3 years ago

What are the answers to these??

Mathematics

1 answer:

QveST [7]3 years ago

5 0

8)23a+13

9)-21b+84

10)17c+2

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Brainliest is given to the correct answer!

OlgaM077 [116]

Answer:

a. $p = 2\pi r + 8r$

b. $r = \frac{p}{2\pi + 8}$

Step-by-step explanation:

a. Radius of semicircle (r) = r

Diameter of semicircle (d) = 2r

Length of rectangle (l) = 2*diameter of semicircle = 2*2r = 4r

Distance around the track (p) = circumference of circle + 2(l)

Note: the two semicircles of the track = 1 full circle

Circumference of full circle = πd = π*2r = 2πr

Distance around the track:

p = 2πr + 2(4r)

p = 2πr + 8r

b. Rewriting the formula to make radius, r, the subject of the formula in terms of distance around the track.

$p = 2\pi r + 8r$

Factor out r

$p = r(2\pi + 8)$

Divide both sides by (2π + 8)

$\frac{p}{2\pi + 8} = \frac{r(2\pi + 8)}{2\pi + 8}$

$\frac{p}{2\pi + 8} = r$

$r = \frac{p}{2\pi + 8}$

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