document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46407>Question 46407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the period of a simple pendulum is directly proportional to the square root of its length.  If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 second period?\r<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 #30765 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=30765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can start by writing the equation of proportionality:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+k%2Asqrt%28L%29 ALIGN=MIDDLE  ALT=\"P+=+k%2Asqrt%28L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Where: P = period, L = Length, and k is the constant of proportionality.<BR>\n" );
document.write( "We need to find the value of k.  We can do this by substituting the given values of L (6 ft) and P (2 secs) into the above formula and solving for k.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+k%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"2+=+k%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2%2Fsqrt%286%29 ALIGN=MIDDLE  ALT=\"k+=+2%2Fsqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the formula for the period is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%282%2Fsqrt%286%29%29sqrt%28L%29 ALIGN=MIDDLE  ALT=\"P+=+%282%2Fsqrt%286%29%29sqrt%28L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To answer your probem however, we need to solve this equation for L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%282%2Fsqrt%286%29%29sqrt%28L%29 ALIGN=MIDDLE  ALT=\"P+=+%282%2Fsqrt%286%29%29sqrt%28L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and divide by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29P%2F2+=+sqrt%28L%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29P%2F2+=+sqrt%28L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now square both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F4%29P%5E2+=+L ALIGN=MIDDLE  ALT=\"%286%2F4%29P%5E2+=+L\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+%283%2F2%29P%5E2 ALIGN=MIDDLE  ALT=\"L+=+%283%2F2%29P%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can answer your problem. What should L be if P is to be 1 second.<BR>\n" );
document.write( "Just substitute P = 1 into the above equation and solve for L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+%283%2F2%29%281%5E2%29 ALIGN=MIDDLE  ALT=\"L+=+%283%2F2%29%281%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+3%2F2 ALIGN=MIDDLE  ALT=\"L+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+1.5 ALIGN=MIDDLE  ALT=\"L+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft. </SPAN>\n" );
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