document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029598>Question 1029598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> problem solving question \r<BR>\n" );
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document.write( "the depth of water d meters, at a port entrance is given by the function <BR>\n" );
document.write( "d(t) = 4.5 + 1.5 sin pi t/12 <BR>\n" );
document.write( "where t is hours \r<BR>\n" );
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document.write( "a certain ship needs the depth at the port entrance to be more than 5 meters. The ship can be loaded and unloaded in and out of the port in 9 hours. assuming the the ship enters the port just as the depth at the entrance passes 5 meters, will the ship be able to exit 9 hours later? How long will it have to spare? or by how many minutes will it miss out? \r<BR>\n" );
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document.write( "and can you please show me working out and how you got the answer. \r<BR>\n" );
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document.write( "Thankyou </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644584 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d(t) = 4.5 + 1.5 sin pi t/12 <BR>\n" );
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document.write( "5 = 4.5 + (1.5 * sin(pi * t/12))<BR>\n" );
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document.write( "0.5 = 1.5 * sin(pi * t/12)<BR>\n" );
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document.write( "note that pi = 180 degrees<BR>\n" );
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document.write( "1/3 = sin(15t)<BR>\n" );
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document.write( "determine angle from inverse sin function = 1/3<BR>\n" );
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document.write( "15t = 19.471220634<BR>\n" );
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document.write( "t = 1.298081376 approx 1.3 hours<BR>\n" );
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document.write( "we need 9 hours to unload the ship<BR>\n" );
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document.write( "d(10.3) = 4.5 + (1.5 * sin(pi * (10.3)/12)) =<BR>\n" );
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document.write( "4.5 + (1.5 * 0.430511097) = 5.145766646 meters<BR>\n" );
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document.write( "*****yes, the ship will be able to exit 9 hours later<BR>\n" );
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document.write( "the sin curve is periodic, here is a graph of the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C+200%2C+-20%2C+20%2C+-1%2C+7%2C+4.5+%2B+1.5%2Asin%28pi%2A%28x%2F12%29%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C+200%2C+-20%2C+20%2C+-1%2C+7%2C+4.5+%2B+1.5%2Asin%28pi%2A%28x%2F12%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "we want to know the value of t when the sin(15t) = 1/3 again *****<BR>\n" );
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document.write( "note we subtract 19.471220634 from 180 = 160.528779366<BR>\n" );
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document.write( "15t = 160.528779366<BR>\n" );
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document.write( "t = 10.701918624 <BR>\n" );
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document.write( "***The ship has an addition 24 minutes before it can not sale out of the harbor<BR>\n" );
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