document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252428>Question 252428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help.  I cannot figure out the correct formula.  \r<BR>\n" );
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document.write( "Using a Nonlinear System.\r<BR>\n" );
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document.write( "Modeling Circuit Gain.  In electronics, cicuit gain is modeled by G = Bt/R + rt, where “R” is the value of a resister, “t” is temperature, Rt is the value of R at temperature “t”, and B is a constant.  The sensitivity of the circuit to temperature is modeled by S = BR/(R + Rt)^2.  If B = 3.7  and \"t\" is 90K (Kelvin), find the values of R and Rt that will make G = .4 and S = .001.\r<BR>\n" );
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document.write( "Answer:  R= 187  , Rt = 645 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184337 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 2 formulas you have to work with are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G+=+%28%28B%2At%29+%2F+%28R+%2B+R%5Bt%5D%29%29 ALIGN=MIDDLE  ALT=\"G+=+%28%28B%2At%29+%2F+%28R+%2B+R%5Bt%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28B%2AR+%2F+%28%28R+%2B+R%5Bt%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"S+=+%28B%2AR+%2F+%28%28R+%2B+R%5Bt%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R is the nominal value of a resistor.  <BR>\n" );
document.write( "R[t] is the value of the resistor at a certain temperature.<BR>\n" );
document.write( "B is a constant.<BR>\n" );
document.write( "t is the temperature using the Kelvin Scale.<BR>\n" );
document.write( "S is the sensitivity of the circuit to temperature.\r<BR>\n" );
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document.write( "Your problem is:\r<BR>\n" );
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document.write( "\"If B = 3.7 and \"t\" is 90K (Kelvin), find the values of R and Rt that will make G = .4 and S = .001.  (Answer: R= 187 , Rt = 645)\"\r<BR>\n" );
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document.write( "We have:\r<BR>\n" );
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document.write( "B = 3.7<BR>\n" );
document.write( "t = 90<BR>\n" );
document.write( "G = .4<BR>\n" );
document.write( "S = .001\r<BR>\n" );
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document.write( "We want to find R and R[t].\r<BR>\n" );
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document.write( "The first formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G+=+%28%28B%2At%29+%2F+%28R+%2B+R%5Bt%5D%29%29 ALIGN=MIDDLE  ALT=\"G+=+%28%28B%2At%29+%2F+%28R+%2B+R%5Bt%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting in this formula gets:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.4+=+%28%283.7%2A90%29+%2F+%28R+%2B+R%5Bt%5D%29%29 ALIGN=MIDDLE  ALT=\".4+=+%28%283.7%2A90%29+%2F+%28R+%2B+R%5Bt%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We divide both sides of this equation by .4 and we multiply both sides of this equation by (R + R[t]) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R+%2B+R%5Bt%5D%29+=+%28%283.7%2A90%29+%2F+.4%29 ALIGN=MIDDLE  ALT=\"%28R+%2B+R%5Bt%5D%29+=+%28%283.7%2A90%29+%2F+.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We solve for (R + R[t] to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R+%2B+R%5Bt%5D%29+=+832.5 ALIGN=MIDDLE  ALT=\"%28R+%2B+R%5Bt%5D%29+=+832.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28%28B%2AR%29+%2F+%28%28R+%2B+R%5Bt%5D%29%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"S+=+%28%28B%2AR%29+%2F+%28%28R+%2B+R%5Bt%5D%29%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We substitute in this formula to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.001+=+%28%283.7%2AR%29+%2F+%28832.5%5E2%29%29 ALIGN=MIDDLE  ALT=\".001+=+%28%283.7%2AR%29+%2F+%28832.5%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "S and B were given.<BR>\n" );
document.write( "R + R[t] was calculated from the first equation.\r<BR>\n" );
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document.write( "We multiply both sides of this equation by (832.5)^2 and we divide both sides of this equation by 3.7 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+%28.001+%2A+%28832.5%29%5E2%29%2F3.7%29 ALIGN=MIDDLE  ALT=\"R+=+%28.001+%2A+%28832.5%29%5E2%29%2F3.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We solve for R to get R = 187.325\r<BR>\n" );
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document.write( "Since R + R[t] = 832.5, this means that R[t] = 832.5 - 187.325 = 645.1875\r<BR>\n" );
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document.write( "we round these out to get:\r<BR>\n" );
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document.write( "R = 187<BR>\n" );
document.write( "R[t] = 645\r<BR>\n" );
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document.write( "This agrees with the answers you provided.\r<BR>\n" );
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document.write( "The key was solving for R + R[t] together in the first equation and then using that value to solve for R in the second equation.\r<BR>\n" );
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document.write( "Once we knew R, getting R[t] was a simple matter of subtraction.\r<BR>\n" );
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document.write( "I think that's what you were looking for.\r<BR>\n" );
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document.write( "Let me know if otherwise.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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