Given that y varies jointly as the square of x and the square of z.
When:
• x = 3
,
• z = 4
,
• y = 72
Let's write an equation describing the relationship of the given varibles.
In this case, we are to make use of the joint variation equation:
y = kx²z²
Where k is the constant of proportionality.
Let's find the value of k.
To solve for k, substitute the given values of the variables into the equation.
We have:
y = kx²z²
72 = 3²×4²×k
72 = 9 × 16 × k
72 = 144k
Divide both sides by 144:
[tex]\begin{gathered} \frac{72}{144}=\frac{144k}{144} \\ \\ 0.5=k \\ \\ k=0.5 \end{gathered}[/tex]
Therefore, the constant of variation, k, is 0.5
The equation describing the relationship will be:
y = 0.5x²z²
ANSWER:
[tex]y=0.5x^2z^2^{}[/tex]
