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Juliette [100K]
3 years ago
5

Using De-Moivre's theorem, prove that i^2= -1.​

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
3 0

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

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HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
AleksandrR [38]
<h3>Answer: Choice A. 82 websites per year</h3>

=============================================================

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

slope = (y2-y1)/(x2-x1)

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

3 0
3 years ago
Solve and graph the inequality 6 + 3n ≤40
Kazeer [188]
6+3n≤40
Use inverse operations i.e.
4x+2<10
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4x<8
4*x/4<8/4
x<2
7 0
3 years ago
Stephanie has 60 tickets to the carnival.She used 3/4 of her 60 tickets to play games.Then she used 1/5 of her remaining tickets
Lera25 [3.4K]

Answer:

<h2>She gave her brother 6 tickets</h2>

Step-by-step explanation:

This problem is on fractional numbers.

given that she has 60 tickets

1.She used 3/4 of her tickets to play game

=(3/4)*60

=180/4

=45

She is left with (60-45)= 15 tickets

2. She used 1/5 of her remaining tickets for rides

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   =15/5

   =3

She is left with (15-3)= 12 tickets

3. She gave half of her tickets to her brother.

  = (1/2)*12

  =12/2

 = 6

She gave her brother 6 tickets

3 0
4 years ago
Chloe is paid $1,213.15 semimonthly. What is her average monthly net, or take-home, pay?
77julia77 [94]
HI THERE
36390
HOPE THAT HELPS

8 0
3 years ago
Read 2 more answers
Mr. Duncan bought a table at a discount if 30% thus saving $42. what was the marked price of the table?​
katovenus [111]

Answer:

$140

Step-by-step explanation:

if 30% of full price = $42 then 100% = 42/0.3 = 140

5 0
3 years ago
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