclusion as to who will win the race. provide support.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638496 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+20%2B20%2B20 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+20%2B20%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+20+20 = 20n <--- twenty n's here<BR>\n" );
document.write( "(The hare runs 20 meters at every minute.)\r<BR>\n" );
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document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+1000%2B500%2B250 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+1000%2B500%2B250\"   DISABLED_style= \"max-width:90%; height:auto;\" >+125+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2A0.5%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"1000%2A0.5%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum for the first n terms of a geometric sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+1000%2A%28%281-0.5%5En%29%2F%281-0.5%29%29+=+2000%281-0.5%5En%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+1000%2A%28%281-0.5%5En%29%2F%281-0.5%29%29+=+2000%281-0.5%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c)The tortoise will arrive at the finish line after 100 minutes.  (20n = 2000 ==> n=100 minutes.)<BR>\n" );
document.write( "At n=100 minutes, the hare would have traveled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000%281-0.5%5E99%29 ALIGN=MIDDLE  ALT=\"2000%281-0.5%5E99%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters, which is really close to 2000, but not quite the finish line yet, because there is still an infinitesimal distance remaining.<BR>\n" );
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