Consider w=sqrrt2/2(cos(225°) + isin(225°)) and z = 1(cos(60°) + isin(60°)). What is w+ z expressed in rectangular form?
Answers
Answer:
Option (3)
Step-by-step explanation:
w = [tex]\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)][/tex]
Since, cos(225) = cos(180 + 45)
= -cos(45) [Since, cos(180 + θ) = -cosθ]
= -[tex]\frac{\sqrt{2}}{2}[/tex]
sin(225) = sin(180 + 45)
= -sin(45)
= -[tex]\frac{\sqrt{2}}{2}[/tex]
Therefore, w = [tex]\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})][/tex]
= [tex]-\frac{2}{4}(1+i)[/tex]
= [tex]-\frac{1}{2}(1+i)[/tex]
z = 1[cos(60) + i(sin(60)]
= [tex][\frac{1}{2}+i(\frac{\sqrt{3}}{2})[/tex]
= [tex]\frac{1}{2}(1+i\sqrt{3})[/tex]
Now (w + z) = [tex]-\frac{1}{2}(1+i)+\frac{1}{2}(1+i\sqrt{3})[/tex]
= [tex]-\frac{1}{2}-\frac{i}{2}+\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]
= [tex]\frac{(i\sqrt{3}-i)}{2}[/tex]
= [tex]\frac{(\sqrt{3}-1)i}{2}[/tex]
Therefore, Option (3) will be the correct option.
Related Questions
hey, can someone please help me solve this? it’s a test.
Answers
Answer:
c
Step-by-step explanation:
3x+75=180
-75 -75
3x=105
x=35
35*2=70
Marissa got a lot of Halloween candy. She collected 7,965 candy bars. She wants to split it between her and her 7 friends. How much candy will be left over after dividing it?
Answers
Answer:
6 candies
Step-by-step explanation:
Marissa collected 7,965 candy bars during Halloween.
She wants to split it between 7 of her friends
= 7965/7
= 1137 remainder 6
Hence 6 candies will be left after dividing
Please help
I will give brainliest
A farmer is painting a new barn. He will need to calculate the surface area of the bath to purchase the correct amount of paint in which following unit can the farmer expect to calculate the surface area?
M, m^3, ft, ft^2
Answers
Answer:
Step-by-step explanation:
Ft is 4 m35
Answer:
The answer would be B
Step-by-step explanation:
meter's squared is literally the basic unit of measurement for surface area
I need help, please u will get 20 points
Answers
Answer:
the answer is going to be 9
Answer:
13
Step-by-step explanation:
9 3/4 feet = 3/4 minutes
39/4 = 3/4
= 13
In the regular octagon shown below, which of the following is the minimum angle of rotation about center point C will carry the figure onto itself?
1) 15°
2) 30°
3) 45°
4) 90°
Answers
Answer: 4)90˚
Step-by-step explanation:
(90˚ is more towards the middle
A regular octagon is a shape with 8 congruent sides.
The minimum angle of rotation is 45 degrees
The number of sides of a regular octagon is:
[tex]\mathbf{n = 8}[/tex]
The total angle at the center of the regular octagon is:
[tex]\mathbf{\theta = 360}[/tex]
So, the minimum angle of rotation is calculated as follows:
[tex]\mathbf{\alpha = \frac{\theta}{n}}[/tex]
This gives
[tex]\mathbf{\alpha = \frac{360}{8}}[/tex]
[tex]\mathbf{\alpha = 45}[/tex]
Hence, the minimum angle of rotation is 45 degrees
Read more about rotations at:
https://brainly.com/question/1571997
Nora has 16 muffins that she wants to give to 4 friends.
She wants each friend to have the same number of muffins.
Select the three statements that describe how Nora should give the muffins to her
friends.
Answers
Answer:
16 ÷ 4, 16/4, each friend gets 4 of the muffins.
Step-by-step explanation:
Dividing it by four will give them all an equal amount.
Hope this helps.
