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
what is the answer to this question it is called (Solve Linear System Graphically (Lev. 1)
Answers
x≥ 0 , everthing to the right of the y-axis
y≥ 0 , everthing above the x-axis
So far you are in quadrant I of the x-y plane
y ≤ 3 , everthing from the above, but also below the horizontal line y = 3
lastly y ≤ -x + 5
sketch a line leaning 45° to the left with a y-intercept of 5, shade in everthing below that line
My diagram has a simple trapezoid consisting of a
rectangle with a right-angled triangle attached
now our Objective Function is
C = -5x + 3y , which is a line with slope 5/3
letting that line go through the origin, let it slide parallel to itself over the shaded region until you reach the farthest point from the origin.
On my diagram that looks like (5,0)
Samir's sister goes for kathak dance lessons on Tuesday ,Thursday and Saturday every week .If each lesson lasts 50 minutes ,how much time did he practice dance at her class in 3 weeks?
Answers
Answer:
450 minutes or 7.5hours
Step-by-step explanation:
for 1 week = 50 *3 (min)
=150 minutes
for 3 weeks = 150* 3(min )
=450 minutes
PLEASE HELP!
Use a compass and straightedge to complete the following construction Leave all construction marks. Having a sharpened pencil will allow for more precise arcs. Make sure that your construction marks are dark enough to see.
Construct a perpendicular line to the given line through the point on the line.
link to the plot: https://www.mathopenref.com/constperplinepoint.html
Answers
Answer:
draw a line straight down through p
A polygon undergoes a combined transformation of T3.2) (Ro, 90). The vertex (5,2) of the polygon maps to what final image?
А
(-4,8)
B.
(-2,5)
С
(1,7)
D
(5.-3)
Answers
The final image of the vertex of the polygon after a translation and rotation would be (- 4, 8).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The preimage of the vertex of a polygon is, (5, 2).
Now, After a transformation of T(3, 2) the image of the vertex of the polygon would be, (5 + 3, 2 + 2) ⇒ (8, 4).
Now, Another transformation is the rotation of 90° (counterclockwise as it is positive).
We know a rotation of 90° counterclockwise to (x, y) becomes (- y, x).
Therefore, The vertex of the polygon will be at (- 4, 8).
learn more about transformations here :
https://brainly.com/question/11709244
#SPJ2
I'll also give brainliest to the first to answer
1+1=x
A) x=1
B) x=2
C) x=3
D) x=4
Answers
Answer:
B) x = 2
Step-by-step explanation:
1 + 1 = x
2 = x
1 + 1 = 2
1. Two angles added together to produce 90 degrees a) Supplementary b) Complementary c) Right od) Vertical
Answers
Answer: B: complementary
Step-by-step explanation: :)
Help ME ASAP
Zach solved the problem 124.8 / 24 = 5. Complete the following model with partial products to check Zach’s work with multiplication.
Part A
Drag values to the boxes to complete the partial products. Not all choices will be used.
{ 0.4 }
{ 0.8 }
{ 2 }
{ 4 }
{ 8 }
{ 10 }
{ 20 }
{ 100 }
The product for A=
The product for B =
The product for C =
The product for D =
Part B
Choose the words to complete the statement
Zach's work is ______
because the total of the partial products is _______ as the dividend.
Answers
The partial products in Zach's work are the result of multiplying each digit
in turn based on their place values.
The given problem is [tex]\dfrac{124.8}{24} = 5[/tex]
Part A
The values to be placed in the boxes are presented as follows;
[tex]\begin{array}{|c|c|c|}&5&0.2\\&&\\20&\underline{100}&\underline{4}\\&&\\4&\underline{20}&\underline{0.8}\end{array}\right][/tex]
The total of the partial product is 100 + 20 + 4 + 0.8 = 124.8 = The dividend
Part B
The completed statement is; Zach's work is correct because the total of
the partial product is the same as the dividend.
Learn more here:
https://brainly.com/question/18613539
Solve by substitution. x=y-9,5x+2y=11
Answers
We have two equations :
x=y-9
5x+2y = 11
We just have to plug the value of x in the second equation to find y :
5(y-9) + 2y = 11
5y - 45 + 2y = 11
7y - 45 = 11
7y = 11 + 45
7y = 56
y = 56/7 = 8
Finally, since x = y -9
x = 8-9 = -1
Good Luck
Answer:
X = -1 Y = 8
try downloading mathaway it might help with these problem types
Choose the best compatible numbers to find an estimated product or quotient.
2,127 ÷ 405
A. 2,100 ÷ 300 = 7
B. 2,000 ÷ 500 = 4
C. 2,400 ÷ 400 = 6
D. 2,000 ÷ 400 = 5
Answers
-
6 less than the product of a number and 3 is -18.. What is the
number?
Answers
Answer:X= -4
Step-by-step explanation:
6 less than the product of a number and 3 is -18.
Make each part of the sentence into numbers:
"the product of a number and 3": becomes X*(3), where X is the "number."
"6 less than": is -6, so we have:
X*(3) - 6
"is -18" means = -18
Put the segments into one equation and solve:
X*(3) - 6 = -18
3X-6=-18
3X = -12
X = -4
====
See if this works: If X=-4, then the product of it and 3 is -12. Six less than -12 is -18. And that is correct. X= -4
A farmer has 24 bushels of apples and can harvest 22 bushels of apples each day?
Answers
Answer:
................ I don"t know sorry I hate you
An envelope is 6 in. wide and 4 in. high. Will a card with an 8 in. diagonal fit in it? Identify the correct explanation.
A) Because 7.2 < 8, it is possible that the card fits in the envelope.
B) Because 8.9 > 8, it is possible that the card fits in the envelope.
