How do you find the scientific notation of:<br> 29,678,900,522?

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

seven people arrive to dinner, but the circular table only seats six. if two seatings such that one is a rotation of the other a

Alenkinab [10]

6 different people chosen from 7 can sit around the circular table in 840 ways.

Given that there are 7 people who have arrived for dinner.

But the circular table only seats 6.

Hence 1 person can be left out.

This can be done in 7 ways, which is a simple case of permutation.

A permutation is a combination of objects arranged in a particular sequence. The elements of sets are arranged in this case in a linear or sequential sequence.

Now 6 people will have to sit on the circular table.

Now from the properties of combination we know that , if n people sit around a circular table, then they can sit in n! ways.

Therefore 6 people can sit around a circular table in 6! ways.

6! = 120

Therefore total number of ways = 120 × 7 = 840

Hence 6 different people chosen from 7 can sit around the circular table in 840 ways.

To learn more about table visit:

brainly.com/question/16885576

#SPJ4

5 0

1 year ago

You owe $1,000 on a credit card that has an interest rate of 27.99% and make only the minimum payment of $20 each month. Which a

mel-nik [20]

Answer: The credit card will paid off within 10 years, therefore the correct option is D.

Explanation:

Let the number of years in which the credit card will aid of be x.

It is given that amount owed on credit card is $1000 with interest rate 27.99%.

So the amount of interest is calculated as,

$1000\times \frac{27.99}{100} =\$27.9$

The total amount have to pay is,

$\$1000+\$279.9=\$1279.9$

The minimum payment is $20 each month.

$x=\frac{1279.9}{20}$

$x=63.995$

So, the credit card will paid of in 63.995 months. We know that 1 year =12 months.

$\frac{63.995}{12} =5.33$

Therefore, the will paid of in 5.33 years, s we can say that the credit card will paid off within 10 years, therefore the correct option is D.

7 0

3 years ago

Read 2 more answers

What is the volume of a rectangular prism that is 3 cm by 7 cm by by 7 cm?

natali 33 [55]

Answer:

147 $cm^{3}$

Step-by-step explanation:

7*7*3 = 147

volume of a rectangular prism = length*width*height, in this case, 7*7*3

hope this helps :)

3 0

3 years ago

Lisa drank 7/16 of a bottle of water during the soccer game. Julianne drank 2/3 of the water in a bottle that was the same size

frez [133]

Answer:

julianne drank by about .1 tenth

Step-by-step explanation:

5 0

3 years ago

How do you find the scientific notation of: 29,678,900,522?