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OleMash [197]
3 years ago
11

Mrs. Portillo's cat weighs 6 kilograms. Her dog weighs 22 kilograms more than her cat. What is the total weight of her cat and d

og ?
Mathematics
2 answers:
topjm [15]3 years ago
5 0
Cat=6
dog=22+6
total kilograms = 6+(22+6)= 34
Strike441 [17]3 years ago
3 0
We already know how much the cat weights so the first step is to find the weight of Mrs. Portillo's dog.

cat = 6 kg

dog = cat + 22 kg
dog = 6kg + 22kg
dog = 28 kg

Weight of the dog and cat = dog + cat
Weight of the dog and cat = 28 kg + 6 kg
Weight of dog and cat = 34 kg
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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
3 years ago
7. Olivia purchases gifts for her mom and
slega [8]

Answer:

$23.40

Step-by-step explanation:

3 0
3 years ago
What is the answer to this question ?
mixer [17]
What the heck is this
5 0
2 years ago
Please help ill give brainliest
Naddik [55]
I think it’s option a
8 0
3 years ago
Please help:)<br><br> See pic attached
Lostsunrise [7]

Answer:

Adults: 75, girls: 100, Boys: 75

Step-by-step explanation:

2/5 x 250 = 100( girls)

3/10 x 250 = 75 (boys)

250 - (100 + 75) = 250 - 175 = 75 (Adults)

5 0
2 years ago
Read 2 more answers
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