Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
Answer:
bro no one cares
Step-by-step explanation:
Step-by-step explanation:
![= ( - 3c + 6) + ( - c + 8)](https://tex.z-dn.net/?f=%20%3D%20%28%20-%203c%20%2B%206%29%20%2B%20%28%20-%20c%20%2B%208%29)
![= - 3c + 6 - c + 8](https://tex.z-dn.net/?f=%20%3D%20%20-%203c%20%2B%206%20-%20c%20%2B%208)
![= - 3c - c + 6 + 8](https://tex.z-dn.net/?f=%20%3D%20%20-%203c%20-%20c%20%2B%206%20%2B%208)
= -4c + 14
hence -4c + 14 is the answer ...
hope it helped !!
Answer:
C
Step-by-step explanation:
If you take the points (1,50), and (2,100) and (3,150) you can see that the graph is increasing by 50 each time
1) we calculate the volume of the first carton:
volume=length x width x height
volume=3 ft * 2 ft * 2 ft=12 ft³
Therefore:
A machine can fill 12 ft³ in 3 seconds.
2) we calculate the volume of the second carton.
volume=length x width x heigth
volume=4 ft * 5 ft * 6 ft=120 ft³
3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.
12 ft³---------------------3 seconds
120 ft³-------------------- x
x=(120 ft³ * 3 seconds) / 12 ft³=30 seconds.
answer: 30 seconds.