document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126910>Question 126910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi could you help me solve his problem.  The section im working on is graphing square root and other radicals functions.\r<BR>\n" );
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document.write( " The formula t=2(pi symbol)square root of (L/9.8)<BR>\n" );
document.write( "can be used to estimate the number of seconds t it takes a pendulum of length L meters to make one complete swing.  Graph the equation on a graphing calculator. Then use the graph to estimate the values of t for pendulums of lengths 1.5 meters and 2.5 meters.  (1 point)\r<BR>\n" );
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document.write( "Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92961 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=92961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let t (the number of seconds for 1 complete swing of the pendulum) be represented on the<BR>\n" );
document.write( "vertical axis (y-axis). And let L (the length of the pendulum arm in meters) be represented<BR>\n" );
document.write( "on the horizontal axis (x-axis)<BR>\n" );
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document.write( "You can easily calculate a couple of points on the graph of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2%2Api%2Asqrt%28L%2F9.8%29 ALIGN=MIDDLE  ALT=\"t+=+2%2Api%2Asqrt%28L%2F9.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "just to check what your calculator shows as the graph. First you can tell that L has to be<BR>\n" );
document.write( "a positive value. Why? Because if it were negative you would be taking the square root of<BR>\n" );
document.write( "a negative number and this means that the answer would not be a real number. (Also it doesn't make<BR>\n" );
document.write( "sense that a pendulum would involve a negative length.)<BR>\n" );
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document.write( "What if L is zero? If you substitute zero for L in the equation, the square root term becomes zero<BR>\n" );
document.write( "and this makes the whole right side of the equation become zero. So when L = 0 then t also<BR>\n" );
document.write( "equals zero. This means that the point (0,0) is on the graph. Note that this is just a <BR>\n" );
document.write( "mathematical solution. It really makes no sense to have a pendulum with an arm of zero length.<BR>\n" );
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document.write( "What if L is 9.8? Then the term in the radical becomes 1 and the square root is 1. This<BR>\n" );
document.write( "makes the right side of the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2%2Api%2A1+=+2%2Api ALIGN=MIDDLE  ALT=\"t+=+2%2Api%2A1+=+2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > is approximately 6.28. So the point (L, t) is (9.8, 6.28) and it should be<BR>\n" );
document.write( "on the graph. <BR>\n" );
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document.write( "These are points on the graph just to help us get a feel that our graph is correct.<BR>\n" );
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document.write( "When you do the graph on your calculator it should look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-3%2C15%2C-3%2C10%2C2%2A3.141592654%2Asqrt%28x%2F9.8%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-3%2C15%2C-3%2C10%2C2%2A3.141592654%2Asqrt%28x%2F9.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that (0,0) is a point on the graph. And when you go to 9.8 on the horizontal<BR>\n" );
document.write( "axis, the corresponding value in the vertical direction appears to be 6.28 just as we had<BR>\n" );
document.write( "said. The graph appears to be correct.<BR>\n" );
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document.write( "Now all you have to do to answer the problem is:<BR>\n" );
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document.write( "First, go out to 1.5 on the horizontal axis and determine how many vertical units you have to go<BR>\n" );
document.write( "up to get to the graph. (You should get an answer of about 2.458 seconds.)<BR>\n" );
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document.write( "Then go out to 2.5 on the horizontal and determine from that point how many vertical units<BR>\n" );
document.write( "you have to go up to get to the graph. (You should get an answer of about 3.173 seconds.)<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
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