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Popular >

10x^3=(4/3)pia^3

Solution

10 x^{3} = (\frac{4}{3}) π a^{3}

Solution

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Solution steps

10 x^{3} = (\frac{4}{3}) π a^{3}

Divide both sides by

10

x^{3} = \frac{2 π a ^{3}}{15}

For

x^{3} = f (a)

the solutions are

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

x = 3 \frac{2 π a ^{3}}{15}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2}

Simplify

3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Simplify

3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Graph

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