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anastassius [24]
3 years ago
12

.....................................................

Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0

(a) The perimeter of the shape is the sum of half a circumference and the diameter itself.

The circumference of a circle with radius r is 2\pi r, and since d=2r we can write the circumference as

C=\pi d

So, half a circumference is

\dfrac{C}{2}=\dfrac{\pi d}{2}

Ad we get the perimeter by addind the diameter:

P=\dfrac{\pi d}{2}+d

(b) Given the perimeter, we can solve for d:

51.42=\dfrac{\pi d}{2}+d=d\left(\dfrac{\pi}{2}+1\right)

So, we can divide both sides by the parenthesis and we have

d=\dfrac{51.42}{\frac{\pi}{2}+1}=\dfrac{51.42}{2.571}=20

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