Answer:

Step-by-step explanation:
We can determine the power of a complex number by the De Moivre's Theorem, which states that for all
, where
, the power of the complex number is:
(1)
Where:
- Magnitude of the complex number, dimensionless.
- Direction of the complex number.
If we know that
,
and
, then the fourth power of the complex number is:
![z^{4} = 1^{4}\cdot \left[\cos\left(\frac{8\pi}{3} \right)+i\,\sin\left(\frac{8\pi}{3}\right)\right]](https://tex.z-dn.net/?f=z%5E%7B4%7D%20%3D%201%5E%7B4%7D%5Ccdot%20%5Cleft%5B%5Ccos%5Cleft%28%5Cfrac%7B8%5Cpi%7D%7B3%7D%20%5Cright%29%2Bi%5C%2C%5Csin%5Cleft%28%5Cfrac%7B8%5Cpi%7D%7B3%7D%5Cright%29%5Cright%5D)

Answer:
The exact values of the tangent, secant and cosine of angle theta are, respectively:



Step-by-step explanation:
The components of the unit vector are
and
. Since
, then
and
. By Trigonometry, tangent and secant can be calculated by the following expressions:


Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:



Answer:
a. 176 feet b. 2640 feet
Step-by-step explanation:
a. Since the diameter of the Ferris wheel is D = 56 feet, the distance Toni travels in one revolution is the circumference of the Ferris wheel, C = πD.
So C = 22/7 × 56 ft = 22 × 8 ft = 176 feet
b. The distance traveled in 15 revolutions is thus D' = 15 × distance of one revolution = 15 × 176 = 2640 feet
The answer would be 8.5. 8.54 rounds down to 8.54.
Hope this helps!
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Answer: The greatest common factor is 2.
Step-by-step explanation: We are given to find the greatest common factor of the following expressions:

<u>Greatest Common Factor:</u> The GCF of two or more numbers (expressions) is the greatest factor that divides all the numbers or expressions.
We have

Therefore, the greatest common factor will be

Thus, the required greatest common factor is 2.