Rectangular coordinates (73,73) and polar coordinates (6,0) = (V6,4) both represent the same complex number z.
Which set of equations demonstrates why both sets of coordinates represent the same number?
Or=v3 + V3 = V6 and 8 = tan-|(1) =

Or=V3 + V3 = V6 and 8 = tan-(3)
4
Or=763)2 + (13)2 = V and a = tan-f(1) = = I
TT
O r=(73)+ (73)2 = 76 and 8 = tan-(73) = 1
+
-

Rectangular Coordinates (73,73) And Polar Coordinates (6,0) = (V6,4) Both Represent The Same Complex

Answers

Answer 1

well, let me put it this way.

[tex]r^2=x^2+y^2\qquad \qquad \qquad \theta =tan^{-1}\left( \cfrac{y}{x} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{\sqrt{3}}~~,~~\stackrel{y}{\sqrt{3}})\qquad \qquad \begin{array}{llll} \stackrel{\textit{is assuming that}}{r^2=(\sqrt{3})^2+(\sqrt{3})^2}\implies r=\sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\ \stackrel{\textit{is also assuming that}}{\theta =tan^{-1}\left( \cfrac{\sqrt{3}}{\sqrt{3}} \right)}\implies \theta =tan^{-1}(1)\implies \theta =\cfrac{\pi }{4} \end{array}[/tex]


Related Questions

please answer these questions my mom is really mad at me because I have a 73 in math and I need to higher my grade pls help

Answers

Answer:

1. D

2.A

Step-by-step explanation:

Hey, with question 1 you add all the numbers and divide them by the number of blue marbles. Then we simply simplify it.

Woth question 2 we divide 20 by 200 and simplify it.

Lily threw a ball. The balls equation that demonstrated its height and velocity is:
h(x) = -16x2 + 3x + 35
What was the initial height that she threw the ball from?

Answers

The initial height of the ball is the y-intercept of the function

The initial height she threw the ball from is 35

How to determine the initial height

The function is given as:

[tex]h(x) = -16x^2 + 3x +35[/tex]

Set x = 0.

So, we have:

[tex]h(0) = -16 * 0^2 + 3*0 +35[/tex]

Evaluate the exponent

[tex]h(0) = -16 * 0 + 3 * 0 + 35[/tex]

Evaluate the products

[tex]h(0) = 0 + 0 + 35[/tex]

Evaluate the sum

[tex]h(0)= 35[/tex]

Hence, the initial height she threw the ball from is 35

Read more about quadratic functions at:

https://brainly.com/question/14477557

A clearance rack is marked as 60% off the regular price to be taken at the register. If a jacket on the clearance rack is marked $239. 99, what will it ring up for at the register? a. $14. 40 b. $60. 00 c. $96. 00 d. $143. 99.

Answers

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{60\% of 239.99}}{\left( \cfrac{60}{100} \right)239.99}\implies 143.994~\hfill \underset{\textit{sale price}}{\stackrel{239.99-143.994}{\approx 96}}[/tex]

There are 10 teachers and 5 school guards in the school. The principal wants to form a 4-member safety committee for the upcoming Grade 10 night. In how many ways can the committee be formed if there are 3 teachers and 1 guard?

a. 35
b. 50
c. 125
d. 600

Answers

B
10 x 5=50
50 combinations

the radius of a circle is 7 cm .the circle is divided into two equal parts .what is the perimeter of the semi circular part

Answers

Answer:

P = 35.98 cm

Step-by-step explanation:

The Perimeter of a shape is the distance around the outside of it. This semi-circle (half circle) has a straight part and the curved part. See image. The straight part is the diameter (distance through the center) it is double the radius that was given, 7 cm.

The circumference of a circle is the perimeter of the whole circle.

C = 2pi•r or pi•d

C = 2pi•7 = 14pi

But you only need half, so 14pi/2 is 7pi.

ADD the straight part and the curved part to get the whole distance around the shape

P = 14 + 7pi

P ~= 35.98 cm

See image

Nilai akar pangkat dua dari bilangan 144, 225 dan 400 adalah

Tolong dijawab ya kakk

Answers

Answer:

harap ia membantu kamu ya saya itu dari negara lain mungkin syllables nyahh lain jadi jawapan nyahh bisa lain ia kan

i try my best for sure gudluckk

Step-by-step explanation:

144

225

400

729

1296


Please help quick !

Answers

Answer:

1. Quadrant 2

2. Quadrant 3

Step-by-step explanation:

The quadrants are ordered in a 'c' pattern. The first quadrant has coordinates (x,y). The second quadrant has coordinates (-x,y). The third quadrant has coordinates (-x,-y). The fourth quadrant has coordinates (x,-y).

Answer:

quadrent 2 for question 1 ( negative x positive y) quadrant 3 for number 2 ( negative x and y)

Formula for area of a triangle

Answers

Answer: half x base x height

I hope that will help you have a great day bye and Mark brainlist if the answer is correct .......

