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2 years ago

De moirve's (√3-i ÷ √3+i)^6 = 1

1 answer:

7 0

(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)

… = ((√3)² - 2√3 i + i ²) / (3 - i ²)

… = (3 - 2√3 i - 1) / (3 - (-1))

… = (2 - 2√3 i ) / 4

… = 1/2 - √3/2 i

… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))

… = exp(i arctan(-√3))

… = exp(-i arctan(√3))

… = exp(-iπ/3)

By DeMoivre's theorem,

[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1

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Naily [24]

Answer:

$92492.40

Step-by-step explanation:

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3 years ago

The dimensions of a rectangle can be given by x+9 and x-2. If the area is 60ft^2, what is the value of X?

Veronika [31]

Answer:

Step-by-step explanation:

(x + 9) * (x - 2) = 60

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x^2 + 7x - 18 = 60

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3 years ago

Use the theoretical probability formula to solve the problem. Express the probability as a fraction

serg [7]

Answer:

c. 3 / 13

d. 2 / 13

Step-by-step explanation:

A deck of cards has 52 cards. There are cards of 4 suits- Spades, Hearts, Diamonds and Clubs.

So, there are 52/4= 13 cards of each suit.

Among these 13 cards, there are 3 picture cards or face cards as they are called. These are the Jack, Queen and King cards.

So, the number of total picture cards = 4*3 = 12

the number of cards are 52

theoretical probability formula: P = favorable events/ possible events

P = 12 / 52

P = 3 / 13

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so favorable events = 4 + 4 = 8

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2 years ago

Applications: Sarah's Pet Store never has more than a combined total of 16 cats and dogs. She also never has more than 9 cats. W

ankoles [38]

The possible solution is 12 cats and 4 dogs in Sarah's store.

Let x represent the number of cats and y represent the number of dogs.

Since Sarah's Pet Store never has more than a combined total of 16 cats and dogs. Hence:

x + y ≤ 16

Also, She also never has more than 9 cats. Therefore:

x > 9

The solution to the inequality is graphed. From the graph, the possible solution is 12 cats and 4 dogs

Find out more on inequalities at: brainly.com/question/24372553

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2 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

1 | 2 -5 3

| 2 -5 3 0

1 | 2 -3

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

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| 1 -1 0 -4

2 | 2 2

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Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

-2 | -12 10 -2

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2 years ago