Answer:
See below
Step-by-step explanation:
Given that:
![\displaystyle{DC^2 = 2a^2(1+\cos 2\theta)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7BDC%5E2%20%3D%202a%5E2%281%2B%5Ccos%202%5Ctheta%29%7D)
Where
and
. Substitute these values in the expression:
![\displaystyle{\left(\sqrt{12}\right)^2 = 2\cdot 2^2(1+\cos 2\theta)}\\\\\displaystyle{12= 2\cdot 4(1+\cos 2\theta)}\\\\\displaystyle{12= 8(1+\cos 2\theta)}\\\\\displaystyle{\dfrac{12}{8}= 1+\cos 2\theta}\\\\\displaystyle{\dfrac{3}{2}=1+\cos 2\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cleft%28%5Csqrt%7B12%7D%5Cright%29%5E2%20%3D%202%5Ccdot%202%5E2%281%2B%5Ccos%202%5Ctheta%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B12%3D%202%5Ccdot%204%281%2B%5Ccos%202%5Ctheta%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B12%3D%208%281%2B%5Ccos%202%5Ctheta%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B12%7D%7B8%7D%3D%201%2B%5Ccos%202%5Ctheta%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D1%2B%5Ccos%202%5Ctheta%7D)
Substitute ![\displaystyle{\theta = 30^{\circ}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Ctheta%20%3D%2030%5E%7B%5Ccirc%7D%7D)
![\displaystyle{\dfrac{3}{2}= 1+\cos (2 \cdot 30^{\circ})}\\\\\displaystyle{\dfrac{3}{2}= 1+\cos 60^{\circ}}\\\\\displaystyle{\dfrac{3}{2}= 1+\dfrac{1}{2}}\\\\\displaystyle{\dfrac{3}{2}= \dfrac{2}{2}+\dfrac{1}{2}}\\\\\displaystyle{\dfrac{3}{2}= \dfrac{3}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D%201%2B%5Ccos%20%282%20%5Ccdot%2030%5E%7B%5Ccirc%7D%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D%201%2B%5Ccos%2060%5E%7B%5Ccirc%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D%201%2B%5Cdfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D%20%5Cdfrac%7B2%7D%7B2%7D%2B%5Cdfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%7B%5Cdfrac%7B3%7D%7B2%7D%3D%20%5Cdfrac%7B3%7D%7B2%7D%7D)
Therefore, since both sides are the same after substituting theta = 30 degrees.
Hence, proved.
Answer:
K (- 10, - 2 )
Step-by-step explanation:
To obtain the original coordinates multiply by the reciprocal of ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
That is multiply the image coordinates by 4
K' (- 2.5, - 0.5 ) → K (-2.5(4), (- 0.5(4) ) → K (- 10, - 2 )
Answer:
I can’t really explain this bc i did it mentally, but i got 162.5
Answer:
50 because if u divide ic 1101 by milky way
5 x 10^22 ÷ 1 x 10^21 = 50
The denominator must be the same, so just think of the LEAST COMMON MULTIPLE, The LCM here is 8, because you can multiply 4 by 2 to get 8.
so when you multiply, you multiply both on the top and on the bottom, so this would be:
3 x 2 / 4 x 2 = 6 / 8
Now you can add or subtract: 6/8 - 1/8 = 5/8