WORTH 20 POINTS
help ASAP
Answers
Answer:
She will use 32
Step-by-step explanation:
Every 1 model she adds 2 just do 16x2=32
A faucet dripped 1/4 cup of water in 11/2 hours. What is the rate in cups per hour?
Answers
Answer:1/6th of the Cup
Step-by-step explanation:
Is the following equation an example of direct variation?
y equals 5 x
Answers
A grocery store sells cashews. The relationship between the mass and cost of cashews is shown in the following graph. Which statements about the graph are true? Select all that apply.
Answers
Answer:
hope this helps! The answer is in the photo <3
Step-by-step explanation:
4+5(p-1) =34 solve it fast
Answers
Answer:
P=7
Step-by-step explanation:
4+5(7-1) = 34
4 + 5(6) = 34
4+30=34
34=34
help asap please !!!!
Answers
Answer:
65,69,81,87,88
Step-by-step explanation:
E.81
Billy bought Katie a present wrapped in this box. How much wrapping paper would He need to wrap the present in this box, PLEASE HELP! WILL MARK BRAINLIEST
Answers
Answer:
284mm²
Step-by-step explanation:
S.A.= 2(lw) + 2(lh)+ 2(wh)
2[12.6(8)] + 2[12.6(2)] + 2[8(2)]
201.6 + 50.4 + 32
S.A.= 284mm²
Answer:
B
Step-by-step explanation:
You need a top and bottom (same size)
You need a front and back (same size for them as well)
You need a left and right covering.
Top and bottom = 2 * 12.6 * 8 = 201.6
Left Right = 2 * 8 * 2 = 32.0
Front/Back= 2 * 2 * 12.6 = 50.4
Total 284
Kristin is filling 3 jars with jellybeans. If she has 1,856 jellybeans and wants to split them evenly between the jars, will Kristin have any jellybeans left over? If so, how many?
Answers
Answer:
Yes, Kristin will have 2 jelly beans left
Step-by-step explanation:
Total jelly beans = 1,856
Total jars = 3
Kristin is filling 3 jars with jellybeans
She wants to split them evenly between the jars, will Kristin have any jellybeans left over?
Jellybeans in a jar = total jellybeans / total jar
= 1,856 / 3
= 618 remainder 2
Yes, Kristin will have jelly beans left
Kristin will have 2 jellybeans left
Check:
618 × 3 = 1,854
Remaining jellybeans = 1,856 - 1,854
= 2 jellybeans
The prime factorization of 1080 is ____
.
List the factors from least to greatest and be sure to use the * between different the factors. For example, the prime factorization for 12 can be entered as 2*2*3. Do not use exponents.
Answers
Answer:
1080 = 2 * 2 * 2 * 3 * 3 * 3 * 5
Step-by-step explanation:
Start dividing by prime numbers.
1080 / 2 = 540
540 / 2 = 270
270 / 2 = 135
135 / 3 = 45
45 / 3 = 15
15 / 3 = 5
5 / 5 = 1
So we have 3 2s, 3 3s, and 1 5.
Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because is less than pi. Do you agree with Han? Copied for free from openupresources.Org
Answers
Given :
Han says that we can wrap a 5 foot rope around a wheel with a 2 foot rope.
To Find :
It this true or false.
Solution :
Radius of wheel, r = 1 foot.
Circumference of wheel is given by :
[tex]C = 2\pi r\\\\C = 2\times 3.14\times 1\\\\C = 6.28 \ foot[/tex]
Since, circumference is greater than 5 foot, therefore, we cannot wrap a 5-foot rope around a wheel with a 2-foot diameter.
Hence, this is the required solution.
agree Step-by-step explanation:
This recipe makes 18 shortbread fingers.
Rose follows this recipe, but only wants to make 6 fingers.
How much of each ingredient does she need?
Recipe: Makes 18
120 g butter
60 g sugar
180 g flour
Answers
Answer:
Butter: 40 g
Sugar: 20 g
Flour: 60 g
Step-by-step explanation:
The recipe makes 18 fingers.
Rose wants to make 6 fingers.
6/18 = 1/3
Rose wants to make 1/3 of the recipe, so she needs 1/3 of each ingredient.
