document.write( "Question 830764: a boy start studying from 8am in the morning and the angle of the sun is 15 degree . now the angle of the sun is 55 degree ... what will.be the time now... \n" ); document.write( "
Algebra.Com's Answer #500871 by Edwin McCravy(20056)\"\" \"About 
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a boy start studying from 8am in the morning and the angle of the sun is 15 degree . now the angle of the sun is 55 degree ... what will.be the time now...
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document.write( "We will assume that at 12 noon the angle of the sun is 90°\r\n" );
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document.write( "Let x = the angle of the sun in degrees\r\n" );
document.write( "Let y = the time of day in hours after midnight\r\n" );
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document.write( "Then when x is 15, y is 8, and when x = 90, y is 12\r\n" );
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document.write( "So we have two points on a line, (15,8) and (90,12)\r\n" );
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document.write( "So we find the equation of the line that passes through\r\n" );
document.write( "those two points:\r\n" );
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document.write( "Slope formula:\r\n" );
document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (15,8)\r\n" );
document.write( "and where (x2,y2) = (90,12)\r\n" );
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document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "m = \"%2812-8%29%2F%2890-15%29\"\r\n" );
document.write( "m = \"4%2F75\"\r\n" );
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document.write( "Point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
document.write( "where (x1,y1) = (15,8)\r\n" );
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document.write( "y - 8 = \"4%2F75\"(x - 15)\r\n" );
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document.write( "y - 8 = \"4%2F75\"x - \"4%2F5\"\r\n" );
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document.write( "    y = \"4%2F75\"x - \"4%2F5\" + 8\r\n" );
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document.write( "    y = \"4%2F75\"x - \"4%2F5\" + \"40%2F5\"\r\n" );
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document.write( "    y = \"4%2F75\"x + \"36%2F5\"\r\n" );
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document.write( "So if we substitute the angle of the sun in that\r\n" );
document.write( "equation, we will get the time of day.\r\n" );
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document.write( "So we substitute x=55\r\n" );
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document.write( "    y = \"4%2F75\"(55) + \"36%2F5\"\r\n" );
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document.write( "    y = \"44%2F15%2B36%2F5\" = \"44%2F15%2B108%2F15\" = \"152%2F15\" = \"10%262%2F15\" = \"10%268%2F60\" \r\n" );
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document.write( "\"8%2F60\"ths of an hour is 8 minutes,\r\n" );
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document.write( "so the time is 10:08AM\r\n" );
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document.write( "-------------------------\r\n" );
document.write( "FYI, after 12 noon the sun starts going down, so to use the formula\r\n" );
document.write( "in the afternoon, you must subtract the angle from 180 degrees, Then\r\n" );
document.write( "the formula will give you military time, which you will convert to\r\n" );
document.write( "ordinary time by subtracting 12 hours.  \r\n" );
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document.write( "For instance, if the angle of the sun were 55° and it were in the \r\n" );
document.write( "afternoon instead of the morning, we would subtract 180°-55° and \r\n" );
document.write( "get 125, we would substitute that in the equation and get \"13%2613%2F15\" or\r\n" );
document.write( "\"13%2652%2F60\" and we would subtract 12 hours and get \"1%2652%2F60\" \r\n" );
document.write( "so the time would be 1:52PM, which is the same amount of time AFTER\r\n" );
document.write( "12 noon that 10:08AM (the answer to your problem) was BEFORE 12 noon.  \r\n" );
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document.write( "Edwin
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