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3 years ago

Is 3, 1, 1/3, 1/9,... a geometric sequence?

1 answer:

7 0

$a_1;\ a_2;\ a_3;\ a_3;\ ...;\ a_n;\ a_{n+1};...\ is\ a\ geometric\ sequence\\if\ a_{n+1}:a_n=const.\\-------------------\\a_1=3;\ a_2=1;\ a_3=\dfrac{1}{3};\ a_4=\dfrac{1}{9}\\\\a_4:a_3=\dfrac{1}{9}:\dfrac{1}{3}=\dfrac{1}{9}\cdot\dfrac{3}{1}=\dfrac{1}{3}\\\\a_3:a_2=\dfrac{1}{3}:1=\dfrac{1}{3}\\\\a_2:a_1=1:3=\dfrac{1}{3}\\\\Answer:Yes.\ It's\ the\ geometric\ sequence.$

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Precal help if you could could you answer both. Me finishing this helps me graduate.

oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

$z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))$

In this form, you have

$z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))$

The magnitude of the number is given by

$z=a+bi \implies \rho = \sqrt{a^2+b^2}$

So, we have

$z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2$

As for the angle, we have

$z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}$

So, we have

$z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}$

Finally,

$z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64$

Exercise 2:

You simply have to compute the trigonometric function:

$\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}$

So, we have

$z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i$

7 0

3 years ago

PQ=RQ <br> i’m looking for A in the problem

Naddik [55]

Answer:

i think the answer is 43 degrees but i dont know

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3 years ago

If carbon dioxide, methane, and water vapor were not in the atmosphere, then

Savatey [412]

<h2>Answer:</h2>

D. The Earth's surface would be much colder than it is.

<h3>Step-by-step explanation:</h3>

This is because warm temperatures and high levels of atmospheric carbon dioxide happen at about the same time. So if atmospheric carbon dioxide concentrations double warm up by between 2 and 4.5 degrees Celsius. On the other hand, water vapor promotes, as the greatest contributor, to the Earth’s greenhouse effect. In this way, if carbon dioxide, methane, and water vapor were not in the atmosphere, then it's obvious that the Earth's surface would be much colder than it is.

3 0

2 years ago

What is 4/20 + 11/20 in its simplest form

vivado [14]

Answer:

Step-by-step explanation:

4/20 + 11/20 = 15/20

15/20 = 3/4 or 0.75

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3 years ago

Read 2 more answers

DUE FIVE MINUTES HELPPPPPP!!!!!!!!!!!!!!!!

iris [78.8K]

Answer:

This is late you said it was due 5 min. yet I this was posted 5 hours. No one can help now.

Step-by-step explanation:

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2 years ago