URGENT!!!!!!! Find all seventh roots of unity and sketch them on the axes below.

URGENT!!!!!!! Find All Seventh Roots Of Unity And Sketch Them On The Axes Below.

Answers

Answer 1

Answer:

The 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]

Step-by-step explanation:

The roots of unity are evenly spread around the unit circle.      

The roots of unity can be find by using the relation

[tex]$ 1= 1 ( \cos 0 ^\circ +i \sin ^\circ )$[/tex]

[tex]$\sqrt[n]{1} = 1 [\cos (\frac{2k \pi}{n}})+ i \sin (\frac{2k \pi}{n}) ] $[/tex]

Now z be a polynomial.

[tex]$z^7=1 \Rightarrow z = 1^{\frac{1}{7}}$[/tex]

therefore, cos 0 = 1.

[tex]$ z = \cos (2k \pi)^{\frac{1}{7}}$[/tex]                [tex]$ (\cos \theta)^n = \cos n \theta $[/tex]

[tex]$ z = \cos \frac{2k \pi}{7} $[/tex]

Now, for k=0, z = 1

[tex]$ k=1 \Rightarrow z = \cos \frac{2 \pi}{7} = \cos 3 \frac{2 \pi}{7}+ i \sin \frac{2 \pi}{7}$[/tex]

[tex]$ k=2 \Rightarrow z = \cos \frac{4 \pi}{7} = \cos \frac{4 \pi}{7}+ i \sin \frac{4 \pi}{7}$[/tex]

[tex]$ k=3 \Rightarrow z = \cos \frac{6 \pi}{7} = \cos \frac{6 \pi}{7}+ i \sin \frac{6 \pi}{7}$[/tex]

[tex]$ k=4 \Rightarrow z = \cos \frac{8 \pi}{7} = \cos \frac{8 \pi}{7}+ i \sin \frac{8 \pi}{7}$[/tex]

[tex]$ k=5 \Rightarrow z = \cos \frac{10 \pi}{7} = \cos \frac{10 \pi}{7}+ i \sin \frac{10 \pi}{7}$[/tex]

[tex]$ k=6 \Rightarrow z = \cos \frac{12 \pi}{7} = \cos \frac{12 \pi}{7}+ i \sin \frac{12 \pi}{7}$[/tex]

[tex]$ k=7 \Rightarrow z = \cos \frac{14 \pi}{7} = \cos \frac{14 \pi}{7}+ i \sin \frac{14 \pi}{7}$[/tex]

Then the 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]

                                              

URGENT!!!!!!! Find All Seventh Roots Of Unity And Sketch Them On The Axes Below.

Related Questions

The cost to download music from an Internet site is shown.

According to the information in the table, which equation describes the relationship between the number of songs downloaded and the cost to download?

A. c = 1.5n
B. c = 1.5n + 25
C. c = 7.75n
D. c = 7.75n + 25

Answers

Answer:

Option (B)

Step-by-step explanation:

If we graph the points given in the table, a straight line is obtained which shows that the table given represents a linear function.

Let the two points on the graph are (4, 31) and (8, 37)

Slope of the line passing through these points,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

   = [tex]\frac{37-31}{8-4}[/tex]

   = 1.5

Equation of the line passing through a point (4, 31) and slope = 1.5 will be,

y - y' = m(x - x')

y - 31 = 1.5(x - 4)

y = 1.5x - 6 + 31

y = 1.5x + 25

Therefore, Option (B) will be the answer.

One of the digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number and add the resulting number to the original number you get 88 . Find the original number

Answers

Answer:

62

Step-by-step explanation:

well, we start by expressing the number:

a b

we understand that using the above expression, the value of the number is 10a + b

using the information in the question,

a = 3b (1)

and,

11b + 11a = 88 (2) (derived using 10a + b form)

hence, when substituting (1) into (2):

11b + 33b = 88

44b = 88

b = 2 (3)

sub (3) into (1)

a = 6

hence, the number is 62

(70) Find the volume. Don't forget your label.

