es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

100= 4/3 pir^3

Solución

100 = \frac{4}{3} π r^{3}

Solución

r = 3 \frac{75}{π}, r = - \frac{3 75 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}, r = - \frac{3 75 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}

Pasos de solución

100 = \frac{4}{3} π r^{3}

Intercambiar lados

\frac{4}{3} π r^{3} = 100

Simplificar

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 100

Multiplicar ambos lados por

3

4 π r^{3} = 300

Dividir ambos lados entre

4 π

r^{3} = \frac{75}{π}

Para

x^{3} = f (a)

las soluciones son

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

r = 3 \frac{75}{π}, r = 3 \frac{75}{π} \frac{- 1 + 3 i}{2}, r = 3 \frac{75}{π} \frac{- 1 - 3 i}{2}

Simplificar

3 \frac{75}{π} \frac{- 1 + 3 i}{2} : - \frac{3 75 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}

Simplificar

3 \frac{75}{π} \frac{- 1 - 3 i}{2} : - \frac{3 75 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}

r = 3 \frac{75}{π}, r = - \frac{3 75 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}, r = - \frac{3 75 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 25 π ^{\frac{2}{3}}}{2 π}

Gráfica

Ejemplos populares

z^{4} - 81 = 0

5 x^{3} = 6

x^{2} x + 3 x = 5 x

54 x^{4} - 3 x^{2} - 1 = 0

2x^4-x^3-2x+23x=-2

2 x^{4} - x^{3} - 2 x + 23 x = - 2