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3 years ago

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

1 answer:

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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What is the correct label of the line?

Schach [20]

The correct label could be MN or NM
It doesn't matter because the line could be going left or right.
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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

#SPJ10

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