Answers

Answer: If the lengths are 3 1/2, 2, and 4 2/3, the volume is 32 2/3

Step-by-step explanation:

3 1/2 * 2 * 4 2/3 = 32 2/3.

ASAP. please.. need answer. please
sugar is sold at MVR 4 1/2 per kg
find the cost of 10kg sugar.
if you got it correct will mark your answer as brainliest.
please help me. ​

Answers

Answer:

$45.00

Step-by-step explanation:

each kilogram of sugar costs $4.50

we want to find the cost of 10 kg

multiply the cost of 1 kg ($4.50) by 10 kg:

4.50*10=$45.00

The cost of 10 kg is $45.00.

Is 6837 cm less than, greater than or equal to 68hm

Answers

Answer:

6837 cm is less than 68 hm

Step-by-step explanation:

1 hectometres  = 100 meters

1 centimetres = 0.01 meters

Therefore;

6837 centimetres = 6837 × 0.01 meters = 68.37 meter

6837 centimetres = 68.37 meter

Also, we have;

68 hectometres  = 68 × 100 meters = 6800 meters

68 hectometres  = 6800 meters

Therefore,

6837 centimetres = 68.37 meter < 68 hectometres  = 6800 meters

6837 centimetres < 68 hectometres  

6837 cm < 68 hm

6837 cm is less than 68 hm.

12-(4) - 1
2

Please helppp!!! :)

Answers

Answer:

17

Step-by-step explanation:

Simplify:

[tex]12\frac{1}{2} = \frac{25}{2}[/tex]  

[tex]-4\frac{1}{2} = \frac{-9}{2}[/tex]

[tex]\frac{25}{2} - (\frac{-9}{2} ) = \frac{25}{2} + \frac{9}{2} = \frac{34}{2} = 17[/tex]

When you have a subtraction sign next to a negative number, the negative number will turn positive since it's understood as -1 multiplied by the number when it's a negative number.  

mark the wheat and rice product in areas in the map of India
PLS MAKE AND SHOW ON THE MAP
I will definitely mark you brainliest​

Answers

Answer:

uttar pradesh

Step-by-step explanation:

see map

Answer:

S.No. State/ UT Wheat (Th. tonnes)

1 Uttar Pradesh    26,874

2 Madhya Pradesh    17,689

3 Punjab                 16,081

4 Haryana                 11,352

5 Rajasthan         9,871

6 Bihar                 4,753

7 Gujarat                 2,484

8 West Bengal         960

9 Uttarakhand         761

10 Maharashtra         758

Step-by-step explanation:

Refer this link for map!

HOPE IT HELPS AND THANK ME BY MARKING AS BRAINLIEST!

A chord subtends an angle 120° at the centre of the circle of radius 3.5cm. Find the perimeter of the minor sector.[r=22/7]​

Answers

Answer:

Step-by-step explanation:as we know that arc length is

s=r*∅

as given angle in degree so  convert it in radian we get

angle=2.09 rad

r=3.5 cm

hence we get

s=3.5*2.09 =7.315 cm

perimeter of sector = s +d  where d=2*r=2*3.5=7 cm

perimeter of sector=7.315+7=14.315 cm

if you like it then hit the stars and tag it a brain-list

Please answer this quick

Answers

Answer:

x = 18

∠A = 83

Step-by-step explanation:

Since you have a line intersecting two parallel lines, the angles formed from the intersection will be equal to 180.  This means that you can add up the two angle measures and set them equal to 180.

(6x - 35) + (3x + 53) = 180

6x - 35 + 3x + 53 = 180

9x + 18 = 180

(9x + 18) - 18 = 180 - 18

9x = 162

x = 18

Now to solve for ∠A, plug in the x-value and solve.

∠A = 6x - 35

∠A = 6(18) - 35

∠A = 118 - 35

∠A = 83

10 subtracted from the sum of a triple number and 12

Answers

Answer:

(3x+12)-10

Step-by-step explanation:

the two legs of a right triangle are 33 and 56. The missing hypotenuse length is ?

