$\bf \stackrel{\textit{perimeter}}{\textit{circumference}}\textit{ of a circle}\\\\ C = 2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=x \end{cases}\implies x = 2\pi r\implies \boxed{\cfrac{x}{2\pi }=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=x \end{cases}\implies x = \pi \left( \boxed{\cfrac{x}{2\pi }} \right)^2\implies x = \pi \cdot \cfrac{x^2}{2^2\pi^2}$

$\bf x = \cfrac{x^2}{4\pi }\implies 4\pi x = x^2\implies \cfrac{4\pi x}{x}=x\implies \blacktriangleright 4\pi = x\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since the radius is}}{r = \cfrac{x}{2\pi }}\implies r =\cfrac{4\pi }{2\pi }\implies \blacktriangleright r = 2\blacktriangleleft$

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4 years ago

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Mark is solving the equation 4x2 = 12x - 9 using the quadratic formula.

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3 years ago