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3 years ago

10

Alexis saves up her monthly allowance over a period of six months to buy a pair of high-resolution headphones. She lends her fri

end, Janet $32.80 from her savings. If Alexis has $216.20 now, calculate her monthly allowance.

2 answers:

Anika [276]3 years ago

6 0

Her monthly allowance should be $41.50

tino4ka555 [31]3 years ago

5 0

Answer:

$41.50

Step-by-step explanation:

:))) please mark me brainliest!

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What is the value of the 8th term of the sequence 4, 8, 16, 32, ...?

vladimir1956 [14]

Answer:

512

Step-by-step explanation:

The sequence is doing the number times 2, so 4 times 2 equals 8,

8 x 2 = 16, ect

If you do this enough, you will get 512 as the 8th term.

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2 years ago

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Lynna [10]

Answer:

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2 years ago

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

Macs farm has a total of 18 horses and 27 cows. what is the ratio of horses to cows in simplest form?

Evgesh-ka [11]

The ratio is basically finding the quotient of two numbers. If you want to find the ratio of horses to cows, divide the number of horses to that of cows.

Ratio = 18/27

When expressing it to its simplest form, make sure it is reduced. 18 and 27 are both factors of 9. So,

Ratio = 9*2/9*3
Cancelling out 9, the ratio at its simplest form is: <em>2/3</em>

7 0

3 years ago

PLEASE HELP I DONT KNOW

Reptile [31]

Answer:

290ft

Step-by-step explanation:

First, add 40 and 50 together to get the side across giving you 90.

Next, take 60 and subtract 25 for the oposite side giving you 25.

Finally, add all sides together to get 290.

6 0

3 years ago