document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762427>Question 762427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12 8 14 18 _____\r<BR>\n" );
document.write( "\n" );
document.write( "whts d nxt numbr...???? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463944 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Presume that 0 maps to 12, 1 maps to 8, 2 to 14 and 3 to 18, then with 4 points you can uniquely define a 3rd degree polynomial.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \gamma(x)\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So if the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (0, 12)\"> is on the graph, then\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \gamma(0)\ =\ a(0)^3\ +\ b(0)^2\ +\ c(0)\ +\ d\ =\ 12\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Which is to say <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\ =\ 12\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, if the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (1, 8)\"> is on the graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \gamma(1)\ =\ a(1)^3\ +\ b(1)^2\ +\ c(1)\ +\ d\ =\ 8\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or simplified:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ +\ d\ =\ 8\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using similar reasoning, write the next two linear equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8a\ +\ 4b\ +\ 2c\ +\ d\ =\ 14\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 27a\ +\ 9b\ +\ 3c\ +\ d\ =\ 18\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we know the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d\">, we can simplify this to a 3X3 system:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ -4\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8a\ +\ 4b\ +\ 2c\ =\ 2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 27a\ +\ 9b\ +\ 3c\ =\ 6\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve the 3X3 linear system to determine the values of the coefficients for \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \gamma(x)\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ 12\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \gamma(4)\"> to determine the next number in the sequence.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By the way, next time you post show us a little respect by using the English language correctly instead of of using your nearly unintelligible teenager text-speak.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );