Answered

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If m varies directly as n and inversely o, when m = 8, n = 4 and o = 2,

find m, when n = 14 and o = 7.

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Sagot :

KAntoineDoixidn

✒️VARIATIONS

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

  • If m varies directly as n and inversely o, when m = 8, n = 4 and o = 2, find m, when n = 14 and o = 7.

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

[tex] \qquad \Large \: \rm{m = 8} [/tex]

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

» Formulate the equation of a combined variation in which k is the constant of the variation.

  • [tex] m = \frac{\,kn\,}{o} \\ [/tex]

» Find the constant.

  • [tex] 8 = \frac{\,k(4)\,}{2} \\ [/tex]

  • [tex] 8 = k(2) \\ [/tex]

  • [tex] \frac{\,8\,}{2} = \frac{\,k(2)\,}{2} \\ [/tex]

  • [tex] 4 = k [/tex]

» The constant is 4. Find m when n is 14 and o is 7

  • [tex] m = \frac{\,4n\,}{o} \\ [/tex]

  • [tex] m = \frac{\,4(14)\,}{7} \\ [/tex]

  • [tex] m = \frac{\,56\,}{7} \\ [/tex]

  • [tex] m = 8 [/tex]

[tex] \therefore [/tex] The value of m is 8

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