Step-by-step explanation:

[tex]kai6417 [/tex]

#carry on learning

PLS HELPP ASP

Whats the sum of
8 1/2 2 1/2

Answers

Answer:

11

Step-by-step explanation:

1/2 + 1/2 is 1

8 + 2 = 10

1 + 10 = 11

3(5+6) distributave property

Answers

Answer:

3(5+6)

3x5 + 3x6

15 + 18

33


need this by midnight please show your work :)

Answers

Answer:

See below

Step-by-step explanation:

Part 1P = $800r = 2% (since P > $500)I = $100t = ?

Find t:

I = Prt100 = 800*0.02t0.16t = 1t = 1/0.16t = 6.25 yearsPart 2P = $100r = 1.5% (since P < $500)I = $50t = ?

Find t:

I = Prt50 = 100*0.015t0.03t = 1t = 1/0.03t = 33.33 yearsPart 3P = $10000r = 3% (since P > $5000)I = $750t = ?

Find t:

I = Prt750 = 10000*0.03t300t = 750t = 750/300t = 2.5 years

My little brother spent $53 on comic books and magazines. He bought 17 items. If comic books cost $4 and magazines cost $3, how many of each item did my brother buy?

Answers

Answer:

comic books = 2

magazines = 15

Step-by-step explanation:

Let c = number of comic books bought

Let m = number of magazines bought

He bought 17 items, so

c + m = 17

Comic books cost $4 each and magazines cost $3 each.

He spent $53 on comic books and magazines, so

4c + 3m = 53

Rearrange c + m = 17 to make m the subject:

m = 17 - c

Substitute  m = 17 - c  into  4c + 3m = 53  and solve for c:

4c + 3(17 - c) = 53

⇒ 4c + 51 - 3c = 53

⇒ c = 2

Substitute c = 2  into m = 17 - c to and solve for m:

m = 17 - 2 = 15

Find the perimeter of the trapezoid
(5,1)( 5,-4) (1,1) (-2,-4)

Answers

Answer:

i cold not find the answer

Step-by-step explanation:

Simplify the expressions
1. x - 2 + 3x + 8
2. 2(-1.5x + 3) + (5x - 2)
3. (x + 3) - (2x - 1)
4. (4 - x) - 2 (-5x + 3)
5. (-4x + 3) + (9x - 5)
6. 3 (-3x - 4) - (3x + 5)
7. (-8x + 4) - (7x - 7)
8. 1/2 (x - 6) + 1/4 (x + 12)
9. (-2x - 3) - (2x - 10)
10. (-4x - 2) + 1/2 (12x - 22)
11. 2 (4.4 - 2x) + 4 (-x + 3)
12. (-2x + 5) - (-3x + 11)

Answers

Answer:

1) 2(2x+3)

2) 2x+4

3) - X + 4

4) 9x - 2

5) 5x−2

6) - 12x - 17

7) - 15x + 11

8) 3x/4

9) - 4x + 7

10) 4x-26/2

11) - 8x + 20.8

12) x - 6

Khloe made 20% of her free throws over the season. If she shot 240 free throws, how many did she make?

Answers

20% is the same as saying 0.2, so if you multiply 0.2 by 240, you should get your answer. Or an alternate way of seeing it is 2 times 24.

Anita can iron a dress shirt in 15 minutes, but

it takes Michelle 18 minutes to do the same.

Working together, how many minutes will it take

them to iron 11 dress shirts?

Answers

The number of minutes it will take both of them to iron 11 dress shirt is 90 minutes

Rate:

Rate is the ratio between two related quantities in different units. Therefore,

Anita iron a shirt in 15 minutes. Therefore,

rate  = 1 / 15

Michelle iron the same shirt for 18 minutes. Therefore,

rate = 1 / 18

Let the time they use to work together = x

Therefore,

1  / x  = 1 / 15 + 1  / 18

1  / x =  18 + 15 / 270

1 / x = 33 / 270

cross multiply

270 = 33x

x = 270 / 33

x = 90 / 11

Both of them will use 90 / 11 minutes to iron a dress shirt

Therefore, 11 dress shirt will be ?

number of minutes to iron 11 dress shirt together = 11 × 90  / 11 = 90 minutes

learn more on rate here: https://brainly.com/question/1119145

The point V(4, –1) is rotated 90° clockwise around the origin. What are the coordinates of its image V’? V’(1, 4) V’(–1, 4) V’(–1, –4) V’(4, 1)

Answers

Answer:

V' = (-1, -4)

Step-by-step explanation:

the original point V (4, -1) is 4 units to the right and 1 unit down.

now we turn this 90° clockwise (upper right to down to upper left).

that means the right part of the x-axis turns into the bottom part of the y-axis, and the bottom part of the y-axis into the left part of the x-axis.

so, positive x turns into negative y, and the negative y turns into negative x.

therefore, (4 -1) turns into (-1, -4).

Answer:

C     V'(-1,-4)

Step-by-step explanation:

Finding the Coordinate for a 90° Rotation

The point V(4, –1) is rotated 90° clockwise around the origin.

What are the coordinates of its image V’?

V’(1, 4)

V’(–1, 4)

(V’(–1, –4)) this one <-------

V’(4, 1)

Rob eats a hamburger that has 415 calories for lunch. He also eats French fries that are 10 calories each. If Rob consumed 645 calories, how many French fries did he eat?​

Answers

Answer: Rob ate 23 fries.

How do you work out 803.309-133.36?​

Answers

669.949 should be your result hope it helps and ask me anything you didn’t understand!

Factorise fully 7y+84​

Answers

Answer:

7 (y + 12)

Step-by-step explanation:

7 times y = 7y

7 times 12 = 84

7 (y + 12)

Answer:

y+12

Step-by-step explanation:

Divide 7y and 84 by 7

find yz 11x+1 and 19x-31

Answers

The length of a segment is the number of units between its endpoints

The length of YZ is 45 units

How to determine length YZ

The given parameters are:

WX = 11x + 1

YZ = 19x - 31

Lengths WX and YZ are congruent.

So, we have:

[tex]19x - 31 = 11x +1[/tex]

Collect like terms

[tex]19x - 11x = 31 +1[/tex]

Evaluate the like terms

[tex]8x = 32[/tex]

Divide both sides by 32

[tex]x = 4[/tex]

Recall that:

YZ = 19x - 31

So, we have:

[tex]YZ = 19*4- 31[/tex]

[tex]YZ = 45[/tex]

Hence, the length of YZ is 45 units

Read more about line segments at:

https://brainly.com/question/18315903

Solve for X round to the nearest tenth of a degree if necessary

Answers

Answer:

  63.4

Step-by-step explanation:

x° is an acute angle in a right triangle with the opposite and adjacent sides given. That means the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(x°) = 18/9 = 2

The value of the angle is found using the inverse tangent function:

  x° = arctan(2) ≈ 63.4°

  x = 63.4 . . . . . . . rounded to tenths

Evaluate |c 2 + b 2|, given a = 5, b = -3, and c = -2.

Answers

Hey there!

|c^2 + b^2|

= -2^2 + -3^2

= -2^2 - 3^2

= -4 - 9

= -13


Therefore, your answer is: -13


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Answer:

10

Step-by-step explanation:

|-2(2)-3(2)|

|-4-6|

|-10|

=10

One angle of a parallelogram measures 162°. What are the measures of the other three angles in the parallelogram?

Answers

Answer:

The important properties of parallelograms to know are:

-Opposite sides of parallelogram are equal (AB = DC).

-Opposite angles of parallelogram are equal (D = B).

-Consecutive angles in a parallelogram are supplementary (A + D = 180°).

-If one angle is 90 degrees, then all other angles are also 90 degrees.

FROM

SURAJ SAINI

Answer:

162,162,18,18

Step-by-step explanation:

each two opposite angles are equal

since there is an angle equals 162° then the opposite angle equals 162°

since the sum of all angles equal 360°

360-(162+162)= 36

so the sum of the other two opposite angle = 36 then the measure of one angle =36/2 =18°

Write a function in the form y=mx+b for the line that contains the points (2, 4) and(5, 10).

Answers

Step-by-step explanation:

gradient=∆y/∆x

=(10-4)/(5-2))

=6/3

=2

(x,y) (2,4)

y-4/x-2=2

y-4=2(x-2)

y=2x-4+4

y=2x

Which values are solutions to this inequality?

x>−5

Choose each correct answer.


8

5

1

−2

−6

−9

Answers

Answer:

8,5,1,-2

Step-by-step explanation:

> = Greater than or equal to -5

what is
(588/2)9=n
a)n=294
b)n=2646
c)n=1323

Answers

Answer:

b)

Step-by-step explanation:

9 × (588/2)

= 9 × (294)

= 2646

I NEER HELP ON KHAN ACADEMY PLS
A board game has players roll two 6-sided dice and subtract the numbers showing on the faces. The game
only looks at nonnegative differences. For example, if a player rolls a 4 and a 6, the difference is 2.
um
Here is the sample space showing the possible (equally likely) outcomes of a single roll:
uctio
2nd die
1st die
1
2
3
4
5
6
1
0
1
2
3
4
5
2
1
1:50
0
1
2
3
4
3
2
1
0
1
2
3
4
3
2
1
0
1
2
5
4
3
2
1
0
1
6
5
4
3
2
1
0
Which graph represents the theoretical probability distribution of the differences?

Answers

It can be deduced that the sample space is the collection of the set of possible outcomes in a random experiment.

What is a sample space?

Your information is incomplete as the graphs aren't provided. Therefore, an overview of the sample space will be given.

A sample space simply means the collection of the set of possible outcomes in a random experiment.

It should be noted that a sample space is usually represented by the symbol S.

Also, the theoretical probability distribution states that the probability of occurence of an event will be equal to the number of the favorable outcomes divided by the total outcomes possible.

Learn more about sample space on:

https://brainly.com/question/5750471

AREA OF TRIANGLE BASE=7 and 4

Answers

Answer:

area: 14

Step-by-step explanation:

An object with a mass of 4.0 kg accelerates 2.0 m/s² when an unknown force is applied to it. What is the
amount of the force

Answers

Answer:

F=ma

Mass is in kg, so we have mass= 4.0kg

since we have a= 2.0 m/s² and m= 4.0kg

F=ma

F= 4.0 x 2.0

F= 8.0N

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