The circumference of a circle is 60 pi cm. What is the radius of the circle?

1 answer:

3 0

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{60\pi }{2\pi }=r\implies 30=r$

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Given f (x) = x2 + 4x + 5, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?

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By evaluating the quadratic function, we will see that the differential quotient is:

$\frac{f(2 + h) - f(2)}{h} = 8 + h$

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So we need to replace the x-variable by "2 + h" and "2" respectively.

Replacing the function in the differential quotient:

$\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}$