Butter: 1/3 * 120 g = 40 g
Sugar: 1/3 * 60 g = 20 g
Flour: 1/3 * 180 g = 60 g
Answer:
40g butter
20g sugar
60g flour
Step-by-step explanation:
simplify 5+3.2n−6−4.8n
Answers
Answer: -1.6n - 1
Step-by-step explanation:
1. Rearrange the expression so like terms are next to each other
3.2n - 4.8n + 5 -6
2. Combine like terms
-1.6n - 1
3. Check your work, and your simplified expression should be correct!
Marcella wants a job as a sales representative. She receives two job offers that sell office machines to businesses.
Office Essentials offers Marcella a set monthly salary of $2,500 plus a commission (additional $) of $120 for every office machine she sells
Everything Office offers her a set monthly salary of $2000 plus a commission (additional $) of $150 for every office machine she sells
If T is the total amount (combined salary and commission) of money Marcella makes each month M is the total number of office machines she sells
1. Write an equation to represent the Total money she would make in one month at Office Essentials
2. Write an equation to represent the Total money she would make in one month at Everything Office
Answers
Answer:
$4,000
Step-by-step explanation:
Part A
Marcella wants a job as a sales representative. She receives two job offers from companies that sell office machines to businesses.
Office Essentials offers Marcella a salary of $2,500 per month, plus a commission of $125 for every office machine she sells.
Everything Office offers Marcella a salary of $2,000 per month, plus a commission of $150 for every office machine she sells.
Let M represent the total monthly earnings, in dollars, and let n represent the number of office machines sold in a month. For each company, write an equation that represents the relationship between M and n.
Enter your equations in the space provided.
Part B
Marcella wants to earn a total of at least $4,000 per month. For each company, find the least number of office machines she would need to sell each month in order to meet this goal. Show your work.
Enter your answers and your work in the space provided.
Part C
Compare Marcella’s possible earnings at Office Essentials to her possible earnings at Everything Office. How many machines would Marcella have to sell for the earnings at both companies to be the same? Find the interval of machines sold for which the total earnings at Everything Office are greater than the total earnings at Office Essentials. Show your work.
Simplify the following expression: b + b + b
Answers
Answer:
3b
Step-by-step explanation:
repeated addition is multiplication
Answer:
3b
Step-by-step explanation:
heres why:
there are 3 b's right
so heres wut i did
b+b+b=3b
i add it
the sum of y and the difference of 9 and j
as an expression
Answers
Answer: I think it would be Y+(9-j)
last question i will give brainliest
Answers
-2.47
-2 1/2 is -5/2 or -2.5
21/4 is 5.25
5
least to greatest would be
-2 1/2
-2.47
-2/5
5
21/4
answer is H
All corresponding angles in congruent figures are congruent.
True or false
Answers
Please tell me if wrong
gjkv ksfirjeogjagkfs fnremfsjkzd ewafeji frefnrzf fjnfjrbgbege frfnr frne frefaznj refjinrf
Answers
Answer:
THIS ANSWER IS REVENGE
muhahaha
Please help me on this problem:)
Answers
There are 24 bottles of water in 2 cases of water. If each case of water contains the same number of bottles, what is the minimum number of cases needed to have 76 bottles of water?
Answers
Answer:
7
Step-by-step explanation:
yw
Answer:
7
Step-by-step explanation:
What is the soul it ion or | 3x -4 | =8
Answers
Answer:
true
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
8+4=12 12 divided by 3=4
Help pls!
13x - 14 = - 118
- 13x =
x=
Answers
-13x=
x=-8
I need help I WILL MARK BRAINLIEST JUST PLS TELL ME WHAT 2+2 IS PLSSSSS IM DESPERATE
Answers
Answer:
4
Step-by-step explanation:
2+2=4
the difference between
8,-7 and -3,-7
Answers
Answer:
1) is 15.
2) is 4.
Step-by-step explanation:
hope this helps :)
Answer:
8,-7 is over in ll
-3,-7 is over in 4
thatsone big difference
lmk if this helped