make-r-the-subject-of-the-formula-y-pr-m-p-3-1-3-2-find-r-if-y-8-m-1-p-3-

Question Number 171437 by solomonwells last updated on 15/Jun/22

make r the subject of the formula

y = {(\frac{pr}{m} - \frac{p^{3}}{1})}^{- 3 / 2}

find r if y = - 8, m = - 1, p = 3

Answered by alephzero last updated on 15/Jun/22

y = {(\frac{p r}{m} - p^{3})}^{- 3 / 2}

\Rightarrow y^{- 2 / 3} = \frac{p r}{m} - \frac{{m p}^{3}}{m}

\Rightarrow y^{- 2 / 3} = \frac{p r - {m p}^{3}}{m}

\Rightarrow {m y}^{- 2 / 3} = p r - {m p}^{3}

\Rightarrow p r = {m y}^{- 2 / 3} + {m p}^{3}

\Rightarrow r = \frac{{m y}^{- 2 / 3} + {m p}^{3}}{p}

Commented by alephzero last updated on 17/Jun/22

y = - 8, m = - 1, p = 3

\Rightarrow r = \frac{- {(- 8)}^{- 2 / 3} - 3^{3}}{3} =

= - \frac{\sqrt[3]{{(- 8)}^{2}} - 27}{3} = - \frac{\sqrt[3]{64} - 27}{3} =

= - \frac{4 - 27}{3} = \frac{27 - 4}{3} = \frac{23}{3} = 7 \frac{2}{3}

Answered by elviselloin719A last updated on 18/Jun/22

A n s : 7.667