document.write( "Question 457399: The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the Bay of Fundy can be modeled by d=35-28cos(pi/6.2)t, where d is the depth in feet and t is the time in hours.\r
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\n" ); document.write( "\n" ); document.write( "a. consider a day in which t=0 represents 12:00 am. For that day, when do the high and low tides occur?\r
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\n" ); document.write( "\n" ); document.write( "I've been doing sine and cosine stuff in class \n" ); document.write( "

Algebra.Com's Answer #313914 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We find the period of that function as that is the number of\r\n" );
document.write( "hours from the time the ocean is a certain number of feet\r\n" );
document.write( "deep until it is that same number of feet deep again. \r\n" );
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document.write( "The period of that function is  or \r\n" );
document.write( " = 12.4 hours.\r\n" );
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document.write( "Low tide is when t=0 or midnight or 12:00AM. So there will\r\n" );
document.write( "be another low tide again at 12.4 hours later or t=12.4 at \r\n" );
document.write( "12:24PM.  Half-way between those two low tides there will be a \r\n" );
document.write( "high tide and that will be at t=6.2 hours after midninght, at \r\n" );
document.write( "6:12AM.  12.4 hours later there will be another high tide at \r\n" );
document.write( "t=18.6 hours after midnight and that will be at 6:36PM.\r\n" );
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document.write( "The low tide is when t=0, substituting t=0 in the equation\r\n" );
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document.write( "d = 35 - 28cos(pi/6.2)t\r\n" );
document.write( "d = 35-28cos(pi/6.2)0\r\n" );
document.write( "d = 35-28cos(0)\r\n" );
document.write( "d = 35-28(1)\r\n" );
document.write( "d - 35-28\r\n" );
document.write( "d = 7\r\n" );
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document.write( "So the lowest possible depth is 7 feet, so it will never be\r\n" );
document.write( "3.5 feet there.  The green line on the graph is at 3.5 feet\r\n" );
document.write( "and we see that the ocean there never gets that shallow.\r\n" );
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document.write( "So there is no solution to the b part.\r\n" );
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document.write( "Edwin

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