Express( (√3 +i )^60 )in polar form​

Answers

Answer 1

Observe that

|√3 + i| = √((√3)² + 1²) = √4 = 2

and

arg(√3 + i) = arctan(1/√3) = π/6

so that

√3 + i = 2 exp(i π/6)

By de Moivre's theorem, we get

(√3 + i)⁶⁰ = 2⁶⁰ exp(i π/6 • 60) = 2⁶⁰ exp(i 10π) = 2⁶⁰


Related Questions

Identify the terms and like terms in the question 3n+7-n-3

Answers

Answer:

like terms: (3n,-n),(7,-3)

Step-by-step explanation:

Answer:=2n+2

Step-by-step explanation:

3n+7-n-3=2n+2

Help fast please, AC= ?

Help fast please, AC= ?

Answers

AC = 14 (do sine method) with degree measure and sides

Can someone pls help me I feel like I am going to die

Can someone pls help me I feel like I am going to die

Answers

Answer:

the first si the correct

Answer:

It's A.

It says he wrote checks for 20 dollars and 30 dollars, which takes away 20 dollars and then 30 more dollars, then he deposited 40 more dollars.

Step-by-step explanation:

Evaluate (10 – 4i) ÷ (5 + i).
Fifty-four twelfths minus fifteen twelfths i
Twenty-three twelfths minus fifteen twelfths i
Fifty-four thirteenths minus fifteen thirteenths i
Twenty-three thirteenths minus fifteen thirteenths i

Answers

The quotient of the given complex number is 7/13 - 15/13i


Division of Complex number

Given the division expression

(10 – 4i) ÷ (5 + i).

This can also be expressed as:

10-4i/5+i

On rationalizing, we will have:

10-4i/5+i * 5-i/5-i

50-10i-20i-4(-1)/25-(-1)

50-30i+4/26

54-30i/26

27/13 - 15/13i

Hence the quotient of the given complex number is 7/13 - 15/13i

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Answer: D \(\frac{23}{13} - \frac{15}{13} i\)

Step-by-step explanation:

solve by using elimination. 12x + 36y = −3
−12x − 36y = 0

Answers

The given system of equations has no solution.

Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,

We know for a system of equations =

a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.

If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.

If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.

comparing the coefficients given,

-12/12 = -1

-36/36 = -1

-3/0 = -3

We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.

Hence the given system of equations has no solution.

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Three increased by one equals the quotient of eight and two

Answers

Answer: 3 + 1 = 8/2

Step-by-step explanation:

Don't really get what this question was asking...? But I put it in equation form.

Answer:

8 / 2 = 3 + 1

Step-by-step explanation:

3 increase by 1 = 3 + 1

quotient of 8 and 2 = 8/2

*quotient is the answer to a division problem*

Put it all together:

8/2 = 3 + 1

Extra Info

8/2 = 3 + 1 --> 8/2 = 4 ---> 4 = 4

This problem/equation is a TRUE statement.

You decide to work out your weekly pay by using the following formula:

p = 5hr
p is weekly pay
h is hours worked
r is rate of pay per hour
This week you worked 8 hours a day, for 5 days, at an hourly rate $6.88.
How much did you earn? $

Answers

Answer:

p = 5(8)(6.88)

p = $275.20

x-2>5
I need a person that can give me answers
Skpe at Kazuto Kirigaya king jolt 07

Answers

Answer:

no identity will escape! I know where you live

if 2^4x = 16, then x = ?

Answers

Answer:

x = 1

Step-by-step explanation:

if 2^4x = 16, then x = ?

2^4x = 16

2^4x - 16 = 0

(16) ⋅ x + (−16) = 0

x = [- (- 16)] : 16

x = 1

Answer: The value of x is 1.

Step-by-step explanation: solution :

Here,

       2^4x = 16

    or, 2^4x = 2^4    (we should factor 16 by 2)

    or, 4x = 4            (Here coefficient 2 is same. so, we shouldn't write it)

     or, x = 4 ÷ 4

     or, x = 1

Therefore, the value of x is 1.

list the angles of ABC in order from smallest to largest

Answers

The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.

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Graph and find the area of the figure with the vertices (-3, 0), (1, 4), (2, 0).
A = 20 Units^2
B = 10 Units^2
C = 12 Units^2

Answers

Answer:

B

Step-by-step explanation:

The points with these coordinates form a triangle with a side 5 units and height 4 units. It' area is equal to 5*4÷2=10units^2

Find the sum and express it in simplest form.
(-4s 9a + 4) + (2s + 2a - 8)
008
Clear all
Enter the correct answer.
000
+?
DONE

Answers

The sum of the expression is (-4s 9a + 4) + (2s + 2a - 8) is -2x + 11a - 4

What are algebraic expressions?

These are expressions that are made up of variables, terms, coefficients, factors and constants.

They are also made up of operations, such as addition, multiplication, division, floor division, subtraction, bracket and parentheses.