Answers

Answer:

65

Step-by-step explanation:

a^2+b^2=c^2

33=a, 56=b

Put them into the equation, then do the algebra and solve it for c.

Answer:

65

Step-by-step explanation:

33²+56²=c²

1089+3136=c²

4225=c²

c=√4225

c=65

does this table show y as a function of x ?
: (-3,1) (0,-5) (4,7) (-3,0)

Answers

Answer:

No.

Step-by-step explanation:

The definition of a function is that every output (x) has only one input (y).

Here -3 gives two different outputs which contradicts the definition of a function.

If the third term in an arithmetic sequence is 7 and the common difference is -5, what is the value of the fourth term? A) 12 B) 2 C) -35 D) 35

Answers

Answer:

B) 2

Step-by-step explanation:

a3 = 7 , d = -5 (GIVEN)

a4 = a3 + d

= 7 + (-5)

= 7 - 5

a4 = 2

HOPE IT HELPS (✷‿✷)

Answer:

[tex]\Huge \boxed{a_4=2}[/tex]

Step-by-step explanation:

The third term in an arithmetic sequence is 7.

The common difference is -5.

The common difference of an arithmetic sequence is found by subtracting a term in the sequence with the previous term.

[tex]d=a_4-a_3[/tex]

Solving for the fourth term.

[tex]a_4 = a_3 + d[/tex]

Plugging in the values and evaluating.

[tex]a_4=7+-5[/tex]

[tex]a_4=2[/tex]

The value of the fourth term is 2.

Simplify the following expression:
-6x + 4(-x - 3)

Answers

Answer:

[tex] - 10x - 12[/tex]

Step-by-step explanation:

[tex] - 6x + 4( - x - 3) \\ - 6x - 4x - 12 \\ - 10x - 12 \\ = - 2(5x + 6)[/tex]

What is the square root of 5

Answers

Hey There!

Answer:

2.23

Step-by-step explanation:

[tex]\sqrt{x} 5[/tex]= 2.23The square root of 5 is 2.23

Hope this helps!!

Have a nice day!!:)

       [✖‿X]

Answer:

Hey!

The square root of 5 is precisely 2.23606797749979

If you want to round it up...

(1.d.p) -- 2.2

(2.d.p) -- 2.24

(3.d.p) -- 2.236

I HOPE THIS HELPED YOU!

A 15 foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the wall. How high up the wall is the ladder? Round to the nearest tenth if necessary.

Answers

Answer:

13.26

Step-by-step explanation:

The computation of the height should be computed by using the Pythagoras theorem

As we know that

Hypothenuse^2 = base^2 + height^2

where,

Hypothenuse is 15 foot

And, the foot of the ladder i.e base is 7

So now placing these values

The height is

15^2 = 7^2 + height^2

225= 49 + height^2

After solving this, the height is 13.26

8 mph above the speed limit. -8 8+8 8 8-8

Answers

Answer:

Below

Step-by-step explanation:

Hey there!

Well, 8 mph over the speed limit is speeding because you can only go 5 above.

If the speed limit is 40 it's okay to go 45 but bot 48.

Hope this helps :)

find
[tex] \frac{dy}{dx \: } of \: \frac{x {}^{2} }{a {}^{2} } + \frac{y {}^{2} }{b { }^{2} } = 1 \\ \\ if \: x = a \cos( \alpha \:) \: and \: \: y \: = b \sin( \alpha ) [/tex]
pls help me ​

Answers

Answer:

dy/dx = -b/a cot α

Step-by-step explanation:

x² / a² + y² / b² = 1

Take derivative with respect to x.

