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Cerrena [4.2K]
4 years ago
8

The figure shown at the right is known as pascal triangle

Mathematics
1 answer:
Nadya [2.5K]4 years ago
4 0
What is the question?


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Use DeMoivre's Theorem to find the following. Write your answer in<br> standard form.
valina [46]

Answer:

Option C.

Step-by-step explanation:

The given expression is

\left(\sqrt{2}cis \dfrac{9\pi}{20}\right)^5

It can be rewritten as

\left(\sqrt{2}\cos \dfrac{9\pi}{20}+i\sin\dfrac{9\pi}{20}\right)^5

According to De moivre's Theorem:

[r(\cos\theta+i\sin \theta)]^n=r^n(\cos n\theta +i\sin n\theta)

Using De moivre's Theorem, we get

(\sqrt{2})^5\left(\cos \dfrac{9\pi\times 5}{20}+i\sin\dfrac{9\pi\times 5}{20}\right)

=4\sqrt{2}\left(\cos \dfrac{9\pi}{4}+i\sin\dfrac{9\pi}{4}\right)

=4\sqrt{2}\left(\cos (2\pi +\dfrac{\pi}{4})+i\sin (2\pi+\dfrac{\pi}{4})\right)

=4\sqrt{2}\left(\cos \dfrac{\pi}{4}+i\sin \dfrac{\pi}{4}\right)

=4\sqrt{2}\left(\dfrac{1}{\sqrt{2}}+i\dfrac{1}{\sqrt{2}}\right)

=4+4i

Therefore, the correct option is C.

5 0
3 years ago
Can someone pls help me<br> Solve for x <br> Please show your work
Arlecino [84]

Answer:

I don't see photo...........

5 0
3 years ago
Read 2 more answers
1.What is the elapsed time between 11:50 a.m. and 4:05 p.m.?
never [62]
1) D.
2) I’d need the AM or PM to tell unless it’s world clock.
3) C.
4) A.
5) B.
6) A.
7) Can’t see the thermometer.
8) B. and C.
6 0
4 years ago
Order these fraction from to : 2/3 , 7/12 , 3/4
lora16 [44]

I didn't really know whether to do it from least to greatest or greatest to least, so I did it from least to greatest.

Steps:

1. Find a common denominator

Let's do 12

2. Convert

7/12 is already in its simplest form, so 2/3 = 8/12 and 3/4 = 9/12

3. Order

7/12, 8/12, 9/12

4. Back to original form

7/12, 2/3, 3/4

ANSWER: 7/12, 2/3, 3/4

7 0
3 years ago
Read 2 more answers
Cos^2(2theta)+ 2cos(2theta)+1=0
Tema [17]

Answer:

θ = π n + π/2 for n element Z

Step-by-step explanation:

Solve for θ:

1 + 2 cos(2 θ) + cos^2(2 θ) = 0

Write the left hand side as a square:

(cos(2 θ) + 1)^2 = 0

Take the square root of both sides:

cos(2 θ) + 1 = 0

Subtract 1 from both sides:

cos(2 θ) = -1

Take the inverse cosine of both sides:

2 θ = 2 π n + π for n element Z

Divide both sides by 2:

Answer:  θ = π n + π/2 for n element Z

4 0
3 years ago
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