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2 years ago

Find the prime factorization of the number 20. If the number is prime, state this

Mathematics

1 answer:

mihalych1998 [28]2 years ago

3 0

Answer:

Some of the prime factors are 1,2,4,5,10,20,-1,-.2,-4,-5,-10,-20, and since 5 is prime you can just start with 5 and 4

Step-by-step explanation:

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Use DeMoivre's theorem to evaluate the expression

natima [27]

Answer:

B. $\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}$

Step-by-step explanation:

DeMoivre's theorem:

If the complex number $z=r(\cos \alpha+i\sin\alpha),$ then for natural number n

$z^n=r^n(\cos n\alpha+i\sin n\alpha).$

In your case,

$z=\sqrt{3}\left(\cos\dfrac{5\pi}{12}+i\sin\dfrac{5\pi}{12}\right)$

and you have to evaluate $z^4.$

By DeMoivre's theorem,

$z^4=(\sqrt{3})^4\left(\cos 4\cdot \dfrac{5\pi}{12}+i\sin 4\cdot \dfrac{5\pi}{12}\right)=9\left(\cos \dfrac{5\pi}{3}+i\sin\dfrac{5\pi}{3}\right)=9\left(\dfrac{1}{2}-i\dfrac{\sqrt{3}}{2}\right)=\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}.$

7 0

2 years ago

The number 64 is a perfect ___ A. Square B. Cube C. Both

Advocard [28]

Answer:

The answer is both.

Step-by-step explanation:

It is both because 8^{2} is 64 and 4^{3} is 64.

hope this helps :)

8 0

3 years ago

Read 2 more answers

Find the perimeter of a square whose sides are 7.

allochka39001 [22]

Hey there,

Your question states: Find the perimeter of a square whose sides are 7.

When finding the perimeter, we need to multiply each side because it is a square. So 7 times 4 would be 28

~Jurgen

5 0

3 years ago

7 cos x+1=6 secx solve for x

jonny [76]

7cos(x) + 1 = 6sec(x)
7cos(x) + 1 = 6/cos(x)
7cos^(x) + cos(x) = 6
7cos^(x) + cos(x) - 6 = 0
[7cos(x) - 6][cos(x) + 1] = 0
cos(x) = 6/7 , x = arccos(6/7) and
cos(x) = -1, x = 180

6 0

2 years ago

15:59:26

Viefleur [7K]

Answer:

Step-by-step explanation: I just took the quiz.

5 0

2 years ago