What is the modulus and argument after (StartRoot 3 EndRoot) (cosine (StartFraction pi Over 18 EndFraction) + I sine (StartFraction pi Over 18 EndFraction) ) gets raised to the 6thpower?
modulus = StartRoot 3 EndRoot ; argument = StartFraction pi Over 18 EndFraction
modulus = StartRoot 18 EndRoot; argument = StartFraction pi Over 3 EndFraction
modulus = 27; argument = StartFraction pi Over 3 EndFraction
modulus = 729; argument = StartFraction pi Over 18 EndFraction
Answers
Answer:
[tex]|z| = 27[/tex] -- Modulus
[tex]\theta = \frac{\pi}{3}[/tex] --- Argument
Step-by-step explanation:
Given
[tex]((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6[/tex]
Required
Determine the modulus and the argument
We have that:
[tex]z = ((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6[/tex]
Expand:
[tex]z = (\sqrt 3)^6(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6[/tex]
[tex]z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6[/tex]
A complex equation can be expressed as:
[tex]z = |z| e^{i\theta}[/tex]
Where
[tex]|z| = modulus[/tex]
[tex]\theta = argument[/tex]
Where
[tex]e^{i\theta} = (cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})[/tex]
So:
[tex]z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6[/tex] becomes
[tex]z = 27(e^{i\frac{\pi}{18}})^6[/tex]
By comparison:
[tex]e^{i\theta} = (e^{i\frac{\pi}{18}})^6[/tex]
This gives:
[tex]{i\theta} = i\frac{\pi}{18}}*6[/tex]
[tex]{i\theta} = i\frac{6\pi}{18}}[/tex]
[tex]{i\theta} = i\frac{\pi}{3}}[/tex]
Divide through by i
[tex]\theta = \frac{\pi}{3}[/tex]
Hence, the modulus, z is:
[tex]|z| = 27[/tex]
And the argument [tex]\theta[/tex] is
[tex]\theta = \frac{\pi}{3}[/tex]
Answer: C. M=27 A=pi/3
Step-by-step explanation:
edge
Related Questions
PLS HELP FAST!! 20 POINTS!!
Overall, the river festival made £12 858.56. The organisers spent £6429.28 running the festival. How much was the profit, as a percentage of the total money made?
Answers
Step-by-step explanation:
it made £12,858.56.
the costs were £6,429.28
so, the profit was
12,858.56 - 6,429.28 = £6,429.28
since cost and profit are equal, that means they are both exactly half of the total income.
and half means 50%.
formally, to do the full % calculation :
100% = 12,858.56
1% = 100%/100 = 12,858.56/100 = 128.5856
how many % are 6,429.28 ?
as many % as times that 1% fits into 6,429.28 :
6,429.28 / 128.5856 = 50
so, it is 50%.
1222445666161616145435463465364534534534
Answers
Estimate 28.4707
explain how to do it
Answers
Answer:
28.4707 is rounded up to 28.5
Explanation: you have to round up any number higher than 5 to the number on the left
Find the slope between points (1,-1) and (2,-2)
Answers
Answer:
The slope should be -1.
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Hope this helps!
Have a great day and God bless! :)
================================================
Work Shown:
[tex](x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (2,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-1)}{2 - 1}\\\\m = \frac{-2 + 1}{2 - 1}\\\\m = \frac{-1}{1}\\\\\boldsymbol{m = -1}\\\\[/tex]
--------------------
Side notes:
Slope = rise/run
rise = change in y value = [tex]y_{2} - y_{1}[/tex]
run = change in x value = [tex]x_{2} - x_{1}[/tex]
Make sure you subtract in the same order each time.
Here I need help with this question
Answers
C=5
Explain explain Explain
5. Write the letter of the correct explanation next to each step in the chart. (Each blank is worth
2 points)
A. Distributive property
B. Simplify using addition
C. Add 9 to each side and simplify
D. Use multiplication to simplify
+
E. Multiply each side by
Steps
-
and simplify
Explanation
-(x + 4) - 6 = 54 Original equation
-(x) (4) - 6 = 54
-(x) + (-3) - 6 = 54
- (x) - 9 = 54
-(x) = 63
x=- 84
Answers
The solution to the equation and the explanation for each step is given below.
