document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133032>Question 1133032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help please I have been trying to figure this out most of the day\r<BR>\n" );
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document.write( "A person bungee cord jumping oscillates up and down. The distance from their highest point to their lowest point is 10m. and the person takes 7 s to complete 2 cycles. For the first few cycles the distance from the mean position, d metres, with respect to t seconds, is modelled by a cosine function. \r<BR>\n" );
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document.write( "A)Sketch a graph of this function for two cycles.<BR>\n" );
document.write( "B) Write an equation that describes the distance of the person from their mean position as a function of time.<BR>\n" );
document.write( "c) at what height is the person after 9 seconds?\r<BR>\n" );
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document.write( "Thank you!!!!<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 #750190 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=750190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the following graph models what you are looking for.\r<BR>\n" );
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document.write( "the equation is y = 5 * cos ( 72 /.7 * x)\r<BR>\n" );
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document.write( "the bungee cord starts at 5 meters above the mean position and drops to 5 meters below the mean position and ten back up to 5 meters above the mean position.\r<BR>\n" );
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document.write( "that's one full cycle.\r<BR>\n" );
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document.write( "it does this two times for two full cycles.\r<BR>\n" );
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document.write( "to model as 7 seconds for two full cycles, model as 3.5 seconds for one full cycle.\r<BR>\n" );
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document.write( "make the period of one full cycle equal to 3.5 degrees rather than 360 degrees.\r<BR>\n" );
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document.write( "the general formula of the cosine function is y = a * cos (b * (x - c)) + d\r<BR>\n" );
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document.write( "a is the amplitude.<BR>\n" );
document.write( "b is the frequency<BR>\n" );
document.write( "c is the horizontal displacement.<BR>\n" );
document.write( "d is the vertical displacement.\r<BR>\n" );
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document.write( "the horizontal displacmeent will be 0 and the vertical displacement will be 0, so the formula becomes y = a * cos (b * x)\r<BR>\n" );
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document.write( "you want the cycle to peak at 5 units above the mean of 0 and bottom at 5 units beloe the mean of 0.\r<BR>\n" );
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document.write( "that makes the amplitude equal to 5.\r<BR>\n" );
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document.write( "the formula becomes y = 5 * cos (b * x).\r<BR>\n" );
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document.write( "your want the period to be 3.5 rather than 360.\r<BR>\n" );
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document.write( "period = 360 / frequency and frequency = 360 / period.\r<BR>\n" );
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document.write( "if the period is going to be 3.5, then frequency = 360 / period applies.\r<BR>\n" );
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document.write( "it becomes frequency = 360 / 3.5 which can also be shown as 720 / 7 if you just want to deal with integers.\r<BR>\n" );
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document.write( "the graph of the function of y = 5 * cos (720 / 7 * x) is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011908.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "after 9 seconds, the person will be at y = 5 * cos (720 / 7 * 9) = 4.505 meters below the center line, which is what i think they mean by the mean.\r<BR>\n" );
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document.write( "this can be seen visually in the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011909.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graph shows 3 full cycles of the cosine wave.\r<BR>\n" );
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document.write( "the first cycle ends at 3.5 seconds.<BR>\n" );
document.write( "the second cycle ends at 7 seconds.<BR>\n" );
document.write( "the third cycle ends at 10.5 seconds.\r<BR>\n" );
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document.write( "9 seconds is just a little past the midpoint of the third cycle.\r<BR>\n" );
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