Answer:
See below for all the cube roots
Step-by-step explanation:
DeMoivre's Theorem
Let [tex]z=r(cos\theta+isin\theta)[/tex] be a complex number in polar form, where [tex]n[/tex] is an integer and [tex]n\geq1[/tex]. If [tex]z^n=r^n(cos\theta+isin\theta)^n[/tex], then [tex]z^n=r^n(cos(n\theta)+isin(n\theta))[/tex].
Nth Root of a Complex Number
If [tex]n[/tex] is any positive integer, the nth roots of [tex]z=rcis\theta[/tex] are given by [tex]\sqrt[n]{rcis\theta}=(rcis\theta)^{\frac{1}{n}}[/tex] where the nth roots are found with the formulas:
[tex]\sqrt[n]{r}\biggr[cis(\frac{\theta+360^\circ k}{n})\biggr][/tex] for degrees (the one applicable to this problem)[tex]\sqrt[n]{r}\biggr[cis(\frac{\theta+2\pi k}{n})\biggr][/tex] for radiansfor [tex]k=0,1,2,...\:,n-1[/tex]
Calculation
[tex]z=27(cos330^\circ+isin330^\circ)\\\\\sqrt[3]{z} =\sqrt[3]{27(cos330^\circ+isin330^\circ)}\\\\z^{\frac{1}{3}} =(27(cos330^\circ+isin330^\circ))^{\frac{1}{3}}\\\\z^{\frac{1}{3}} =27^{\frac{1}{3}}(cos(\frac{1}{3}\cdot330^\circ)+isin(\frac{1}{3}\cdot330^\circ))\\\\z^{\frac{1}{3}} =3(cos110^\circ+isin110^\circ)[/tex]
First cube root where k=2
[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(2)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+720^\circ}{3})\biggr]\\3\biggr[cis(\frac{1050^\circ}{3})\biggr]\\3\biggr[cis(350^\circ)\biggr]\\3\biggr[cos(350^\circ)+isin(350^\circ)\biggr][/tex]
Second cube root where k=1
[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(1)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+360^\circ}{3})\biggr]\\3\biggr[cis(\frac{690^\circ}{3})\biggr]\\3\biggr[cis(230^\circ)\biggr]\\3\biggr[cos(230^\circ)+isin(230^\circ)\biggr][/tex]
Third cube root where k=0
[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(0)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ}{3})\biggr]\\3\biggr[cis(110^\circ)\biggr]\\3\biggr[cos(110^\circ)+isin(110^\circ)\biggr][/tex]
The estimated brand value $188,000,000,000 rounded to the nearest ten billion
Answer:
180,000,000,000
Step-by-step explanation:
What is the simplified expression for x-(x+7)
What two numbers add and give you -4 and multiply and give you 5
Answer:
your answer would be: no number
Step-by-step explanation:
to get a positive 5, you have to multiply 2 negative numbers, which are -1 and -5. and negative -1 + -5 =-6. For you to get -4, the 5 would have to be -5, in this case, it's a +5.
I don't get it, I just need some help.
Answer:
Which part do you want? I can easily help you
3=39
2=108
1=72
Hellppp please 10 points
toAnswer:
x ≥ 1
[] See attached
Step-by-step explanation:
[Given]
-6 ≤ -7 + x
[Add 7 to both sides]
1 ≤ x
For the graph, we will plot the point 1 and fill it in since x is greater than or equal to 1. Next, we will draw an arrow to the right showing greater than.
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.
- Heather
1)) An angle measures 144º more than the measure of its supplementary angle. What is the
measure of each angle?
Supplementary angles add to 180 degrees.
180 - 144 = 36
36/2 = 18
18 + 144 = 162
One angle is 18 and the other one is 162
The table below shows the amount of money that Samantha has in her retirement account during the months of January and February.
January February
$29,000 $28,000
What could happen in March to make the net change in her account $0 from January to March?
A.
She withdraws $1,000 from her retirement account.
B.
Her retirement account value decreases by $1,000.
C.
She gets a loan of $1,000 from her retirement account.
D.
Her company puts a $1,000 bonus into her retirement account.
Answer:
D. Her company puts a $1,000 bonus into her retirement account.Step-by-step explanation:
Since the amount in the retirement account has decreased in February, she needs the increase by same amount, $1000 to make it same as in January.
