Express 8e^i16pie in rectangular, polar and trignometric form?

Answers

Answer 1

Euler's formula immediately gives

[tex]8e^{i\cdot16\pi}=8\cos(16\pi)+8i\sin(16\pi)=8[/tex]

and the equation above lists, from left to right, the polar, trigonometric, and rectangular forms.


Related Questions

What value of a makes the following equation true?
a−8a=210

Answers

Answer:

a=-30

Step-by-step explanation:

Which polynomial was factored? x2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4

Answers

Answer:

x^2+2x-8

Step-by-step explanation:

x^2+2x-8 = (x+4)(x-2)

Answer: A. x^2 -2x -8

Step-by-step explanation:

A 115​-inch is cut into two pieces. One piece is four times the length of the other. Find the lengths of the two pieces.

Answers

Answer:

Shorter piece: 23 inches

Longer piece: 92 inches.

Step-by-step explanation:

Since the longer piece is four times the length of the other, we multiply 23*4 and we get 92 inches.

simplify this complex fraction 1 2/3 divided by 2 1/9

Answers

Answer:

[tex]\frac{5}{3} \times\frac{9}{19}[/tex]

Step-by-step explanation:

In order to simplify this equation you need to convert these whole number fractions into improper fractions and then use KCF. (Keep, Change, Flip)

[tex]1\frac{2}{3} \div2\frac{1}{9}[/tex]

Convert into improper fractions:

[tex]1\frac{2}{3} = 3\times1+2=\frac{5}{3}[/tex]

[tex]2\frac{1}{9} =9\times2+1=\frac{19}{9}[/tex]

(Remember to keep the denominators the same)

[tex]\frac{5}{3} \div\frac{19}{9}[/tex]

Now use KCF

[tex]\frac{5}{3} \div\frac{19}{9} = \frac{5}{3} \times\frac{9}{19}[/tex]

[tex]= \frac{5}{3} \times\frac{9}{19}[/tex]

Hope this helps.

The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7), what are the
coordinates of B?

Answers

Answer:

(8,1)

Step-by-step explanation:

(8,1) you have to add do to the same to B

Pont B is located at coordinates at the line AB (8, 1)

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)

From the general formula of midpoints of a line

coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)

where,

(x₁, y₁) are the coordinates of A

(x₂, y₂) are the coordinates of B

And in our case Coordinates of the midpoint are (6, -3)

Thus,

6 = (4 + x₂)/2

x₂ = 8

-3 = (-7 + y₂)/2

y₂ = 1

therefore, the coordinates of Pont B at line AB are (8, 1)

Learn more about coordinates here:

https://brainly.com/question/20282507

#SPJ2

How is 2+ (2) similar to adding 2+2 how is different explain your answer

Answers

Answer:

2+2 is 4-1=3 quick maths

Step-by-step explanation:

Answer:

2+(2) is the same to adding 2+2 because the "(" " )" just mean the you have to add the 2 + 2 just like----- 2+2

Pls help thanks :)


..................

Answers

The answer would be -1/2
-1/2 yes sirrrrrrrrrr

find the radii of a circle 6.16ha

Answers

Answer:

88m

Step-by-step explanation:

area = 6.16msq

πrsq=6.16

22/7*rsq=6.16/100

22/7*rsq=616

rsq=616*7/22

rsq=4321/22

rsq=196

r=√196

r=14m

diameter=14*2=28m

radius=14m

circumfrence=2πr

=2*22/7*14

=44*2

=88m

Describe how to round 3.987 to the nearest tenth.​

Answers

Answer:

4

Step-by-step explanation:

You see the hunderth digit has a 8, so you round up. 0.9+0.1=1 so you add 1 to 3, so 3.987 rounded is 4

To round it to the nearest tenth you have to look at the number beside the tenths place and if that number is 5 or above u round the tenths place up. So since that number is an 8 u round the 9 to 0 which then changes the 3 to 4 so your final answer should be 4.0

What is the equation of the line that passes through the point (-3. 4) and has a
slope of 1/3?

Answers

Y= mx+c
So m= the gradient (slope)
And c=the y intercept (x,y= -3,4)
So it should be
Y=1/3x+4

don’t understand sb help

Answers

Answer:

the 3rd one

Step-by-step explanation:

Answer:

It is the second one

Step-by-step explanation:

please help me for a question ​

Answers

What question do you need help with

Answer:

there is no question??

The original price of a bottle
of dish soap is $2. How much
will Sasha PAY if she buys it
during the sale when it is 50%
off?

Answers

Answer:

$1

Step-by-step explanation:

i hope i read it right

Answer:

1

Step-by-step explanation:

cuz half of 2 is 1

Three points on the function are (-1, 1) (0,3) and blank

Answers

Answer:

well assuming this is a normal function, the next point would be (1,5)

h(x) = x2 + 3x - 2; 12 - h(7)

Solve

Answers

The answer to the question is -56

Which one are functions

Answers

Answer:

A

Step-by-step explanation:

PLEASE MARK BRAINLIEST IT WILL HELP SM

Answer:

its hard to see but I think all of them except the first and the last ones r

Step-by-step explanation:

an x can't repeat

If {x) = 3x + 2, what is (5)?​

Answers

You mean f(x) = 3x+2 and what is f(5)?

f(5) = 3(5)+2

f(5) = 15+2

f(5) = 17

So f(5) = 17

This is statistics. Please answer fast

Answers

Answer:

This is a normal distribution and we can use the standard score to compute for probabilities. We compute the standard score of the given.

Step-by-step explanation:

z = (x - mu)/sd

z = (2625 - 2600)/50 = 25/50 = 0.5.

Consulting the z-table, P(z <= 0.5) = 0.6915.

P(z > 0.5) = 1 - P(z <= 0.5) = 1 - 0.6915 = 0.3085.

I hope this helped! <3

To prepare for a bake-off, Kent used 560 grams of flour each day for 2 weeks. How many kilograms did Kent use in those 2 weeks?

Answers

Answer:

7.840

Step-by-step explanation:

560 grams times the number of days

560×14=7840grams

1000grams = 1 kilogram soo

7840g=7.840kg

Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?

Answers

Complete Question:

Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters.  This year he wants to make the garden three times as long and two times as wide.  

Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.  

How many more meters of fencing is needed for this year’s garden than last year’s?

Answer:

26 meters of fencing needed

Step-by-step explanation:

Given

Last Year:

[tex]Width = 5m[/tex]

[tex]Area = 20m^2[/tex]

This Year:

[tex]Length = 3\ times\ longer[/tex]

[tex]Width = 2\ times\ wider[/tex]

Required

Determine how many more meters is needed

Represent last year's length of Fence with L and last year's width with W

First, we need to calculate L

[tex]Area = L * W[/tex]

Where

[tex]Area = 20m^2[/tex]

[tex]W = 5m[/tex]

[tex]20m^2 = L * 5m[/tex]

Divide both sides by 5m

[tex]\frac{20m^2}{5m} = \frac{L * 5m}{5m}[/tex]

[tex]\frac{20m^2}{5m} = L[/tex]

[tex]L = \frac{20m^2}{5m}[/tex]

[tex]L = 4m[/tex]

So, we have that:

For Last Year

[tex]Length = 4m[/tex] and [tex]Width = 5m[/tex]

For this year:

[tex]Length = 3\ times\ longer[/tex]

[tex]Length = 3 * 4m[/tex]

[tex]Length = 12m[/tex]

[tex]Width = 2\ times\ wider[/tex]

[tex]Width = 2 * 5m[/tex]

[tex]Width = 10m[/tex]

So, for this year, we have:

[tex]Length = 12m[/tex] and [tex]Width = 10m[/tex]

Next, we calculate perimeter of fencing in both years.

[tex]Perimeter = 2 * (Length + Width)[/tex]

Last Year:

[tex]Perimeter = 2 * (4m + 5m)[/tex]

[tex]Perimeter = 2 * 9m[/tex]

[tex]Perimeter = 18m[/tex]

This Year:

[tex]Perimeter = 2 * (12m + 10m)[/tex]

[tex]Perimeter = 2 * 22m[/tex]

[tex]Perimeter = 44m[/tex]

To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.

[tex]Difference = 44m - 18m[/tex]

[tex]Difference = 26m[/tex]

Hence, there are 26 meters of fencing needed

James went to the store and bought a pair of shoes on sale for $40.00. This week they were a regular price of $64.50. What was the percent discount that he bought the shoes for?
I need work shown.

Answers

Answer:

A. 62%

Step-by-step explanation:

64.50x = 40

x = 0.62015 or 62%

This means 62% of original price is $40, discount is 38%. From your options seem to be asking for percent of original price paid and not discount.

In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 151 lb, that the standard deviation is 25 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:

a. What is the expected value of the sample mean of their weights?
b. What is the standard deviation of the sampling distribution of the sample mean weight?
c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb?
d. What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit?

Answers

Answer:

Explained below.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

a

The expected value of the sample mean of their weights is same as the population mean, μ = 1515 lbs.

b

The standard deviation of the sampling distribution of the sample mean weight is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{16}}=6.25[/tex]

c.

