Answer:
The value of x is 108.
Step-by-step explanation:
Mathematical Equation:
[tex]\LARGE\text{$x=\frac{ky^2}{z}$}[/tex]
For the constant of variation (y):
Given: [tex]x=12[/tex], [tex]y=3[/tex], [tex]z=6[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]x=\frac{ky^2}{z}[/tex]
[tex]x=\frac{ky^2}{z}[/tex]
[tex]12=\frac{(3)^2k}{6}[/tex]
[tex](12)(6)=9k[/tex]
[tex]72=9k[/tex]
[tex]\frac{72}{9}=\frac{9k}{9}[/tex]
[tex]\boldsymbol{8=k}[/tex]
For the value of x:
Given: [tex]k=8[/tex], [tex]y=9[/tex], [tex]z=6[/tex]
Find: [tex]x=?[/tex]
Formula: [tex]x=\frac{ky^2}{z}[/tex]
Solution:
[tex]x=\frac{ky^2}{z}[/tex]
[tex]x=\frac{(8)(9)^2}{6}[/tex]
[tex]x=\frac{(8)(81)}{6}[/tex]
[tex]x=\frac{648}{6}[/tex]
[tex]\boxed{\boldsymbol{x=108}}[/tex]
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