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3 years ago

HELP PLEASE FIND THE VALUE OF THE FOLLOWING EXPRESSION

Mathematics

1 answer:

AleksAgata [21]3 years ago

3 0

The answer is 3,359,232.

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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

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

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3 years ago

What is the volume of a hemisphere with a diameter of 7.7 ft, rounded to the nearest tenth of a cubic foot?

Nady [450]

Answer: 119.57 cu. ft.

Step-by-step explanation:

Volume of a hemisphere = (2/3)πr^3

= (2/3) * 22/7 * 3.85^3

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3 years ago

The parking meter charges $2 for the first hour, then $.75 for each hour thereafter. Nate only has $5. How many hours can he par

frozen [14]

Answer:5 hours

Step-by-step explanation:

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An isosceles triangle has a base of 8 inches and legs measuring 12 inches how wide is the base of a similar triangle with legs m

VARVARA [1.3K]

If the triangles are similar, the base should be 24 inches. The legs on the first triangle are 12 inches. To get 36 inches (the other triangle), we multiply 12 by 3. 12 x 3 = 36. Because you did that to the legs, you must also do it to the base. 8 x 3 = 24. Therefore, the base of the second triangle is 24 inches.

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3 years ago

THIS IS 6TH GRADE please help me! thanks

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Answer:

Step-by-step explanation:

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2 years ago

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