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If a varies directly as b and c and inversely as d , find the constant of variation when =6 and b=5, c=4 and d=10

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KAntoineDoixgo

✏️MATH VARIATIONS

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[tex] \underline{\mathbb{PROBLEM}:} [/tex]

  • If a varies directly as b and c and inversely as d, find the constant of variation when a=6 and b=5, c=4 and d=10

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[tex] \underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad\LARGE » \tt\: \green{k = 3} [/tex]

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[tex] \underline{\mathbb{SOLUTION}:} [/tex]

» Make an equation of the variation.

  • [tex] a = \frac{kbc}{d} \\ [/tex]

» Find the value of [tex] k [/tex] in which it is the constant of the variation.

  • [tex] 6 = \frac{k(5)(4)}{10} \\ [/tex]

  • [tex] 6 = \frac{20k}{10} \\ [/tex]

  • [tex] 6 = 2k [/tex]

  • [tex] \frac{\,6\,}{2} = \frac{\cancel2k}{\cancel2} \\ [/tex]

  • [tex] 3 = k [/tex]

[tex] \therefore [/tex] The value of [tex] k [/tex] or the constant of the variation is 3.

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(ノ^_^)ノ

Eloudlygo

[tex]\sf\red{= = = = = = = = = = = == = = = = = = = = = =}[/tex]

[tex] \large \red{ \tt Problem:}[/tex]

  • If a varies directly as b and c and inversely as d , find the constant of variation when =6 and b=5, c=4 and d=10

[tex] \red{ \large \tt Answer: }[/tex]

[tex] \blue{ \boxed { \large{ \pink{ \boxed{ \red{ \bold{K = 3}}}}}}}[/tex]

[tex]\sf\red{= = = = = = = = = = = == = = = = = = = = = =}[/tex]

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[tex] \red{ \rm \#CarryOnLearning}[/tex]

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