PLEASE I NEED THIS NOW!! Please
Which of the following is a third root of the given complex number?
JE
27| COS
2700
+ i sin
5
5
Check all that apply.
O
A. 27| cos
1 172
15
+ i sin
1117
15
872
8z
B. 3COS
15
isin
15
117
O C. 3 cos
+ i sin
1 177
15
15
().-()
Hisin
3
O D. 3
+ i sin
JC
15
15
Answers
Suppose that r (cos(θ) + i sin(θ)) is a third root of 27 (cos(π/5) + i sin(π/5)), i.e.
[r (cos(θ) + i sin(θ))]³ = 27 (cos(π/5) + i sin(π/5))
Expand the left side using de Moivre's theorem:
r³ (cos(3θ) + i sin(3θ)) = 27 (cos(π/5) + i sin(π/5))
Matching up real and imaginary parts, we have
r³ cos(3θ) = 27 cos(π/5)
r³ sin(3θ) = 27 sin(π/5)
Right away we see that r³ = 27 ⇒ r = 3, which eliminates A.
We also have
(r³ sin(3θ)) / (r³ cos(3θ)) = (27 sin(π/5)) / (27 cos(π/5))
tan(3θ) = tan(π/5)
3θ = tan⁻¹(tan(π/5))
3θ = π/5 + nπ
(where n is an integer)
θ = π/15 + nπ/3
Now,
• n = 0 ⇒ θ = π/15 ⇒ D is a third root
• n = 1 ⇒ θ = π/15 + π/3 = 2π/5
• n = 2 ⇒ θ = π/15 + 2π/3 = 11π/15 ⇒ C is a third root
Related Questions
Find the odds agasinst getting a number less than 4
Answers
Answer:
3 out of 4 I think
Step-by-step explanation:
because the total amount is 4 so there's a 3/4 chance youll get less than 4
Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect? y2 + x2 = 100 g(x) graph of the function y squared plus x squared equals 100 x g(x) −1 −22 0 −20 1 −18
Yes, at positive x coordinates
Yes, at negative x coordinates
Yes, at negative and positive x coordinates
No, they will not intersect
Answers
Answer:
Yes, at positive x coordinates
Step-by-step explanation:
Find the equation of g(x)
Given ordered pairs of g(x): (-1, -22) (0, -20) (1, -18)
[tex]\sf let\:(x_1,y_1)=(0,-20)[/tex]
[tex]\sf let\:(x_2,y_2)=(1,-18)[/tex]
[tex]\sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-18-(-20)}{1-0}=2[/tex]
Point-slope form of linear function: [tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-20)=2(x-0)[/tex]
[tex]\implies \sf y=2x-20[/tex]
Substitute the equation of g(x) into the equation of the circle and solve for x
Given equation: [tex]y^2+x^2=100[/tex]
[tex]\implies (2x-20)^2+x^2=100[/tex]
[tex]\implies 4x^2-80x+400+x^2=100[/tex]
[tex]\implies 5x^2-80x+300=0[/tex]
[tex]\implies x^2-16x+60=0[/tex]
[tex]\implies x^2-10x-6x+60=0[/tex]
[tex]\implies x(x-10)-6(x-10)=0[/tex]
[tex]\implies (x-6)(x-10)=0[/tex]
Therefore:
[tex](x-6)=0 \implies x=6[/tex]
[tex](x-10)=0 \implies x=10[/tex]
So the linear function g(x) will intersect the equation of the circle at positive x coordinates.
[20 points]
Write the polynomial in standard form. (Look at the Photo)
Answers
Answer:
[tex]5x^4+5x^3+3x^2-4[/tex]
1 +5x2 + (1 + 3) to the second power
Answers
Answer:
27
Step-by-step explanation:
1 + (5)(2) + (1 + 3)^2
1 + 10 + (1 + 3)^2
11 + (1+3)^2
11+4^2
11+16
27
Hope this helps! Have an amazing day!A cylinder has a height that is twice the length of the diameter. The diameter of the cylinder is 10 centimeters. What is the surface area of the cylinder?
Type the correct answer in the box. Use numerals instead of words.
The surface area is square centimeters.
Answers
Answer:
Step-by-step explanation:
Givens
pi = 3.14
d = 10 cm
h = 2*d
Formula
The top of the cylinder is a solid circle. So the area of the circle is pi r^2There is both a top and bottom to the circle so the fomula is 2*pi*r^2The surrounding area of the cylinder is the circumference of the circle times the height. The circumference of the circle is 2*pi*r. Then you just multiply by the height.formula = 2*pi * r * hThe combined formula is given below.
