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4 years ago

13

tickets to a science expedition cost $5.75 each for students and seven dollars for adults how many students and adults went if t

he ticket charge was $42.75

1 answer:

zysi [14]4 years ago

6 0

7 students and 6 adults (I think lol sorry if I'm wrong)

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using <span>De Moivre's theorem:
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>

Part (A) <span>find the modulus for all of the fourth roots
</span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

4 years ago

Recently, the Dow opened at 26,428 ad closed at 26,340. what was the change in the Dow for the day?

IRISSAK [1]

Answer:

88.

Step-by-step explanation:

428-360 = 88

5 0

3 years ago

Kevin said that if you triple his age the result will be 1 less than his mother age

Ivahew [28]

Basically, this problem is saying that if you multiply x by 3, then you will get a number that is one less than y. So, if you switch that around a bit, then the problem is saying that if you subtract 3x from y, you'll get 1.

Your final answer should be y - 3x = 1.

8 0

4 years ago

The point (6, 7) is reflected across the y axis. what are the coordinates of the reflection

aev [14]

Answer:

Hello!!

the point (6, 7) is reflected across the y axis. what are the coordinates of the reflection?

(-6, 7)

Step by Step Explanation:

When reflecting (x, y) over the x axis is (x, -y)

When reflecting (x, y) over the y axis is (-x, y)

Hope this helps!

7 0

2 years ago

Read 2 more answers

2/3x=20 help mee if you dont mind

Ksenya-84 [330]

The answer I got was 30

7 0

3 years ago