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One week you tell 3 of your friends a secret. The next week, each of them tells 3 people the secret and the

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yawa3891 [41]3 years ago

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By the 7th week, 2,187 people will have found out the secret.

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A sector of a circle makes a 127° angle at its centre. If the arc of the sector has length 36 mm, find

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Approximately $68.5\; \rm mm$ .

Step-by-step explanation:

Convert the angle of this sector to radians:

$\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}$ .

The formula $s = r\, \theta$ relates the arc length $s$ of a sector of angle $\theta$ (in radians) to the radius $r$ of this sector.

In this question, it is given that the arc length of this sector is $s = 36\; \rm mm$ . It was found that $\theta = 2.22$ radians. Rearrange the equation $s = r\, \theta$ to find the radius $r$ of this sector:

$\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}$ .

The perimeter of this sector would be:

$\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}$ .

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