SA = 2*pi*r^2 + 2*pi*r * h
Conversions
d = 10 cm
h = 2*10
h = 20 cm
r = d/2
r = 10 / 2
r = 5cm
Solution
SA = 2*pi*r^2 + 2*pi*r * h
SA = 2*3.14*5^2 + 2*3.14*5*20
SA = 157 + 628
SA = 785 cm^2
Answer: The surface area is 785 cm^2
Answer:
the surface area is 250 Pi square centimeters
HELPPP ME BAE!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I think it would be B
Step-by-step explanation:
Because if you look at it neither of the x or y's are the same and if you multiply the second equation by 2 than you would have the same y in both problems which is 4y
Please help me out ;)
Answers
Answer:
for every 21 votes for A there were 6 for b or 9 for c
Step-by-step explanation:
63 divided by 3
18 divided by 3
27 divided by 3
Which expressions are equivalent to 6m+5(n+m)?
7m + 5n
11m + 5n
12m + n
6m + 5n + 5m
6(m + 5n + 5m)
Answers
Answer:
it's 11m+5m
Step-by-step explanation:
Rearrange term
6m+5(n+m)
6m+5(m+n)
Distribute
6m+5m+5n
Combine like terms
6m+5m+5n
=11m+5n
20 In a village,
if it rains on one day, the probability
that it will rain on the next day is 0.8
if it does not rain on one day, the probability that it will rain on the next day is 0.6
A weather forecaster says,
“There is a 70% chance that it will rain in the village on Monday.”
Work out an estimate for the probability that it will rain in the village on Wednesday.
lou must show all your working.
Answers
Using it's concept, it is found that there is a 0.643 = 64.3% probability that it will rain in the village on Wednesday.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, considering Monday - Tuesday - Wednesday, the possible outcomes are as follows:
R - R - R(0.7 x 0.7 x 0.7)
R - N - R(0.7 x 0.2 x 0.6)
N - R - R(0.3 x 0.6 x 0.8)
N - N - R(0.3 x 0.4 x 0.6)
Then, the probability is given by:
p = 0.7 x 0.7 x 0.7 + 0.7 x 0.2 x 0.6 + 0.3 x 0.6 x 0.8 + 0.3 x 0.4 x 0.6 = 0.643.
0.643 = 64.3% probability that it will rain in the village on Wednesday.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Math 8: One-step equations word problems (writing algebraic expressions)
Answers
Answer:
x puls four is equal to
Step-by-step explanation:
need help
complete solution and correct aanswer
Answers
Answer:
17.0 m/s
Step-by-step explanation:
Using SUVAT:
[tex]s= \\u=7.0\:\textsf{m/s}\\v=v \\a=2.0\:\textsf{m/s}^2\\t=5\: \sf s[/tex]
[tex]\begin{aligned}\textsf{Using}\quad v & =u+at\\ \implies v & = 7.0+2.0(5)\\ & = 7.0+10.0\\ & = 17.0\:\textsf{m/s} \end{aligned}[/tex]
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
Answers
Answer:
at least 10 visits
Step-by-step explanation:
Given:
75 rewards points for signing up
10.5 points for each visit
Total Number of Points are :
75 + 10.5 · number of visits he makes
How many visits must Tyler make to earn a free movie ticket?
75 + 10.5 · x ≥ 180 points for a free movie ticket
Where, x is how many visits must Tyler make to earn a free movie ticket
10.5 · x ≥ 180 -75
x ≥ 105/ 10.5
x ≥ 10
Since the number of visits to reach 180 points is 10 then Tyler has to visit the movie theater 10 times or more.
Check our answer:
75 + 10.5 · 10 = 180 will earn him a free movie ticket
Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
what is the value of X in the following diagram?
Answers
Answer:
x = 98 degrees
Step-by-step explanation:
The sum of angles in a pentagon is 540 degrees. You can find this with the formula where n is the number of sides: 180(n-2). This formula will find the angle sum of a polygon. Now, since you know the value of every other angle except X, we can construct the equation 112+100+113+117+x=540
Solving this equation yields x=98 degrees
Sum of angles in a pentagon is 540°
x = 540 - (117+113+100+112)
x = 540 - 442
x = 98°
what is 2/8 simplified
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
when the numerator and denominator are no longer divisible by the same number, that's when it is in simplest form:
[tex]\frac{2}{8}[/tex] divides by [tex]\frac{2}{2}[/tex] to give you [tex]\frac{1}{4}[/tex]
2÷2 = 1
8÷2 = 4
x2 + 8x + 19 = 0 What is the equivilent that results from completing the square?
