document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275518>Question 275518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships.\r<BR>\n" );
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document.write( "1.   z varies inversely with x and directly with y.  (1 point)\r<BR>\n" );
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document.write( "2.   z varies jointly with x and y  (1 point)\r<BR>\n" );
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document.write( "3.   z varies directly with x and inversely with the square of y  (1 point)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200942 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=200942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem states:\r<BR>\n" );
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document.write( "When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships.\r<BR>\n" );
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document.write( "1. z varies inversely with x and directly with y. (1 point)\r<BR>\n" );
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document.write( "formula would be z = ky/x\r<BR>\n" );
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document.write( "substitute:\r<BR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "z = 42\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "42 = k*3/2 **************************************************\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 2*42/3 = 28\r<BR>\n" );
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document.write( "2. z varies jointly with x and y (1 point)\r<BR>\n" );
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document.write( "formula is z = kxy\r<BR>\n" );
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document.write( "substitute:\r<BR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "z = 42\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "42 = k*2*3 *******************************************************\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 42/6 = 7\r<BR>\n" );
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document.write( "3. z varies directly with x and inversely with the square of y (1 point) \r<BR>\n" );
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document.write( "formula is:\r<BR>\n" );
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document.write( "z = kx/y^2\r<BR>\n" );
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document.write( "substitute:\r<BR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "z = 42\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "42 = k*2/(3^2) = k*2/9 ************************************************\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 42*9/2 = 189\r<BR>\n" );
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document.write( "they did not ask you to solve the equations.\r<BR>\n" );
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document.write( "they only asked you to write the functions.\r<BR>\n" );
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document.write( "functions with the ****************************************** next to them should be your answers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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