What are the solutions to the equation 972pi= 4/3 pir^3 ?

The solutions to the equation 972pi= 4/3 pir^3 are r=9,r=-9/2+(9sqrt(3))/2 i,r=-9/2-(9sqrt(3))/2 i

Find the zeros of 972pi= 4/3 pir^3

The zeros of 972pi= 4/3 pir^3 are r=9,r=-9/2+(9sqrt(3))/2 i,r=-9/2-(9sqrt(3))/2 i

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972 π = \frac{4}{3} π r^{3}

r = 9, r = - \frac{9}{2} + \frac{9 3}{2} i, r = - \frac{9}{2} - \frac{9 3}{2} i

Solution steps

972 π = \frac{4}{3} π r^{3}

Switch sides

\frac{4}{3} π r^{3} = 972 π

Simplify

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 972 π

Multiply both sides by

3

4 π r^{3} = 2916 π

Divide both sides by

4 π

r^{3} = 729

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}

r = 3729, r = 3729 \frac{- 1 + 3 i}{2}, r = 3729 \frac{- 1 - 3 i}{2}

3729 = 9

Simplify

3729 \frac{- 1 + 3 i}{2} : - \frac{9}{2} + \frac{9 3}{2} i

Simplify

3729 \frac{- 1 - 3 i}{2} : - \frac{9}{2} - \frac{9 3}{2} i

r = 9, r = - \frac{9}{2} + \frac{9 3}{2} i, r = - \frac{9}{2} - \frac{9 3}{2} i

13 x^{3} + 182 x^{2} - 184 x + 2503 = 0

x^{4} + 2 x^{3} - x^{2} - 6 x - 3 = 0

x^{4} - 17 x^{2} = - 16

x^{3} - 5 x - 1 = 0

4 x^{9} - 4 x = 0

What are the solutions to the equation 972pi= 4/3 pir^3 ?
The solutions to the equation 972pi= 4/3 pir^3 are r=9,r=-9/2+(9sqrt(3))/2 i,r=-9/2-(9sqrt(3))/2 i
Find the zeros of 972pi= 4/3 pir^3
The zeros of 972pi= 4/3 pir^3 are r=9,r=-9/2+(9sqrt(3))/2 i,r=-9/2-(9sqrt(3))/2 i