document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012885>Question 1012885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profit P for a product whose sales fluctuate with the seasons is estimated to be P= 14 + 5sin(pit/52), where t is given in weeks and P is in thousands of dollars. Determine the number of weeks it would take for the profit to initially reach $18,000.\r<BR>\n" );
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document.write( "I attempted this problem, but when I plug the sin inverse of a number into my calculator, it says there is a math error. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629018 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The greatest positive value for ANY<BR>\n" );
document.write( "sin function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+14+%2B+5%2A1+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+14+%2B+5%2A1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+19+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+19+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in thousands, so<BR>\n" );
document.write( "that is $19,000.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "The problem makes sense, so I can continue<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+18+ ALIGN=MIDDLE  ALT=\"+P+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+ ALIGN=MIDDLE  ALT=\"+18+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++5%2Asin%28+pi%2A%28+t%2F52+%29+%29+=+4+ ALIGN=MIDDLE  ALT=\"++5%2Asin%28+pi%2A%28+t%2F52+%29+%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+pi%2A%28+t%2F52+%29+%29+=+4%2F5+ ALIGN=MIDDLE  ALT=\"+sin%28+pi%2A%28+t%2F52+%29+%29+=+4%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2A%28+t%2F52+%29+=+theta+ ALIGN=MIDDLE  ALT=\"+pi%2A%28+t%2F52+%29+=+theta+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin+%28+theta+%29+=+4%2F5+ ALIGN=MIDDLE  ALT=\"+sin+%28+theta+%29+=+4%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+arc+sin+%28+4%2F5+%29+=+.9273+ ALIGN=MIDDLE  ALT=\"+arc+sin+%28+4%2F5+%29+=+.9273+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that I had to get the angle measured in radians<BR>\n" );
document.write( "because of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi+ ALIGN=MIDDLE  ALT=\"+pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+.9273+ ALIGN=MIDDLE  ALT=\"+theta+=+.9273+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2A%28+t%2F52+%29+=+.9273+ ALIGN=MIDDLE  ALT=\"+pi%2A%28+t%2F52+%29+=+.9273+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%2F52+=+.9273+%2F+3.1416+ ALIGN=MIDDLE  ALT=\"+t%2F52+=+.9273+%2F+3.1416+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%2F52+=+.2952+ ALIGN=MIDDLE  ALT=\"+t%2F52+=+.2952+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+15.3488+ ALIGN=MIDDLE  ALT=\"+t+=+15.3488+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the 15th week, the profit will reach $18,000<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+5%2Asin%28+pi%2A%28+t%2F52+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+5%2Asin%28+pi%2A%2815.3488%2F52+%29+%29+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+5%2Asin%28+pi%2A%2815.3488%2F52+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+5%2Asin%28+.9273+%29+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+5%2Asin%28+.9273+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+5%2A.8+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+5%2A.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14+%2B+4+ ALIGN=MIDDLE  ALT=\"+P+=+14+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+18+ ALIGN=MIDDLE  ALT=\"+P+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );