Consider the numbers z = 3√2(cos(135°) + i sin(135o) and w = cos(180o) + i sin(180°).
Which expression is closest to the polar form of z + w?
Answers
Answer: A
5(cos(143o) + i sin(143o))
Step-by-step explanation:
The expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"
What is polar form of the complex number?"The polar form of the complex number z = x + iy is [tex]z=r(cos(\theta)+i~sin(\theta))[/tex] where [tex]r=\sqrt{x^{2} +y^{2} } , ~\theta=tan^{-1}(\frac{y}{x} )[/tex] "
For given question,
We have been given two complex numbers.
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})[/tex] and [tex]w = cos(180^{\circ}) + i~sin(180^{\circ})[/tex]
We know that,
[tex]cos(135^{\circ})\\=cos(90^{\circ}+45^{\circ})\\=-sin(45^{\circ})\\=-\frac{1}{\sqrt{2} }[/tex]
And
[tex]sin(135^{\circ})\\=sin(90^{\circ}+45^{\circ})\\=cos(45^{\circ})\\=\frac{1}{\sqrt{2} }[/tex]
So, the first complex number would be,
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})\\\\z = 3\sqrt{2} (-\frac{1}{\sqrt{2} } + i~\frac{1}{\sqrt{2} } )\\\\z=-3+3i[/tex]
We know that [tex]cos(180^{\circ})=-1,~~sin(180^{\circ})=0[/tex]
So the second complex number would be,
[tex]w = cos(180^{\circ}) + i~sin(180^{\circ})\\\\w = -1 + 0i[/tex]
So, the sum of complex numbers z and w would be,
[tex]z+w\\=(-3+3i)+(-1+0i)\\=-4+3i[/tex]
We write the complex number -4 + 3i in the polar form.
Comparing above number with x + iy, we have x = -4 and y = 3
[tex]\Rightarrow r=\sqrt{(-4)^2+3^2}\\ \Rightarrow r=5[/tex]
Also, the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{3}{-4} )\\\\\theta= -36.86^{\circ}\\\\\theta=180^{\circ}-36.86^{\circ}\\\\\theta=143.14^{\circ}[/tex]
So the complex number -4 + 3i in the polar form would be, [tex]5(cos(143.14^{\circ})+i~sin(143.14^{\circ}))[/tex]
Therefore, the expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
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Related Questions
How can you solve linear equations and inequalities in one variable, including equations with coefficients represented by letters?
Answers
Answer:
X=3
Step-by-step explanation:
For a linear equation like 2x + 3 = 9 you would start with subtracting 3 from both sides. Then you would divide both sides by 2 to get x by itself. You get x=3
For linear inequalities it’s the same but with a less than or equal sign. You just solve the same way. However if you divide a negative the sign flips like in my second example. I’m not sure if this is exactly what you are looking for since I don’t know what your problems look like but I hope it helps.
Anyone???
Mathematics
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The rise is 1
The run is 2
So the slope would be 1/2
Estimate the following sum by first rounding each decimal to the nearest hundred. Is the answer 800?
Answers
A dime (0.10) is what percent of a dollar (1.00)?
Answers
1.00 / 0.10 = 10
Answer:
10%
Step-by-step explanation:
A meteorologist records the temperature as - 7.5°C at 7 a.m. and as-4.3°C at 10p.m. Which statement is true?
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Answer:
Step-by-step explanation:
its maybe A
3/4x+2-1/3x=12
What is the answer?
Answers
Answer:
x=24 or 25
Step-by-step explanation:
90% is x=24
89.999999 repeat% is x =25
Tyler is packing his bags for vacation. He plans to pack two outfits for each day of vacation.
Let d = the number of days of his vacation.
Write an expression for the total number of outfits WILL BRIANLIST
Answers
=========================================
Work Shown:
d = number of days of his vacation
1 day = 1*2 = 2 outfits
2 days = 2*2 = 4 outfits
3 days = 3*2 = 6 outfits
4 days = 4*2 = 8 outfits
5 days = 5*2 = 10 outfits
and so on.
In general we can say,
d days = d*2 = 2d outfits
d is simply a placeholder or a box where we'll place a number inside. For example, if he's on vacation for d = 7 days, then he'll bring 2*d = 2*7 = 14 outfits.
The expression 2*d is the same as 2d. We can leave out the multiplication sign since having a number next to a variable like this implies multiplication.
The expression for the total number of outfits is 2d
The total number of outfits Tyler plans to pack for his vacation can be expressed as 2 multiplied by the number of days of his vacation, which we'll denote as 'd'. Since Tyler plans to pack two outfits for each day, multiplying 'd' by 2 will give us the total number of outfits.
In this expression, 'd' represents the number of days of Tyler's vacation, and multiplying it by 2 accounts for the two outfits planned for each day. This expression allows us to calculate the total number of outfits based on the length of Tyler's vacation.
For example, if Tyler's vacation is 7 days long, the expression 2d would yield:
2 * 7 = 14
Therefore, Tyler would plan to pack 14 outfits for his 7-day vacation. The expression 2d allows flexibility to calculate the total number of outfits based on the specific number of vacation days.
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Adele mows lawns in her neighborhood each weekend to save money for college.She uses her parents lawn mower,but is responsable for buying gas and other supplies she’ll need.The table below shows her profit after the first two lawns she moved last weekend.Adele charges the same amount of every lawn she mows.Select the function that models the relationship between her profit and the number of lawns she mows.
Answers
Answer:
P = 25m - 15
Step-by-step explanation:
Kindly find attached the table of values for your reference.
Step one:
given data
let us set up the coordinate using the value of p and m
p=35
p1=10
m=2
m1=1Tthe cordinate is (p1,p),(m1,m)= (y1,y),(x1,x)
(1,10), (2, 35)
the slop is given as, slope m = (p- p1)/(m - m1)
m=(35-10)/(2-1)
m = 25
from the equation of line y=mx+c
y = 25x + c
10 = 25(1) + bc
c= -15
y = 25x - 15
in term of m and p we have P = 25m - 15
help plsss hurryyyyyy
Answers
Given f(x) = 7 - 4x. If the domain of the function is {-4, 0, 1.75, 3}, what is the range of the function?
Answers
Answer:
[-5,23]
Step-by-step explanation:
f(-4)=23
f(3)= -5
put the maximum and minimum values for x which at domain
Is 1¾ a rational numbers
Answers
Answer:
Yes 1¾ is a rational number
Step-by-step explanation:
1¾ is written as a fraction of two integer and is therefore rational.
Use the digits 5, 3 and 2 two only once in each number how many different three digit numbers can you make
Answers
Question 1 of 10
What is the slope of the line shown below?
10
(3,9)
O A.
5
B. 4
(1,1)
-5
10
15
O C. -
1
4
O D.-4
SUBMIT
Answers
The slope of the given line is 4.
What is slope?The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Given that, a line passing through points (3, 9) and (1, 1) we need to find the slope of the line,
Slope = y₂ - y₁ / x₂ - x₁
So,
Slope = 9-1 / 3-1 = 8/2 = 4
Hence, the slope of the given line is 4.
Learn more about slopes, click;
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what is 5/ 16 expressed as a percentage
Answers
Answer:
31.25%Step-by-step explanation:
To express a number as a percent we will first divide the top number by the bottom number.
5/16 = 0.3125
A percent is expressed by moving the decimal two places to the left.
31.25%22a) PLEASE HELP BEST ANSWER BRAINLIEST
Endpoints of segment MN have coordinates (0, −3), (−2, −4). Endpoints of segment AB have coordinates (2, 5), (4, k).
a
What value of k makes these segments perpendicular?
Answers
Answer:
the answer is k=1
Step-by-step explanation:
pls help pls ill mark brainliest
Answers
Answer:
Area/Circumference is the length of a circle!
