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Answered

if y varies inversly as x and y=1/5 when x=9, find y when x=-3 ​

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KAntoineDoixgo

✒️VARIATIONS

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

  • if y varies inversely as x and y=1/5 when x=9, find y when x=-3

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

[tex] \qquad \LARGE \: \rm{y = \text- \frac{\,3\,}{5}} \\ [/tex]

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

» Formulate an equation of an inverse variation in which k is the constant of the variation.

  • [tex] y = \frac{\,k\,}{x} \\ [/tex]

» Find the constant.

  • [tex] \frac{\,1\,}{5} = \frac{\,k\,}{9} \\ [/tex]

  • [tex] 5k = 9 [/tex]

  • [tex] \frac{5k}{5} = \frac{\,9\,}{5} \\ [/tex]

  • [tex] k = \frac{\,9\,}{5} \\ [/tex]

» Find y when x is -3.

  • [tex] y = \frac{\,9\,}{5} \div x \\ [/tex]

  • [tex] y = \frac{\,9\,}{5} \div (\text-3) \\ [/tex]

  • [tex] y = \frac{\,9\,}{5} \cdot \bigg(\text-\frac{\,1\,}{3}\bigg) \\ [/tex]

  • [tex] y = \text-\frac{9}{15} \\ [/tex]

  • [tex] y = \text-\frac{3}{5} \\ [/tex]

[tex] \therefore [/tex] The value of y is -3/5

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(ノ^_^)ノ

JuniorZxgo

✒️[tex]\large \bold{QUESTION} [/tex]

If y varies inversly as x and y = 1/5 when x = 9, find y when x = -3

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✒️[tex]\large \bold{ANSWER} [/tex]

[tex]y = - \frac{3}{5} [/tex]

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✒️[tex]\large \bold{SOLUTION} [/tex]

Step 1 : Formulate

Base on the given conditions, formulate:

[tex]y = \frac{k}{x} [/tex]

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Step 2 : Subtitute

  • [tex]y = \frac{1}{5} [/tex]
  • [tex]x = 9[/tex]
  • [tex]into \: y = \frac{k}{x} [/tex]

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Step 3 : Solve the Equation

  • [tex] \frac{1}{5} = \frac{k}{9} [/tex]
  • [tex] \frac{k}{9} = \frac{1}{5} [/tex]
  • [tex]k = \frac{1}{5} \times 9[/tex]
  • [tex]k = \frac{9}{5} [/tex]

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Step 4 : Find the Function

Find the equation of the function.

  • [tex]y = \frac{9}{5x} [/tex]

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Step 5 : Subtitute

Subtitute x = -3 into [tex]y = \frac{9}{5x} [/tex]

  • [tex]y = \frac{9}{5x( - 3)} [/tex]

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Step 6 : Solve the Equation

  • [tex]y = \frac{9}{5x( - 3)} [/tex]
  • [tex]y = - \frac{ 9}{5x + 3} [/tex]
  • [tex]y = \frac{9}{15} [/tex]
  • [tex]y = - \frac{ 3}{5} [/tex]

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  • So the Correct Answer is [tex]y = - \frac{ 3}{5} [/tex]