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Likurg_2 [28]
3 years ago
14

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations.

Mathematics
1 answer:
Nostrana [21]3 years ago
4 0
x^3-27i=0
x^3=27i
x^3=27e^{i\pi/2}
x=\left(27e^{i\pi/2}\right)^{1/3}
x=3e^{i(\pi/2+2\pi k)/3}
x=3e^{i\pi(4k+1)/6}

where k\in\{0,1,2\}. This means you have

x=3e^{i\pi/6}=\dfrac32(\sqrt3+i)
x=3e^{i5\pi/6}=\dfrac32(-\sqrt3+i)
x=3e^{i9\pi/6}=-3i

as the solutions to the original equation.
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Schach [20]
The correct label could be MN or NM
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3 0
2 years ago
30 POINTS For Answers To Questions 1-10
DochEvi [55]

QUESTION 1

The angle 33x+3 and 135\degree are alternate exterior angles.

Since alternate interior angles are congruent, we must have;

33x+3=135\degree

Group similar terms.

\Rightarrow 33x=135-3

\Rightarrow 33x=132

QUESTION 10

We solve the following equation for the two alternate exterior angles to find x.

x+134=130

\Rightarrow x=130-134

\Rightarrow x=-4

\Rightarrow x=\frac{132}{33}

\Rightarrow x=4.

QUESTION 2

The angle 120\degree and 31x-4 degree angle are alternate interior angles.

Alternate interior angles are also equal

\Rightarrow 31x-4=120\degree

\Rightarrow 31x=120+4

\Rightarrow 31x=124

\Rightarrow x=\frac{124}{31}

\Rightarrow x=4

QUESTION 3

The angle 120\degree and x+124 degree angle are alternate interior angles.

Alternate interior angles are congruent

\Rightarrow x+124=120\degree

\Rightarrow x=120-124

\Rightarrow x=-4

QUESTION 4

The given angles, 40x+5 and 42x-1 are alternate interior angles.

\Rightarrow 40x+5=42x-1

Group like terms;

\Rightarrow 5+1=42x-40x

\Rightarrow 6=2x

Divide both sides by 2 to get;

\Rightarrow x=3

QUESTION 5

The given angles, 20x+4 and 19x+9 are alternate interior angles.

\Rightarrow 20x+4=19x+9

Group like terms;

\Rightarrow 20x-19x=9-4

\Rightarrow x=5

QUESTION 6

The given angles, 11x and -9+12x are alternate exterior angles.

Since the alternate exterior angles are congruent, we have;

-9+12x=11x

We group similar terms to obtain;

12x-11x=9

\Rightarrow x=9

QUESTION 7

The two angles, x+88 and 80.

The two alternate interior angles are congruent.

\Rightarrow x+88=80\degree

\Rightarrow x=80-88

\Rightarrow x=-8

QUESTION 9

The two angle alternate interior angles.

These angles are congruent.

This implies that;

x+75=70

\Rightarrow x=70-75

\Rightarrow x=-5

QUESTION 10

We solve the following equation for the two alternate exterior angles.

x+134=130

\Rightarrow x=130-134

\Rightarrow x=-4

6 0
3 years ago
Ava and Maria went shopping together. Eva spent $20 more than Maria. Together they spent $209.84. Write and solve an equation to
ad-work [718]

Answer:209.84 - 20.00 = 189.84 / 2 = 94.92

94.92 + 20.00 = 114.92 Eva spent and Martha spent $94.92

Step-by-step explanation:

5 0
3 years ago
If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.
alexgriva [62]

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]

The inverse of the matrix is

\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]

So, the Inverse Transformation is given by

T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})

So, no option is correct. And the answer is

T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})

Learn more about linear transformations here-

brainly.com/question/13005179

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5 0
2 years ago
4. Use the substitution method to determine the solution to this system of equations.
N76 [4]

Answer:

No solution

Step-by-step explanation:

6X - 3Y = -9--------------(1)

- 2 X +Y= 5---------------(2)

from equation two,

Y = 5+2X------------------(3)

substitute equation (3) into equation (1)

6X-3(5+2X)= -9

opening bracket

6X-15-6X= -9

6X- 6X = -9+15

0 = 6

<h2>therefore the answer is no solution</h2>

3 0
1 year ago
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