Step-by-step explanation:
Answer: the answer is area/ circumference
Step-by-step explanation:
1) g(x) = 4x + 3
h(x) = 3x + 3
Find g(x) + (x)
Answers
Answer:
Step-by-step explanation:
g(x) = 4x + 3
h(x) = 3x + 3
g(x) + h(x) = 7x + 6
To complete her holiday wrapping, bella needs identical strips of ribblon measuring 3.5 feet each. She has 85 feet of ribbon in total. About how many pieces of ribbon can she cut from this long strip
Answers
Answer:
85/3.5 = 17/0.7 = 24.29 pieces of ribbon .
Step-by-step explanation:
The given equation shows the relationship between the price, in dollars, y, of x gallons of gasoline.
y = 2.251
Which graph represents the proportional relationship?
Cost of Gasoline
3.5
Cost of Gasoline
3.5
3
3
2.5
2.5
Price ($)
2
Price ($)
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5 1 1.5 2 2.5 3 3.5
Gallons of Gasoline
w.
0.5 1 1.5 2 2.5 3 3.5
Gallons of Gasoline
X.
Cost of Gasoline
Cost of Gasoline
Y
3.5
3.5
3
3
2.5
2.5
Price ($)
2
Price ($)
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5 1 1.5 2 2.5
1.5 2 2.5 3 3.5
Gallons of Gasoline
Y.
0.5 1 1.5 2
1.5 2 2.5 3 3.5
Gallons of Gasoline
z.
1 of 10 Answered
Session Score: 0% (0/1)
Answers
log_6(x+1)+log_6x=1
Answers
This is pretty simple once you figure out the trick.
All you have to do is make the args common.
Meaning [tex]log_{6}(x + 1) + log_{6}(x) = 1[/tex] is nothing but [tex]log_{6}(x(x + 1)) = 1[/tex]
Which is nothing but: [tex]log_{6}(x^2 + x) = 1[/tex].
Now using the scorpion tail method, this equation can be reframed to being: [tex]6 = x^2 + x[/tex]. You bring 6 to the other side and it'll become: [tex]x^2 + x - 6 = 0[/tex]
Factorise it and you get: [tex](x - 2) * (x + 3)[/tex]
Henceforth, the solution would be [tex]2[/tex] and [tex]-3[/tex]. :D
Answer:
D. x = 9
Step-by-step explanation:
edge 2022
Which algebraic expression is equivalent to the expression below? 6(3x - 4/3) + 44
A. 18x - 36
B. 18x - 52
C.18x + 52
D.18x + 36
Answers
Answer:
D
Step-by-step explanation:
first distribute 6 to get
(18x - 8) +44
combine like terms
18x + 36
Answer: D.) 18x+36
-4/3×6=-8
-8+44=36
6×3x=18x
I hope this is good enough:
How do you do these questions?
Answers
Part (a)
The equilibrium price occurs at the intersection of the supply and demand curves. See the diagram below to see how this looks. Ignore the red line and green lines for now. Those will apply for part (b).
If the price was below equilibrium, then we would have a shortage and it would lead to a pressure to push prices upward. If the price was below equilibrium, then there would be a surplus or oversupply, leading to a downward pressure in prices. So inevitably the price lands on the equilibrium if given enough time and there are no external forces acting on the market.
==============================================================
Part (b)
Let's say we have two people labeled person A and person B. If person A gets a higher education, while person B does not, then person A is likely to earn more money. Person B will see this and want to may want to earn more money as well, so that makes their demand for higher education go up. While of course this rule doesn't work for everyone, in general we'll have enough people to effectively push the demand curve to the right while the supply curve remains where it is. Check out the diagram below to see what I mean.
==============================================================
Part (c)
Refer to the diagram in part (b). We have a new demand curve which intersects the supply curve to produce a new equilibrium point with price P1 and quantity Q1. So effectively the tuition has gone up due to higher demand.
==============================================================
Part (d)
If a government provides a subsidy, then this would lower the cost of education to provide people with more opportunities to improve their earning potential. The subsidy would provide a portion of the tuition which gives the illusion of the tuition price being lowered. In a way it's like getting a grant from the government to then pay that money toward your tuition.
