How do you rewrite the formula to solve for r?

Question 1

Question 2

Answer :

C

$r = \sqrt[3]{ \frac{ {T}^(2)GM} {4 {\pi}^(2) } }$

Step-by-step-explanation :

${t}^(2) = ( \frac{4 {\pi}^(2) }{gm} ) {r}^(3) \\ {t}^(2) = \frac{4 {\pi}^(2) {r}^(3) }{gm}$

${t}^(2) gm = 4 {\pi}^(2) {r}^(3) \\ \frac{ {t}^(2) gm}{4 {\pi}^(2) } = \frac{4 {\pi}^(2) {r}^(3) }{4 {\pi}^(2) }$

${r}^(3) = \frac{ {t}^(2) gm}{4 {\pi}^(2) }$

$\sqrt[3]{ \frac{ {t}^(2) gm}{4 {\pi}^(2) } } = \sqrt[3]{r}$

$r = \sqrt[3]{ \frac{ {t}^(2) gm}{4 {\pi}^(2) } }$

Question 3

Answer:

The answer is C.

The steps are :

${T}^(2) = ( \frac{4 {\pi}^(2) }{GM} ) * {r}^(3)$

${T}^(2) / ( \frac{4 {\pi}^(2) }{GM}) = {r}^(3)$

${T}^(2) * \frac{GM}{4 {\pi}^(2) } = {r}^(3)$

$\frac{GM {T}^(2) }{4 {\pi}^(2) } = {r}^(3)$

$\sqrt[3]{ \frac{GM {T}^(2) }{4 {\pi}^(2) } } = r$

$r = \sqrt[3]{ \frac{GM {T}^(2) }{4 {\pi}^(2) } }$

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