Question 1059524
z varies directly as x^2  and inversely as y^2 .  If  z = 165  
when x = 4  and  y = 7 , find z  if x = 9  and y = 6 .  (Round 
off your answer to the nearest hundredth.) 
<pre><font size = 4><b>
For all proportion problems, start with this:

Varying           "directly" or product of "jointlys" or 1 if none 
quantity  = k · ----------------------------------------------------------
                inversely variable or product of "inverselys" or 1 if none

In this problem the varying quantity is z.
We have one "directly", x².  We have one inversely, y².  So we have x² 
on top and y² on the bottom:

z = k·{{{x^2/y^2}}}

one set of values is</pre>z = 165  when x = 4  and  y = 7<pre>

Substitute these values:

165 = k·{{{4^2/7^2}}}

165 = k·{{{16/49}}}

Multiply both sides by {{{49/16}}}

{{{8085/16}}} = k

Now substitute {{{8085/16}}} for k in the first equation:

z = k·{{{x^2/y^2}}}

z = {{{8085/16}}}·{{{x^2/y^2}}}

>>...find z  if x = 9  and y = 6 ...<<

Substitute those values

z = {{{8085/16}}}·{{{9^2/6^2}}}

z = {{{8085/16}}}·{{{81/36}}}

z = 1136.953125

Round to

z = 1136.95

Edwin</pre>