C) Because 7.2 < 8, it is NOT possible that the card fits in the envelope.
D) Because 8.9 > 8, it is NOT possible that the card fits in the envelope.
Answers
= 6^2 + 4^2
=36 + 16
= 52
A^2= 52
Sqrt A^2 = sqrt 52
A = 7.2
Since the envelopes diagonal is 7.2 inches and the card’s diagonal is 8 inches and 7.2<8. Your answer is c)
Write an equation for the line in the given form.
Contains the points (5, 2) and (8, 11); slope-intercept form
Answers
Answer:
y = 3x-13
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
= ( 11-2)/(8-5)
= 9/3
=3
Then using slope intercept form
y= mx+b
Using one of the points and the slope
2 = 3(5) +b
2 = 15 +b
2-15 = b
-13 =b
y = 3x-13
What is 968.1 as a fraction
Answers
I believe it is 9681/10.
Answer:
the answer is 9681/10
Step-by-step explanation:
9681/10
A snail moves through a garden and travles 1 1/8 meters in 1 1/2 minutes. What is the snail's rate in minutes per meter? Show your work
Answers
Answer:
4/3mpm
Step-by-step explanation:
(1 1/2)/(1 1/8)
convert to improper fraction
(3/2)/(9/8)
solve
1/(3/4)
4/3
If 2x = 3y + 11 and 2 to the power of x = 2 to the power of 4(y+1), determine the value of x + y
Answers
Z = -2
Y = 5
is your answer
T
Зл
Solve for the interval <<
2
2
3. 2 cos? 0-5 cos e = 3
(it put it in wrong so i put a picture of the question)
Answers
Answer:
540 g m/s.
Step-by-step explanation:
PLEASE HURRY!
Nicholas started a canned-food drive at school. The equation representing this is y = 235x + 15, where x is the number of days, and y is the number of cans collected. Explain how to determine how many days it would take to collect 2600 cans.
Answers
Answer:
11 days
Step-by-step explanation:
because Nicholas was given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Answer:
11 days
Step-by-step explanation:
what is the desimal for
Answers
Answer:
A decimal is used to identify a unit of measure with precision because not all whole numbers cannot represent a unit of measure in a respective situation.
Answer:
Decimals are used to express the whole number and fraction together.
Step-by-step explanation:
0.35 is best classified as a ________ number.
Fill the blank
why this stuff hard
Answers
Answer:
rational number (might be wrong)
Write an equation of the line in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
Y=1/2x+3
What is the solution for the system of equations?
y=−x+4y=x−2
Question 1 options:
(1, 3)
(−2, 1)
(3, 1)
(1, −2)
Answers
Answer:
(3, 1)
Step-by-step explanation:
y = −x + 4
y = x − 2
-x + 4 = x - 2
4 = 2x - 2
6 = 2x
3 = x
y = (3) − 2
y = 1
Answer:
x = 3 and y = 1
Step-by-step explanation:
5 4/6-4 2/3 ÷ 3 2/3?
Answers
Answer:
145/33
Step-by-step explanation:
Assuming what you wrote was mixed fractions, this is how to do the question.
Do the division first and then subtract that from 5 4/6/
How would you slove ;
-2x+2y=3 & 2×-2y=2
in order to get y by itself ?
Answers
Answer:
simultaneous linear equation
Step-by-step explanation:
you can use two methods:
substitution method
elimination method
what´s the answer to this?
Answers
Step-by-step explanation:
it is a linear function, if the increases in y are constant from point (ordered pair of x and y) to point reissue to the increase in x.
the first table (top left) increases x constantly by 1.
but y increases first by 2 and then by 3 and then again by 3.
this is not constant, so it does not follow the pattern of x.
in technical terms : the slope of the function is not the same for every point of the function.
in other words : it is not a straight line all the way.
so, it is not a linear function.
the second table (top right) increases x constantly by 2.
and y increases constantly by 2.
this is constant also in relation to x.
in technical terms : the slope of the function is the same for every point of the function.
in other words : it is a straight line all the way.
so, it is a linear function.
the third table (bottom left) increases x constantly by 1.
but y increases first by 4 and then by 1 and then again by 1.
this is not constant, so it does not follow the pattern of x.
in technical terms : the slope of the function is not the same for every point of the function.
in other words : it is not a straight line all the way.
so, it is not a linear function.
the fourth table (bottom right) increases x constantly by 2.
but y increases first by 2 and then by 3 and then again by 3.
this is not constant, so it does not follow the pattern of x.
in technical terms : the slope of the function is not the same for every point of the function.
in other words : it is not a straight line all the way.
so, it is not a linear function.
Help Please. It's 10:11 AM right now. This due by 12 PM or in 2 more hours. I don't know this.
Answers
Answer:
B) 2,000.
Step-by-step explanation:
As the mean is 6000 the total number of students = 5*6000
= 30,000.
If graduates are excluded we have 4*7000 = 28,000 students.
So the number at graduate level
= 30,000 - 28,000
= 2,000.
Which of the following correct shows the next two
terms after -40 in the pattern?
Answers
Answer:
I believe the answer is B. 80, -160
Step-by-step explanation:
The pattern involves multipling by -2 so the term after that would be 320!
Please help me with this MATH question.
Answers
Answer:
y=4
Step-by-step explanation:
84=30y-9y, first you collect like terms.
84=21y, swap the sides
21y=84, devide both sides and you get y =4
I need help with this please! It’s due tonight and I don’t know.
Answers
Answer:
b
Step-by-step explanation:
Find zeroes of quadratic polynomial p(x) = x2 -3x - 4.
Answers
Here is ur answer
- BRAINLIEST answerer