document.write( "Question 1194135: 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
\n" ); document.write( "\n" ); 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? \n" ); document.write( "
Algebra.Com's Answer #826280 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The info below is for your education\r
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                Tides and Water Levels\r
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\n" ); document.write( "\n" ); document.write( "            Frequency of Tides - The Lunar Day

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document.write( "Most coastal areas, with some exceptions, experience two high tides and two low tides every day.\r\n" );
document.write( "Almost everyone is familiar with the concept of a 24-hour solar day, which is the time that it takes \r\n" );
document.write( "for a specific site on the Earth to rotate from an exact point under the sun to the same point under the sun.\r\n" );
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document.write( "Similarly, a lunar day (also known as a \"tidal day\") is the time it takes for a specific site on the Earth \r\n" );
document.write( "to rotate from an exact point under the moon to the same point under the moon. Unlike a solar day, \r\n" );
document.write( "however, a lunar day is 24 hours and 50 minutes. The lunar day is 50 minutes longer than a solar day \r\n" );
document.write( "because the moon revolves around the Earth in the same direction that the Earth rotates around its axis. \r\n" );
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document.write( "So, it takes the Earth an extra 50 minutes to “catch up” to the moon.\r\n" );
document.write( "Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience \r\n" );
document.write( "two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. \r\n" );
document.write( "It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See this site with nice illustration\r
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\n" ); document.write( "\n" ); document.write( "https://oceanservice.noaa.gov/education/tutorial_tides/tides05_lunarday.html\r
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\n" ); document.write( "\n" ); document.write( "Regarding the three solutions you obtained so far, the solution by @greenestamps is correct. You may use it.\r
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\n" ); document.write( "\n" ); document.write( "The solution by @Theo is incorrect due to different reasons; in particular,
\n" ); document.write( "he counts the time starting from midnight, while the problem asks to count time starting from 9:15 am.\r
\n" ); document.write( "\n" ); document.write( "The period of the cosine function is also incorrect in the Theo' solution.\r
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\n" ); document.write( "\n" ); document.write( "The solution by Alan has wrong sign at cosine function.\r
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document.write( "  //  O-o-o-p-s ! Sorry. The solution by @Alan is correct.\r\n" );
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document.write( "      It was my mistake to say that it is wrong . . . Sorry for that.\r\n" );
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document.write( "      I simply ran too fast by my eyes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar solved problems,  look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on Trigonometric functions \r
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