2x / a² + 2y / b² dy/dx = 0

2y / b² dy/dx = -2x / a²

dy/dx = -b²x / (a²y)

Substitute:

dy/dx = -b²a cos α / (a²b sin α)

dy/dx = -b cos α / (a sin α)

dy/dx = -b/a cot α

The Y is the diameter

Find Y

Area of the circle ​

Answers

Answer:

Y = 22.56 cm

Step-by-step explanation:

To find the diameter Y of the circle we must first find the radius of the circle

Area of a circle = πr²

where

r is the radius

From the question

Area = 400cm²

Substitute the value into the above formula and solve for the radius

That's

400 = πr²

Divide both sides by π

We have

[tex] {r}^{2} = \frac{400}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{400}{\pi} } [/tex]

radius = 11.28 cm

Since we have the radius we can use it to find the diameter Y using the formula

diameter = radius × 2

radius = 11.28

Y = 11. 28 × 2

We have the final answer as

Y = 22.56 cm

Hope this helps you

7. Which of the following statements is NOT true? a. All integers are rational numbers. b. Some rational numbers are whole numbers. c. All whole numbers are natural numbers. d. All irrational numbers are real numbers.

Answers

Here, a,c and d are not true because,

a) all integers are not rational numbers because 2/10 is a rational number but not an integer.

c) all whole numbers are not natural numbers because 0 is not a natural number.

d) all irrational numbers are not real numbers because root2 is not a real number.

b) it is true.

Hope it was helpful,

pls mark this as a brainliest answer.

thank you.

^_^

   

Statements (1), (3), and (4) are correct these are NOT true after using the definition of the numbers.

What is the number?

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

As we know,

The integer can be defined as the whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

Thus, statements (1), (3), and (4) are correct these are NOT true after using the definition of the numbers.

Learn more about the number here:

brainly.com/question/17429689

#SPJ2

find the distance between (-3,-5) (4,8)

Answers

Answer:

14.765 units

Step-by-step explanation:

distance formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(4 + 3)² + (8 + 5)²]

d = √(7²) + (13²)

d = √(49 + 169)

d = √218

d = 14.765

Jeremy spends 44 minutes eating dinner with his family. Jeremy finishes eating dinner at 6:09. What time did the clock show when Jeremy started eating dinner?

Answers

Answer:

5:25

Step-by-step explanation:

Borrow 1 hour from 6 hours, change it to 60 minutes, and add it to 9 minutes.

6:09 is the same as 5:69.

6:09 = 5:69

Now subtract 44 minutes from 69 minutes.

5:69 = 0:44 = 5:25

Answer: 5:25

Answer:

5:25

Step-by-step explanation:

Borrow 1 hour from 6 hours, change it to 60 minutes, and add it to 9 minutes.

6:09 is the same as 5:69.

6:09 = 5:69

Now subtract 44 minutes from 69 minutes.

5:69 = 0:44 = 5:25

Answer: 5:25

Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10

Answers

Answer: p = 1/6.

Step-by-step explanation:

First, we have two fair dice, so we have two events.

The number of outcomes for each dice is 6, then the total number of outcomes for the two dice is equal to the product of the number of outcomes in each event.

C = 6*6 = 36.

Now, the combinations that have a sum larger than 10 are:

4 and 6.

6 and 4

5 and 5

5 and 6

6 and 5

6 and 6.

So we have 6 outcomes where the sum of both numbers is larger than 10.

Now, the probability will be equal to the quotient between the number of outcomes where the sum is larger or equal than 10, and the total number of outcomes:

P = 6/36 = 1/6.

James truck shows that his average gas mileage per day is 29 miles per gallon of gas. If james drives about 87 miles each day about how much gas does he use in 14 days of driving

Answers

Answer: 42 gallons

Step-by-step explanation:

given data:

average gas mileage/day = 29miles/gallon

distance travelled each day by James = 87miles

How much gas does he use in 14days drive.

solution:

james drives 87miles daily, so in 14 days he would have travelled

= 87miles * 14

= 1218miles travelled.

gas used in 14days

1218miles distance traveled in 14 days

29miles/gallon

= 1218miles / 29miles

= 42gallons of gas have been used by janew to fuel his truck in 14days.

