document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018075>Question 1018075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that u^2 is directly proportional to cube of w.find the value of w when u=27,if u=8 when u=8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634261 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=634261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula for direct variation is y = kx\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = u^2 and x = w^3, this formula becomes u^2 = k * w^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when u = 8 and w = 8,m this formula becomes 8^2 = k * 8^3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for k to get k = 8^2 / 8^3 = 1/8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when u = 27 and k = 1/8, the formula becomes 27^2 = 1/8 * w^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by 8 to get 27^2 * 8 = w^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the cube root of each side of this equation to get cube root of (27^2 * 8) = cube root of (w^3).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get cube root of (27^2 * 8) = w.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be expressed as cube root of (27 * 27 * 8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since cube root of 27 is 3 and cube root of 8 is 2, this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cube root of (3^3 * 3^3 * 2^3) which can then be expressed as cube root of (3^3) * cube root of (3^3) * cube root of (2^3) which can then be expressed as 3 * 3 * 2 which is equal to 18.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cube root of (27^2 * 8) is equal to 18.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can use your calculator to confirm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when u = 27, w is equal to 18.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get u^2 = k * w^3 becomes 27^2 = 1/8 * 18^3 which becomes 729 = 5832 / 8 which becomes 729 = 729.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this ocnfirms the solution is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );