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if x varies inversely as y and x =8 when y=2,find d when y =4.

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Problem: If x varies inversely as y and x = 8 when y = 2, find x when y = 4.

Solution: Make the equation for inverse variation in which k is the constant.

  • [tex] \begin{gathered} x = \frac{k}{y} \end{gathered}[/tex]

- Find the constant.

  • [tex] \begin{gathered} 8 = \frac{k}{2} \end{gathered}[/tex]

  • [tex] \begin{gathered} 8 \cdot 2= \frac{k}{2} \cdot2 \end{gathered}[/tex]

  • [tex] \begin{gathered} 8 \cdot 2= \frac{k}{ \cancel2} \cdot \cancel2 \end{gathered}[/tex]

  • [tex]8 \cdot2 = k[/tex]

  • [tex]k = 16[/tex]

- Find x when y = 4.

  • [tex] \begin{gathered} x = \frac{16}{4} \end{gathered}[/tex]

  • [tex]x = 4[/tex]

- Therefore, the value of x is:

  • [tex] \large \boxed{ \sf{ \green{ \: \: 4\: \: }}}[/tex]

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