From the information given, we have the expressions;

(-4s + 9a + 4) + (2s + 2a - 8)

expand the bracket

-4s + 9a + 4 + 2s + 2a - 8

Now, collect the like terms

-4s + 2s + 9a + 2a + 4 - 8

add or subtract the like terms

-2x + 11a - 4

Hence, the expression is -2x + 11a - 4

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help ugent!
12 + 2 + 2 + 2 + 2 + 2 ^ 2=

Answers

\(24.\)

Step-by-step explanation:

\(12 + 2 = 14.\)

\(14 + 2 = 16.\)

\(16 + 2 = 18.\)

\(18 + 2 = 20.\)

\(20 + {2}^{2} = 24.\)

Note:- 2² = 2×2 = 4. So, 2² = 4.

Answer:

24

make sure you calculate the answer next time!

Homework: 7.4
LIOL
What is the probability of getting either a sum of 6 or at least one 5 in the roll of a pair of dice?

Answers

the probability of rolling it is possible/likely. you have a chance of almost ever dice roll you might be able to roll a sum of 6 or 5

trouve trois nombres entiers consécutifs dont la somme vaut 513

Answers

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

put a digit in the gap, such that the answer is a whole number 10x + 11 = 144

Answers

Answer:

13.3 or 13

Step-by-step explanation:

10x+11=144

10x=144-11

10x=133

x=133/10

x=13.3

help fast please
i have no idea what to do in math so i need help

help fast pleasei have no idea what to do in math so i need help

Answers

Answer:

see the attachment photo!

help fast pleasei have no idea what to do in math so i need help


Si 10 obreros construyen un consultorio médico en 12 dias.¿Con cuántos obreros se hará la misma obra en 15 dias?

Answers

A total of 8 workers are required for a building time of 15 days.

How many workers are needed to complete a building?

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Please help! I will give brainliest and 65 points!

The joint probability mass function of X and Y, p(x,y), is given by p(1,1) = 1, p(2,1) = 1, p(3,1) = 1, 939 p(1,2) = 1, p(2,2) = 0, p(3,2) = 1 , 9 18 p(1,3) = 0, p(2,3) = 1, p(3,3) = 1 69

Compute E[X|Y = i] for i = 1,2,3 and explain if the random variables X and Y are independent?

Answers

By definition of conditional expectation,

\(\mathrm E\left[ X \mid Y = y \right] = \displaystyle \sum_x x\, p_{X\mid Y}(x \mid y) = \sum_x x \frac{p_{X,Y}(x,y)}{p_Y(y)}\)

where \(p_Y(y)\) is the marginal probability mass function (pmƒ) of Y. We find this by summing up all joint probabilities over the possible values of X :

\(p_Y(y) = \displaystyle \sum_x p_{X,Y}(x,y) = p_{X,Y}(1,y) + p_{X,Y}(2,y) + p_{X,Y}(3,y)\)

Consult the given values of the joint pmƒ. The values you actually list are unclear… if p(1, 1) = 1, then all other probabilities should be 0, so you must mean something else.

To get around this, I'll just make up a valid joint pmƒ of my own, and show you how to get what you need **using this pmƒ**.

\(\begin{array}{c|c|c|c} & A=1 & A=2 & A=3 \\ ---&---&---&--- \\ B=1 & 0.3 & 0.1 & 0.05 \\ B=2 & 0.02 & 0.02 & 0.01 \\B=3 & 0.25 & 0 & 0.25 \end{array}\)

The marginal pmƒ for B is

\(p_B(b) = \begin{cases} p_{A,B}(1,1)+p_{A,B}(2,1)+p_{A,B}(3,1) = 0.45 & \text{if }b = 1 \\ p_{A,B}(2,1)+p_{A,B}(2,2)+p_{A,B}(3,1) = 0.05 & \text{if }b = 2 \\ p_{A,B}(3,1)+p_{A,B}(3,2)+p_{A,B}(3,3)=0.5 & \text{if }b = 3\\0&\text{otherwise}\end{cases}\)

Now get the conditional expectation:

\(\mathrm E\left[A \mid B = b\right] = \begin{cases}\dfrac{1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1)}{p_B(1)} \approx 1.44 & \text{if }b = 1 \\\\\dfrac{1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2)}{p_B(2)} = 1.8 & \text{if }b = 2\\\\\dfrac{1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3)}{p_B(3)} = 2 & \text{if }b = 3\end{cases}\)

If A and B are independent, then \(p_{A,B}(a,b)=p_A(a)p_B(b)\) and it follows that E[A | B] = E[A]. Compute the expectation of A :

\(\mathrm E\left[A\right] = \displaystyle \sum_a a \, p_{A,B}(a,b)\)

\(\mathrm E[A] = \begin{cases}1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1) = 0.65 & \text{if }b = 1 \\ 1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2) = 0.9 & \text{if }b = 2\\ 1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3) = 1 & \text{if }b = 3\end{cases}\)

But E[A | B] ≠ E[A], so A and B are not independent.

multiply [4, 0, -1, 2, -3, -1]x[0, 1, -3, 1]

Please Help...

