Geometric sequence

gokturkv · December 16, 2014

Hi guys,

I couldn't solve the "b"

Can you please help ?

Vioh · December 17, 2014

Hi guys, I couldn't solve the "b" Can you please help ?

I would assume that the "perimeter" of a sector (which is mentioned in the question) means the sum of the arc length of that sector with the 2 sides of the sector (which are basically equal to the radius of the circle).

From the assumption, the perimeter of the first sector is $gif.latex?2r + r\theta = 4 + 2\theta$

Now it's obvious that the angle of the third sector is $gif.latex?\varphi = \theta k^2$ ; this means that the perimeter of the third sector is $gif.latex?2r + r\varphi = 4 + 2\theta k^$ . Thus, from the information provided by the question, we have the 2 following equations:

$gif.latex?\theta = 2\pi(1-k)$

$gif.latex?2(2\theta k^2 + 4) = 2\theta +$

Expanding, simplifying, & combining the equations, we get the polynomial:

$gif.latex?2k^3-2k^2-k+ \left(1-\frac{1}{$

Using graphing calculator, we get $gif.latex?k\approx0.456$ , which means that $gif.latex?\theta = 2\pi(1-k) = 2\pi(1-0.$

Not completely sure that this is right though. Or maybe i have even misunderstood the question. So it's best if you could check my result against the answer key

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Geometric sequence

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