What are the solutions to the equation 450pi=2pi*r^2+2*pi*r^{15} ?

The solutions to the equation 450pi=2pi*r^2+2*pi*r^{15} are r\approx 1.43399…

Find the zeros of 450pi=2pi*r^2+2*pi*r^{15}

The zeros of 450pi=2pi*r^2+2*pi*r^{15} are r\approx 1.43399…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

450 π = 2 π \cdot r^{2} + 2 \cdot π \cdot r^{15}

r \approx 1.43399 \dots

Solution steps

450 π = 2 π r^{2} + 2 π r^{15}

Switch sides

2 π r^{2} + 2 π r^{15} = 450 π

Move

450 π

to the left side

2 π r^{2} + 2 π r^{15} - 450 π = 0

Write in the standard form

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

2 π r^{15} + 2 π r^{2} - 450 π = 0

Find one solution for

6.28318 \dots r^{15} + 6.28318 \dots r^{2} - 1413.71669 \dots = 0

using Newton-Raphson:

r \approx 1.43399 \dots

Apply long division:

\frac{2 π r ^{15} + 2 π r ^{2} - 450 π}{r - 1.43399 \dots} = 6.28318 \dots r^{14} + 9.01002 \dots r^{13} + 12.92029 \dots r^{12} + 18.52758 \dots r^{11} + 26.56839 \dots r^{10} + 38.09882 \dots r^{9} + 54.63336 \dots r^{8} + 78.34373 \dots r^{7} + 112.34418 \dots r^{6} + 161.10052 \dots r^{5} + 231.01665 \dots r^{4} + 331.27574 \dots r^{3} + 475.04635 \dots r^{2} + 687.49524 \dots r + 985.86180 \dots

6.28318 \dots r^{14} + 9.01002 \dots r^{13} + 12.92029 \dots r^{12} + 18.52758 \dots r^{11} + 26.56839 \dots r^{10} + 38.09882 \dots r^{9} + 54.63336 \dots r^{8} + 78.34373 \dots r^{7} + 112.34418 \dots r^{6} + 161.10052 \dots r^{5} + 231.01665 \dots r^{4} + 331.27574 \dots r^{3} + 475.04635 \dots r^{2} + 687.49524 \dots r + 985.86180 \dots \approx 0

Find one solution for

6.28318 \dots r^{14} + 9.01002 \dots r^{13} + 12.92029 \dots r^{12} + 18.52758 \dots r^{11} + 26.56839 \dots r^{10} + 38.09882 \dots r^{9} + 54.63336 \dots r^{8} + 78.34373 \dots r^{7} + 112.34418 \dots r^{6} + 161.10052 \dots r^{5} + 231.01665 \dots r^{4} + 331.27574 \dots r^{3} + 475.04635 \dots r^{2} + 687.49524 \dots r + 985.86180 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solution is

r \approx 1.43399 \dots

4 x - 5 = 5 x - 4

3 = 0.5 k (0.11)^{2}

x (3 x + 2) = 1

\frac{12 x ^{7} y ^{8}}{4 x ^{3} y}

4 (w - 2) - 3 w = 2 (w - 6)

What are the solutions to the equation 450pi=2pi*r^2+2*pi*r^{15} ?
The solutions to the equation 450pi=2pi*r^2+2*pi*r^{15} are r\approx 1.43399…
Find the zeros of 450pi=2pi*r^2+2*pi*r^{15}
The zeros of 450pi=2pi*r^2+2*pi*r^{15} are r\approx 1.43399…