document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169577>Question 1169577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls answer my question\r<BR>\n" );
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document.write( "When a ball is tossed to a height of 4 meters above the ground, it always rebounds to 40% of it's previous height until it stops. Find the total distance that the ball has covered when it strikes the ground for the fifth time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794393 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> each time the ball is tossed, it rebounds to 40% of the previous height.<BR>\n" );
document.write( "when it is tossed, the height is 4 meters.<BR>\n" );
document.write( "on the first rebound, the height is .4 * 4 = 1.6 meters.<BR>\n" );
document.write( "on the second rebound, the height is .4 * 1.6 = .64 meters.<BR>\n" );
document.write( "on the third rebound, the height is .4 * .64 = .256 meters.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "at some point the height will decrease to 0.\r<BR>\n" );
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document.write( "this appears to be a geometric series.\r<BR>\n" );
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document.write( "the formula for the nth term of a geometric series is An = A1*r^(n-1).\r<BR>\n" );
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document.write( "the formula for the sum of the n terms of a geometric series is Sn = A1*(1-r^n)/(1-r).\r<BR>\n" );
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document.write( "if r is less than 1, than the infinite sum of the geometric series is S = A1/(1-r)\r<BR>\n" );
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document.write( "in your series, r is less than 1.<BR>\n" );
document.write( "it is .4 to be exact.\r<BR>\n" );
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document.write( "the formula for the infinite sum of your series would be:<BR>\n" );
document.write( "S = 4 / (1-r) = 4/.6 = 6.66666667 rounded to 8 decimal places.\r<BR>\n" );
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document.write( "to find the total distance traveled when the ball strikes the ground for the fifth time, the formula of Sn = A1*(1-r^n)/(1-r) is used.<BR>\n" );
document.write( "that becomes:\r<BR>\n" );
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document.write( "S5 = 4*(1-.4^5)/.6 = 6.5984.\r<BR>\n" );
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document.write( "the ball will have traveled 6.5984 meters by the time it strikes the ground for the 5th time.\r<BR>\n" );
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document.write( "here's what the series looks like in excel.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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