Answer:
The value of y is 8.
Step-by-step explanation:
Mathematical Equation:
[tex]\LARGE\text{$y=\frac{kx^2}{z}$}[/tex]
For the constant of variation (k):
Given: [tex]y=1[/tex], [tex]x=2[/tex], [tex]z=10[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]y=\frac{kx^2}{k}[/tex]
Solution:
[tex]y=\frac{kx^2}{y}\\1=\frac{(2)^2k}{10}\\1=\frac{4k}{10}\\4k=(10)(1)\\4k=10\\\frac{4k}{4}=\frac{10}{4}\\k=\frac{10}{4}\\\boldsymbol{k=\frac{5}{2}}[/tex]
For the value of y:
Given: [tex]k=\frac{5}{2}[/tex], [tex]x=4[/tex], [tex]z=5[/tex]
Find: [tex]y=?[/tex]
Formula: [tex]y=\frac{kx^2}{z}[/tex]
Solution:
[tex]y=\frac{kx^2}{z}\\y=\frac{(\frac{5}{2})(4)^2}{5}\\y=\frac{(\frac{5}{2})(16)}{5}\\y=\frac{(5)(8)}{5}\\\boxed{\boldsymbol{y=8}}[/tex]
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