Uma barraca de tiro ao alvo de um parque de diversão dará um prêmio de r$ 20ao participante cada vez que ele acertar o alvo por outro lado cada vez que ele errar o alvo da deverápagar r$ 10 não há cobrança inicial para participar do jogo um participante deu 80 tiros e ao final recebeu r$ 100 qual foi o número de vezes que esse participante acertou o alvo

Answers

Resposta: 30

Explicação passo a passo:

Dado o seguinte:

Preço para atingir a meta = $ 20

Penalidade por falta de alvo = $ 10

Se 80 tiros forem disparados e os participantes receberem $ 100.

Número de vezes que o participante atinge o alvo.

Deixe o número de erros = m

Deixe o número de acertos = h

h + m = 80 - - - - (1)

20h - 10m = 100 - - - (2)

h = 80 - m

Substitua h = 80 - m em (2)

20 (80 - m) - 10m = 100

1600 - 20m - 10m = 100

-30m = 100 - 1600

-30m = - 1500

m = 50

De (h = 80 - m)

h = 80 - 50

h = 30

Número de acertos = 30

O participante acerta o alvo 30 vezes

13. Distributive Property
3(x - 1) = 3x - ?

Answers

Answer:

[tex]\huge\boxed{3x-3}[/tex]

Step-by-step explanation:

[tex]3(x-1)=\\\\\text{Distribute: }\left \{ {{3*x=3x} \atop {3*-1=-3}} \right.\\\\3(x-1)=\boxed{3x-3}[/tex]

3(x - 1) = 3x - 3

The distributive property is a very important property used in algebra.

It states that when we have the statement a(b + c), we can "distribute" the

a by multiplying a times both terms that are inside the parenthses.

So that would give us a(b) + b(c) or ab + bc.

The same process is done here.

Distribute the 3 through both terms to get 3(x) - 3(1) or 3x - 3.

c. The cost price of 12 bananas is equal to the SP of 15 bananas.Find loss or gain percent.​

Answers

Answer:

20% loss.

Step-by-step explanation:

Suppose the cost of each banana is $1

Then cost of 12 = $12.

You sell 15 bananas for  $12, therefore the price of each banana is 12/15

= $0.80.

So the loss percent is  (1 - 0.80) * 100

= 20%.

Can someone please help me with this question ASAP...

Answers

Answer:

A = 1.11

n = - 6

Step-by-step explanation:

[tex] \frac{0,0001\times 1,11}{0,1\times 10^4} = A \times 10^n\\\\

\frac{1\times 1,11}{1\times 10^4} = A \times 10^n\\\\

\frac{1,11}{10^4} = A \times 10^n\\\\

{1,11\times 10^{-4} } = A \times 10^n\\\\

{1.11\times 10^{-6} } = A \times 10^n\\\\[/tex]

Equating like terms on both sides :

A = 1.11

n = - 6

PLEASE HELP ME :(((((

Umar drove his taxi from Ipoh to Kuala Lumpur via the highway. He stopped at Tapah to
pick up some goods before proceeding to Kuala Lumpur. He drove from Ipoh to Tapah at an
average speed of 100 km/h over a distance of 60 km. If the average speed of his taxi from Ipoh
to Kuala Lumpur is 110 km/h over a distance of 220 km, calculate the average speed of Umar's
taxi from Tapah to Kuala Lumpur.

Answers

Answer:

approximately 114.28 km/h

Step-by-step explanation:

Distance = rate * time (d = rt)

The distance from Ipoh to Tapah is 60 km, and the rate is 100 km/h. Therefore, the time it took to drive from Ipoh to Tapah is:

60 = 100t

t = 0.6 hours

The total distance from Ipoh to Kuala Lumpur is 220 km, and the average rate is 110 km.

