document.write( "Question 1189907: Hi, can someone please help me out with this question?\r
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Algebra.Com's Answer #821459 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
not sure if they wanted you to do this manually.
\n" ); document.write( "if so, let me know and i'll work on a manually derived solution configuration.\r
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\n" ); document.write( "\n" ); document.write( "the easiest way i can see is to use the desmos.com calculator.\r
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\n" ); document.write( "\n" ); document.write( "here's a video on how to do that.\r
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\n" ); document.write( "\n" ); document.write( "https://www.youtube.com/watch?v=b75PEalga4c\r
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\n" ); document.write( "\n" ); document.write( "i followed the directions on the video and this is what i got.\r
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\n" ); document.write( "\n" ); document.write( "the little hourglass on the left allows you to zoom in on the graph automatically.\r
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\n" ); document.write( "\n" ); document.write( "othrwise, use her instructions to set the x and y limits.\r
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\n" ); document.write( "\n" ); document.write( "the equation is entered from the keyhboard using the tilde rather than the equal sign.\r
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\n" ); document.write( "\n" ); document.write( "here's the link to the desmos.com calculator.\r
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\n" ); document.write( "\n" ); document.write( "https://www.desmos.com/calculator\r
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\n" ); document.write( "\n" ); document.write( "your regression eqution of y = a * (b * (x - c)) + d becomes:\r
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\n" ); document.write( "\n" ); document.write( "y = 13.8091 * sin(.509283 * (x - 4.11135)) + 13.4074.\r
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\n" ); document.write( "\n" ); document.write( "to find the value for next march, just add 12 to 3 to get x = 15 and solve the equation for x = 15.\r
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\n" ); document.write( "\n" ); document.write( "the equation becomes y = 13.8091 * sin(.509283 * (15 - 4.11135)) + 13.4074.\r
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\n" ); document.write( "\n" ); document.write( "you should get y = 4.1187.\r
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\n" ); document.write( "\n" ); document.write( "to find the month when the average tmperature first reaches 17 degrees centigrade, solve the equation for y = 17.\r
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\n" ); document.write( "\n" ); document.write( "the equation becomes 17 = 13.8091 * sin(.509283 * (x - 4.11135)) + 13.4074.
\n" ); document.write( "subtract 13.4074 from both sides of the equation to get:
\n" ); document.write( "17 - 13.4074 = 13.8091 * sin(.509283 * (x - 4.11135))
\n" ); document.write( "simpliy to get:
\n" ); document.write( "3.5926 = 13.8091 * sin(.509283 * (x - 4.11135))
\n" ); document.write( "divide both sides of the equation by 13.8091 to get:
\n" ); document.write( "3.5926 / 13.8091 = sin(.509283 * (x - 4.11135))
\n" ); document.write( "simplify to get:
\n" ); document.write( ".2601617774 = sin(.509283 * (x - 4.11135))
\n" ); document.write( "find the arcsin of .260167774 to get:
\n" ); document.write( "arcsin(.260167774) = .263189746
\n" ); document.write( "solve for .509283 * (x - 4.11135)) = .263189746 as follows:
\n" ); document.write( "divide both sides of the equation by .509283 to get:
\n" ); document.write( "x - 4.11135 = .5167848642.
\n" ); document.write( "add 4.11135 to both sides of the equation to get:
\n" ); document.write( "x = 4.628134864.
\n" ); document.write( "that should be some time in april.\r
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\n" ); document.write( "\n" ); document.write( "there's an easier way to do this using the desmos.com graph.
\n" ); document.write( "set x = 15 to find next march.
\n" ); document.write( "set y = 17 to find where the graph goes above 17 deegrees.\r
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\n" ); document.write( "\n" ); document.write( "it will look like this.\r
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\n" ); document.write( "\n" ); document.write( "check out the video.
\n" ); document.write( "it's pretty good.
\n" ); document.write( "let me know if you get hung up trying to do it yourself.\r
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\n" ); document.write( "\n" ); document.write( "theo\r
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