document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998962>Question 998962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)\r<BR>\n" );
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document.write( "(a) Explain why speed S is a linear function of temperature T.<BR>\n" );
document.write( "Because S always increases by 1.1 when T increases by ...., S has a constant rate of change and is a linear function of T.\r<BR>\n" );
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document.write( "Identify the slope of the function.<BR>\n" );
document.write( ".....\r<BR>\n" );
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document.write( "(b) Use a formula to express S as a linear function of T.<BR>\n" );
document.write( "S =  .....\r<BR>\n" );
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document.write( "(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.<BR>\n" );
document.write( "T =  .....\r<BR>\n" );
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document.write( "(d) Explain in practical terms the meaning of the slope of the function you found in part (c).<BR>\n" );
document.write( "The slope of T as a linear function of S is ..... , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..... degree in temperature.<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616646 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The speed of sound in air changes with the temperature. <BR>\n" );
document.write( " When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second.<BR>\n" );
document.write( " For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)<BR>\n" );
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document.write( "(a) Explain why speed S is a linear function of temperature T.<BR>\n" );
document.write( "Because S always increases by 1.1 ft/sec when T increases by .one degree,<BR>\n" );
document.write( " S has a constant rate of change and is a linear function of T.<BR>\n" );
document.write( "Identify the slope of the function.<BR>\n" );
document.write( "slope = rise/run, therefore 1.1/1, or just +1.1<BR>\n" );
document.write( ".....<BR>\n" );
document.write( "(b) Use a formula to express S as a linear function of T.<BR>\n" );
document.write( "S = 1.1(t-32) + 1087.5<BR>\n" );
document.write( "S = 1.1t - 35.2 + 1087.5<BR>\n" );
document.write( "S = 1.1t + 1052.3 <BR>\n" );
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document.write( "(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.<BR>\n" );
document.write( "1.1t + 1052.3 = S<BR>\n" );
document.write( "1.1t = S - 1052.3<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28S-1052.3%29%29%2F1.1 ALIGN=MIDDLE  ALT=\"%28%28S-1052.3%29%29%2F1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2F1.1 ALIGN=MIDDLE  ALT=\"S%2F1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1052.3%2F1.1 ALIGN=MIDDLE  ALT=\"1052.3%2F1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(d) Explain in practical terms the meaning of the slope of the function you <BR>\n" );
document.write( "found in part (c). Approx 1 ft/sec change indicates 1 degree of temperature change<BR>\n" );
document.write( "The slope of T as a linear function of S is .91 , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..one... degree in temperature. </SPAN>\n" );
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