Therefore, the time it took to drive from Ipoh to Kuala Lumpur is:

220 = 110t

t = 2 hours

So since we know that the time taken to go Ipoh -> Tapah is 0.6 hours and the time taken to go Ipoh -> Tapah -> Kuala Lumpur is 2 hours, the time taken to go Tapah -> Kuala Lumpur must be:

2 - 0.6 = 1.4 hours

And the distance from Tapah to Kuala Lumpur must be:

220 - 60 = 160 km

So the speed driven from Tapah to Kuala Lumpur must be:

160 = r * 1.4

r ≈ 114.28 km/h

Answer:

114.3 km/h

Step-by-step explanation:

We need to find te average speed from Tapah to Kuala Lumpur.

speed = distance/time

We need to find the distance and time from Tapah to Kuala Lumpur.

Ipoh to Tapah:

100 km/h over a distance of 60 km

Ipoh  to Kuala Lumpur:

110 km/h over a distance of 220 km

The total distance is from Ipoh to Kuala Lumpur.

speed = distance/time

distance = speed * time

time = distance/speed

time = 220 km / 110 km/h = 2 hours

Ipoh to Tapah.

time = distance/speed

time = 60 km / 100 km/h = 0.6 hour

Distance & time from Tapah to Kuala Lumpur:

220 km - 60 km = 160 km

2 hours - 0.6 hours = 1.4 hours

average speed from Tapah to Kuala Lumpur:

speed = distance/time = 160 km  /  1.4 hours

speed = 114.3 km/h

Can someone help pleassssssseeeeee!!!!!!!!!????????? ILL MARK BRAINLIEST!!!!

Answers

Answer:

[tex]b-17[/tex]

Step-by-step explanation:

So, Tanvi started with b buttons.

And she gave away 17.

Since she "gave away," this means that we should use subtraction.

Therefore, she now has b-17 buttons.

Our expression is:

[tex]b-17[/tex]

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Empathy is the ability to understand the thoughts, feelings, and emotions of your athletes and to convey your sensitivity to them.A. trueB. false If you had to come to a new world how would you have survived Give at least two examples Read the excerpt from "An Image of Africa: Racism in Conrads Heart of Darkness by Chinua Achebe. In the fall of 1974 I was walking one day from the English Department at the University of Massachusetts to a parking lot. It was a fine autumn morning such as encouraged friendliness to passing strangers. Brisk youngsters were hurrying in all directions, many of them obviously freshmen in their first flush of enthusiasm. An older man going the same way as I turned and remarked to me how very young they came these days. I agreed. Then he asked me if I was a student too. I said no, I was a teacher. What did I teach? African literature. Now that was funny, he said, because he knew a fellow who taught the same thing, or perhaps it was African history, in a certain community college not far from here. It always surprised him, he went on to say, because he never had thought of Africa as having that kind of stuff, you know. By this time I was walking much faster. "Oh well," I heard him say finally, behind me: "I guess I have to take your course to find out." A few weeks later I received two very touching letters from high school children in Yonkers, New York, whobless their teacherhad just read Things Fall Apart. One of them was particularly happy to learn about the customs and superstitions of an African tribe. How do these two anecdotes help readers understand Achebes purpose for writing the essay? by suggesting that Achebe is excited about peoples interest in Africa and wants to teach people about it by suggesting that Achebe wants to correct false perceptions about the African continent by suggesting that Achebe is trying to draw attention to his essay by beginning with two interesting stories by suggesting that Achebe is upset that older and younger people have conflicting views of Africa Describe three strength training exercises that can be performed by adults at an average fitness level and then discuss at least two health benefits of strength training. Leslie McCormack is in the spring quarter of her freshman year of college. She and her friends already are planning a trip to Europe after graduation in a little over three years. Leslie would like to contribute to a savings account over the next three years in order to accumulate enough money to take the trip. Assume an interest rate of 16%, compounded quarterly. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) How much will she accumulate in three years by depositing $520 at the end of each of the next 12 quarters, beginning three months from now In which of the following biomes would one likely find wolf, elk, moose, bear, lynx, beaver, wolverine, and a number of migratory birds?a) tropical rain forest.b) tropical savanna.c) desert.d) boreal and montane forest.e) temperate rain forest.