Answers
Answer:
[tex](x+4)^2+3=0[/tex]
Step-by-step explanation:
Hey there!
Standard form is what this equation is in
Standard form is this: [tex]ax^2+bx+c[/tex]
So order to complete the square, you need to take the [tex]b[/tex] term out of the equation, divide it by two, and then square it
In this case, the [tex]b[/tex] term is 8
We need to divide 8 by 2 ---> 4
Then square 4 ---> 16
So now you should add 16 to both sides
[tex]x^2+8x+16+19=16[/tex]
Now you can simplify the LHS
[tex](x+4)^2 +19=16[/tex]
Now you subtract 16 from both sides
[tex](x+4)^2+3=0[/tex]
So this is as far as you can go since you cannot take the square root of a negative number
In Ms. March's class, 7/10 of the students walk to school. Another 1/5 of the students ride thier bikes. The other students ride on the school bus. What fraction of the class rides on the school bus?
A. 1/10
B. 1/5
C. 2/5
D. 1/2
(I will mark brainliest!)
Answers
Answer:
1/10 of the class
Step-by-step explanation:
We already know:
Total students: 10/10Determining the fraction of the total students rides on school bus
[tex]\implies\dfrac{7}{10} = \text{Walk}[/tex] [tex]\dfrac{10}{10} - \dfrac{7}{10} = \boxed{\dfrac{3}{10}} \ \text{students remain}[/tex]
[tex]\implies\dfrac{1}{5} = \dfrac{2}{10} = \text{Ride bikes}[/tex] [tex]\dfrac{3}{10} - \dfrac{2}{10} = \boxed{\dfrac{1}{10} }\ \text{student remain}[/tex]
Thus, 1/10 of the class rides on the bus.
what is x > 7 j don't get it pls help me
Answers
Answer:
j < x/7
Step-by-step explanation:
Solve for y. y /4 + 15 = 17
Answers
Answer:
y = 2 x ± [tex]\sqrt{2}[/tex] =± 2.8284
Step-by-step explanation:
y*y/4+15-(17)=0
Answer:
[tex]4 + 15 \div y = 17 \\ \\ 4 + 15 = 17y \\ \\ 19 = 17y \\ \\ y = \frac{19}{17} [/tex]
Find b, glven that a = 20, angle A = 30°, and angle B= 45 triangle ABC.
Answers
Answer:
b =28.28
Step-by-step explanation:
SinA/x = sinB/x
Sin30°/20=sin45°/b
Cross multiplication
20×sin45=b×sin30
20×sin45/sin30 =b
b=28.28
Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game? a spinner is divided into 4 equal sections. each section is a different color and is labeled 1 through 4. red is 1; 2 is blue; 3 is green; 4 is yellow. the odd numbered regions will add one point. the even numbered regions lose one point. red will add one point. any other color will lose one point. a number less than or equal to 3 will add one point. a 4 will lose two points. odds will add a point value equal to the number on the space. evens will lose a point value equal to the number on the space.
Answers
The correct option is C: A number less than or equal to 3 will add one point and A.4 will lose two points.
Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game
Therefore a spinner is divided into 4 equal sections.
What is the favorable game?
A favorable game is one in which, loosely speaking, there are opportunities for favorable bets.
each section is a different color and is labeled 1 through 4.
red is 1; 2 is blue; 3 is green; 4 is yellow.
The odd-numbered regions will add one point.
The even-numbered regions lose one point.
red will add one point.
any other color will lose one point. a number less than or equal to 3 will add one point.
Therefore the option a and c is correct
C: A number less than or equal to 3 will add one point.
A.4 will lose two points.
Edge
To learn more about the favorable game visit:
https://brainly.com/question/1393329
Answer:
A number less than or equal to 3 will add one point.
A 4 will lose two points.
Step-by-step explanation:
The answer above is correct.
Lucy Garcia took out a loan for $40,000 at 10 percent interest for 10 years. Her monthly payments are $528. 60. She made payments for one year and has paid the principal down to $37,546. 36. She now wants to repay the loan early. The loan specifies a $300 prepayment penalty if she pays the loan now. How much will she save by paying the loan early (round final answer to nearest dollar)?
Answers
The amount saved due to early payment is $19,242
Data;
Monthly payment = 528.60Number of payment = 10 years * 12 = 120 Total payment if not prepaid = 528.60 * 120 = $63,432Total Payment for the whole termThe total payment for the whole term is the equal to the product of monthly payment and the number of payment as calculated above.
