9514 1404 393
Answer:
16. 134°
17. 20°
18. 94°
Step-by-step explanation:
An inscribed angle is half the measure of the arc it intercepts.
__
16. Arc QT is twice the measure of inscribed angle QST, given as 67°.
Arc QT = 2×67°
Arc QT = 134°
__
17. Angle STR is half the measure of arc SR, so is ...
m∠STR = (arc SR)/2 = 40°/2
m∠STR = 20°
__
18. Arc RST is a semicircle, so has a measure of 180°. Then arc ST is the difference between that and arc RS:
arc ST = 180° -40° = 140°
Angle RST subtends a semicircle, so is 180°/2 = 90°. We know angle QST is 67°, so the remaining portion, angle QSR must be the complement of that:
m∠QSR = 90° -67° = 23°
Arc RQ will be twice this measure, or 46°.
So, the desired difference is ...
mST -mRQ = 140° -46° = 94°
I am gonna do what you did to me and say its easy.
Answer:

Step-by-step explanation:
The formula of a volume of a sphere:

We have

Substitute:
<em>divide both sides by π</em>
<em>multiply both sides by 3</em>

<em>divide both sides by 4</em>
![R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}](https://tex.z-dn.net/?f=R%5E3%3D%5Cdfrac%7B1%7D%7B2%7D%3A4%5C%5C%5C%5CR%5E3%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5C%5CR%5E3%3D%5Cdfrac%7B1%7D%7B8%7D%5Cto%20R%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B1%7D%7B8%7D%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B%5Csqrt1%7D%7B%5Csqrt8%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B1%7D%7B2%7D)