How to Solve an Equation?Given the equation, -3/4(x + 4) - 6 = 54, the steps to find the value of x is given below:
-3/4(x + 4) - 6 = 54 [given]
-3/4(x) -3/4(4) - 6 = 54 [Distributive property]
-3/4x + (-3) - 6 = 54 [Use multiplication to simplify]
-3/4x - 9 = 54 [Simplify using addition]
-3/4x = 63 [Add 9 to each side and simplify]
x = -84 [Multiply each side by -4/3 and simplify]
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A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 171 yd^2, determine the radius of the region (the radius is the length of the stream of water). Round the answer to the nearest yard.
The radius is approximately ___ yd.
Answers
The radius of the sprinkler is approximately 7 yards.
How long is the arm of the sprinkler?
In this situation we find the case of a sprinkler that rotates until a complete revolution is done, that is, the area of complete circle is covered due to the rotation. That area can be found by using this formula:
A = (θ / 360) · π · r²
Where:
A - Area of rotation, in square yards.θ - Angle of rotation, in degrees.r - Radius of the sprinkler, in yards.If we know that A = 171 yd² and θ = 360°, then the radius is approximately:
171 = π · r²
r = √(171 / π)
r ≈ 7.378 yd (approx. 7 yd)
The radius of the sprinkler is approximately 7 yards.
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What are the domain and range of the function f(x) = x^2 + 5x + 4/ x+4
Answers
This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.
How to find the domain and range of the given function?Here we have the function:
f(x) = (x^2 + 5x + 4)/(x + 4)
The numerator can be rewritten if we find the zeros:
x = (-5 ± √( 5^2 - 4*1*4))/(2*1)
x = (-5 ± 3)/2
Then the zeros are:
x = (-5 - 3)/2 = - 4
x = (-5 + 3)/2 = -1
So the numerator can be rewritten to (x + 4)*(x + 1)
And the function is rewritten to:
f(x) = (x^2 + 5x + 4)/(x + 4) = (x + 4)*(x + 1)/(x + 4) = (x + 1)
This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.
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Use the map shown below to find the distance between cities A and B to the nearest tenth.
Answers
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{(~~0 - (-3)~~)^2 + (~~0 - 6~~)^2} \implies BA=\sqrt{(0 +3)^2 + (0 -6)^2} \\\\\\ BA=\sqrt{( 3 )^2 + ( -6 )^2} \implies BA=\sqrt{ 9 + 36 } \implies BA=\sqrt{ 45 }\implies BA\approx 6.7[/tex]
Determine if the following functions are inverses algebraically.
F(x) = 2x + 7 and h(x) = x-7/2
Answers
Answer:
(x) = 2x
Step-by-step explanation:
Puja claims that any fraction can be thought of as a division problem and any
division problem can be thought of as a fraction. Is Puja's claim true? Give two
examples-one division problem as a fraction and one fraction as a division
problem to explain your answer.
Answers
Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.
What is a fraction and division problem?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. Represented as [tex]\frac{a}{b}[/tex].A division problem has three primary components: the dividend, the divisor, and the quotient. The amount that will be divided is the dividend. The quantity of "people" among whom the number is divided is referred to as the divisor. The answer is the quotient.As seen by the definition of fraction, in terms of division problem, it involves only the the dividend and the divisor and not the quotient.
Hence, the two cannot be used inter-changeably, i.e., a fraction is not a division problem and vice versa.
Hence, Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.
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Answer:
Step-by-step explanation:
yesterday
Find the missing values in the ratio table.
Pounds
Weeks
Answers
The missing values in the ratio are 2.5 and 17.5.
What is mean by Ratio?
A Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
Now, The missing values are find as;
Ratio of Pounds to the weeks are;
In first column,
Pounds : Weeks = 10 : 4
In second column,
Pounds : Weeks = x : 1
In third column,
Pounds : Weeks = y : 7
Since, All ratio are equal.
Hence,
10 : 4 = x : 1
It can be written as,
10/4 = x / 1
After cross multiplication we get;
x = 10/4
x = 2.5
And,
10 : 4 = y : 7
It can be written as,
10/4 = y/7
After cross multiplication we get,
10 * 7 = y * 4
y = 70/ 4
y = 17.5
Hence, The missing values in the ratio are 2.5 and 17.5.
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It takes 3 people 4 hours to paint a wall. Assume that all people paint at the same rate. How long would it take 5 people to paint the same wall?
Answers
Answer:
2 [tex]\frac{2}{5}[/tex] hours or 2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
x-y=-3
y-6=-1/4(x+12
Answers
Answer:
(0,3)
Step-by-step explanation:
x - y = -3
y = -1/4x + 3
x - (-1/4x + 3) = -3
x = 0
y = -1/4 x 0 + 3
y = 3
(0,3)
Answer: 24
Step-by-step explanation:
−3−6=−
4
1
(x+12)
Subtract 6 from −3 to get −9.
−9=−
4
1
(x+12)
Use the distributive property to multiply −
4
1
by x+12.
−9=−
4
1
x−
4
1
×12
Express −
4
1
×12 as a single fraction.
−9=−
4
1
x+
4
−12
Divide −12 by 4 to get −3.
−9=−
4
1
x−3
Swap sides so that all variable terms are on the left hand side.
−
4
1
x−3=−9
Add 3 to both sides.
−
4
1
x=−9+3
Add −9 and 3 to get −6.
−
4
1
x=−6
Multiply both sides by −4, the reciprocal of −
4
1
.
x=−6(−4)
Multiply −6 and −4 to get 24.
x=24
A 17 foot ladder is leaning on a wall. the bottom of the ladder on the ground is at a distance of 3 feet from the base of the wall.
What is the distance, in feet, between the griund and the top of the ladder? round your answer to the nearest tenth
Answers
The distance in feet between the ground and the top of the ladder is 16.7 feet.
Let the distance in feet between the ground and the top of the ladder be x.
According to the given question.
Length of the ladder = 17 foot
The distance of the ladder from the base of the wall is 3 feet.
From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.
Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
Therefore,
17^2 = 3^2 + x^2
⇒ 289 = 9 + x^2
⇒ 280 = x^2
⇒ x = 16.7 feet
Hence, the distance in feet between the ground and the top of the ladder is 16.7 feet.
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what is the greatest possible error of 5.78 mi.?
Answers
Answer:
2.89
Step-by-step explanation:
GPE = U * 1/2
GPE = 5.78 * 1/2
GPE = 2.89
2001
(is A force of 200 is exerted on an area of 50meters square
Calculate the pressure exerted by the force.
Answers
Given : Force applied is given as : 200 N
Area : 50m²
We know that the pressure is the force applied perpendicular to the surface of an object per unit area. or
Pressure = Force/Area=> P = 200N / 50m²
=> P = 40Nm² or 40 pascalVicky has 12 clear crystals in her collection. She has c more colored than clear ones. Write an expression that shows the number of colored crystals VIcky has in her collection
Answers
Answer:
y = 12 + c
Step-by-step explanation:
Well, let's begin with what you're given, and that is that there are 12 clear ones, and there is a number of colored ones which succeeds that, which is represented by the variable c. So, we can use the equation:
y = 12 + c
To show the amount of colored ones that Vicky has in her collection, with y = number of colored crystals.
convert 1100 feet per second into miles per hour
Answers
Answer: 0.681818
Hope this helps!
The table shows the percent of each type of doughnut sold at a bakery. A store clerk put all of the cream filled and powered sugar doughnuts on a display in the front of the store. Both of these types of doughnuts completely sold out on Tuesday morning. If the clerk put 108 doughnuts in front of the store, how many doughnuts were there in all at the beginning of the day on Tuesday.
Answers
Using proportions, it is found that 240 doughnuts were there in all at the beginning of the day on Tuesday.
What is the missing information?The percentages are missing and are given in the graph at the end of the answer.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures using the unit rates and operations such as multiplication and division.
One example of application of proportions is for percentage problems, as the decimal equivalent of the percentages are used to find either the equivalent amount or the total amount, by multiplication operations.
The percentages of doughnuts displayed are given as follows:
Cream filled: 20%.Powdered sugar: 25%.Hence 45% of the total amount is equivalent to 108 doughnuts, hence:
0.45n = 108.
n = 108/0.45
n = 240.
Which is the number of doughnuts that were there in all at the beginning of the day on Tuesday.
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Westside Energy charges its electric customers a base rate of $8.00 per month, plus 12¢ per kilowatt-hour (kWh) for the first 300 kWh used and 4¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month. Express the monthly cost E as a piecewise defined function of x. (Assume E is measured in dollars.)
