document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204408>Question 1204408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average temperature of a fictious town is given by the equation: f(x) = 20 sin (π/13x) + 2 where x represents the number of weeks since beggining of year. During the course of the year for how many weeks was the average temperature higher than 15° celcius </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840633 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "1 year = 52 weeks approximately\r<BR>\n" );
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document.write( "Desmos Graph<BR>\n" );
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document.write( "The Desmos graph shows the sine function f(x) = 20*sin( (pi/13)x ) + 2, along with the horizontal line y = 15.\r<BR>\n" );
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document.write( "On the domain 0 < x < 52, the intersection points are approximately:<BR>\n" );
document.write( "A = (2.928,15)<BR>\n" );
document.write( "B = (10.072,15)<BR>\n" );
document.write( "C = (28.928,15)<BR>\n" );
document.write( "D = (36.072,15)\r<BR>\n" );
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document.write( "The gap from A to B is one chunk of time when the temperature is above 15 degrees Celsius.<BR>\n" );
document.write( "10.072-2.928 = 7.144, which is about 7 weeks.\r<BR>\n" );
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document.write( "The gap from C to D is another chunk of time when the temperature is above 15 degrees Celsius.<BR>\n" );
document.write( "36.072-28.928 = 7.144, also about 7 weeks.\r<BR>\n" );
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document.write( "The total would then be roughly 7+7 = 14 weeks out of the 52 week timespan.\r<BR>\n" );
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document.write( "Edit: The student has mentioned the textbook's answer is 14.29<BR>\n" );
document.write( "This is because 2*7.144 = 14.288 which rounds to 14.29<BR>\n" );
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