Solve for the variable

Algebra

Solve for the variable

Postby Guest » Tue Jul 02, 2019 11:54 am

Solve the following equation for the indicated variable.

A = 2πr² + 2πrh

Solve for positive r
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Re: Solve for the variable

Postby Baltuilhe » Fri Jul 05, 2019 9:25 pm

Good night!

[tex]2 \pi r^2 + 2 \pi r h = A\\
2 \pi r^2 + 2 \pi h r - A = 0\\
\Delta = \left( 2 \pi h \right)^2 - 4 \left( 2 \pi \right) \left( -A \right)\\
\Delta = 4 \pi^2 h^2 + 8 \pi A\\
r = \dfrac{-2 \pi h \pm \sqrt{ 4 \pi^2 h^2 + 8 \pi A } }{ 2 \left( 2 \pi \right) }\\
r = \dfrac{-2\pi h \pm 2 \sqrt{ \pi^2 h^2 + 2 \pi A }}{4 \pi}\\
r = \dfrac{-2\pi h \pm 2 \sqrt{ \pi^2 \left( h^2 + \dfrac{2 A}{ \pi } \right) } }{4 \pi}\\
r = \dfrac{-2\pi h \pm 2 \pi \sqrt{ h^2 + \dfrac{2 A}{ \pi } } }{4 \pi}\\[/tex]
[tex]\boxed{ r = \dfrac{ -h + \sqrt{ h^2 + \dfrac{2 A}{ \pi } } }{ 2 } }[/tex]

I hope to have helped! :)

Baltuilhe
 
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