document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166394>Question 166394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following question:<BR>\n" );
document.write( "Find an equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x=-0.5, z=4, and w=5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122644 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y varies jointly as x and z means y = k*x*z (equation 1)<BR>\n" );
document.write( "y varies inversely as square of w means y = k/w^2 (equation 2)<BR>\n" );
document.write( "y varies jointly as x and z, and inversely as w^2 means y = k*x*z/w^2 (equation 3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "given y = 20 when x = -.5, z = 4, and w = 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plug these into equation 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "20 = k*((-.5)*(4))/(5^2)<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "20 = -2*k/25<BR>\n" );
document.write( "multiply both sides of equation by 25<BR>\n" );
document.write( "25*20 = -2*k<BR>\n" );
document.write( "simplify<BR>\n" );
document.write( "500 = -2*k<BR>\n" );
document.write( "divide both sides of equation by 2<BR>\n" );
document.write( "250 = -k<BR>\n" );
document.write( "multiply botrh sides of equation by -1<BR>\n" );
document.write( "-250 = k<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "k = -250<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now that you have k, plug it back into the equation to see that it is correct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "20 = [-250*(-.5)*(4)]/25<BR>\n" );
document.write( "20 = [-250*(-2)]/25<BR>\n" );
document.write( "20 = 500/25<BR>\n" );
document.write( "20 = 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is how it works:<BR>\n" );
document.write( "k = constant of proportionality.<BR>\n" );
document.write( "if y varies directly with x, then y = k*x<BR>\n" );
document.write( "if y varies directly ,and jointly, with x and z, then y = k*x*z<BR>\n" );
document.write( "if y varies inversely with x, then y = k/x<BR>\n" );
document.write( "if y varies inversely with x^2, then y = k/x^2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );