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受欢迎的代数 >

371= 4/3 pir^3

解答

371 = \frac{4}{3} π r^{3}

解答

r = 3 \frac{1113}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

求解步骤

371 = \frac{4}{3} π r^{3}

交换两边

\frac{4}{3} π r^{3} = 371

化简

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 371

在两边乘以

3

4 π r^{3} = 1113

两边除以

4 π

r^{3} = \frac{1113}{4 π}

对于

x^{3} = f (a)

解为

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

r = 3 \frac{1113}{4 π}, r = 3 \frac{1113}{4 π} \frac{- 1 + 3 i}{2}, r = 3 \frac{1113}{4 π} \frac{- 1 - 3 i}{2}

化简

3 \frac{1113}{4 π} \frac{- 1 + 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

化简

3 \frac{1113}{4 π} \frac{- 1 - 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

r = 3 \frac{1113}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

作图

流行的例子

x^{3} - x^{2} + x = 6

4/3 pir^3=4pir^2

\frac{4}{3} π r^{3} = 4 π r^{2}

2x^3-26x^2+84x=0

2 x^{3} - 26 x^{2} + 84 x = 0

n c^{3} - n c^{4} = n c^{1}

4m^3-40m^2+36m=0

4 m^{3} - 40 m^{2} + 36 m = 0