Question 960784
To review:

    "{{{y}}} varies as {{{x}}}" means {{{y = kx}}}

    "{{{y}}} varies jointly as {{{x}}} and {{{y}}}" means {{{y = kxy}}}

    "{{{y}}} varies as {{{x + y}}}" means {{{y = k(x + y)}}}

    "{{{y}}} varies inversely as {{{x}}}" means {{{y  = k/x}}}


find the equation of variation:

 if {{{y }}} varies jointly as {{{w }}}and the {{{x^2}}}, then
{{{y =kwx^2}}}

 and if{{{y }}} varies  inversely  as {{{z}}}, then
{{{y =kwx^2/z}}}

and if {{{ y=9 }}}when {{{x=5}}}, {{{x=3}}} and {{{z=10}}}, we have

{{{9 =kw*5^2/10}}}

{{{90 =kw*25}}}

{{{90/25 =kw}}}

{{{kw=18/5 }}}

{{{kw=3.6}}}
{{{w=3.6/k}}}


{{{9 =kw*3^2/10}}}

{{{90 =kw*9}}}

{{{90/9 =kw}}}

{{{w=10k}}}

find k
{{{3.6/k=10k}}}
{{{3.6=10k^2}}
{{{3.6/10=k^2}}
{{{0.36=k^2}}
{{{k=sqrt(0.36)}}}
{{{k=0.6}} or {{{k=-0.6}} 

now find {{{w}}}

{{{w=10k}}}=>{{{w=10*0.6}}}=>{{{w=6}}}
or
{{{w=10k}}}=>{{{w=10*(-0.6)}}}=>{{{w=-6}}}

so, {{{y =0.6*6x^2/z}}} or {{{y =-0.6*(-6)w^2/z}}} (both are same)

{{{y =3.6x^2/z}}}