The total amount in cash in case of prepayment is
[tex]total amount in case of prepayment = monthly payment * number completed + balance + penalty[/tex]
The number of payment completed = 12
Balance = $37,546.36
Penalty for prepayment = 300
The amount of prepayment is
[tex]528.60 * 12 + 37546.36 + 300 = 44,189.56[/tex]
The amount saved due to early payment is
[tex]63432 - 44189.56 = 19,242[/tex]
The amount saved due to early payment is $19,242
Learn more on payment plans here;
https://brainly.com/question/251701
Fill in the table using this function rule.
y=3x+3
Answers
Answer:
9
24
27
30
Step-by-step explanation:
f(2) = 3(2) + 3 = 9
f(7) = 3(7) + 3 = 24
f(8) = 3(8) + 3 = 27
f(9) = 3(9) +3 = 30
Hope this helps!
What steps are used to solve the equation 146 + f = 225
Answers
Answer:
f = 79
Step-by-step explanation:
You need to perform one-step equations process
146 + f = 225 (You're trying to solve for "f")
*First way, you could subtract both sides by 146 which makes the 146 cancel out then do 225-146 = 79. So f is 79
*A rule to remember is that the opposite of addition is subtraction. If you move 146 to 225 side you must switch it to negative 146.
someone please please help me i need this asap and i’m struggling so much !!!
Answers
Answer:
21.5 square units
Step-by-step explanation:
The 4 circles touching eachother have a total combined length of 20.
There are 4 circles. 20/4 = 5. The diameter of each circle is 5 units.
The length ofthe rectangle is 20 units. the width of the rectangle is 5 units.
The area of the shaded region is the area of the rectangle minus the ares of 4 circles.
A = area of rectangle - area of 4 circles
A = LW - 4 × πr²
The radius of each ciorcle is d/2 = 5/2 = 2.5
A = 20 × 5 - 4 × 3.14 × 2.5²
A = 100 - 78.5
A = 21.5
Help me please I don’t understand
Answers
Answer:
Area of composite shape = 36 square units
Step-by-step explanation:
Area of composite shape:
Rectangle I:
Length = 3 units
width = 6 - 4 = 2 units
Area of rectangle I = length *width
= 3* 2
= 6 square units
Rectangle II:
length = 6 units
width = 5 units
Area of rectangle II = 6 * 5
= 30 square units
Area of composite shape = area of rectangle I + area of rectangle II
= 6 + 30
= 36 square units
Question 8 (1 point)
21 A student must complete the column of the table that lists the dates of the full moons.
Dates of New Moons Dates of Full Moons
February 10
March 11
April 10
May 9
What are the most likely dates of the full moons?
A February 5, March 7, April 5, May 4
B February 15, March 17, April 15, May 14
CFebruary 25, March 27. April 25, May 24
D February 29, March 31, April 29, May 28
Answers
The most likely dates of the full moons will be C. February 25, March 27, April 25, and May 24.
What is a full moon?It should be noted that a full moon simply means the lunar phase when the moon appears illuminated from the perspective of the Earth.
In this case, the most likely dates of the full moons will be February 25, March 27, April 25, May 24. The Full moon usually lasts for a night.
Learn more about moon on:
brainly.com/question/398659
A basketball team scored a total of 747 points for the season. This was 9 times the number of points scored in the first game. How many points were scored during the first game?
Answers
You can set it up as an equation.
X * 9 = 747
X = 83
What is the perimeter of kite obde? 17 units 23 units 27 units 60 units
Answers
All sides add up to the perimeter. The perimeter of the kite is 27 units then the correct option is C.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D forms.
The Pythagoras theorem will determine the kite's length (x).
H² = P² + B²
H² = 15² + 8²
H² = 225 + 64
H² = 289
H = 17
Then
[tex]\rm x = \dfrac{H}{2} \\\\x = \dfrac{17}{2}\\\\x = 8.5[/tex]
And another length of the kite is 5 units.
Then the perimeter of the kite will be
Perimeter = 2(8.5 + 5)
Perimeter = 27
More about the geometry link is given below.
https://brainly.com/question/7558603
Answer:27 units
Step-by-step explanation:
trust
The value of a company equipment is $25000 and decreases at a rate of 15% per year. What is the value of the equipment after 8 years.
Answers
Answer: $6812.3
Step-by-step explanation: Just solve decreasing 15% each year
3) Solve 5(x + 3) - 3x = 55 for x. Use mathematical properties to justify each step in the process.
Step 1
Step 2
Step 3
Step 4
Step 5
Answers
solution
5(x+3)-3x=55
5x+15-3x=555x-3x+15=552x+15=552x=55-152x=402x/2=40/2x=20