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2 years ago

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A DJ has a total of 1075 dance, rock, and country songs on her system. The dance selection is three times the size of the rock s

election. The country selection has 105 more songs than the rock selection. How many songs on the system are dance? rock? country?

1 answer:

Alexus [3.1K]2 years ago

7 0

582 dance, 194 rock, 299 country.

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garri49 [273]

Answer:

the answer is c

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3 years ago

Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of

jeka57 [31]

Answer:

c = 60.65 cm

Step-by-step explanation:

Given that,

The two sides of a triangle are 33 cm and 37 cm.

The angle between these two sides is 120°.

We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,

$c^2=a^2+b^2-2ab\cos C$

a = 33 cm, b = 37 cm and C is 120°

So,

$c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm$

So, the length of the third side of the triangle is 60.65 cm.

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2 years ago

The difference between eight times a number and three is equal to negative nineteen. What is the number? 2 -2 -3 3

castortr0y [4]

The answer is -2 because 8(-2)-3=-19
8(-2)= -16-3=-19

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3 years ago

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rosijanka [135]

Answer:

HI TO YOU HAVE A GOOD DAY AND NICE DAY

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2 years ago

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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 = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

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3 years ago