document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194135>Question 1194135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 am. High tide occurs at 3:30 pm. What is a cosine function that models the variation in inches above and below the water level as a function of time and hours since 9:15 am?\r<BR>\n" );
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document.write( "Please tell me what should I put as answer for the a cosine function. From chegg I got the answer as f(x) = 20 (x -0.99 ) + 32. Is that correct?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826263 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The starting point for the function (t=0) is at low tide.  Since the maximum of the basic cosine function is at t=0, we can use a negative cosine function with no horizontal shift.<br><BR>\n" );
document.write( "High tide is 52 inches and low tide is 12 inches.  The difference is 40 inches, so the amplitude is 20; the midline is 32.  So the function is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-20%2Acos%28bx%29%2B32 ALIGN=MIDDLE  ALT=\"y=-20%2Acos%28bx%29%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The only missing part is the coefficient b, which is (2pi) divided by the period.<br><BR>\n" );
document.write( "Half the period is between low tide and high tide, which is 6.25 hours; so the period is 12.5 hours.  The desired function is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-20%2Acos%28%282pi%2F12.5%29x%29%2B32 ALIGN=MIDDLE  ALT=\"y=-20%2Acos%28%282pi%2F12.5%29x%29%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph, showing low tide of 12 inches at t=0 (9:15am) and high tide of 52 inches at t=6.25 (3:30pm) -- and the next low tide 12.5 hours after the first one (9:45pm):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-pi%2F2%2C9pi%2F2%2C-10%2C70%2C-20%2Acos%28%282pi%2F12.5%29x%29%2B32%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-pi%2F2%2C9pi%2F2%2C-10%2C70%2C-20%2Acos%28%282pi%2F12.5%29x%29%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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document.write( "Commenting on tutor @ikleyn's comments about the other responses, note that the response from alan3354 is in fact correct, because he used a horizontal shift of pi radians, making the positive coefficient on the cosine function correct.<br><BR>\n" );
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document.write( "To the student, who asked a completely different question in a \"thank you\" note regarding this problem....<br><BR>\n" );
document.write( "We generally can't answer questions that you ask in that way.  You need to post your questions in the normal way.<br><BR>\n" );
document.write( "However, there is a quick answer to the question you asked this time.<br><BR>\n" );
document.write( "The angle t goes from 0 to 2pi; but the angle in the problem is 2t, so 2t goes from 0 to 4pi.  The two answers you didn't find are each simply 2pi more than the answers you DID find, because the range is 0 to 4pi instead of 0 to 2pi.<br>\r<BR>\n" );
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