z = 1/2
Explanation:[tex]\begin{gathered} z\text{ }\alpha\text{ x} \\ z\text{ }\alpha\text{ 1/}y^2 \end{gathered}[/tex]
combining both:
[tex]\begin{gathered} z\text{ }\alpha x/y^2 \\ z\text{ = }\frac{kx}{y^2} \\ \text{where k = constant of proportionality} \\ \text{and }\alpha\text{ means varies } \end{gathered}[/tex]
when z = 12, x = 3, y = 1
Inserting the values, we get k:
[tex]\begin{gathered} 12\text{ = }\frac{k(3)}{1^2} \\ 12\text{= }\frac{3k}{1} \\ 12\text{ = 3k} \\ k\text{ = 12/3} \\ k\text{ = 4} \end{gathered}[/tex][tex]z\text{ = }\frac{4x}{y^2}\text{ (relationship connnecting the variables)}[/tex]
when x = 8, y = 8, z= ?
[tex]\begin{gathered} \text{Inserting into the relationship:} \\ z\text{ = }\frac{4(8)}{8^2} \\ z\text{ = }\frac{32}{64} \\ z\text{ = 1/2} \end{gathered}[/tex]