Answers

Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Can someone please help me

Can someone please help me

Answers

Answer:

D. -2/5

Step-by-step explanation:

Slope=  \(\frac{delta Y}{Delta X} =\frac{-2}{5}\)

Answer:

D

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (14, - 2)

m = \(\frac{-2-4}{14+1}\) = \(\frac{-6}{15}\) = - \(\frac{2}{5}\) → D

A line segment has endpoints E(–2, 8) and F(10, –6). What is the midpoint? ( , )

Answers

The midpoint of the line segment with the endpoints is (4, 1)

How to determine the midpoint of the line segment with the endpoints?

The endpoints are given as:

E= (-2,8) and F = (10, -6)

The midpoint of the line segment with the endpoints is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-2 + 10, 8- 6)

Evaluate the sum

So, we have:

Midpoint = 0.5 * (8, 2)

Evaluate the products

So, we have:

Midpoint = (4, 1)

Hence, the midpoint of the line segment with the endpoints is (4, 1)

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In ΔDEF, f = 33 inches, mm∠F=140° and mm∠D=5°. Find the length of e, to the nearest 10th of an inch.

Answers

The length of e is given as follows:

e = 29.5 inches.

What is the law of sines?

Suppose we have a triangle in which:

Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.

The lengths and the sine of the angles are related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle E is given as follows:

<E = 180 - (140 + 5)

<E = 35º.

Hence the length e is obtained applying the law of sines as follows:

sin(35º)/e = sin(140º)/33

e = 33 x sine of 35 degrees/sine of 140 degrees

e = 29.5 inches.

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NEEED HELP FROM BRAINLIEST??????




If the point (1,4) is on the graph of an equation, which statement must be
true?
A. The values x= 1 and y= 4 make the equation true.
B. The values x= 4 and y= 1 make the equation true.
C. The values x= 1 and y= 4 are the only values that make the
equation true.
D. There are solutions to the equation for the values x= 1 and x= 4.

NEEED HELP FROM BRAINLIEST??????If the point (1,4) is on the graph of an equation, which statement must

Answers

Answer:

A

Step-by-step explanation:

Helppp meee Pleaseee

Helppp meee Pleaseee

Answers

Answer:

4

Step-by-step explanation:

I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.

In this question, the binomial is (x + 2)².

You can expand this to be (x + 2)(x + 2).

When you expand it using the FOIL method, you get x times x, which is .

Next, the outside/outer terms are x and 2, which is 2x.

Then, you multiply the inside/inner terms 2 and x, which is 2x.

Last, you multiply the last terms, which are 2 and 2, which is 4.

When you put them together, it looks like this:

x² + 2x + 2x + 4.

You can simplify this to x² + 4x + 4.

So your answer is 4.

Helppp meee Pleaseee

Find the surface area of the composite figure.
20 in.
11 in.
5 in.
I
I
19 in
12 in.
12 in.
SA
=
11 in.
5 in.
20 in.
[?] in.2

Answers

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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Which figure can be formed from the net?
__________________________________
(Reporting any spams/wrong answers)
(Giving brainliest to correct answer)
___________________________

Which figure can be formed from the net?__________________________________(Reporting any spams/wrong

Answers

Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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8
Select the correct answer.
Which would you use to estimate the demand for a product at various prices?
O A
a demand table
B.
a demand chart
Ос.
a demand schedule

Answers

Answer:you would use a demand chart

Step-by-step explanation:

Answer:

C. A demand schedule.

Step-by-step explanation:

The demand curve is a visual representation of how many units of a good or service will be bought at each possible price. It plots the relationship between quantity and price that's been calculated on the demand schedule, which is a table that shows exactly how many units of a good or service will be purchased at various prices.

As you can see in the chart below, the price is on the vertical (y) axis, and the quantity is on the horizontal (x) axis. This chart plots the conventional relationship between price and quantity. The lower the price, the higher the quantity demanded. As the price decreases from p0 to p1, the quantity increases from q0 to q1.

Key words and Phrases:

quantity, price, demand, good, service, demand curve, demand schedule

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8Select the correct answer.Which would you use to estimate the demand for a product at various prices?O

for f(x)=4x+1 and g(x)=x^2-5, find (f-g) (x) need help guys!

for f(x)=4x+1 and g(x)=x^2-5, find (f-g) (x) need help guys!

Answers

Answer:

-x^2 +4x +6

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f-g)(x) = 4x+1 - (x^2-5)

Distribute the minus sign

           = 4x+1 - x^2 +5

           = -x^2 +4x +6

Miguel bought 8 equally priced pens for $3.84.

How much will 15 of these pens cost?


$10.42

$7.20

$5.89

$2.05

Answers

Answer:

For 15 pens, the cost is $7.2

Step-by-step explanation:

We know that:

8 pens = $3.84

Work:

8 pens = $3.84

Divide the RHS:

=> 1 pen = 3.84/8=> 1 pen = 0.48

Multiply the RHS:

=> 15 pens = 0.48 x 1=> 15 pens = $7.2

Hence, for 15 pens, the cost is $7.2

Hoped this helped.

\(BrainiacUser1357\)

The cost of 15 pens is $7.20.


3.48 divided by 8 is 0.48. Multiply that by 15 and you get 7.2 or $7.20
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