Answers
The linear function that gives the monthly cost E for x > 300 is given by:
E(x) = 44 + 0.04x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When x > 300, we have that:
The base rate of $8.00 was paid.The 12 cents for each kWh up to 300 was paid.Hence the intercept is given by:
b = 8 + 0.12 x 300 = 44.
The slope is the cost per kWh of 4 cents, hence the function is:
E(x) = 44 + 0.04x.
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Sophie needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4 hours and charged her $127 for
parts. The total was $227. Write and solve an equation which can be used to
determine x, the cost of the labor per hour.
Answers
Answer: 227=4x+127
x=$25
Step-by-step explanation:
227=4x+127 ==> equation
227-127=4x+127-127
4x=227-127
4x=100
4x/4=100/4
x=100/4
x=$25
A formula for v is given as v=u+ 9.8t The value for u after truncation to 2 decimal places is 4.7 Given also that t, measured to the nearest whole number is 17, calculate the smallest possible value for V
Answers
Answer:
V = 86.06
Step-by-step explanation:
V = u + 9.8t
V = 4.7 + 9.8(17)
V = 86.06
4.08 x 29.7 preferably show work
Answers
Answer: 121.176
Step-by-step explanation:
First, multiply out the decimal points. To get 408 from 4.08, multiply by a hundred. Likewise, with 29.7, multiply it by 10.
Then, do long multiplication with 408 and 297 (you get 121176 from that).
Finally, use your answer from the long multiplication and divide it by how many times you multiplied your original numbers. So, you have to divide by 100, and then also divide by 10.
From that, you get 121.176
pls help 50 if corrret
Answers
Answer:
-4.2
Step-by-step explanation:
Check the attached photo for work.
The temperature is-2°C. if the temperature reses by 15°C, what is the new temperature?
Answers
Explanation:
Draw a vertical number line (see below). Mark -2 on it. Then move up 2 units to arrive at 0. Move up the remaining 13 units to arrive at 13
This shows that -2+15 = 13
A parking garage charges $2.00 for the first hour and $0.75 for each additional hour. If a customer gave the parking attendant $35 for parking from 10 AM to 3 PM, how much did the garage charge?
Which piece of information is not necessary to solve the problem?
$2.00 parking charges for the first hour
$0.75 parking charges for each additional hour
O
Amount of time the customer was parked
$35 the customer gave the parking attendant
None of the information provided
How much did the garage charge?
Answers
Answer:
The information that I do not need is how much the customer gave the parking attendant.
The garage charged $5.00
Step-by-step explanation:
2 + .75h h stands for the number of hours the car was parked.
2 + .75 (4)
2 + 3 = 5
Douglas Noel went to Home Depot and bought thirteen doors at $43.44 each and six bags of fertilizer at $8.71 per bag.
Round your answers to 2 decimal places.
What was the total cost to Douglas?
If Douglas had $660 in his pocket, what does he have left to spend?
Answers
The total cost is $616.98.
The amount he has left to spend is $43.02.
What is the total cost?The total cost to Douglas is the sum of the total cost of the thirteen doors and the sum of the six bags of fertilizers
The total cost of the thirteen doors = (cost of one door x total number of doors that would be bought)
$43.44 x 13 = $564.72
The total cost of six bags of fertilizers = (cost of one bag x total number of bags)
$8.71 X 6 = $52.26
Total cost = $564.72 + $52.26 = $616.98
Amount he has left to spend = $660 - $616.98 = $43.02
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Total cost (5)
Moving Van Costs
2889222
0
10 20 30 40
Distance driven (mi)
W
Q. What is the slope?
the
ve
Answers
Answer:
Here's a screenshot of the work i've done
Step-by-step explanation:
Your welcome
6 people are evenly sharing 5 blueberry muffins.
How many blueberry muffins should each person get?
Choose 1 answer:
Answers
Each person will get 1.2 of the Blueberry muffins
How to calculate the number of blueberry muffins each person will get ?The number blueberry muffins in 5
6 people wants to share the 5 blueberry muffins
Therefore the number of blueberry muffins each person will get can be calculated by dividing 6 by 5
= 6/5
= 1.2
Hence each person will get 1.2 blueberry muffins if the muffins are shared equally.
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