What are the solutions to the equation 208pi=2pir^2+2pir^5 ?

The solutions to the equation 208pi=2pir^2+2pir^5 are r\approx 2.50046…

Find the zeros of 208pi=2pir^2+2pir^5

The zeros of 208pi=2pir^2+2pir^5 are r\approx 2.50046…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

208 π = 2 π r^{2} + 2 π r^{5}

r \approx 2.50046 \dots

Solution steps

208 π = 2 π r^{2} + 2 π r^{5}

Switch sides

2 π r^{2} + 2 π r^{5} = 208 π

Move

208 π

to the left side

2 π r^{2} + 2 π r^{5} - 208 π = 0

Write in the standard form

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

2 π r^{5} + 2 π r^{2} - 208 π = 0

Find one solution for

6.28318 \dots r^{5} + 6.28318 \dots r^{2} - 653.45127 \dots = 0

using Newton-Raphson:

r \approx 2.50046 \dots

Apply long division:

\frac{2 π r ^{5} + 2 π r ^{2} - 208 π}{r - 2.50046 \dots} = 6.28318 \dots r^{4} + 15.71090 \dots r^{3} + 39.28460 \dots r^{2} + 104.51308 \dots r + 261.33160 \dots

6.28318 \dots r^{4} + 15.71090 \dots r^{3} + 39.28460 \dots r^{2} + 104.51308 \dots r + 261.33160 \dots \approx 0

Find one solution for

6.28318 \dots r^{4} + 15.71090 \dots r^{3} + 39.28460 \dots r^{2} + 104.51308 \dots r + 261.33160 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solution is

r \approx 2.50046 \dots

x^{3} = 995

a^{6} + \frac{a}{2} = 28

\frac{21 x ^{7}}{2} = 7

(x + 2) (x - 3) (x^{2} + x - 2) = 0

x^{6} = 16 x^{3}

What are the solutions to the equation 208pi=2pir^2+2pir^5 ?
The solutions to the equation 208pi=2pir^2+2pir^5 are r\approx 2.50046…
Find the zeros of 208pi=2pir^2+2pir^5
The zeros of 208pi=2pir^2+2pir^5 are r\approx 2.50046…