Answer:
The answer to your question is below
Step-by-step explanation:
Write an equation for the cost of fish at each fish store.
a) Wet pets
We must consider the initial price and the cost of each fish.
total cost = C
kit cost = $15
cost of each fish = $0.60
cost of one fish = f
C = 15 + 0.60f
Example, if the number of fish is 4, then the total cost will be
C = 15 + 0.60(4)
C = 15 + 2.4
C = $ 17.4
b) Grips and Frills
total cost = C
kit cost = $13
cost per fish = $0.80
cost of one fish = f
Equation
C = 13 + 0.8f
The given proof of De Moivre's theorem is related to the operations of
complex numbers.
<h3>The Correct Responses;</h3>
- Step C: Expanding and collecting like terms
- Step D: Trigonometric formula for the cosine and sine of the sum of two numbers
<h3>Reasons that make the above selection correct;</h3>
The given proof is presented as follows;
![\mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%5E%7Bk%20%2B%201%7D%7D)
- Step A: By laws of indices, we have;
![\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1} = \mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}](https://tex.z-dn.net/?f=%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%5E%7Bk%20%2B%201%7D%20%3D%20%5Cmathbf%7B%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%5E%7Bk%7D%20%5Ccdot%20%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%7D)
![\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] = \mathbf{\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}](https://tex.z-dn.net/?f=%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%5E%7Bk%7D%20%5Ccdot%20%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%20%3D%20%20%5Cmathbf%7B%5Cleft%5Bcos%28k%20%5Ccdot%20%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28k%20%5Ccdot%20%5Ctheta%29%20%5Cright%5D%20%5Ccdot%20%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%7D)
- Step B: By expanding, we have;
![\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] = cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right]](https://tex.z-dn.net/?f=%5Cleft%5Bcos%28k%20%5Ccdot%20%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28k%20%5Ccdot%20%5Ctheta%29%20%5Cright%5D%20%5Ccdot%20%5Cleft%5Bcos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%20%3D%20cos%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20cos%28%5Ctheta%29%20-%20sin%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20sin%28%5Ctheta%29%20%2B%20i%20%20%5Ccdot%20%5Cleft%20%5Bsin%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20cos%28%5Ctheta%29%20%2B%20cos%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D)
- Step D: From trigonometric addition formula, we have;
cos(A + B) = cos(A)·cos(B) - sin(A)·sin(B)
sin(A + B) = sin(A)·cos(B) + sin(B)·cos(A)
Therefore;
![cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right] = \mathbf{ cos(k \cdot \theta + \theta) + i \cdot sin(k \cdot \theta + \theta)}](https://tex.z-dn.net/?f=cos%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20cos%28%5Ctheta%29%20-%20sin%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20sin%28%5Ctheta%29%20%2B%20i%20%20%5Ccdot%20%5Cleft%20%5Bsin%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20cos%28%5Ctheta%29%20%2B%20cos%28k%20%5Ccdot%20%5Ctheta%29%20%5Ccdot%20sin%28%5Ctheta%29%20%5Cright%5D%20%3D%20%5Cmathbf%7B%20cos%28k%20%5Ccdot%20%5Ctheta%20%2B%20%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28k%20%5Ccdot%20%5Ctheta%20%20%2B%20%5Ctheta%29%7D)
Learn more about complex numbers here:
brainly.com/question/11000934
Answer:
no
the point (4,3) is not within the shaded region
Answer:
14
Step-by-step explanation:
ratio of glue sticks to glue bottles is 5:2 so number of glue bottles = 35×2=14 or you can think that for every 5 glue sticks, you will have 2 glue bottles. Since 35means 5×7, then the number of glue sticks will be 2×7 which is 14
