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
(x^2+ 6x + 9) / (x-3)
Answers
Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
The second of three numbers is 8 more than the first,
and the third number is 3 less than 3 times the first.
If the third number is 15 more than the second, find
the three numbers.
1st___
2nd___
3rd___
Answers
Answer:
1st = 13
2nd = 21
3rd = 36
Step-by-step explanation:
Let the first number be
f
The second of three numbers is 8 more than the first,
f + 8
third number is 3 less than 3 times the first.
3f - 3
---------------------------
the third number is 15 more than the second,
3f - 3 = (f + 8) + 15
3f - 3 = f + 23
Subtract f from both sides
2f - 3 = 23
add 3 to both sides
2f = 26
Divide both sides by 2
f = 13
f + 8 = 13 + 8 = 21
3f - 3 = 3(13) - 3 = 36
Ricardo camina 2 km
en 2 hora. ¿Cuántos
minutos tardará si
DESCANSO
A 2KM
camina 12 km?
Answers
The time it will take ricardo to walk 12km is 12 hours
If Ricardo walks 2 km in 2 hours, the speed of Ricardo is expressed as:
Speed = Distance/Time
Speed = 2km/2hr
Distance = 1km/hr
To find the time it will take to walk 12km, we will use the same formula:
Time = Distance/Speed
Time = 12km/1km/hr
Time = 12hours
Hence the time it will take ricardo to walk 12km is 12 hours
Learn more on speed here: https://brainly.com/question/13262646
Question 13 options:
Isaac drops an apple from the top of a lighthouse, 154 feet above the ground.
The equation to represent the height of the apple at a given time is h=−16t2+154,
where h is the height of the apple, and t is the number of seconds after the apple is dropped.
How many seconds (t) will it take for the apple to hit the ground (h = 0)?
[Find the value of t, rounded to the nearest tenth.]
Answers
Answer:
3.1 sec.
Step-by-step explanation:
please someone help. I really need help with this question. I will give brainliest
Answers
Answer:
3/200
Step-by-step explanation:
total medicine = 9/50 liter
evenly divided into 12
so 1 prescription = 9/50 / 12
= 9/50*12
=3/50*4
=3/200
Find the positive root of x^2+2x-35=0 in math Please.
Answers
Answer:
x2+2x−35=0
Step 1: Factor left side of equation.
(x−5)(x+7)=0
Step 2: Set factors equal to 0.
x−5=0 or x+7=0
x=5 or x=−7
Step-by-step explanation:
<=> x^2 - 5x + 7x - 35 = 0
<=> x(x-5) + 7(x-5)=0
<=> (x+7)(x-5)=0
<=> x+7=0 or x-5=0
<=> x = -7 or x = 5
Ok done. Thank to me :>
A family on a trip budgets $1,338 for meals and gasoline. If the price of a meal for the family is $90 and if gasoline costs $2.80 per gallon, then how many gallons of gasoline can the family buy if they buy 13 meals
Answers
’creating a system linear equation, the number of possible gallons of gasoline that can be purchased is 60 gallons
Given the Parameters :
Total budget = 1338Meal cost = $90Gasoline cost = $2.80 per gallon Number of meals = 13 Number of gallons of gasoline = gHence, we have :
90(13) + 2.80g = 13381170 + 2.80g = 1338
2.80g = 1338 - 1170
2.80g = 168
g = 168/2.80
g = 60
Therefore, only 60 gallons of gasoline can be purchased.
Learn more : https://brainly.com/question/18796573
Help?????????????????
Answers
Answer:
the first option is the answer
Step-by-step explanation:
y = -7x - 21
What is the slope of this equation and what is the Y intercept.
Answers
Answer:
Slope is -7
Y intercept = -21
Step-by-step explanation:
The equation is Y=mx+b
M is the slope so -7 would equal the slope
B is where your Y- intercept already is so that would equal -21
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
3 less than the quotient of a number and 5 is -7
Answers
Answer: The number is -20
Step-by-step explanation:
Take each part of the sentence and write what it is telling us:
3 less than the quotient of a number and 5 is -7
The quotient of a number and 5 is (X/5), where X is the "number."
3 less than is (X/5) - 3
is -7 is = -7
Therefore:
3 less than the quotient of a number and 5 is -7 is: (X/5) - 3 = -7
---
(X/5) - 3 = -7
(X/5) = -4
X = -20
===
See if this works:
3 less than the quotient of -20 and 5 is -7
(-20/5) = -4
Three kless than -4 is -7: It works
(b+3)(b+7) FOIL method
Answers
b^2+10b+21
Step-by-step explanation:
(b + 3)(b + 7) = ...
= b² + (3 + 7)b + (3•7)
= b² + 10b + 21
will give brainliest !!
Answers
Answer:
Triangle A'B'C'
A'B'= 7.81
B'C'= 6
A'C'=5
C) Perimeter= 18.81 Area 15
Triangle ABC
AB=5
BC=4
AC=3
c) Perimeter = 12 Area = 6
Step-by-step explanation:
Triangle ABC work
Perimeter 4+3+√4^2+3^2=12
Area 4*3/2=6
Triangle A'B'C' work
Area 6*5/2=15
Perimeter 6+5+√6^2+5^2=18.81025
Please give brainliest
Please answer below :) I will mark the brainiest answer
Answers
Answer:The last option is correct.
Step-by-step explanation:
The number of ways to choose three different pizza toppings from a group of six is called a ?
Answers
Answer:
Uh, 16.
Step-by-step explanation:
We need to choose three different toppings. So here we need to find the number of ways in which we can choose three different toppings out off. 16. So a number of ways are takes three at a time, from a total of 16. That is civilians combination. Here are formula for combination is 16 factorial over three factorial into 16 minus three. Factorial this candidate and a 16 factorial over three factorial into 16 minus trees. 13. Authority in factorial, now 16. Factory converted on a 16 in 2 15 into 14 into 13. Factorial over three factorial into 30. In fact, a real as we can see that 13 factorial is common toward denominator and numerator so we can get through this. Now I remaining times are 16 into 15 into 14. Over three in Toto into one has three factories, three in tow, one So calculating this ticket. Find 60 Soviet 56 TVs to select three different topics. Talked to select three different toppings out off 16 on a bizarre
If given DG ≅ JK, which congruence postulate or theorem must you use before proving FG ≅ HK?
Answers
Answer:
the correct answer choice is marked (AAS)
Step-by-step explanation:
All the corresponding angles are marked congruent. If one corresponding side is marked congruent, you can claim AAS or ASA congruence for the triangles: one side and two angles. Of these, AAS is among the answer choices.
You must use AAS to show triangle congruence before claiming FH ≅ HK by CPCTC.
what slope is parallel to m = 3/4
Answers
Answer:
3/4
Step-by-step explanation:
For lines to be parallel, only their y-intercepts have to be different.
Answer:
3/4
Step-by-step explanation:
My sweatshirt rhat i want to buy is $36 today the price is 30% off what is the price of the sweatshirt today
Answers
Your answer 10.8$
You research rowboat rentals at a local lake. The total charge to rent a rowboat for 2 hours is $22 for each boat, plus a fee of f dollars for each passenger, up to 5 passengers.
The day you decide to go to rent a rowboat, you take n friends with you and decide to rent one boat for 2 hours. Your total cost is $34.
Using f, n, and the other information provided, model this situation by completing the equation: __________________________ = $34.
Answers
Answer:
f=2 N=5
Step-by-step explanation:
solve the following equations
A) 2 (A + 5) = 16
b) 4 p - 2/3 = 7/3
c) 3y/2 + 8 = (-4)
pls pls pls pls pls pls answer steps
Answers
Answer:
A. 2(a+5) = 16
2a + 10 = 16
2a = 16-10
2a = 6
2a÷2 = 6÷2
a = 3
B. 4p-2/3 = 7/3
4p = 7/3 + 2/3
4p = 3
4p÷4 = 3÷4
p = 3/4
C. 3y/2 + 8 = -4
3y/2 = -4 - 8
3y/2 = -12
[ 3y/2 = -12 ] 2
3y = -24
3y ÷ 3 = -24 ÷ 3
y = -8
[tex] \: \: \: \: \: [/tex]
A.) a = 3
B.) p = ¾
C.) y = -8
hope it helpsrefer to the attachment
[tex] \: \: \: \: \: \: \: \: [/tex]
In the figure, lines j and k intersect to form the
angles shown. What is the measurements of angle 1
Answers
ANSWER ONLY IF U KNOW, OR THINK U KNOW.
(ILL MARK U BRAINLIEST)
Answers
Answer:
I KNOW FOR SURE
Step-by-step explanation:
if that's all the question is then I definitely know the answer ;)
if you forgot to write the rest then hmu haha
Determine which postulate can be used to prove the triangles are congruent then identify the valid congruency statement (SELECT TWO ANSWERS)
Options:
A) AAS
B)ASA
C) HL
D) CDE ≅ FDE
E) DEC ≅ EDF
F) ECD ≅ DFE
Answers
Answer:
A) AAS
D) CDE ≅ FDE
Step-by-step explanation:
∠C ≅ ∠F Given
∠DEC ≅ ∠EDF Given
DE ≅ DE Reflexive property
ΔCDE ≅ ΔFDE AAs congruent
what equation represents the line that passes through the points (3, -2) and (-1, 10)
Answers
Answer:
y=-3x-9
Step-by-step explanation:
Let's find the slope of the line
m=-2-10/3--1
m=-12/4=-3
The equation is given as
y-y1=m(x-x1)
y--2=-3(x-3)
y+2=-3x+9-2
y=-3x-7-2
y=-3x-9
you could give away 70 coffee mugs without charging anything.
If you charge $10.00, nobody will buy the coffee mugs. You also figured out that your sales will be decreasing
following straight line. Your job is to find the maximum possible revenue from selling the coffee mugs.
Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S.
Hint: To give away 70 coffee mugs means when the price p=0, S(0) = 70. Plot that point on the graph. Find one
more point using the other given condition. Keep in mind S(p) is a linear function. Be careful what will be
represented on the x-axis, and what will be represented on the y-axis.
2. Find the equation of the linear function S(p) that describes the quantity sold as a function of the price p.
3. The revenue is determined by R = Sp. Express the revenue as a function of the price p.
Help: You may look at the examples from the power point for section 2.6
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be sold to maximize the revenue?
8. What is the maximum revenue?
9. What price per coffee mug you should charge to collect at least $70 in revenue?
Your project will be graded based on the following:
1. Turned in a hard copy, and an electronic version as a PDF file on Blackboard on time (due date Dec 7
or before ) (5pts. deduction per day)
2. Completeness (no missing part, show all of your work, calculations, formulas used etc.
3. Precision ( correct answers )
4. Complete graph
the graph has a title
the axes are labeled ( make sure you have included the units of measurement)
-
Answers
At $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
Since you could give away 70 coffee mugs without charging anything, and if you charge $ 10.00, nobody will buy the coffee mugs, and you also figured out that your sales will be decreasing following straight line, and your job is to find the maximum possible revenue from selling the coffee mugs, to determine at which price per coffee mug do you not make any money; the price per coffee mug that makes the most revenue; how many coffee mugs must be sold to maximize the revenue; what is the maximum revenue; and what price per coffee mug you should charge to collect at least $ 70 in revenue; the following calculations must be performed:
70 = 0 0 = 10 35 = 5 63 x 1 = 63 56 x 2 = 112 49 x 3 = 147 42 x 4 = 168 35 x 5 = 175 28 x 6 = 168
Therefore, at $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
Learn more about quantities in https://brainly.com/question/25797049
Two of the angles in a triangle measure 154° and 20°. What is the measure of the third angle?
Answers
Answer:
6°
Step-by-step explanation:
The angles in a triangle always add up to 180°. Let’s call the third angle x. That means that:
154 + 20 + x = 180 ->
174 + x = 180 ->
x = 180 - 174 ->
x = 6°
Hope that help! :)
Please help I’ll mark u as brilliant
Answers
Answer:
-2,3
Step-by-step explanation:
So that is the highest point marked on the graph.
Order the numbers from least to greatest.
1,553
1,347
1,644; 1,553; 1,347
b. 1,347; 1,553; 1,644
1,644
a.
C.
1,553; 1,347; 1,644
Please select the best answer from the choices provided
Ο Α
Ο Ο Ο
B
Answers
Answer:
b even though you made this hard to read lol, its b
Step-by-step explanation:
The diagram below shows how the tables and chairs are arranged in the school cafeteria. A table seats 3 people and the tables can be pushed together. When two tables come together, 4 people can sit around the table. Complete this table to show the relationship between the number of tables, n, and the number of students, S, who can sit around the table.
Answers
Answer:
well in theory on tabe has to be smaller so I guess the number of people in all is 4 and the difference between the tables are size
A car's value depreciates by 18% in its first year and is now worth £6789.
What was the original price of the car?
Answers
Answer:
£8279.27
Step-by-step explanation:
The given relationship is ...
(original price) × (1 - 18%) = £6789
Dividing by the coefficient of the original price, we find it to be ...
original price = £6789/0.82 = £8279.27
The original price of the car was £8279.27.