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.
<span>50-8t<90
50-90<8t
-40<8t
8t>-40
t>-5
Solutions should go to the right.
Mary probably was solving it as following
</span>50-8t<90
<span>-8t<90-50
-8t<40 (here, when she divided both sides by -8, she had to change sign < to the sign >)
But she did not change the sign, and got
t<-5
</span>
That's false. If they share a congruent angle and the sides adjacent to it are
also congruent, then the triangles are also congruent. In order for them to be
similar, all that's necessary besides the congruent angle is that each side
adjacent to it be in the <em>same ratio</em> between the two triangles.
Answer:
6
+ 5x² - 2x + 3
Step-by-step explanation:
Given
( + 2x² - 4) - (-5 - 3x² + 2x - 7)
Remove the parenthesis on the first factor and distribute the second by - 1
= + 2x² - 4 + 5 + 3x² - 2x + 7 ← collect like terms
= 6 + 5x² - 2x + 3 ← in standard form
The stright side of the hula hoop would be 2 inches
