Answers
Answer: Choice C
==========================================================
Explanation:
Recall that the form
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
can be abbreviated to
[tex]z = r*\text{cis}(\theta)[/tex]
The "cis" stands for the first letters of "cosine i sine" in that order.
The original fairly messy quotient can be shortened down to
[tex]\frac{90\text{cis}(\pi/4)}{2\text{cis}(\pi/12)}[/tex]
We have 90cis(pi/4) all over 2cis(pi/12) as one big fraction.
-------------------------------
Now we'll use this rule to divide two complex numbers
[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\\frac{z_1}{z_2} = \frac{r_1}{r_2}*\text{cis}(\theta_1-\theta_2)\\\\[/tex]
As you can see, we divide the r1 and r2 values to form the final coefficient out front. The theta angles are subtracted to form the new argument.
-------------------------------
Let's apply that idea to what your teacher gave you
[tex]z_1 = 90*\text{cis}(\pi/4)\\\\z_2 = 2*\text{cis}(\pi/12)\\\\\frac{z_1}{z_2} = \frac{90}{2}*\text{cis}(\pi/4 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(3\pi/12 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(2\pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(\pi/6)\\\\[/tex]
That last step then converts directly to the expression shown in choice C.
Related Questions
For a ride on a rental scooter, Rafael paid a $6 fee to start the scooter plus 8 cents per minute of the ride. The total bill for Rafael's ride was $18.64. For how many minutes did Rafael ride the scooter?
Answers
Answer:
158 minutes
Step-by-step explanation:
If m represents the number of minutes Rafael rode, his total bill is ...
0.08m +6.00 = 18.64 . . . . cost to start plus cost based on time
0.08m = 12.64 . . . . . . . . . . subtract 6
m = 12.64/0.08 = 158 . . . . divide by 0.08
Rafael rode the scooter for 158 minutes.
How much would it cost Matt to buy 2½ metres? when it is 9.50 per metre
Answers
Answer: 23.75
Step-by-step explanation:
can someone help with this question
Answers
Answer:
<1= 60
<2=120
<3=60
<4=60
<5=120
<6=120
<7=60
Step-by-step explanation:
How many minutes is 6:45 to 9:25 ?
Answers
Answer:
It is 15 minutes from 6:45 to 7:00. From 7:00 to 9:25 it is 2 hours and 25 minutes. Note: one hour is 60 minutes.
15 + 60(2) + 25
15 + 120 + 25
160 minutes
:)
Help me with this hw plz
Answers
Answer:
here
Step-by-step explanation:
А. parallelogram .............
Step-by-step explanation:
Which is the graph of linear inequality 6x + 2y > –10?
On a coordinate plane, a dashed straight line with negative slope goes through (negative 2, 0) and (0, negative 6). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line with negative slope goes through (0, 6) and (2, 0). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line with positive slope goes through (0, negative 6) and (2, 0). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line with positive slope goes through (negative 2, 0) and (0, 4). Everything to the right of the line is shaded.
Answers
Hope it helps :) and let me know if you want me to explain why
Answer:
A
Step-by-step explanation:
DECYPHERED
Could someone help me with these all these questions below
And no file please.
Use the information below to answer the questions:
Hastings 45 km Dover 108 km
Brighton 22 km Coventry 209 km
London 77 km Birmingham 172 km
1. How far is Hastings to the nearest 10 km?
2. How far is Brighton to the nearest 10km?
3. How far is London to the nearest 100km?
4. How far is Dover to the nearest 100km?
5. Approximately how far would you travel if you drive to London and then to Coventry?
6. Approximately how far would you have travel if you drive to Brighton, London and then Birmingham?
Answers
Answer:
1. 50km 2. 20 3. 100km 4. 100 5. 300 (rounded to the 100's) or 290 (rounded to the 10's) 6. 270 (to the nearest 10's) 300 (to the nearest 100's)
Step-by-step explanation:
1.
45
5=>5
Answer 50
2.
22
2<5
Answer 20
3.
77
7>5
Answer 100
4.
108
0<5
Answer 100
5.
Answer 300 or 290
(Based on the answer above)
6.
300 or 270
(Based on the answer above)
Written as a rate, 15 miles in 10 hours would be ____ miles per hour.
Answers
Answer:
1.5 mph
Step-by-step explanation:
To find the Unit Rate, you need to divide 15 miles by 10 hours to get the # of miles per hour.
15/10 = 1.5
1.5 miles per hour.
PLZ HELP ASAP
Find the length of X
Answers
x = 5
explanation:
3 + 4.5 = 7.5 to get the side of the big triangle
set up a proportion
[tex]\frac{3}{7.5} =\frac{2}{x}[/tex]
3x=7.5(2)..........cross multiply
3x=15.................multiply
x=5.....................divide both sides by 3
Answer:
Step-by-step explanation:
[tex]\frac{3}{2} =\frac{7.5}{x} \\[/tex]
3x = 15
x = 5
Red At Santa's workshop, Jingles
the Elf sampled candy canes. He found
that 18 candy canes were broken. This
number represented 15% of the total
number of candy canes he inspected.
What was the total number of candy
canes Jingles sampled?
Answers
Based on the total number of candy canes damaged and the proportion of the total it was, the total inspected was 120 candy canes.
Assuming the total number of candy canes inspected is x, the relevant formula would be:
18 = x × 15%
Solving for x would give us:
18 = 0.15x
x = 18 / 0.15
= 120 candy canes
In conclusion, 120 canes were sampled.
Find out more at https://brainly.com/question/529563.
I need help on this question
Answers
In the number 78.018, how does the value of the 8 in the thousandths place compare to the value of the 8 in the ones place?
Drag and drop a fraction into the box to correctly complete the statement.
The value of the 8 in the thousandths place is Response area the value of the 8 in the ones place.
Answers
Each digit the decimal place moves can be thought of as multiplying or dividing the original value by 10 (depending on which way it is moved)
Answer:
1/1000
Step-by-step explanation:
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck
Answers
Answer:
The answer is not finished but if John is buying the materials and paying for the labor then the answer will be $510.
Step-by-step explanation:
I’m sorry if I didn’t help but the answer is not written out enough…
Solve for the unknown side of each right triangle
Answers
x is 9.1 accordingly to the phytagores therom
What is the equation of the line in slope-intercept form?
Answers
Answer:
y=2x+1/2 or its y=2x+2
Step-by-step explanation:
Y intercept is when the line intercepts with the y axis, the straight line. In this case it is 4, so b=4
Slope is choosing two imaginary points and appyling the y2-y1/x2-x1 formula in this case is 5/2
Y=5/2x+4
What is the length of the altitude to the longest side of a triangle, if the lengths
of its sides are
15 cm, 17 cm, 8 cm
Answers
Answer:
hb ≈ 7.06cm
Step-by-step explanation:
Using the formulas:
A=hbb
2
A=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving for hb
hb=﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4
2b=﹣154+2·(15·17)2+2·(15·8)2﹣174+2·(17·8)2﹣84
2·17
≈7.05882cm
Please help! urgent! A-E questions
no links!!!!!
A. Name a line parallel to KI.
B. Name a line skew to KI
C. Name a plane parallel to plane KIJ.
D. Name a line parallel to plane GJI.
E. What is a difference between parallel lines and skew lines?
Answers
Answer:
a. KJ
b. GF
c. HFG
d. FIJ
e. parallel lines will never intersect, skew lines are crooked and not in line with another specified line.
Step-by-step explanation:
hope this helps :)
On a coordinate plane, 4 points are plotted. The points are (1, 4), (2, 6), (3, 9), (4, 13.5).
Which statements are true for the given geometric sequence? Check all that apply.
The domain is the set of natural numbers.
The range is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = Three-halves(f(x )) when f(1) = 4.
An explicit formula representing the sequence is
f(x) = 4(three-halves) Superscript x
The sequence shows exponential growth.
Answers
Answer: See below.
Step-by-step explanation:
The domain is the set of natural numbers. Yes
The range is the set of natural numbers. Yes
The recursive formula representing the sequence is f(x + 1) = Three-halves(f(x )) when f(1) = 4. Yes See attachment
An explicit formula representing the sequence is
f(x) = 4(three-halves) Superscript x No See attachment
The sequence shows exponential growth. Yes
Answer:
1,3,5 are correct. please ignore the other person.
Step-by-step explanation:
if you are graphing a system of equations, but the graph doesn't give you enough space to plot the y intercept or slope, what do you do? HELP ASAP
Answers
Fatima writes down three square numbers.
The total of the square numbers is 30.
Which square numbers did Fatima write down?
Answers
Answer:
10
Step-by-step explanation:
Fatima wrote down 3 square numbers
since we don't know the three square we will represent it by any variable (X)
3x=30
so you divide both sides by 3
so we have 3x/3=30/3=10
therefore the answer is 10
The total of the square numbers is 30.
The squares can be from the following.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
1 + 4 + 25 = 30
The three square numbers are 1, 4, and 25.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total of the square numbers is 30.
The squares can be from the following.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
We can take three squares.
1 + 4 + 25 = 30
This is a perfect case.
Thus,
The three square numbers are 1, 4, and 25.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
I am really lost in this statistics problem and I would truly appreciate it if someone can help me with it
Answers
Answer:
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. ... Any measurement or data collection effort is subject to a number of sources of variation.
Step-by-step explanation:
soo yeah
Help anyone please and thank you
Answers
the answer would 1/4 of a gallon
simply because 4 of the containers equals one gallon
what is 6/2(1+2)=?give with expiation
Answers
Step-by-step explanation:
6/2 (1+2) = 3(3) = 9.
hope this helps you.
Answer:
9
Step-by-step explanation:
First you need to multiply 6/2 or 3 by the numbers in the ( ) 6/2 x 1 and 6/2 x 2. You will get 3 and 6. 3+6= 9
50 points!! :D
not sure how to do this :/
Answers
Answer:
1
Step-by-step explanation:
x - 5 = -2( x + 1 )
=> x - 5 = -2x - 2
=> x + 2x = 5 - 2
=> 3x = 3
∴ x = 1
A-project-of-construction-of-a-building-can-be-completed-by-150-workers-in-40-days-But-project-manager-brought-30-more-workers-after-16-days-In-how-many-days-will-the-remaining-work-be-finished
Answers
Answer:
In the second scenario after 16 days, 150 workers would have completed 150*16=2400 worker days. That leaves 6000-2400=3600 worker days remaining. If you add 30 workers, it would take 3600/180=20 days longer to complete. So, the entire project would take 16+20=36 days to complete.
I need help on this pls
Answers
[1] Complementary means the angles will add up to 90 degrees
() Blank one is BOC
() Blank two is 90
() Reason blank I am unsure as I do not know the wording that is being looked for, but it is either "given," "complementary angles" or something similar
[2] Since AOC is equal too BOC + 30, we can decide the following is true
() First blank is BOC
() Second blank is 30
[3] 30°
() BOC + BOC + 30 = 90 [Given]
2(BOC) = 60 [Subtract 30 from both sides & combine like terms]
BOC = 30 [Divide by 2]
[4] 60°
() 90 - 30 = 60
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Which number is greater explain your reasoning .375 or 3/8? help!
Answers
Answer: Neither is greater, they are perfectly equal. Or If it's a trick question, 0.375
Step-by-step explanation:
3 divided by 8 equals 0.375, no rounding or anything. I'm not sure if it is more of a trick, brain melting question, then in that case 0.375 because I suppose it could be a rounded number that represents numbers such as 0.3751, 0.3752, etc.
Marc has 45 books on his bookshelf, and Corinna has 61. If Marc buys 4 new books each month and Corinna buys 2 new books each month, after how many months will Marc and Corinna have the same number of books?
Define the variable:_________________________________________
Write the equation: _________________________________________
Solve the equation in the space below. Show your work
Answers
45 +4x= 61 +2x
4x- 2x= 61-45
2x= 16
x= 8
Answer correctly and u get the brainiest and 20 points! Which equation has a solution of r = 1/3?
3r=1/3
2/2/3+r=3
r−1=2/3
4r = 12
Answers
Answer:
Your answer is the second one.
Hope this helps!
Step-by-step explanation:
3 * 1/3 is 1, not 1/3
2 2/3 + 1/3 is equal to 3 and the answer is 3
1/3 - 1 is negative 2/3, not 2/3
4 * 1/3 is 4/3, not 12
Answer: I just keep getting [tex]r=\frac{1}{3}[/tex]
Use the solution for the system to find x - y
3x - 2y = 10
2x + 3y = -2
Answers
Answer:
solution is (3,-1/2)
Step-by-step explanation: