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The cube root of our varies inversely with the square of S which to equations model this relationship?

The cube root of our varies inversely with the square of S which to equations model-example-1

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The question states as follows;

"The cube root of r varies inversely with the square of s."

The general form of an inverse relationship is shown below;


y=(k)/(x)

Substituting the variables, we would now have;


\sqrt[3]{r}=(k)/(s^2)

Therefore, the third option is correct.

Also;


\begin{gathered} \sqrt[3]{r}=(k)/(s^2) \\ \text{Observe that}_{} \\ \sqrt[3]{r}=r^{(1)/(3)} \end{gathered}

Therefore, we can alo have the expression;


\begin{gathered} r^{(1)/(3)}=(k)/(s^2) \\ \text{Cross multiply, and we'll have;} \\ s^2r^{(1)/(3)}=k \end{gathered}

The fifth option is also correct.

ANSWER:

The third and fifth options are both correct models of the inverse relationship given.

User Unixmiah
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