Respuesta :

CHERLYNnotCHERRY

Answer:

The answer is C.

The steps are :

[tex] {T}^{2} = ( \frac{4 {\pi}^{2} }{GM} ) \times {r}^{3} [/tex]

[tex] {T}^{2} \div ( \frac{4 {\pi}^{2} }{GM}) = {r}^{3} [/tex]

[tex] {T}^{2} \times \frac{GM}{4 {\pi}^{2} } = {r}^{3} [/tex]

[tex] \frac{GM {T}^{2} }{4 {\pi}^{2} } = {r}^{3} [/tex]

[tex] \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } = r[/tex]

[tex]r = \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } [/tex]

Answer :

C

[tex]r = \sqrt[3]{ \frac{ {T}^{2}GM} {4 {\pi}^{2} } } [/tex]

Step-by-step-explanation :

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

[tex] {t}^{2} gm = 4 {\pi}^{2} {r}^{3} \\ \frac{ {t}^{2} gm}{4 {\pi}^{2} } = \frac{4 {\pi}^{2} {r}^{3} }{4 {\pi}^{2} } [/tex]

[tex] {r}^{3} = \frac{ {t}^{2} gm}{4 {\pi}^{2} } [/tex]

[tex] \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } = \sqrt[3]{r} [/tex]

[tex]r = \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } [/tex]

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