COMBINED VARIATION
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Solve:
[tex]\implies \sf \large x = \frac{k {y}^{2} }{z} \\ [/tex]
[tex]\large \tt \red{given} \begin{cases} \sf \: x = 12 \\ \sf \: y = 3 \\ \sf \: z = 6\end{cases} \\ \\ [/tex]
[tex]\implies \sf \large 12 = \frac{k {(3)}^{2} }{6} \\ [/tex]
[tex]\implies \sf \large 12 = \frac{k (9) }{6} \\ [/tex]
[tex]\implies \sf \large 12 \times \frac{6}{9} = \frac{k (9) }{6} \times \frac{6}{9} \\ [/tex]
[tex]\implies \sf \large \frac{72}{9} = \frac{k ( \cancel{54}) }{ \cancel{54}} \\ [/tex]
[tex]\implies \sf \large \therefore \: k = 8 [/tex]
[tex] \: [/tex]
[tex]\large \tt \red{given(2)} \begin{cases} \sf \: k = 8 \\ \sf \: y = 9 \\ \sf \: z = 6\end{cases} \\ \\ [/tex]
[tex]\implies \sf \large x = \frac{8( {9)}^{2} }{6} \\ [/tex]
[tex]\implies \sf \large x = \frac{8(81) }{6} \\ [/tex]
[tex]\implies \sf \large x = \frac{648 }{6} \\ [/tex]
[tex]\implies \sf \large \therefore \: \orange{ x = 108 }[/tex]
[tex] \: [/tex]
Final Answer:
[tex] \large\implies \sf \huge \orange{ x = 108 }[/tex]
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