Answer:
24192 hope it helps and sorry if i get it wrong
Step-by-step explanation:
Answer:
![\rm\cos({600}^{ \circ} ) =-1/2](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%28%7B600%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D-1%2F2%20)
Step-by-step explanation:
we would like to solve the following using double-angle formula:
![\displaystyle \cos( {600}^{ \circ} )](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%20%5Ccos%28%20%7B600%7D%5E%7B%20%5Ccirc%7D%20%29%20)
there're <u>4</u><u> </u>double Angle formulas of cos function which are given by:
![\displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}](https://tex.z-dn.net/?f=%20%20%5Cdisplaystyle%20%20%5Ccos%282%20%5Ctheta%29%20%20%3D%20%20%5Cbegin%7Bcases%7D%20i%29%5Ccos%5E%7B2%7D%20%28%20%5Ctheta%29%20%20-%20%20%7B%20%5Csin%7D%5E%7B2%7D%28%20%20%5Ctheta%29%20%20%5C%5Cii%29%202%20%7B%20%5Ccos%7D%5E%7B2%7D%28%20%5Ctheta%29%20-%201%20%5C%5Ciii%29%201%20-%20%20%7B%20%5Csin%7D%5E%7B2%7D%20%20%5Ctheta%20%20%5C%5C%20%20iv%29%5Cdfrac%7B1%20-%20%20%7B%20%5Ctan%7D%5E%7B2%7D%20%20%5Ctheta%7D%7B1%20%2B%20%20%7B%20%5Ctan%7D%5E%7B2%7D%20%5Ctheta%20%7D%20%20%5Cend%7Bcases%7D)
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
![\displaystyle \cos( {2(300)}^{ \circ} )](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%20%5Ccos%28%20%7B2%28300%29%7D%5E%7B%20%5Ccirc%7D%20%29%20)
so,
Step-2: substitute:
![\rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%282%20%5Ccdot%20%7B300%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D%202%20%5Ccos%20%5E%7B2%7D%20%20%7B300%7D%5E%7B%20%5Ccirc%7D%20%20-%201)
recall unit circle thus cos300 is ½:
![\rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%282%20%5Ccdot%20%7B300%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D%202%20%20%5Cleft%28%20%5Cdfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%20%20%20-%201)
simplify square:
![\rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%282%20%5Ccdot%20%7B300%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D%202%5Ccdot%20%5Cdfrac%7B1%7D%7B4%7D%20%20-%201)
reduce fraction:
![\rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%282%20%5Ccdot%20%7B300%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%20-%201)
simplify substraction and hence,
![\rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}](https://tex.z-dn.net/?f=%20%20%5Crm%5Ccos%28%7B600%7D%5E%7B%20%5Ccirc%7D%20%29%20%20%3D%20%5Cboxed%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
Answer:
400.5 miles
Step-by-step explanation:
227.5 + 173=400.5
Answer:
The other factor is (x + 2).
Step-by-step explanation:
If x - 10 is a factor of x^2 - 8x - 20 then we must find another factor that includes +2x, so that we have -10x + 2x = -8x. That factor is (x + 2):
x^2 - 8x - 20 = (x - 10)(x + 2)
As a test, multiply -10 and +2. We get -20, matching the constant of the given polynomial. Also, -10x + 2x = -8x, another match.