Can you please help me with this

By using the De Moivre's formula, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).

Complex numbers are numbers of the form a + i b, where a and b are the real and imaginary component, respectively. In other words, complex numbers are an expansion from real numbers. The n-th root of a complex number is found by using the De Moivre's formula:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n} \right) + i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for i = {0, 1, 2, ...,  n - 1}.

Where:

The norm of the complex number is found by Pythagorean theorem:

[tex]r = \sqrt{(2\sqrt{3})^{2}+(-2)^{2}}[/tex]

r = 4

And the direction is determined below:

[tex]\theta = \tan^{-1} \left(\frac{2\sqrt{3}}{-2} \right)[/tex]

θ = 2π/3 rad

Then, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).

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Answer: Hope this helps you.

1,3

Step-by-step explanation:

(6, 4) and (0,2)

4-2/6-0 =2,6 (1,3)

Step-by-step explanation:

please mark me as brainlest

Answer:-8.3

Step-by-step explanation:-8.3

Answer:

-8.3333333333

Step-by-step explanation:

First you want to start by multiplying (-2) * 3.

Next you want to multiply 1/2 * 1/3

Finally you add you answers together to get what you need.

Also this was very very very easy so go to summer school if you are this dum.

Answer:

20 for $8

Step-by-step explanation:

Answer:

119 4/7

Step-by-step explanation:

Perimeter is all of the lengths of the sides added together. I started by adding all of the whole numbers:

35+10+12+15+24+12+10=118

Then I added the fractions (after making the denominators equal by multiplying the 3/7, 1/7, 2/7 all by 2)

6/14+2/14+4/14+3/14+1/14+4/14+2/14= 22/14

Then I subtracted 14 from 22 to take out our whole number (which would be 14/14 or 1), and see that we are left with 8.

This means that our answer is 119 8/14 or 119 4/7

When the height of the prism doubles, the percentage increase in the volume is 100%

The volume of a prism is:

V₁ = BH

Where:

B represents the base area and H represents the height.

When the height doubles, the volume becomes

V₂ = 2BH

The percentage increase is then calculated using:

%Increase = (V₂ - V₁)/V₁

So, we have:

%Increase = (2BH - BH)/BH

Evaluate

%Increase = 1

Express as percentage

%Increase = 100%

Hence, the percentage increase is 100%

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                  [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

         [refer to attachment for question] ~

    [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

✫ First of all, Slope-intercept form is written as follows:-

                                        [tex]\longmapsto\Large\textbf{y=mx+b}[/tex]

Where:-

To find:-

Solving,

           Replace m with -1/5 And b with -3:-

                 [tex]\large\text{$y=-\displaystyle\frac{1}{5} x-3$}[/tex]

[tex]\Uparrow[/tex]  [tex]\sf{the\:equation}[/tex]

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[tex]\rule{300}{1}[/tex]

half the diagonal is shown as 20cm.

The full diagonal would be 20 x 2 = 40 cm.

area of a square using the diagonal is 1/2 x diagonal^2

Area = 1/2 x 40^2 = 800 square cm

answer: 800 square cm.

Answer: it might be 8

Step-by-step explanation: Write a distance formula:  x^2  - x^1    

substituted -3.8, 4.2 into  x^2  - x^1   and u will get 4.2 + 3.8 and u will calculate and it gets 8

I hope its right

Answer:

[tex]r \: = \: \boxed{ \bold{\frac{2}{3} }}[/tex]

Step-by-step explanation:

[tex]r \: = \: \frac{36}{54} \\ \\ r \: = \: \frac{24}{36} \\ \\ r \: = \: \frac{16}{24} [/tex]

[tex]r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} \\ \\ r \: = \: \frac{2}{3} [/tex]

Since the ratio is the same, that is the common ratio.

Answer:

36

Step-by-step explanation:

[tex]-2[-6(-4+7)]\\\\=(-2)(-6)(3)\\\\=12(3)\\\\=36[/tex]

Answer:

For no solution,

2x + 9 + 3x + x = 6x

For one solution,

2x + 9 + 3x + x = 15

For infinitely many solutions,

2x + 9 + 3x + x = 6x + 9

Step-by-step explanation:

Step-by-step explanation:

1.  2x + 9 + 3x + x = 6x

6x + 9 = 6x

Subtract 6x from both sides,

9 = 0 which is absurd and hence the equation has no solution.

2.  2x + 9 + 3x + x = 15

6x + 9 = 15

Subtract 9 from both sides.

