Answer:
The correct option is C.
Step-by-step explanation:
The given complex number is
![z=64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])](https://tex.z-dn.net/?f=z%3D64%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29)
We need to find the third root of the given complex number.
![z^{\frac{1}{3}}=(64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}]))^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%2864%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![z^{\frac{1}{3}}=64^{\frac{1}{3}}(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D64%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
De moivre's theorem:
where, n is an integer.
Using de moivre's theorem, we get
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}\times \frac{1}{3}]-i\sin[\frac{\pi}{7}\times \frac{1}{3}])](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5D%29)
![z^{\frac{1}{3}}=4(\cos[\frac{\pi}{21}]-i\sin[\frac{\pi}{21}])](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D4%28%5Ccos%5B%5Cfrac%7B%5Cpi%7D%7B21%7D%5D-i%5Csin%5B%5Cfrac%7B%5Cpi%7D%7B21%7D%5D%29)
Therefore the correct option is C.
Lets w width, l length, y amount add, A area, P perimeter
A=lw=(3+y)(2)=6+2y ft²
p= 2l+2w= 2(3+y)+2(2)= 6+2y+4 =10+2y
Your rate of change would be 3/4 lb/week.
You could model this with a linear eq:
y = 8+ 3/4x
2,500 subtracted by 372 equals 2148. 2148 dollars is how much savings he has left.
Answer: the first one.
Step-by-step explanation:
because distance on a number line will always be positive. :D
