Answer:
20
Step-by-step explanation:
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
Answer:
Dustin has 42 cards.
Mike has 54 cards.
Kevin has 39 cards
Step-by-step explanation:
subtract (Dustin + Mike) – (Dustin + Kevin) or 96 – 81.
Think of it like....
Dustin + Mike – Dustin – Kevin
Dustin – Dustin + Mike – Kevin
Mike – Kevin
Since 96 – 81 = 15, Mike – Kevin = 15
Add (Kevin + Mike) + (Mike – Kevin) or 93 + 15.
Think of it like...
Kevin + Mike + Mike – Kevin
Kevin – Kevin + Mike + Mike
Mike + Mike
Since 93 + 15 = 108, Mike + Mike = 108. If you divide, Mike had 54 cards. That means that you can find Kevin’s cards by using 93 – 54 or 39. You can then find Dustin’s cards by using 81 – 39 = 42.
Check:
Dustin’s cards + Kevin’s cards = 42 + 39 = 81
Dustin’s cards + Mike’s cards = 42 + 54 = 96
Mike’s cards + Kevin’s cards = 54 + 39 = 93
I just checked and the answer should be 3786.25