Answer:
B
Step-by-step explanation:
![\cos( \alpha ) + i\sin( \alpha ) = {e}^{i (\alpha + 2\pi)}](https://tex.z-dn.net/?f=%20%5Ccos%28%20%5Calpha%20%29%20%20%2B%20%20i%5Csin%28%20%5Calpha%20%29%20%20%3D%20%20%7Be%7D%5E%7Bi%20%28%5Calpha%20%20%20%2B%202%5Cpi%29%7D%20)
z = 3(cos π/2 + i sin π/2) =→
![3 {e}^{i \frac{\pi}{2} }](https://tex.z-dn.net/?f=3%20%7Be%7D%5E%7Bi%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%7D%20)
z⁷ =
![{3}^{7} {e}^{i \frac{7\pi}{2} } = {3}^{7} {e}^{i \frac{(7 - 4)\pi}{2} } = {3}^{7} {e}^{i \frac{3\pi}{2} } = {3}^{7} ( \cos( \frac{3\pi}{2} ) + i \sin( \frac{3\pi}{2} ) ) = 2187( \cos( \frac{3\pi}{2} ) + i \sin( \frac{3\pi}{2} ) )](https://tex.z-dn.net/?f=%20%7B3%7D%5E%7B7%7D%20%20%7Be%7D%5E%7Bi%20%5Cfrac%7B7%5Cpi%7D%7B2%7D%20%7D%20%20%3D%20%20%20%7B3%7D%5E%7B7%7D%20%20%7Be%7D%5E%7Bi%20%5Cfrac%7B%287%20-%204%29%5Cpi%7D%7B2%7D%20%7D%20%20%3D%20%20%7B3%7D%5E%7B7%7D%20%20%7Be%7D%5E%7Bi%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%7D%20%20%3D%20%20%7B3%7D%5E%7B7%7D%20%28%20%5Ccos%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%29%20%20%2B%20i%20%5Csin%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%29%20%29%20%3D%202187%28%20%5Ccos%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%29%20%20%2B%20i%20%5Csin%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%29%20%29)
A boy stands 1 meter away from a lamppost. He is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp
The diagram is attached below using the given information
We have two similar triangle
Triangle ACD is similar to triangle ABE. So the sides are in proportional
![\frac{DC}{EB} =\frac{AC}{AB}](https://tex.z-dn.net/?f=%20%5Cfrac%7BDC%7D%7BEB%7D%20%3D%5Cfrac%7BAC%7D%7BAB%7D%20)
AC = AB + BC = 3m
![\frac{x}{1.8}=\frac{3}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B1.8%7D%3D%5Cfrac%7B3%7D%7B2%7D)
2x = 1.8 * 3 (cross multiply)
2x = 5.4
Divide by 2 on both sides
x = 2.7
Height of Lamppost is 2.7 meter
Answer:
oh yeah thats the 3rd one
Step-by-step explanation:
Product means multiplication, so I would multiply 379 and 8.
379 x 8 = 3032
<span>3032 is directly in between 3031 and 3033</span>
Step-by-step explanation:
![\underline{\large{ \tt{G \: I \: V \: E \: N}}} :](https://tex.z-dn.net/?f=%20%20%5Cunderline%7B%5Clarge%7B%20%5Ctt%7BG%20%5C%3A%20I%20%5C%3A%20V%20%5C%3A%20E%20%5C%3A%20N%7D%7D%7D%20%3A%20)
- Line a & b are parallel
- m ∠ 8 = 150 °
![\underline{ \large{ \tt{T \: O\: \: F \: I \: N \:D}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7BT%20%5C%3A%20O%5C%3A%20%20%5C%3A%20F%20%5C%3A%20I%20%5C%3A%20N%20%5C%3AD%7D%7D%7D%20%3A%20)
![\underline{ \large{ \tt{S\: O \:L \: U \: T \: I \: O \: N}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Clarge%7B%20%5Ctt%7BS%5C%3A%20O%20%5C%3AL%20%5C%3A%20U%20%5C%3A%20T%20%5C%3A%20I%20%5C%3A%20O%20%5C%3A%20N%7D%7D%7D%20%3A%20)
[ Sum of co-interior angles ]
⤑ ![\large{ \tt{150 \degree \: + m \: \angle \: 2}} = 180 \degree](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7B150%20%5Cdegree%20%5C%3A%20%20%2B%20m%20%20%5C%3A%20%5Cangle%20%5C%3A%202%7D%7D%20%3D%20180%20%5Cdegree)
⤑ ![\large{ \tt{m \angle \: 2 \: = \: 180 \degree - 150 \degree}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7Bm%20%5Cangle%20%5C%3A%202%20%5C%3A%20%20%3D%20%20%5C%3A%20180%20%5Cdegree%20-%20150%20%5Cdegree%7D%7D)
⤑ ![\large{ \tt{m \: \angle \: 2 \: = \bold{ \tt{30 \degree}}}}](https://tex.z-dn.net/?f=%20%5Clarge%7B%20%5Ctt%7Bm%20%20%5C%3A%20%5Cangle%20%5C%3A%202%20%5C%3A%20%20%3D%20%20%5Cbold%7B%20%5Ctt%7B30%20%5Cdegree%7D%7D%7D%7D)
![\red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \bold{ \tt{30 \degree}}}}}}}}](https://tex.z-dn.net/?f=%20%5Cred%7B%20%5Cboxed%7B%20%5Cboxed%7B%20%5Ctt%7BOur%20%5C%3A%20final%20%5C%3A%20answer%20%3A%20%20%5Cboxed%7B%20%5Cunderline%7B%20%5Cbold%7B%20%5Ctt%7B30%20%5Cdegree%7D%7D%7D%7D%7D%7D%7D%7D)
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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