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Rectangular coordinates (StartRoot 3 EndRoot, StartRoot 3 EndRoot) and polar coordinates (r, theta) = (StartRoot 6 EndRoot, StartFraction pi Over 4 EndFraction) both represent the same complex number z.
Which set of equations demonstrates why both sets of coordinates represent the same number?
A.) r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi over 4 EndFraction
B.) r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi over 4 EndFraction
correct one - C.) r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi Over 4 EndFraction
D.) r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi Over 4 EndFraction
Answers
Answer:
It is C. r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi Over 4 EndFraction
Step-by-step explanation:
edge2020
The rectangular coordinates (√3,√3) and polar coordinates (√6,[tex]\frac{\pi}{4}[/tex]) represent the same complex number z=x+iy because,
[tex]r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6[/tex] and,
[tex]\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}[/tex]
The question is not written in an understandable manner look at the question in the below-given image.
What is polar coordinate?In terms of Cartesian coordinates, the polar coordinates r (the radial coordinate) and θ (the angular coordinate, often known as the polar angle),
x = rcosθ
(1)
y = rsinθ,
(2)
where r is the radial distance from the origin and θ is the counterclockwise angle from the x-axis. In relation to x and y,
[tex]r=\sqrt{x^2+y^2}[/tex]
(3)
[tex]\theta=\arctan(\frac{y}{x})[/tex]
How to solve it?Using the above explanation of polar coordinates we have that
[tex]r=\sqrt{(\sqrt3)^2+(\sqrt3)^2}=\sqrt6[/tex] and
[tex]\theta=\arctan(\frac{\sqrt3}{\sqrt3})=\arctan(1)=\frac{\pi}{4}[/tex]
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Related Questions
help I need this asap I will give the brainiest
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Plz help. Write the slope intercept form of the equation
Answers
Answer:
2nd option is correct
Step-by-step explanation:
x +2y=14
2y = -x + 14
y= -x/2 +7
Answer:
-1/2
Step-by-step explanation:
So I am not certain but there is a website for things these.
There are 817 students enrolled at school, and 239 are remote. What percentage of school students are remote.
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HELP!!!
Mr. Suarez drives at a speed of 60 miles per hour to visit his brother who lives 200 miles away
from his home. Write an equation is slope intercept form. that represents the distance D in miles from his brothers home and T is the time in hours he had been driving.
the second part is Mr.Suarez is now traveling to her sister after 2 hours she is 75 miles away if she is still driving 60 miles per hour. Write an equation in point slope that represents his new situation
Answers
Answer:
d=-60h+120 First Part
d=-60h+160
hope this helps, if not, your free to give me one star (if you want to).
You are a sales clerk in a clothing store. You receive a salary of $320 per week plus a 5% commission on all sales. Write an equation to represent your weekly salary. (Let y equal the weekly salary and x equal the amount of sales.) What are the slope and y-intercept of your equation?
Answers
Answer:
slope: 0.05
y-intercept: 320
Step-by-step explanation:
y is the total weekly salary and x is the sales
there is a constant salary of $320, which will be the constant in the equation.
y = mx + b
y = mx + 320
we know there is a 5% commission on all sale, which we can convert to the fraction 0.05.
y = .05x + 320
Now we can see that the slope is .05 and the y-intercept is 320
Solve 8x - 5y = 14 for y.
Answers
Answer:
y=-14x/5+8x/5
Step-by-step explanation:
A 12 foot ladder is leaning up against a wall. If the angel made between the ladder and the ground is 80 degrees. How far up can the ladder reach the wall? Round to the nearest tenth of a foot
Answers
Answer:
11.8 feetStep-by-step explanation:
Given
Length of the ladder = 12foot
angle of elevation = 80 degrees
Required
Height of the wall (opposite side)
The set up will form a right angled triangle where
length of the ladder is the hypotenuse
height of the wall is opposite;
Using SOH, CAH, TOA trig identity
According to SOH
sin 80 = opp/hyp
sin80 = opp/12
opp = 12sin80
opp = 11.82 feet
Hence the height of the wall is 11.8feet (to the nearest tenth)
Shawn said that in standard notation,
7.142 x 107 will have 7 zeros after the
2 because the exponent is a 7. Is he
correct? Why or why not?
Answers
Answer:
This is incorrect.
Step-by-step explanation:
You move the decimal 7 places to the right after the 7. Since 2 is the third digit, you're adding 4 more zeros.
What is (5/4)³ ? Just asking-
Answers
Answer: 1.953... or 125/64
Step-by-step explanation:
Machine A makes 12.75 ounces of popcorn in 3 minutes. Machine B makes 18 ounces of popcorn in 4 minutes.
