Answer:
(A) ![\frac{\pi }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B3%7D)
(b) ![1.768\pi](https://tex.z-dn.net/?f=1.768%5Cpi)
Step-by-step explanation:
It is given in the question that ![0\leq x\leq 2\pi](https://tex.z-dn.net/?f=0%5Cleq%20x%5Cleq%202%5Cpi)
(a) We have given equation ![2cosx-1=0](https://tex.z-dn.net/?f=2cosx-1%3D0)
![cosx=\frac{1}{2}](https://tex.z-dn.net/?f=cosx%3D%5Cfrac%7B1%7D%7B2%7D)
![x=cos^{-1}\frac{1}{2}](https://tex.z-dn.net/?f=x%3Dcos%5E%7B-1%7D%5Cfrac%7B1%7D%7B2%7D)
![x=\frac{\pi }{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%20%7D%7B3%7D)
(b) ![3sinx+2=0](https://tex.z-dn.net/?f=3sinx%2B2%3D0)
![sinx=\frac{-2}{3}](https://tex.z-dn.net/?f=sinx%3D%5Cfrac%7B-2%7D%7B3%7D)
![x=sin^{-1}(-0.666)](https://tex.z-dn.net/?f=x%3Dsin%5E%7B-1%7D%28-0.666%29)
![x=-41.75^{\circ}=360-41.75=318.25^{\circ}=1.768\pi](https://tex.z-dn.net/?f=x%3D-41.75%5E%7B%5Ccirc%7D%3D360-41.75%3D318.25%5E%7B%5Ccirc%7D%3D1.768%5Cpi)
Regrouping is only done into lower place values. For example, tens to ones and hundreds to tens.
I first convert it into decimals because it an easier way to do it. So it would be 0.5+0.33+0.4= 1.23. Then I convert it into a fraction which is 37/30.
Answer:
r = 55.2 cm
Step-by-step explanation:
the arc length is calculated as
arc = circumference × fraction of circle
= 2πr ×
( r is the radius )
given arc = 63.48π , then
2πr ×
= 63.48π ( cancel 2π on numerator/ denominator )
r ×
π = 63.48π ( divide both sides by π )
= 63.48 ( multiply both sides by 20 to clear the fraction )
23r = 1269.6 ( divide both sides by 23 )
r = 55.2 cm
The Inner planets, or The Rocky Planets. I'm not 100% sure if this is right, so maybe wait for another answer.