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If p varies directly as the square of q and inversely as the square root of r, and p=60 when q=6 and r=81, find p when q=8 and r=144.

Sagot :

ARMYLidn

If p varies directly as the square of q and inversely as the square root of r, and p=60 when q=6 and r=81

[tex] \\ [/tex]

Formula:

[tex]p = \frac{k {q}^{2} }{ \sqrt{r} } [/tex]

Evaluate the given values

[tex]60 = \frac{k {(6)}^{2} }{ \sqrt{81} } [/tex]

Simplify

[tex]60 = \frac{k(36)}{9} [/tex]

Multiply 9 both sides

[tex](9)60 = \frac{k(36)}{9} (9)[/tex]

[tex](9)60 = \frac{k(36)}{ \cancel{9}} ( \cancel{9})[/tex]

[tex]540 = k(36)[/tex]

Divide both sides by 36

[tex] \frac{540}{36} = \frac{k(36)}{36} [/tex]

[tex] \frac{540}{36} = \frac{k( \cancel{36})}{ \cancel{36} }[/tex]

[tex]k = \frac{540}{36} [/tex]

[tex] \green{ \boxed{ \bold{k = 15}}}[/tex]

Find p when q=8 and r=144

Use k=15

[tex]p = \frac{k {q}^{2} }{ \sqrt{r} } [/tex]

[tex]p = \frac{(15) {(8)}^{2} }{ \sqrt{144} } [/tex]

Simplify

[tex]p = \frac{(15)(64)}{12} [/tex]

Multiply

[tex]p = \frac{960}{12} [/tex]

[tex]p = \frac{960}{12} [/tex]

Divide

[tex] \green{ \boxed{ \boxed{ \bold{p = 80}}}}[/tex]