Step-by-step explanation:
If two objects vary directly, we just divide those two objects.
If two objects vary indirectly, we multiply them.
So here we have
[tex] \frac{v}{ {x}^{2} } {y}^{3} = k[/tex]
where k is a constant.
So let analyze when all variables Except k is given.
[tex] \frac{2}{16} (27) = 3.375[/tex]
So k=3.375
[tex] \frac{v}{ {3}^{2} } (2 {}^{3} ) = 3.375[/tex]
[tex] \frac{v}{9} (8) = 3.375[/tex]
[tex] \frac{v}{9} (8) = \frac{27}{8} [/tex]
[tex]v8 = \frac{243}{8} [/tex]
[tex]v = \frac{243}{64} [/tex]
[tex]3.796875[/tex]
