[tex]y\text{ = }\frac{1}{2}x^2z^2[/tex]
Explanation:
Given:
y varies jointly as the square of x and square of z
Mathematically:
[tex]\begin{gathered} y\text{ }\propto x^2z^2 \\ To\text{ equate the expression:} \\ y\text{ = k}x^2z^2 \\ \text{where k = constant of proportionality} \end{gathered}[/tex]
when x = 3 and z = 4, y = 72
We need to find the value of the constant of proportionality, k
Substitute for x, y and z in the equation above:
[tex]\begin{gathered} 72=k(3^2)(4^2) \\ 72\text{ = k(9)(16)} \\ 72\text{ = }144k \\ \\ \text{divide both sides by 144:} \\ \frac{72}{144}\text{ = }\frac{144k}{144} \\ k\text{ = 1/2} \end{gathered}[/tex]
The equation showing the relationship between x, y, and z:
[tex]y\text{ = }\frac{1}{2}x^2z^2[/tex]