If each machine makes popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags?
A. Yes; Machine A and Machine B make 77.5 ounces in 10 minutes. 77.5 > 72, so there will be enough popcorn.
B. Yes; Machine A and Machine B make 87.5 ounces in 10 minutes. 87.5 > 72, so there will be enough popcorn.
C. No; Machine A and Machine B make 67.5 ounces in 10 minutes. 67.5 < 72, so there will not be enough popcorn.
D. No; Machine A and Machine B make 30.75 ounces in 10 minutes. 30.75 < 72, so there will not be enough popcorn.
Answers
Answer:
B i think
Step-by-step explanation:
can u mark me brainliest plz
A bookstore had 45 copies of a magazine. Yesterday, it sold 2/3 of them. Today, it sold 2/5 of what remained. How many copies does the bookstore have left?
Answers
Answer:
After the first day, 1/3 of the original amount remained:
... (1/3)·45 = 15
After the second day, 2/3 of that amount remained:
... (2/3)·15 = 10
The bookstore has 10 copies left.
Step-by-step explanation:
Answer:
Step-by-step explanation:
45 copies and sold 2/3= 30 sold so 15 left
15 copies and sold 2/5= 6 sold so 9 left
list five common multiples for 8 and 14
Answers
Answer:
56, 112, 168, 224, and more
The common multiples of 8 and 14 are: 56, 112, 168, 224, 280
They are going in intervals of 56
Hope this helps!
Find the slope of the line. (0,-1) (3,-2)
Answers
Answer:
-1/3
Step-by-step explanation:
m = (y2-y1) / (x2-x1)
m = (-2-(-1)) / (3-0)
m = (-2+1) / 3
m = -1/3
Answer:
-1/3
Step-by-step explanation:
equation is y2-y1/x2-x1
So the second y (-2) minus the first y (-1) is -1
And 3-0 is 3. So 3/1
Find the measure of the missing angle.
45 degree angle
X=-8
Answers
Answer:
47238
Step-by-step explanation:
it cost $11 for 15 granola bars what is the unit price in dollars per granola bar, rounded to the nearest hundred
Answers
Answer:
It is $0.73 for each granola bar. 11/15
Step-by-step explanation:
2. need help with this question
Answers
Answer:
First = Poppy seed = 3x10^-4 grams = 0.0003 grams
Second = sesame seeds = 3.64x10^-6 grams = 0.00364 grams
third = 250 pumpkin seeds 21 grams = one seed 0.084 grams
Step-by-step explanation:
3.64x10^-6 kilograms *1000gr/Kilograms = 0.00364 grams
21/250 = 0.0084 grams one seeds
GIVING BRAINLEST TO THE PERSON WHO ANSWERS IT FIRST AND CORRECT!!
Three friends each have some ribbon. Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 2.5 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and yards.
Answers
Answer:
read below explanation
Step-by-step explanation:
KEY= C;CAROL T;TINO B;BAXTER
inches: C=90 T=90 B=90
Feet: C=7.5 T=7.5 B=7.5
Yards C=2.5 T=2.5 B=2.5
|10+4x|<14 how do you solve this?
Answers
Answer:
-6 < x < 1
Step-by-step explanation:
-14 < 10 + 4x < 14
Subtract 10 from both sides
-24 < 4x < 4
Divide both sides by 4
-6 < x < 1
Answer: - 6 < x < 1
|10 + 4x| < 14
⇔ -14 < 10 + 4x < 14
⇔ -14 - 10 < 4x < 14 - 10
⇔ - 24 < 4x < 4
⇔ -24/4 < x < 4/4
⇔ - 6 < x < 1
Step-by-step explanation:
a UPS delivery man earns $0.60 per mile driven.How many miles did he drive if he received at $42
Answers
Answer:
70 miles
Step-by-step explanation:
Divide 42 by 0.60 = 70
Multiply 70 * 0.60 = 42.
A local restaurant serves breakfast. They use 124 cups of pancake mix every hour. It takes 114 cups of mix to make one pancake. The pancakes are all equal in size.
About how many pancakes can the restaurant make in two hours?
A 99 pancakes
B 198 pancakes
C 251 pancakes
D 310 pancakes
Answers
198 pancakes can the restaurant make in two hours.
What is Equation?Two or more expressions with an equal sign is called as Equation.
The restaurant can make 199 pancakes in two hours.
Given: Total number of cups of pancake mix used in 1 hour = 124
Mix required for each pancake 1 1/4=5/4.
Number of cups of pancake mix used in 2 hours = 2 x 124 = 248
Number of pancakes made = (Number of cups of pancake mix used in 2 hours ) ÷ (Mix required for each pancake )
=248÷5/4
=248×4/5
=198.4
Hence 198 pancakes can the restaurant make in two hours.
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7.25 x 2 1/2= WHAT PS HELPPP!!!!
Answers
Answer:
Its either 18.125 or 145 / 8
Step-by-step explanation:
Answer:
sorry, 18.125 what the other person said
Step-by-step explanation:
hope that can help!!
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
a I think
Step-by-step explanation:
I dont know how to explain if its not im sorry
I need help please (+5)+(-2)=
Answers
Which ordered pair is a solution to the linear inequality given below?
3x + 4y > 20
(-5,1)
(0,-3)
(-4,2)
(2,7)
Answers
Answer:
(2, 7 )
Step-by-step explanation:
Substitute the coordinates of each pair into the left side of the inequality and compare the result to the right side.
(- 5, 1 )
- 15 + 4 = - 11 < 20 ← not a solution
(0, - 3)
0 - 12 = - 12 < 20 ← not a solution
(- 4, 2 )
- 12 + 8 = - 4 < 20 ← not a solution
(2, 7 )
6 + 28 = 34 > 20 ← solution
The ordered pair which is correct for the given inequality will be equal to (2, 7). Hence, option D is correct.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given information in the question,
The given inequality is,
3x + 4y > 20
For point (-5, 1)
3(-5) + 4(1) > 20
-11 > 20, this is incorrect.
For point (0, -3)
3(0) + 4(-3) > 20
-12 > 20, this is incorrect.
For points (-4, 2)
3(-4) + 4(2) > 20
-4 > 20, this is incorrect.
For points (2, 7)
3(2) + 4(7) > 20
34 > 21, this is correct.
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Una fábrica envasadora recibe diariamente distintos tipos de aceite en las siguientes cantidades: 195 l, 275 l, 315 l, 460 l y 525 l. Puesto que los aceites son diferentes, los envasarán en diferentes garrafas. Sin embargo, quieren utilizar el menor número posible de garrafas, que todas tengan la misma capacidad y que no sobre ni una gota de aceite.
Answers
Answer:
Se calcula el maximo comun divisor.
195/5 = 39
275/5 =55
315/5 =63
460/5= 92
525/5 =105
Se deben utilizar 354 garrafas
Step-by-step explanation:
Descomponemos cada número en factores primos.
Después, señalamos los factores comunes.
A continuación, en cada uno de los comunes, escogemos el factor con menor exponente.
Y por ultimo, multiplicamos los factores elegidos.
195 3 275 5 315 3 460 2 525 3
65 5 55 5 105 3 230 2 175 5
13 13 11 11 35 5 115 5 35 5
1 1 7 7 23 23 7 7
1 1 1
Help with these 3 please
Answers
The second is 4
The third is -7
1. What absolute value expression can be written to determine the distance between 63 feet above sea level and 48 feet below sea level?
Answers
Given:
The distance between 63 feet above sea level and 48 feet below sea level.
To find:
The absolute value expression for the given situation.
Solution:
We have,
Distance above the sea level = 63 feet
Distance below the sea level = -48 feet
Here, negative sign represents the distance in below the sea level.
So, absolute value expression that can be written to determine the distance between 63 feet above sea level and 48 feet below sea level is
[tex]Distance=|63-(-48)|[/tex]
[tex]Distance=|63+48|[/tex]
[tex]Distance=|111|[/tex]
[tex]Distance=111[/tex]
Therefore, the required absolute expression is [tex]|63-(-48)|[/tex] and distance is 111 feet.
Use the symbols +, -, x, and = to make the number sentence true.
Option 1. (8 ÷ 3) - 2³x 17 = 33
Option 2. (8 + 3) - 2³ x 17 = 33
Option3. (8 x 3) - 2³+ 17 = 33
Option4. (8-3) x 2³+ 17 = 33
Answers
Answer:
it will be option 3 if isnt pls tell me and I'll work if out
(8 x 3) - 2³+ 17 = 33 is the true statement and so Option 3 is the correct answer.
What is an Equation ?An equation is a statement that links variables to constants and even with other variables and is helpful in solving complex problems.
The options given below needs to be checked for
Left Hand Side = Right Hand Side
Option 1
LHS = -133.33
RHS = 33
Option 2
LHS = -125
RHS = 33
Option 3
LHS = 33
RHS = 33
Therefore Option 3 is the correct answer.
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(-8)+(-19) i will give brainllest
Answers
Answer:
-27
Step-by-step explanation:
Answer:
-27 maybeeeeeeeeeeeee
Solve for u.
6u=78
U =
Answers
Because your dividing each term by 6