It is possible by adding $1000, which is the Option D, all other options end up with $1000 less than in February.
How many inches are there in a mile? ASAP
Answer:
63360 inch = 1 miles.
Step-by-step explanation:
Answer:
63360
Step-by-step explanation:
G
O
O
G
L
E
In the least-squares regression line, the desired sum of the errors (residuals) should be a) zero b) positive c) 1 d) negative e) maximized
Explanation:
The key word here is "desired". We wish to make the errors as small as possible. The smallest any individual error can get is 0. Adding the entire collection of zeros will sum in a total of zero.
An error of zero means we hit the mark exactly. The unfortunate reality is that error is going to happen, so we'll have some positive error values with any regression line (or curve). It's only when all points are on the same line is when we have zero error and perfect interpolation rather than regression.
Again, the question is asking about desired error and the ultimate goal is to make the error zero. The next best thing is to minimize it as small as possible.
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts
is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds
y = -(x - 5)2 + 3
y=-3(x-3)2 + x + 1
To make sure the flip is in unison, after how many seconds should the flip occur?
O2 seconds
O 3 seconds
O4 seconds
O 5 seconds
Answer:
05 is your answer
Step-by-step explanation:
hope it helps you
Answer:
it might be 3
Step-by-step explanation:
due to someone getting 5sec wrong me getting 2 wrong another post with only three stars said 4 so id leave it to 4 or 3.(process of elimination)
Question 3: Tyrone gets paid $ 7.25 per hour and a bonus of $ 25 if he finishes his work early. Which of the following expressions represents how much money Tyrone makes when he finishes work early? 7.25 + 25x 7.25 + x + 25 7.25x + 25 7.25 + x − 25
Question 10 of 10
Factor the trinomial below.
x2 - 2x - 35
O A. (x+5)(x-7)
O B. (x + 5)(x + 7)
O C. (x - 5)(x-7)
O D. (X - 5)(x+7)
Answer:
A
Step-by-step explanation:
[tex] { x}^{2} - 2x - 35 = (x + 5)(x - 7)[/tex]
[tex]5 + - 7 = - 2[/tex]
[tex]5 \times - 7 = - 35[/tex]
Sixty students took a math test. The percentages of students who scored an A, B, C, or D are displayed in the circle graph, but the labels are missing. If the largest category in the graph represents those who scored an A, how many students scored an A?
Answer:
30
Step-by-step explanation:
~Calculate :)~
a) −5.68 + 4.73
b) −0.85 − (−2.34)
c) 1.8(−4.5)
d) −3.77 ÷ (−2.9)
Answer:
a)-0.95
b)1.49
c)-8.1
d)1.3
Step-by-step explanation:
a) just add the postive to the negative, pretty simple.
b) the two negatives in this problem cancel out so the new pronlem is adding -.85+2.34
c)Anything multiplied by one negative will have a negative product
d)Divide like regular, but anything that has two negatives equals a postive.
Let me know if you need more or the actual work.
What is the value of x2 + 3 4y when x = 2 and y = 5?
18
20
21
37
Answer:
21
Step-by-step explanation:
x2 + 3.4y, when x = 2, y = 5
(2)2+3.4(5)
2×2+3.4×5
4+5×3.4
4+17
21
Hope it helps! :)
Write an algebraic expression to model the unknown number situation.
the sum of a number and one-third
Which statements are true? Select all that apply.
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "sum" with an multiplication sign.
You can replace "one-third" with 1/3
The correct algebraic expression is 1/3 n
CHART IS BELOW
Answer:
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "one-third" with 1/3.
Step-by-step explanation:
"the sum" means to add.
Let "a number" = x:
The sum of a number and one-third = x + 1/3.
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "one-third" with 1/3.
What’s 20 timas 10 I can’t figure it out I give Brainly for answert
solve 8 x (b + 57) = _____ + _____
Answer:
8xb + 456x
Step-by-step explanation:
8x(b + 456)
8xb + 456x
You multiply 8x by the numbers in the parenthesis. And you add the variables to the coefficents.
I hope it helps! Have a great day!
Lilac~
How to find the value of x of a triangle with all three sides having numbers.
Answer:
20
Step-by-step explanation:
When triangles are similar,
DE/DF=GH/GJ
[tex]\frac{x}{16} =\frac{15}{12} \\\\x=\frac{15*16}{12} \\\\x=20[/tex]
Answer:
x = 24
Step-by-step explanation:
[tex]\frac{16}{x} = \frac{12}{18}[/tex]
[tex]12(x) = 18(16)[/tex]
[tex]12x = 288[/tex]
[tex]x = 24[/tex]
Which of the following answers is the simplified form?
Answer:
the answer is c, 1/81
Step-by-step explanation:
Hope this helps! :)
solve the following equation 6/8 + 1 equals 26 - 2 x
Answer:
x = 97/8
Step-by-step explanation:
6/8 + 1 = 26 - 2x
6/8 + 8/8 = 26 - 2x
14/8 = 26 - 2x
14/8 - 26 = -2x
14/8 - 208/8 = -2x
-194/8 = -2x
194/16 = x
x = 97/8
HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION HELP ME WITH THIS QUESTION
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation: look at the graph dude
What is the equation of this line?
y= - 3/2x
y= 3/2x
y= - 2/3x
y= 2/3x
Answer:
y = 2/3x
Step-by-step explanation:
[] Since the line goes through the origin (0, 0) the line will have no b. This does not rule out any of the options as they all have no b.
[] When we have clear points on a line, we can find the slope by using "rise-over-run." Here is an example using your problem;
-> The slope of the line will be positive because it is going from the bottom left to the top right.
We will start at (0, 0). We count up two units to (0, 2) and to the right three units too our next point, (3, 2). This leaves us with a slope of 2/3.
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.
- Heather
How many kilograms are in 14,500 grams?
Answer: 14.5
Step-by-step explanation: there is 1000 g in a kg
PLEASE HELP WILL MARK BRAINLIEST THANK U
Explain why this equation is wrong
Answer:
The equation is wrongexplanatiowrongexplanwrongo
Step-by-step explanation:
find the volume of a cylinder whose circumference is 110 cm and height is 20 CM
Answer:
Volume is 19277.46 cm
Step-by-step explanation:
Data :
Circumference = C = 110 cm
Height = h = 20 cm
As circumference is
C = 2πr ⇒ r = C/2π = 110/2π =
r = 17.516 cm
Formula for volume of cylinder is
V = πr²h = π × 17.516 × 20
V = 19277.46
MARK BRAINLIEST IF YOU UNDERSTAND
SOMEONE PLEASE HELP ME WITH THIS!! ILL GIVE BRAINLIEST
Answer:
d I think I could be wrong but hey who knows
10. C because if you use the distance formula you get 10.
22 questions
Question 18 of 22
A home has a triangular backyard. The second angle of the triangle is 4º more than the first angle. The third angle is 16° more than three times the first angle. Find the
angles of the triangular yard.
Answer:
32°, 36°, 112°
Step-by-step explanation:
All of the angles are described in terms of the first angle, so we can use a variable to represent that: x. The second angle is (x+4) and the third angle is (3x+16). As always, the sum of angles in a triangle is 180 degrees:
x +(x +4) +(3x +16) = 180
5x +20 = 180 . . . . . collect terms
5x = 160 . . . . . . . subtract 20
x = 32 . . . . . . . divide by 5
x+4 = 36 . . . . find the other two angles
3x+16 = 3(32) +16 = 112
The angles of the triangular yard are 32°, 36°, and 112°.
Marked up 60% new price 80$ what was original price
0.6x=80
6x=800
x=800/6=133.3333333333333333333333333333333...
which is 133 1/3 in a fraction
What is the product of 1/2 x - 1/4 and 5x^2 - 2x + 6? Write your answer in standard form?
a) show your work
b) is the product of 1/2 x - 1/4 and 5x^2 - 2x + 6 equal to the product of 1/4 x - 1/2 and 5x^2 - 2x + 6?
explain your answer
Answer:
for a. you will first solve 5x²-2x+6 with
x=-b ± ✓b²-4ac
----------------
2a
then put the two answers you will get into a bracket then multiply it with 1/2x - 1\4
then write in form of dis :- A ×10^n
Step-by-step explanation:
b. the two products are not the same