document.write( "Question 1179528: I tried to do with examples and couldn't make it!!!\r
\n" ); document.write( "\n" ); document.write( "Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 60 and 80 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 65 degrees?\r
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Algebra.Com's Answer #809090 by ikleyn(52817)\"\" \"About 
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\n" ); document.write( "Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies
\n" ); document.write( "between 60 and 80 degrees during the day and the average daily temperature first occurs at 8 AM.
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document.write( "Temperature varies between 60 and 80 degrees - - - it means that the average daily temperature is 70 degrees.\r\n" );
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document.write( "So, the temperature is 70 degrees at 8 am (given).\r\n" );
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document.write( "Assuming that the temperature is sinusoidal during the 24 hours, we must take it as a given that \r\n" );
document.write( "the temperature is 70 degrees 12 hours after 8 am, i.e. at 8 pm.\r\n" );
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document.write( "Then we can construct this table of temperatures\r\n" );
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document.write( "    average, 70 degs     8 am           = 8 am\r\n" );
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document.write( "    maximum, 80 degs     8 am + 6 hours = 2 pm\r\n" );
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document.write( "    average, 70 degs     2 pm + 6 hours = 8 pm\r\n" );
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document.write( "    minimum, 60 degs     8 pm + 6 hours = 2 am   next day\r\n" );
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document.write( "    average, 70 degs     8 am           = 8 am   next day\r\n" );
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document.write( "           From this table, you see that you should examine\r\n" );
document.write( "        two time intervals: one from  8 pm today to 2 am next day\r\n" );
document.write( "          and the second from 2 am next dat to 8 am next day.\r\n" );
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document.write( "So, after 8 pm, the temperature continues decreasing from 70 degs to the lowest temperature of 60 degs.\r\n" );
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document.write( "In this way, the temperature passes 65 degrees  when  \"sin%28alpha%29\" = 1/2, i.e.  with the shift of 1/12  of the 24-hour period.\r\n" );
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document.write( "        1/12 of the 24-hours period is 2 hours.\r\n" );
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document.write( "So we conclude that for the first time interval, the temperature will reach 65 degrees at  8 pm + 2 hours, which is 10 pm.\r\n" );
document.write( "It is still BEFORE midnight, so we do not count this time moment.\r\n" );
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document.write( "Next time moment with the 65 degs will be 2 hours BEFORE 8 am next day, which is 6 am next day.\r\n" );
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document.write( "So, your  ANSWER  is THIS:  first time after midnight, the temperature will reach 65 degs at 6 am.\r\n" );
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