document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208108>Question 1208108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is given below.\r<BR>\n" );
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document.write( "Let W = a piecewise function. \r<BR>\n" );
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document.write( "Top portion: t if 0 <= v < 1.79\r<BR>\n" );
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document.write( "Middle portion: \r<BR>\n" );
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document.write( "33 - [(10.45 + 10sqrt{v} - v)(33 - t)]/(22.04) <BR>\n" );
document.write( "if 1.79 <= v <= 20\r<BR>\n" );
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document.write( "Bottom portion: 33 - 1.5958(33 - t) if v > 20\r<BR>\n" );
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document.write( "where v represents the wind speed (in meters per second) and t represents the air temperature (°C). \r<BR>\n" );
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document.write( "Compute the wind chill for the following: \r<BR>\n" );
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document.write( "(a) An air temperature of 10°C and a wind speed of 5 m/sec\r<BR>\n" );
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document.write( "(b) An air temperature of 10°C and a wind speed of 25 m/sec </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846277 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Piecewise functions can be a strange beast. <BR>\n" );
document.write( "I think of them as a Frankenstein's monster because we glue together various parts of other functions. \r<BR>\n" );
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document.write( "The function will change its identity based on what the input is.<BR>\n" );
document.write( "The input in this case is variable v (t is the parameter and appears to be fixed to t = 10).\r<BR>\n" );
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document.write( "We have 3 scenarios<ul><li>If 0 <= v < 1.79, then W(v) = t</li><li>If 1.79 <= v <= 20, then W(v) = 33 - (10.45 + 10*sqrt(v) - v)*(33-t)/22.04</li><li>If v > 20, then W(v) = 33 - 1.5958(33-t)</li></ul>-------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "t = 10<BR>\n" );
document.write( "v = 5\r<BR>\n" );
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document.write( "v = 5 fits the interval 1.79 <= v <= 20, so we use the middle piece.\r<BR>\n" );
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document.write( "W(v) = 33 - (10.45 + 10*sqrt(v) - v)*(33-t)/22.04<BR>\n" );
document.write( "W(5) = 33 - (10.45 + 10*sqrt(5) - 5)*(33-10)/22.04<BR>\n" );
document.write( "W(5) = 3.977965752044<BR>\n" );
document.write( "W(5) = 3.98<BR>\n" );
document.write( "The wind chill is approximately 3.98 degrees Celsius.\r<BR>\n" );
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document.write( "-------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "This time we have<BR>\n" );
document.write( "t = 10<BR>\n" );
document.write( "v = 25\r<BR>\n" );
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document.write( "v = 25 fits the interval v > 20 aka 20 < v < infinity.<BR>\n" );
document.write( "So we'll use the 3rd piece of this piecewise function.\r<BR>\n" );
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document.write( "W(v) = 33 - 1.5958(33-t)<BR>\n" );
document.write( "W(25) = 33 - 1.5958(33-10)<BR>\n" );
document.write( "W(25) = -3.7034<BR>\n" );
document.write( "The wind chill is roughly -3.7034 degrees Celsius.\r<BR>\n" );
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document.write( "Side notes:<BR>\n" );
document.write( "10 degrees Celsius = 50 degrees Fahrenheit<BR>\n" );
document.write( "3.98 degrees Celsius = 39.164 degrees Fahrenheit<BR>\n" );
document.write( "-3.7034 degrees Celsius = 25.33388 degrees Fahrenheit<BR>\n" );
document.write( "5 m/s = 18 km/hr = 11.1846815 mph<BR>\n" );
document.write( "25 m/s = 90 km/hr = 55.9234073 mph<BR>\n" );
document.write( "The decimal values are approximate.<BR>\n" );
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