document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164778>Question 1164778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A particle sliding down an inclined plane travels 2 feet the first second. In any second after the first it slides 4 feet farther than it did in the preceeding second. \r<BR>\n" );
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document.write( "A.) How far will it slide in the 7th second? \r<BR>\n" );
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document.write( "B.) How far will it slide in 7 seconds? \r<BR>\n" );
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document.write( "C.) How long will it take to slide 128 feet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789198 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=789198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the formula to use is An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "A1 is equal to 2<BR>\n" );
document.write( "d is equal to 4<BR>\n" );
document.write( "n is equal to the number of seconds\r<BR>\n" );
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document.write( "using this formula, you will find that it will slide 26 feet in the 7th second.<BR>\n" );
document.write( "the formula ia A7 = 2 + 6 * 4 = 2 + 24 = 26\r<BR>\n" );
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document.write( "the formula to find the sum of all the feet that it slid is Sn = n * (A1 + An) / 2.\r<BR>\n" );
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document.write( "n is the number of seconds<BR>\n" );
document.write( "A1 is the first term.<BR>\n" );
document.write( "An is the nth term.\r<BR>\n" );
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document.write( "using this formula, you will find that the total number of feet that it slid in 7 seconds is S7 = 7 * (2 + 26) / 2 = 98.\r<BR>\n" );
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document.write( "you can use this same formula to find out how many seconds it takes to slide a total of 128 feet.\r<BR>\n" );
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document.write( "the formula becomes Sn = n * (2 + An) / 2<BR>\n" );
document.write( "since Sn is equal to 128,  the formula becomes:<BR>\n" );
document.write( "128 = n * (2 + An) / 2<BR>\n" );
document.write( "multiply both sides of this formula by 2 to get:<BR>\n" );
document.write( "256 = n * (2 + An)\r<BR>\n" );
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document.write( "you know that An = A1 + (n-1) * d<BR>\n" );
document.write( "you also know that A1 = 2 and d = 4<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "An = 2 + (n-1) * 4<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "An = 2 + 4n - 4 which becomes:<BR>\n" );
document.write( "An = 4n - 2\r<BR>\n" );
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document.write( "in the formula of 256 = n * (2 + An), replace An with 4n - 2 to get:<BR>\n" );
document.write( "256 = n * (2 + 4n - 2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "256 = 2n + 4n^2 - 2n<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "256 = 4n^2<BR>\n" );
document.write( "divide both sides of this formula by 4 to get:<BR>\n" );
document.write( "64 = n^2<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = sqrt(64) = 8\r<BR>\n" );
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document.write( "this tells you a total of 128 feet will have been slid in 8 seconds.<BR>\n" );
document.write( "use the An formula to find A8 and then use the Sn formula o find the total number of feet that was slid.\r<BR>\n" );
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document.write( "A8 = 2 + 7 * 4 = 2 + 28 = 30<BR>\n" );
document.write( "this makes sense since it slid 26 feet in the 7th second and it now slides 4 more feet in the 8th second.\r<BR>\n" );
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document.write( "S8 = 8 * (2 + 30) / 2 = 128<BR>\n" );
document.write( "this says the particle slides a total of 128 feet in 8 seconds.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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