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r varies inversely as the square of s, when r = 1 then s = 2.

Sagot :

INVERSE VARIATION

[tex] \\ \bold{ GIVEN: } \\ [/tex]

[tex] \\ \bold{ \sf{r \: varies \: inversely \: as \: the \: square \: of \: s}} \\ \\ \implies \: \texttt{r = 1 \: and \: s = 2} \\ [/tex]

[tex] \\ r = \frac{k}{ {s}^{2} } \\ [/tex]

Evaluate values

[tex] \\ 1 = \frac{k}{ {(2)}^{2} } \\ [/tex]

Square 2

[tex] \\ 1 = \frac{k}{4} \\ [/tex]

Multiply 4 to both sides

[tex] \\ (4)(1) = \frac{k}{4} (4) \\ [/tex]

Cancel both 4 from the right side

[tex] \\ (4)(1) = \frac{k}{ \cancel4} ( \cancel4) \\ [/tex]

Multiply 4 by 1

[tex] \\ \large\boxed{ \green{ \sf{k = 4}}} \\ \\ \\ \\ [/tex]

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