Factor 6x^6+4x^4+3x^3+6x

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Answer 1

Answer: Ok so i did it in this app

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Write the complex number 4(cos 60 + i sin 60) in standard form 10. Use DeMoivre's Theorem to find (2+3i)6

Answers

Answer:

a) The standard form of $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ is $z = 2 + i\cdot 2√(3)$ , b) $z = (2+i\cdot 3)^(6) = 1219.585 + i \cdot 1829.381$ .

Step-by-step explanation:

a) The standard form of the complex number is $z = a + i\cdot b$ , $\forall \,a,b \in \mathbb{R}$ . If we get that $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ , whose standard form is obtained by algebraic means:

1) $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ Given

2) $z = (4\cdot \cos 60^(\circ))+i\cdot (4\cdot \sin 60^(\circ))$ Distributive and Associative properties.

3) $z = 2 + i\cdot 2√(3)$ Multiplication/Result.

The standard form of $z = 4\cdot (\cos 60^(\circ)+i\cdot \sin 60^(\circ))$ is $z = 2 + i\cdot 2√(3)$ .

b) The De Moivre's Theorem states that:

$z = (a+i\cdot b)^(n)= r^(n)\cdot (\cos \theta + i\cdot \sin \theta)$

Where:

$r =\sqrt{a^(2)+b^(2)}$ and $\theta = \tan^(-1) \left((b)/(a)\right)$ .

If we know that $z = (2+i\cdot 3)^(6)$ , then:

$r = \sqrt{2^(2)+3^(2)}$

$r =√(13)$

$r \approx 3.606$

$\theta = \tan^(-1)\left((3)/(2) \right)$

$\theta \approx 56.310^(\circ)$

The resulting expression is:

$z = 3.606^(6)\cdot (\cos 56.310^(\circ)+i\cdot \sin 56.310^(\circ))$

$z = 1219.585+i\cdot 1829.381$

Therefore, $z = (2+i\cdot 3)^(6) = 1219.585 + i \cdot 1829.381$ .

Which graph shows the solution to the system of linear inequalities? Y< 1/3x-1 y<1/3-31) All values that satisfy y<1/3-1 are solutions
2) All values that satisfy y<1/3-3 are solutions
3) All values that satisfy either equations are solutions
4) There are no solutions
(Edge 2020)

Answers

The solution of the system of linear inequalities is All values that satisfy y<1/3-3 are solutions. (option 2)

What is inequality?

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a graph of inequalities, y < 1/3x-1 and y < 1/3-3

The solution of the inequality A is the shaded area below the solid blue line and the solution of the inequality B is the shaded area below the solid red line,

That means all the solutions of inequality B will satisfy the inequality A also.

Hence, The solution of the system of linear inequalities is All values that satisfy y<1/3-3 are solutions. (option 2)

For more references on inequality, click;

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I think the best answer would probably be 1

Proportional relationships

Answers

Answer:

relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Step-by-step explanation:

Solve for , , and .
-6x+3y-z=5
3x-y+5z=-10
-x+2y+3z=-1

Answers

Answer:

x=1, z=-2, y=3

Step-by-step explanation:

Substitution Method

Warehouse Club A charges its members $55 to join plus $25 Warehouse Club B charges a $10 to join plus $40 each month.

Answers

Warehouse Club A: y= $25x + $55
Warehouse Club B: y= $40x + $10

This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft. Draw another scale drawing of the apartment using the scale 20 ft to 1 unit from the apartment to the drawing. EXPLAIN your reasoning.

Answers

The attached drawing is the apartment using the scale 20 ft to 1 unit from the apartment to the drawing.

As the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter,

this means that each square is

160 / 16 = 10 ft on a side.

so 10 ft in real life plots to 1 unit on the drawing

If the scale is changed to 20 :1 ,

then the drawing would be exactly the same shape, only each side would have half the original drawing units.

In stead of a 40 ft side being represented by 40 ft / 10 ft/unit = 4 units,

That side would be 40 ft / 20 ft/unit = 2 units

Hence, The attached drawing is the apartment using the scale 20 ft to 1 unit from the apartment to the drawing.

Learn more about perimeter here:

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Answer:

Step-by-step explanation:

As the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is

160 / 16 = 10 ft on a side.

so 10 ft in real life plots to 1 unit on the drawing

If the scale is changed to 20 :1 , then the drawing would be exactly the same shape, only each side would have half the original drawing units.

In stead of a 40 ft side being represented by 40 ft / 10 ft/unit = 4 units, That side would be 40 ft / 20 ft/unit = 2 units

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