document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117795>Question 117795</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534954146/algebrahomeworkh>Fund of Alg and Trig</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to review for a final and would like to get help with A &B:\r<BR>\n" );
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document.write( "a. y= (10^x-10^-x)/ (2)<BR>\n" );
document.write( "b. y= (e^x +e^-x) / (2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85793 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=85793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. y= (10^x-10^-x)/ (2)<BR>\n" );
document.write( "Multiply both sides by 2 to get:<BR>\n" );
document.write( "2y = (10^x -10^-x)<BR>\n" );
document.write( "Multiply both sides by 10^x to get:<BR>\n" );
document.write( "10^x(2y) = 10^2x-1<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "[10^x]^2 - [10^x](2y) + 1 = 0<BR>\n" );
document.write( "Use the Quadratic Formula:\r<BR>\n" );
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document.write( "10^x = [2y +- sqrt((2y)^2-4*1*1)]/2<BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "10^x = [2y +- sqrt(4y^2-4)]/2<BR>\n" );
document.write( "10^x = y +- sqrt(y^2-1)<BR>\n" );
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document.write( "Solve for \"x\" : x = log[y +- sqrt(y^2-1)]<BR>\n" );
document.write( "Solve for \"y\" : y = 10^x + sqrt(y^2-1)<BR>\n" );
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document.write( "b. y= (e^x +e^-x) / (2)<BR>\n" );
document.write( "2y = (e^x + 1/e^x)<BR>\n" );
document.write( "Multiply thru by e^x to get:<BR>\n" );
document.write( "(2y)e^x = e^2x + 1<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "e^2x -(2y)^x + 1 = 0<BR>\n" );
document.write( "Use Quadratic Formula:<BR>\n" );
document.write( "e^x = [2y +- sqrt((2y)^2-4*1*!)]/2<BR>\n" );
document.write( "e^x = [2y +- sqrt(4y^2-4)]/2<BR>\n" );
document.write( "e^x = [y +- sqrt(y^2-1)]<BR>\n" );
document.write( "Solve for x: x = ln[y +- sqr(y^2-1)]<BR>\n" );
document.write( "Solve for y: y = e^x + sqrt(y^2-1)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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