Read the excerpt from "Myths About the Founding Fathers This is the truth Revere did ride from Boston to Lexington to warn Hancock and Adams, but he didn't go alone William Dawes took a different route to Lexington, joining Revere and Dr. Samuel Prescott. All three had been spreading the word that the regulars are coming along the way. There may have been as many as forty others who helped.
How do these sentences contribute to the development of ideas in the passage?
It explains how myths about Paul Revere came to
It highlights the importance of lessons to be learned from myths
It provides evidence that Revere's actions were exaggerated in myths
It shows that this are often based on real events
Answers
Answer: it shows that myths are often based on real events. Hope it helps
Step-by-step explanation:
i took the test on the k-12 site and the was the answer cuz i got it correct.
Is line l parallel to line m? Explain.
Yes, alternate interior angles are congruent.
No; alternate interior angles are not congruent.
No; corresponding angles are not congruent.
Yes; corresponding angles are congruent.
Answers
Answer:
yes, corresponding angles are congruent
Step-by-step explanation:
graph the line with the equation y=-6/5x+1
Answers
sneakychickens please help
Answers
Answer:
16
Step-by-step explanation:
First I plugged in the values like [tex](-2)^{2} |6-(3(-2))|[/tex]
Then I Solved [tex](-2)^{2}[/tex] and got 4
Than I multiplied 3 by -2 and got -6
Now the equation looks like 4|6-(-6)| which will now be 4|6+6|
then add 6 and 6 together and you get 12 now you add 4 and 12 together and you get your answer 16
Hope this helps
three-fourths of a number is at least -18
Answers
Answer:
3/4*X < -18
( put a line underneath the less than sign ) ( Astric's means multiplication )
Step-by-step explanation:
Hope this helped, Have a Wonderful Day!!
Answer:
x ≥ - 24
Step-by-step explanation:
Let's solve this with an equal sign and then decide how to handle the at least part.
3/4 x = -18 Multiply by 4
3/4 * 4 x = -18*4 Cancel the left, multiply the right.
3x = -72 Divide by 3
x ≥ -24
You need the greater than to indicate that 3/4 of a number can give something larger than - 18.
You need the equal sign to fulfill at least.
At least, in this question means "get larger."
so x > - 24
elena receives $200 for a birthday present, which she deposited in a bank account. Every month she withdraws $25. how much will she have left in her bank?
Answers
Answer:
8 months
Step-by-step explanation:
for every 100 four 25s and these two 100s so 8
hope this helps
Mary keeps track of how much time she goes running each week for 10 weeks. the frequency table with the data she collected. How many hours did mary spend running?
Answers
Answer:
One bad b, and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
One bad b, and she do what I say so (yeah, gang)
Two big .40s and a big a Draco (two)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s
I'm with my n*yeah, we some rockstars
And I'm with my n yeah, KK Wokhardt (KK Wokhardt)
This not my d, lil' b, my Glock hard (lil' b)
Straight to the cash, I'm a trapstar (cash)
Straight to the bag, I'm that n, huh (bag, oh)
Got me some gas, rollin' up some
Fft, fft, cash, yeah, I got me some
I ain't f her yesterday (yeah)
I'ma f some
One bad b , and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
3-0 clip in my Nina (oh, oh)
On my toes, Gucci, Valentino (yeah, b)
She on go, your b f the team, uh (lil' b )
'Cause you know your b want a winner (winner)
I just went back to my city (to my city)
And you know they all f with me (big hands)
But it ain't safe, h with me (h)
I'ma chase bands 'til they end me
One bad b, and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
One bad b, and she do what I say so (yeah, gang)
Two big .40s and a big a Draco (two)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s
Step-by-step explanation:
how to get beter at maths
Answers
Answer: to get better in math:-
i) listen to the math class properly
ii) practice the math works thoroughly
iii) do homeworks on time
iv) if there is any doubt still feel free to ask to the teacher
v) do revision of the taken chapters once in month
vi) If u can attend tuition classes then attend them
doing these steps I'm sure u can be better in math.
Hope it helped u, pls mark this as brainliest and put thanks for the ans