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Arturiano [62]
2 years ago
12

What is the correct justification for the indicated steps?

Mathematics
2 answers:
Oliga [24]2 years ago
5 0

Answer:

Step A: Product of Powers

Step C: Distributive Property

Step D: Trigonometric Sum Identity

Step-by-step explanation:

Correct on Edge :)

yanalaym [24]2 years ago
4 0

The given proof of De Moivre's theorem is related to the operations of

complex numbers.

<h3>The Correct Responses;</h3>
  • Step A: Laws of indices
  • Step C: Expanding and collecting like terms
  • Step D: Trigonometric formula for the cosine and sine of the sum of two numbers

<h3>Reasons that make the above selection correct;</h3>

The given proof is presented as follows;

\mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1}}

  • Step A: By laws of indices, we have;

\left[cos(\theta) + i \cdot sin(\theta) \right]^{k + 1} = \mathbf{\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}

\left[cos(\theta) + i \cdot sin(\theta) \right]^{k} \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] =  \mathbf{\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right]}

  • Step B: By expanding, we have;

\left[cos(k \cdot \theta) + i \cdot sin(k \cdot \theta) \right] \cdot \left[cos(\theta) + i \cdot sin(\theta) \right] = cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i  \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right]

  • Step D: From trigonometric addition formula, we have;

cos(A + B) = cos(A)·cos(B) - sin(A)·sin(B)

sin(A + B) = sin(A)·cos(B) + sin(B)·cos(A)

Therefore;

cos(k \cdot \theta) \cdot cos(\theta) - sin(k \cdot \theta) \cdot sin(\theta) + i  \cdot \left [sin(k \cdot \theta) \cdot cos(\theta) + cos(k \cdot \theta) \cdot sin(\theta) \right] = \mathbf{ cos(k \cdot \theta + \theta) + i \cdot sin(k \cdot \theta  + \theta)}

Learn more about  complex numbers here:

brainly.com/question/11000934

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The following list gives the number of siblings for each of 11 students. 0, 8, 9, 6, 5, 7, 2, 4, 3, 1, 11 Find the modes of this
Y_Kistochka [10]

Answer:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11

Step-by-step explanation:

Given

0, 8, 9, 6, 5, 7, 2, 4, 3, 1, 11

Required

Determine the mode

Though, not necessary; it is a good practice to order the given data either in ascending or descending order.

In ascending order, the ordered data are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11

Mode implies that: the data that has the highest number of occurrence.

In the given data, each data has a frequency of 1.

Hence, the mode is:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11

4 0
2 years ago
I'm struggling with this question i need help. please and thank you
soldi70 [24.7K]
The answer is 100X because if you do 5x-4x first it will be 1x. Later on, if you do the exponent you have 1x times 1x. Then you do 1x+9x = 10x

Then you do 10x times 10x because of the exponent is telling you how times you do it and it equals to 100x.

Answer= 100x



I hope this helps YOU!   

7 0
3 years ago
Miguel is making a snack mix. The recipe calls for six parts of spicy tortilla chips to three parts of corn chips. Miguel would
Harlamova29_29 [7]
Equation:
6x + 3x = 45

To find X:
6x = 45
45/6 = 7.5
x = 7.5

To find other X:
3x = 45
45/3 = 15
x = 15

Final answer:

7.5 cups tortilla chips

15 cups corn chips
3 0
3 years ago
Read 2 more answers
URGENT 30 points I need help
Ostrovityanka [42]

Answer:

<em>- 112 + 100 n</em>

Step-by-step explanation:

a_{n} = a_{1} + (n - 1 )d

~~~~~~~

a_{1} = - 12

d = 100

a_{n} = - 12 + 100( n - 1 )

a_{n} = - 12 + 100n - 100

a_{n} <em>= - 112 + 100 n</em>

4 0
2 years ago
(Re-Asking This Question, NO scam answers or LINKS. I will report.)
AlexFokin [52]

Answer:

Yes

Step-by-step explanation:

This is because the first point in the parenthesis is x and the second is y. If we know this, we can substitute -5 in for x and -6 in for y to get that -15 - (-12) > -4. When you subtract by a negative number, it is the same as adding by that number, so -15 - (-12) = -15 + 12, so we get that -3 > -4. This is true because when you have negative numbers, the lesser negative number is the greater one (Ex. -5 > -6).

3 0
3 years ago
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