Question

How do you rewrite the formula to solve for r?

Answer 1

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) } }`

Answer 2

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) } }`