What are the solutions to the equation 30pir^2+4pir^3=4500 ?

The solutions to the equation 30pir^2+4pir^3=4500 are r\approx 5.29111…

Find the zeros of 30pir^2+4pir^3=4500

The zeros of 30pir^2+4pir^3=4500 are r\approx 5.29111…

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30 π r^{2} + 4 π r^{3} = 4500

r \approx 5.29111 \dots

Solution steps

30 π r^{2} + 4 π r^{3} = 4500

Move

4500

to the left side

30 π r^{2} + 4 π r^{3} - 4500 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 π r^{3} + 30 π r^{2} - 4500 = 0

Find one solution for

12.56637 \dots r^{3} + 94.24777 \dots r^{2} - 4500 = 0

using Newton-Raphson:

r \approx 5.29111 \dots

Apply long division:

\frac{4 π r ^{3} + 30 π r ^{2} - 4500}{r - 5.29111 \dots} = 12.56637 \dots r^{2} + 160.73788 \dots r + 850.48249 \dots

12.56637 \dots r^{2} + 160.73788 \dots r + 850.48249 \dots \approx 0

Find one solution for

12.56637 \dots r^{2} + 160.73788 \dots r + 850.48249 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solution is

r \approx 5.29111 \dots

2 m^{3} - 250 = 0

7 x^{4} + 2 = 8 x^{4} + 10

4 x^{3} + 16 x^{2} + 19 x + 5 = 0

- x^{3} - 3 x^{2} + 32 x - 60 = 0

4 x^{3} + 4 x^{2} - 21 x + 9 = 0

What are the solutions to the equation 30pir^2+4pir^3=4500 ?
The solutions to the equation 30pir^2+4pir^3=4500 are r\approx 5.29111…
Find the zeros of 30pir^2+4pir^3=4500
The zeros of 30pir^2+4pir^3=4500 are r\approx 5.29111…