document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026264>Question 1026264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula T = 2&#960;&#8730;(l/g) relates a pendulum's period, T, in seconds (the time it takes to swing back and forth) to its length, l, in centimeters using g, the gravitational acceleration of 981 cm/sec^2.\r<BR>\n" );
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document.write( "How long would the pendulum have to be (to the nearest tenth of a centimeter) to make a pendulum with the given period?\r<BR>\n" );
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document.write( "QUESTION:\r<BR>\n" );
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document.write( "Solve the equation T = 2&#960;&#8730;(l/g) for l  \r<BR>\n" );
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document.write( "NOTE:\r<BR>\n" );
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document.write( "&#8730;(l/g) means square root of l/g   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641498 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=641498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29 ALIGN=MIDDLE  ALT=\"T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "i use capital L because it's less easy to be confused with the number one.\r<BR>\n" );
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document.write( "what you need to do is solve this equation for L.\r<BR>\n" );
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document.write( "the given period is T.\r<BR>\n" );
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document.write( "start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29 ALIGN=MIDDLE  ALT=\"T+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "divide both sides of this equation by (2 * pi) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+%2F+%282+%2A+pi%29+=+sqrt%28L%2Fg%29 ALIGN=MIDDLE  ALT=\"T+%2F+%282+%2A+pi%29+=+sqrt%28L%2Fg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28T%2F%282%2Api%29%29%5E2+=+L%2Fg ALIGN=MIDDLE  ALT=\"%28T%2F%282%2Api%29%29%5E2+=+L%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "multiply both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%2A%28T%2F%282%2Api%29%29%5E2+=+L ALIGN=MIDDLE  ALT=\"g%2A%28T%2F%282%2Api%29%29%5E2+=+L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+g%2A%28T%2F%282pi%29%29%5E2 ALIGN=MIDDLE  ALT=\"L+=+g%2A%28T%2F%282pi%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for example, if the given period is 5 seconds, then the formula would becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29 ALIGN=MIDDLE  ALT=\"5+=+2+%2A+pi+%2A+sqrt%28L%2Fg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you would solve for L to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+g%2A%285%2F%282pi%29%29%5E2 ALIGN=MIDDLE  ALT=\"L+=+g%2A%285%2F%282pi%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since g = 981, the formula would become:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+981%2A%285%2F%282pi%29%29%5E2 ALIGN=MIDDLE  ALT=\"L+=+981%2A%285%2F%282pi%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this results in L = 621.2255072 centimeters.\r<BR>\n" );
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document.write( "if you go back to the original formula, then it becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+2+%2A+pi+%2A+sqrt%28621.255072%2F981%29 ALIGN=MIDDLE  ALT=\"T+=+2+%2A+pi+%2A+sqrt%28621.255072%2F981%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "that results in T = 5.\r<BR>\n" );
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document.write( "any discrepancy will be due to rounding.\r<BR>\n" );
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document.write( "i used internally stored numbers and the answer came exactly to 5.\r<BR>\n" );
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document.write( "the number of 621.255072 that you see has been rounded to the number of digits that the calculator can display.\r<BR>\n" );
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document.write( "using that only will give you an answer that is close to 5, but not right on.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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