By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].
How to determine a fourth root of a complex numberAccording to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)
Where:
r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the magnitude and direction of the complex number:
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]
r = 6
[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]
[tex]\theta = \frac{2\pi}{3} \,rad[/tex]
Now we find the four quartic roots of the complex number:
[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]
[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]
[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]
[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]
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HURRYYY PLEASE AND THANK YOUUMrs. Green wants to make some toys for a store. She starts
working at 8 AM and stops at 12 PM everyday. The store needs
120 toys and requires Mrs. Green to make them in three days.
What must be her average rate of toys made per hour?
toys/hour
I
I
Enter the answer
Answer:
10 per hour
Step-by-step explanation:
Answer: 75
Step-by-step explanation:
Tell me if it’s wrong or not
Please help this is due today!
Calculate the unknown missing angle measures.
Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.
Answer:
x=63+86
Step-by-step explanation:
due to circle theory
PLEASE ANSWER THIS QUESTION!!!!!!!!!!!!!
uhhh... my math grade is a D and i dont have my phone and i want it back so please just help me, this will get my grade up to a C or a B at least so help
Answer:
function one
Step-by-step explanation:
the x intercept in function one is a negative number
Answer: function one
Step-by-step explanation:
One side of a square has a measurement of 2x + 4. Write an expression to represent the perimeter of the shape.
Answer:
4(2x+4)
for example, if 5 were the length of a side you'd do 4(5). 4 because theres 4 sides and the formula for P is P= l+l+w+w OR P=2l+2w
The difference of four times a number and seven is 21. Find the number.
Answer:
7
Step-by-step explanation:
4x-7=21
4x=28
x=7.....
The number is 7.
We have a sentence - "The difference of four times a number and seven is 21".
We have to find the number.
Express the statement - "The difference of 40 and 20 is equal to n" in the form of expression.The expression representing the above statement is -
n = 40 - 20 = 20
According to the question, we have -
The difference of four times a number and seven is 21.
Assume the number be x.
Therefore -
4x - 7 = 21
4x = 28
x = 7
Hence, the number is 7.
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Which of the following inequalities does the graph represent
Answer:
di KO kaya sorry kahit ako dipa KO talks dyan
Find the area of the trapezoid. If the answer is not an integer, leave it in simplest radical form. The figure is not to scale.
A=
Step-by-step explanation:
area of trapezium = 15× 12 + 1/2× 12× 5
= 180 + 30 = 210
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
(WILL MARK BRAINLIEST) 16 POINTS!
GRAPHING LINEAR EQUATIONS. (picture below)
the map below shows certain locations in town. Use the map and the box of equations at the right to answer the questions below.
Step-by-step explanation:
Gas Station (2,7) -> y = [tex]\frac{1}{2}[/tex]x + 6 if you plug in the numbers it becomes 7 = 1 + 6
Grocery Store (6,3) -> x + 6y = 24 plug in the numbers it becomes 6 + 18 = 24
Bowling Ally (1, -3) -> 6x + 3y = -3 plug in numbers 6 -9 = -3
Movies (7, -7) -> y = -7 because the y coordinates for the movies = -7
Park(-2, -4) -> -6x + 2y = 4 plug in the numbers 12 - 8 = 4
Coffee Shop (-6, -8) -> -10x + 5y = 20 plug in the number 60 - 40 = 20
Gym (-8, -3)-> y = - [tex]\frac{1}{2}[/tex]x - 7 plug in the numbers -3 = 4-7
School (-6, 6) -> y = - [tex]\frac{1}{3}[/tex]x +4 plug in the numbers 6 = 2 + 4
6x + 3y = -3 quadrant II is (-x, y)
rearrange the equation:
3y = -6x - 3
y = -2x - 1
if x is -1, y will be 2 -1 = 1. So another solution for this equation is (-1, 1).
Classify the polynomial according to its degree and number of terms 8x.
quadratic binomial
seventh-degree binomial
seventh-degree monomial
linear monomial
Answer:
Linear monomial
Step-by-step explanation:
As here the number of terms is only 8x that is only one hence it is a monomial and as its degree here is 1 hence it is linear.
So it is a linear monomial.
which equation is equivalent to
y + 2(x + 5) = 4x + 5
a) y = 2x + 20
b) y = -4x + 5
c) y = 2x - 5
d) y = 5x + 2
Answer:
C
Step-by-step explanation:
y + 2x + 10 = 4x + 5
y = 4x - 2x + 5 - 10
y = 2x - 5
Answer- C
The line with a slope of 1/3 and a y- intercept of -15 intersects the line passing through which of these pairs of points? Select THREE that apply
If you can buy 4 containers of pudding for $4.20 how much can you buy for $9.45 math problem PARAMETERS
*** 7 STEPS ***
Answer:
9 containers
Step-by-step explanation:
$4.20 for 4 containers
Form that we can find the cost per container, the unit cost.
$4.20 / 4 containers = $1.05/container
Each container costs $1.05
Now we find the number of containers we can buy with $9.45 by dividing $9.45 by the unit cost.
$9.45/($1.05/container) = 9 containers
Answer: 9 containers
Step-by-step explanation:
Four containers of pudding cost $4.20.
4x = 4.20
x = 1.05
Using this we know that one container of pudding costs $1.05.
Then, divide the maximum amount that you have by the cost of one.
9.45/1.05 = 9
With $9.45, you can buy nine cups of pudding.
In the case that you can buy the four containers in bulk (4 at a time)...
You can only buy 8 containers of pudding (two) because $4.20 only fits into $9.45 twice.
se quiere pintar una pared en forma de hexágono regular y se sabe que cada lado mide 3m y que su apotema es de 2,8m cual es el area que se va a pintar?
Answer:
El área total a pintar será:
[tex]A_{tot}=25.2\: m^{2}[/tex]
Step-by-step explanation:
Sabiendo el apotema y la longitu de los lados, podemos encontrar el área de un triangulo. Recordemos que, si trazamos rectas del centro del hexágono a los vértices, se formaran 6 triángulos equiláteros.
El área de un triángulo es:
[tex]A_{t1}=\frac{b*a}{2}[/tex]
b es la longitud de la base (b=3 m)
a es la apotema, osea la altura del triangulo (a = 2.8)
[tex]A_{t1}=\frac{2.8*3}{2}[/tex]
[tex]A_{t1}=4.2\: m^{2}[/tex]
Ahora, solo debemos mutiplicar ese valor por 6 para determianr el área total de la pared.
[tex]A_{tot}=25.2\: m^{2}[/tex]
Espero te haya sido util!
Kevin is designing a cover for a comic book. He wants to have a rectangular grid with x ^ 2 - 3x - 10 squares in it, for some positive whole number x. What are the possible side lengths for the grid?
A. There are no possible whole number side lengths.
B. (x + 2) and (x - 5)
C. (x - 2) and (x + 5)
D. (x + 2) and (x + 5)
Answer:
(X+2) and (x-5)
Step-by-step explanation:
en una casa construida con madera el tejado se sostiene con una estructura triangular en el que se utilizan ángulos complementarios ¿cómo se construye es estructura?¿qué pares de ángulos son congruentes ? ¿cómo se distribuye la carga que soporta?
Answer:
Si me dieras una imagen con esto, podría responderla fácilmente, pero no hay una imagen o modelo para ayudar a disculparme.
Step-by-step explanation:
lo siento, tal vez vuelva a publicarlo con un modelo o una imagen para que pueda ayudar
Martha's bakery started with 200 cupcakes in the morning. After a busy afternoon there were only 60 cupcakes left. By what percent did the cupcake inventory drop?
Answer: 70%
Step-by-step explanation:
Martha's bakery started with 200 cupcakes in the morning and after a busy afternoon there were only 60 cupcakes left, this means that 200 - 60 = 140 cupcakes were sold.
The percentage drop will be:
= 140/200 × 100
= 70%
if a trader make a loss of 10% when he sells a watch for 15,300
a what is the cost price
b how much would he gain if he made a profit of 6%
Answer:
A. original price: 16830
B. Profit gain: 918
10%=1530
6%=918
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Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $450 and has not made any withdrawals or deposits since then.
If her interest rate is 7% each year, how much interest has accrued using simple interest?
Answer:
Step-by-step explanation:
The interest accrued is $258.48.
Step-by-step explanation:
Given that:
Initial balance in the savings account = $359
Interest rate = 8%
Time for which no withdrawals or deposits were done = 9 years
To find:
Simple Interest accrued = ?
Solution:
First of all, let us have a look at the formula for simple interest.
Where P is the Principal Amount.
R is the annual rate of interest
T is the time in years.
Here, we are given:
P = $359
R = 8%
T = 9 years
Let us put all the values in the formula:
So, the interest accrued is $258.48.
which choices are equivalent to the quotient below check all that apply √12/√6
Step-by-step explanation:
I don't see any of the choices, but I'll just give you what it's equal to. The expression is equal to: sqrt2, which is approximately 1.414.
Can Some please help
Answer:
First we need to find out how much is 1 inch in feet
80/5
=16
Now we just simply need to multiply
16x3/4
=12
Your answer is 12
Hope it Helps!!
2 z − 22 facorise fully
Answer:
Factorising fully
then
2z - 22
= 2( z - 11)
Math sucks helppppp pls
Answer:
B
Step-by-step explanation:
Perimeter of the composite shape = ½ of the circumference of a circle + perimeter of a rectangle - Length of the rectangle
= ½*2πr + 2(L + W) - L
Where,
r = 8
π = 3.14
L = 16
W = 12
Perimeter of the composite shape = ½(2*3.14*8) + 2(16 + 12) - 16
= 25.12 + 56 - 16
Perimeter of the composite figure = 65.12 inches
Area of the composite figure = ½(πr²) + L*W
= ½(3.14*8²) + 16*12
= 100.48 + 192
Area = 292.48 square inches
No answer text provided.
No answer text provided.
HA < CH
HM > CH
AM = CK
MH < HC
Answer:
HM > CH
Step-by-step explanation:
You are correct, I didn't see the option HM > CH, which is correct, since the angle 90 degrees is larger than the angle 73, and then the sides opposite to them must follow suit.
Therefore, the correct answer is: HM > CH
The true statement from the triangles is (b) HM > CH
How to determine which must be trueFrom the question, we have the following parameters that can be used in our computation:
The figures
Next, we have
Angles at corresponding points = 90 degrees and 73 degrees
Since the angle 90 degrees is larger than the angle 73 degrees, and then the sides opposite to them must also have the same relationship
Using the above as a guide, we have the following:
The true statement is (b) HM > CH
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Use the discriminant to determine the number of real solutions to the quadratic equation.
6a2−11a+9=0
What is the number of real solutions?
Select the correct answer below:
0
1
2
Answer:
0
Step-by-step explanation:
Use discramnt formula
[tex]b {}^{2} - 4ac[/tex]
Where 6 is a, 11 is b and 9 is c
[tex]11 {}^{2} - 4(6)(9) [/tex]
[tex]121 - 216 = - 95[/tex]
Since the discramnt is negative, there are no real solutions and it will only produce imaginary solutions
Jenny read 12 pages on Monday, 25 pages on Tuesday and
the remaining pages on Wednesday. On average she read
23 pages per day during these three days. How many pages
did she read on Wednesday?
Answer:
32
Step-by-step explanation:
Let Wed pages = x
(12 + 25 + x) / 3 = 23 Multiply both sides by 3
12 + 25 + x = 3 * 23 Combine the right
12 + 25 + x = 69
37 + x = 69 Subtract 37
x = 69 - 37
x = 32
32 pages were read on Wed
If the ratio of AB:BC is 7:4,
what is the length of AB?
If the ratio of AB:AC is 8:7, what is the length of AC?
PLZ HELP
Answer:
The answer will be :-
2. AB = 31.5 in
3. AC = 5.25 in
5 divided by 3670 equals
Answer:
.0013623978
Step-by-step explanation:
Someone please help♀️
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10
-10
(0,0)
(10,-2)
10
Rest of the options are
D.y=- 1/5x
E. Y=5x
F.y=x
Answer:
D. y=-1/5(x)
Step-by-step explanation:
To find the equation of a line, use the formula y=mx+b, where x and y represent your x and y coordinates, m is your slope and b is your y-intercept.
b is you y-intercept, this is where the line cuts the y-axis. We can see from the graph that the line cuts the y-axis at (0,0), so c=0.
Now we have y=mx
Sub in one of our points (10,-2):
-2=m10
m=-1/5
So our equation looks like this:
y=-1/5(x)
help me pls I would really appreciate it
Answer:
A (-3,-3)
B (-4,1)
C (-1,0)
Step-by-step explanation:
help math eeekkkkkkk
Answer:
Step-by-step explanation: