Answer:
Step-by-step explanation:
![\sin 2\theta = 2 \sin \theta \cos \theta\\\\\\~~~~~~~~=2\sqrt{1 -\cos^2 \theta} \cdot \cos \theta~~~~~~~~~~~;[\text{In quadrant I, all ratios are positive.}]\\\\\\~~~~~~~~=2 \sqrt{1- \left( \dfrac{12}{13} \right)^2} \cdot \left(\dfrac{12}{13} \right)\\\\\\~~~~~~~~=\left( \dfrac{24}{13} \right) \sqrt{1- \dfrac{144}{169}}\\\\\\~~~~~~~~=\dfrac{24}{13}\sqrt{\dfrac{25}{169}}\\\\\\~~~~~~~=\dfrac{24}{13} \times \dfrac{5}{13}\\\\\\~~~~~~=\dfrac{120}{169}](https://tex.z-dn.net/?f=%5Csin%202%5Ctheta%20%3D%202%20%5Csin%20%5Ctheta%20%5Ccos%20%5Ctheta%5C%5C%5C%5C%5C%5C~~~~~~~~%3D2%5Csqrt%7B1%20-%5Ccos%5E2%20%5Ctheta%7D%20%5Ccdot%20%5Ccos%20%5Ctheta~~~~~~~~~~~%3B%5B%5Ctext%7BIn%20quadrant%20I%2C%20all%20ratios%20are%20positive.%7D%5D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D2%20%5Csqrt%7B1-%20%5Cleft%28%20%5Cdfrac%7B12%7D%7B13%7D%20%5Cright%29%5E2%7D%20%5Ccdot%20%5Cleft%28%5Cdfrac%7B12%7D%7B13%7D%20%5Cright%29%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cleft%28%20%5Cdfrac%7B24%7D%7B13%7D%20%5Cright%29%20%5Csqrt%7B1-%20%5Cdfrac%7B144%7D%7B169%7D%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B24%7D%7B13%7D%5Csqrt%7B%5Cdfrac%7B25%7D%7B169%7D%7D%5C%5C%5C%5C%5C%5C~~~~~~~%3D%5Cdfrac%7B24%7D%7B13%7D%20%5Ctimes%20%5Cdfrac%7B5%7D%7B13%7D%5C%5C%5C%5C%5C%5C~~~~~~%3D%5Cdfrac%7B120%7D%7B169%7D)
<span>All sides are the same length and all interior angles are the same size.</span>
Answer:
radius = 3 feet
Step-by-step explanation:
V = 1/3πr²h
15π = 1/3πr²·5
you can divide each side by 5π to get:
3 = r²/3
r² = 9
r = 
which is 3
Find the circumference of the metal frame?
C = pi * d
Where 'd' is the diameter.
In this case, the diameter is 14, because that is the given information from the question.
Plug it in along with 3.14 for pi:
C = 3.14 * 14
C = 43.96
So it's approximately 44
