Answer:
16
Step-by-step explanation:
Subtract DE from CE and you will get the value of CD
27 - 11 = 16
Answer:
![x = 19](https://tex.z-dn.net/?f=x%20%3D%2019)
Step-by-step explanation:
Given
Shape: Regular Dodecagon
Interior Angle = 8x - 2
Required
Determine x
The sum of n terms of a regular polygon is:
![Sum=180(n-2)](https://tex.z-dn.net/?f=Sum%3D180%28n-2%29)
Sides of a dodecagon is 12; So, we have:
![Sum=180(12-2)](https://tex.z-dn.net/?f=Sum%3D180%2812-2%29)
![Sum=180(10)](https://tex.z-dn.net/?f=Sum%3D180%2810%29)
![Sum=1800](https://tex.z-dn.net/?f=Sum%3D1800)
Each angle is gotten by dividing 1800 by 12
![Angle = \frac{1800}{12}](https://tex.z-dn.net/?f=Angle%20%3D%20%5Cfrac%7B1800%7D%7B12%7D)
![Angle = 150](https://tex.z-dn.net/?f=Angle%20%3D%20150)
Equate this to 8x - 2:
![8x - 2 = 150](https://tex.z-dn.net/?f=8x%20-%202%20%3D%20150)
Solve for x
![8x = 150 + 2](https://tex.z-dn.net/?f=8x%20%3D%20150%20%2B%202)
![8x = 152](https://tex.z-dn.net/?f=8x%20%3D%20152)
![x = 152/8](https://tex.z-dn.net/?f=x%20%3D%20152%2F8)
![x = 19](https://tex.z-dn.net/?f=x%20%3D%2019)
![\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BSum%20and%20Difference%20Identities%7D%20%5C%5C%5C%5C%20sin%28%5Calpha%20-%20%5Cbeta%29%3Dsin%28%5Calpha%29cos%28%5Cbeta%29-%20cos%28%5Calpha%29sin%28%5Cbeta%29)
well, for both angles A and B we're on the IV Quadrant, meaning, the sine is negative, the cosine is positive, likewise, the opposite side is negative and the adjacent side for the angle is positive.
![\bf cos(A)=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{5^2-3^2}}\implies b = \pm 4 \\\\\\ \stackrel{IV~Quadrant}{b = -4}\qquad \qquad sin(A)=\cfrac{\stackrel{opposite}{-4}}{\underset{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill\\\\ cos(B)=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{13}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{13^2-12^2}}\implies b = \pm 5](https://tex.z-dn.net/?f=%5Cbf%20cos%28A%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B3%7D%7D%7B%5Cunderset%7Bhypotenuse%7D%7B5%7D%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bgetting%20the%20opposite%20side%7D%7D%7Bb%3D%5Cpm%5Csqrt%7B5%5E2-3%5E2%7D%7D%5Cimplies%20b%20%3D%20%5Cpm%204%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7BIV~Quadrant%7D%7Bb%20%3D%20-4%7D%5Cqquad%20%5Cqquad%20sin%28A%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-4%7D%7D%7B%5Cunderset%7Bhypotenuse%7D%7B5%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20cos%28B%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B12%7D%7D%7B%5Cunderset%7Bhypotenuse%7D%7B13%7D%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bgetting%20the%20opposite%20side%7D%7D%7Bb%3D%5Cpm%5Csqrt%7B13%5E2-12%5E2%7D%7D%5Cimplies%20b%20%3D%20%5Cpm%205)
![\bf \stackrel{IV~Quadrant}{b = -5}\qquad \qquad sin(B)=\cfrac{\stackrel{opposite}{-5}}{\underset{hypotenuse}{13}} \\\\[-0.35em] ~\dotfill\\\\ sin(A-B)=\cfrac{-4}{5}\cdot \cfrac{12}{13}-\left( \cfrac{3}{5}\cdot \cfrac{-5}{13} \right)\implies sin(A-B)=\cfrac{-48}{65} - \left( \cfrac{-15}{65} \right) \\\\\\ sin(A-B)=\cfrac{-48}{65} + \cfrac{15}{65}\implies sin(A-B)=\cfrac{-33}{65}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7BIV~Quadrant%7D%7Bb%20%3D%20-5%7D%5Cqquad%20%5Cqquad%20sin%28B%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-5%7D%7D%7B%5Cunderset%7Bhypotenuse%7D%7B13%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20sin%28A-B%29%3D%5Ccfrac%7B-4%7D%7B5%7D%5Ccdot%20%5Ccfrac%7B12%7D%7B13%7D-%5Cleft%28%20%5Ccfrac%7B3%7D%7B5%7D%5Ccdot%20%5Ccfrac%7B-5%7D%7B13%7D%20%5Cright%29%5Cimplies%20sin%28A-B%29%3D%5Ccfrac%7B-48%7D%7B65%7D%20-%20%5Cleft%28%20%5Ccfrac%7B-15%7D%7B65%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20sin%28A-B%29%3D%5Ccfrac%7B-48%7D%7B65%7D%20%2B%20%5Ccfrac%7B15%7D%7B65%7D%5Cimplies%20sin%28A-B%29%3D%5Ccfrac%7B-33%7D%7B65%7D)
Answer: None of the above
Step-by-step explanation:
If you wrap the image around the line m, you get neither a cone or a cylinder (question originally from Khan Academy, High School Geometry)
V (velocity) = distance / time
So distance = velocity x time = 20 x 10 = 200 ft.