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Sever21 [200]
3 years ago
7

Please help me from 1-10

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
6 0
1. Herself
2. She
3. Them
4. Her
6. Themselves
8. They
9. It
10. Us

Couldn't figure out 5 and 7
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Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer t
11Alexandr11 [23.1K]

Answer:

The solution is z = -2.853 - i 0.927.

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

z^{n} = r^{n} \cdot (\cos n\theta + i \sin n\theta)

Where r is the norm of the complex number. In this case, expression can be written as:

-i 243 = 3^{5} \cdot (\cos 5\theta + i \sin 5\theta)

The real component must be equal to zero and complex component must be equal to -1. That is to say:

\cos 5\theta = 0

\sin 5\theta = -1

Possible solutions for each component are, respectively:

Real component

5\theta = \cos^{-1}0

5\theta = \frac{\pi}{2} \pm \pi\cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{\pi}{10} \pm \frac{\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{13\pi}{10}, \frac{3\pi}{2}

Complex component

5\theta = \sin^{-1}(-1)

5\theta = \frac{3\pi}{2} \pm 2\pi \cdot j, \forall j \in \mathbb{N}_{O}

\theta = \frac{3\pi}{10} \pm \frac{2\pi}{5}  \cdot j, \forall j \in \mathbb{N}_{O}

Possible solutions: \frac{11\pi}{10}, \frac{3\pi}{2}

There is one solution whose argument is strictly between 180 degrees (\pi) and 270 degrees (1.5\pi).

z = 3 \cdot \left( \cos \frac{11\pi}{10} + i \sin \frac{11\pi}{10} \right)

z = -2.853 - i 0.927

6 0
3 years ago
A factory can work its employees no more than 6 days a week, and no less than 2 days per
Molodets [167]

Answer:

Step-by-step explanation:

Answer: A.) 2 <= X <= 6

B.) 13 < = X < = 39

Step-by-step explanation:

Given that a factory can work its employees no more than 6 days a week, that is, less than or equal to 6 days a week

And also, no less than 2 days per week. That is, greater than or equal to 2 day a week.

Let X represent the number of days an employee can work per week.

According to the first statement,

X < = 6

According to the second statement,

X >= 2

An inequality to represent the range of days an employee can work will be

2 < = X <= 6

To represent the range in hours, first convert the number of days to hour. Given that an employee can work

1 day = 6.5 hours

2 days = 2 × 6.5 = 13 hours

5 days = 6 × 6.5 = 39 hours

Therefore, the range will be

13 < = X < = 39

6 0
3 years ago
Pleaseeeee helpppp meeeeee
Crank

Answer:

2. -18w + 6

4. 2w - 20w + 6

Step-by-step explanation:

2w +  \frac{1}{2} ( - 40w + 12) \\ 2w - 20w + 6 \\  - 18w + 6 \\

3 0
3 years ago
What is the value of x?
Morgarella [4.7K]

Answer:

91.5

Step-by-step explanation:

I did the math. Add up all the numbers and then, divide the result by two to get 91.5

4 0
3 years ago
What is the slope of the line shown in the graph?
Katarina [22]

Answer:

I'm pretty sure it's -3/2

6 0
3 years ago
Read 2 more answers
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