The average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lbs. is:

[tex]\text{Average Weight}=\frac{2500}{16}=156.25[/tex]

d

Compute the probability that a random sample of 16 persons on the elevator will exceed the weight limit as follows:

[tex]P(\bar X > 156.25)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{156.25-151}{6.25})\\\\=P(Z>0.84)\\\\=1-P(Z<0.84)\\\\=1-0.79955\\\\=0.20045\\\\\approx 0.20[/tex]

Eight sports fans were asked to count the number of baseball
caps and the number of basketball jerseys in their collection.
Create a scatter plot that represents the data that is shown in the
table. The x-axis represents number of baseball caps and the y-
axis represents the number of basketball jerseys.

Answers

Answer:

what grade are you in?

Step-by-step explanation:

There are 4 trucks for every 5 cars in a parking lot. If there are 80 cars, how many trucks are in the parking lot?

Answers

Answer:

There are 64 trucks!

Step-by-step explanation:

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. The distribution of this particular variable is very right skewed.(a) Suppose we let (X-bar) be the mean number of accidents per week at the intersection during 9 randomly chosen weeks. What is the probability that (X-bar) is less than 2?(b) Now let X be the mean number of accidents per week at the intersection during a year (52 weeks). What is the probability that X is less than 2?

Answers

Answer:

The probability that sample mean is less than 2  is 0.1423.

Step-by-step explanation:

Let X denote the number of accidents per week at a hazardous intersection.

It is provided that the mean and standard deviation of X are, μ = 2.2 and σ = 1.4.

(a)

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample size is not large enough, i.e. n = 9 < 30, the Central Limit Theorem cannot be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.

And since the distribution of X is not specified, the probability cannot be computed.

(b)

In this case, the sample size is large enough, i.e. n = 52 > 30, the Central Limit Theorem can be applied to approximate the sampling distribution of the mean number of accidents per week at the intersection.

Compute the probability that sample mean is less than 2 as follows:

[tex]P(\bar X<2)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{2-2.2}{1.4/\sqrt{56}})\\\\=P(Z<-1.07)\\\\=0.14231\\\\\approx 0.1423[/tex]

Thus, the probability that sample mean is less than 2  is 0.1423.

Given that R= 4x +6y find x when y= 4 and R=11

Answers

Answer:

The value of x:

[tex]x=-\frac{13}{4}[/tex]

Step-by-step explanation:

Given the equation

[tex]R=4x+6y[/tex]

substituting the values y=4 and R=11

[tex]R=4x+6y[/tex]

[tex]11=4x+6\left(4\right)[/tex]

[tex]11=4x+24[/tex]

[tex]11-24=4x[/tex]

switching the sides

[tex]4x=11-24[/tex]

Subtract the numbers: 11-24=-13

[tex]4x=-13[/tex]

Divide both sides by 4

[tex]\frac{4x}{4}=\frac{-13}{4}[/tex]

[tex]x=-\frac{13}{4}[/tex]

Therefore, the value of x:

[tex]x=-\frac{13}{4}[/tex]

How did the National Woman Suffrage Association (NWSA) differ from the American Woman Suffrage Association (AWSA)?

Answers

Answer:

The National Woman Suffrage Association advocated for a range of reforms to make women equal members of society, such as the right to own property, etc. The American Woman Suffrage Association lobbied state governments to enact laws granting or expanding women's right to vote in the United States.

Answer:

C: The NWSA wanted to address the voting rights of both women and formerly enslaved people.

Step-by-step explanation:

The NWSA wanted to address and justify the rights of both former slaves and women, while the AWSA only wanted to either help women or former slaves, not simultaneously.

Which algebraic expression represents “Sarah has fives times as much homework today as yesterday”?
5 + h
5 h
h minus 5
StartFraction h Over 5 EndFraction

Answers

The answer is 5h


This is because the phrase “times” represents multiplication, therefore your answer would be 5 x h but you can represent that as just 5h.!

Answer:5h

Step-by-step explanation: i just did the quiz

PLZZZZZZZZZZZZZZZZZZZZZZ HELP!!!
QUESTION: -2(x-6)=8

STUDENT WORK:
-2(x-6)=8
-2x-12=8
-12 -12
-2x+0=-4
-2x=-4
÷2 ÷2
x=-2



1. Explanation of Errors Made

2. Correct Solution (show all work)

Answers

Answer:

The error was made in the division step it should have been divided by negative 2

-2(x-6)=8

-2x+12=8

-2x=-4

-x=-2

X=2

Cooper wrote checks on his checking account for $20 and $35. He also deposited $63 in the account. Which number describes the change in the balance of his account? A.$12 B.$8 C.$15​

Answers

Answer:

the change is b 8. 63-55=8 35+20=55

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