6x = 6

Divide both sides by 6.

x = 1 and this is the only solution.

3. 2x + 9 + 3x + x = 6x + 9

6x + 9 = 6x + 9

Subtract 6x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

First simplify

#No solution

#One solution

#Infinitely many solution

Answer:

dont now the answer but air math app will help you just take photo of problems

Answer:

4.08

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

Anything multiplied by 0 = 0. So the whole right side is 0.

(6x - 9)*3 - 1  = 0                       Add 1 to both sides.

(6x - 9)*3 - 1 + 1 = 0 + 1             Combine

(6x - 9)*3 = 1                             Divide both sides by 3

(6x - 9)*3/3 = 1/3                      Simplify

(6x - 9) = 1/3                             Remove brackets. Add 9 to both sides

6x - 9+9 = 9 1/3                        Combine

6x = 9 1/3

6x = 28/3                                   Divide both sides by 6

6x / 6 = 28/3 // 6                       Invert the 6 and multiply.

x = 28/3 * 1/6

x = 28/18

Answer

x = 14/9

Answer:

[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]

Answer:

3x-3

Step-by-step explanation:

use synthetic division

Answer:

See explanation

Step-by-step explanation:

Since she used only 1/2 of the recipe and the full recipe uses 1 cup, divide 1 by 2. The equation is 1/2=0.5.

For the lemon juice, the equation is 1/4 divided by 2. On the number line, make a dot at 1/4, and then travel backwards halfway. 1/4 divided by 2 is 1/8, or 0.125.

Hope this helps!

Answer:

D1×D2/2sq

445×5= 225

225/2

=112.5

Answer:

4

Step-by-step explanation:

x = 7 - 3

x = 4

Answer:

x = 4

Step-by-step explanation:

3+x = 7

Subtract 3 from each side

3+x-3 = 7-3

x = 4

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.

__

The interior angle at the right end of the line is the supplement of 4x:

  180° -4x

The interior angle at the left end of the line is the supplement of 2x:

  180° -2x

  86° +(180° -4x) +(180° -2x) = 180°

Then the solution to the triangle is ...

  266° = 6x . . . . . . . . . add 6x-180°

  x = 266°/6 = 44 1/3° . . . . . divide by 6

Answer:

see explanation

Step-by-step explanation:

PQRS is a cyclic quadrilateral.

the opposite angles in a cyclic quadrilateral sum to 180° then

∠ Q + ∠ S = 180 ( substitute values )

3x - 8 + 3x + 8 = 180

6x = 180 ( divide both sides by 6 )

x = 30

Then

∠ Q = 3x - 8 = 3(30) - 8 = 90 - 8 = 82°

∠ S = 3x + 8 = 3(30) + 8 = 90 + 8 = 98°

∠ P = x + 15 = 30 + 15 = 45°

∠ R = 180° - ∠ P = 180° - 45° = 135°

The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

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If the volume of each brick will be 64 cubic centimeters. Then the mass of each brick will be 192 grams.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

mass = density × volume

A construction company needs to transport 500 bricks. The dimensions of each brick are 2 cm by 4 cm by 8 cm.

The density of each brick is 3 g/cm³.

Then the mass of each brick will be

The volume of each brick will be

V = 2 x 4 x 8

V = 64 cm³

Then the mass will be

m = 3 x 64

m = 192 gram

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Answer:

i don't know

Step-by-step explanation:

i don't know

The distance around the perimeter would be 120 ft.

Perimeter is the distance around the edge of a shape.

The complete question is

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.

What is the distance around the perimeter of the garden?

let AE is the half of the diagonal AC.

AC = 30 ft.

So, AE = ½ * 30

AE = 15 ft

Now, using trigonometry

sin 30 = 15/AD

0.5= 15/AD

AD= 30 ft

Hence, distance around the perimeter would be: AD+AD+AD+AD=

=30 ft + 30 ft + 30 ft + 30 ft

= 120 ft.

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Answer:A

Step-by-step explanation: just took it

Answer:

t would be steeper

Step-by-step explanation:

Answer:

[tex] \frac{1}{24} miles \\ [/tex]

Step-by-step explanation:

[tex] \frac{7}{8} - \frac{5}{6} = \frac{1}{24} [/tex]

Answer: 0.000000009085

Step-by-step explanation: This expression is rewritten like this because it is multiplied by a negative power of ten. Therefore, applying this principle to scientific notation, the answer would have to be less than 0. That would be your answer. Hope this helps!