The three third roots of the complex number -1 + 4i, expressed in polar form with angles in ascending order (in radians), are:
∛17 (cos(-0.441) + i sin(-0.441)) , ∛17 (cos(1.201) + i sin(1.201)) , ∛17 (cos(2.842) + i sin(2.842))
To find the third roots of the complex number -1 + 4i, we can represent the number in polar form and use De Moivre's theorem.
First, let's find the magnitude and argument of the complex number. The magnitude, denoted as r, is given by the formula r = √(a² + b²), where a and b are the real and imaginary parts, respectively. In this case, a = -1 and b = 4, so r = √((-1)² + 4²) = √(1 + 16) = √17.
The argument, denoted as θ, can be found using the formula θ = arctan(b/a). In this case, θ = arctan(4/(-1)) = arctan(-4) = -1.3258 radians (approximately).
Now, we can express the complex number -1 + 4i in polar form as z = √17 (cos(-1.3258) + i sin(-1.3258)).
To find the third roots, we need to take the cube root of the magnitude and divide the argument by 3. Let's call the cube root of the magnitude as r^(1/3) and the angle divided by 3 as θ/3.
The three third roots are then given by:
r^(1/3) (cos(θ/3) + i sin(θ/3))
r^(1/3) (cos((θ + 2π)/3) + i sin((θ + 2π)/3))
r^(1/3) (cos((θ + 4π)/3) + i sin((θ + 4π)/3))
So, the three third roots of -1 + 4i in polar form, with angles in ascending order (in radians), are given by the above expressions.
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PLEASE HELP due in a few hours!!
Answer:
75 meters²
Step-by-step explanation:
4 cm= 5 m
12 cm= 15 m
15×5=75
Area of Patio=75 m²
Given y[n] = 3" u[n] - 1.5 8[n-1] = A) B) C) What is Y[z]? Draw the graph 3u[n] and 1.58 [n-1]. Simplify y[n] by first solving Y[z]. Use inverse Z for simplification.
The Z-transform of the given sequence y[n] = 3u[n] - 1.5 8[n-1] is Y[z] = (3z)/(z-1) - (1.5z)/(z-1). To simplify y[n], we need to find the inverse Z-transform of Y[z].
The Z-transform is a useful tool for analyzing discrete-time signals and systems. In this case, we are given the sequence y[n] = 3u[n] - 1.5 8[n-1], where u[n] is the unit step function and 8[n-1] represents the delayed unit impulse function.
To find the Z-transform of y[n], we can use the linearity property of the Z-transform. Since the Z-transform of u[n] is 1/(1-z^(-1)), and the Z-transform of 8[n-1] is z^(-1), we can substitute these values into the expression for y[n] to obtain:
Y[z] = 3(1/(1-z^(-1))) - 1.5(z^(-1))/(1-z^(-1))
To simplify Y[z], we need to combine the terms with a common denominator. By finding a common denominator of (1-z^(-1)), we can rewrite Y[z] as:
Y[z] = (3z - 1.5)/(z-1)
Now, to obtain y[n], we need to find the inverse Z-transform of Y[z]. The inverse Z-transform can be computed using techniques such as partial fraction expansion or by referring to Z-transform tables.
The simplified expression for y[n] would be:
y[n] = 3δ[n] - 1.5δ[n-1]
where δ[n] represents the discrete-time unit impulse function. The graph of y[n] would have an impulse of magnitude 3 at n = 0 and an impulse of magnitude -1.5 at n = 1.
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Please find the next fraction in this sequence. No files please
Find the largest possible constant r ∈ (0, 1) such that the function f : [0, r] → [0, r] defined by f(x) = x^2 is a (strict) contraction.
The largest possible constant r ∈ (0, 1) such that the function f : [0, r] → [0, r] defined by f(x) = x^2 is a strict contraction is r = 1/2.
To prove this, we need to show that there exists a positive constant k < 1 such that |f(x) - f(y)| ≤ k|x - y| for all x, y ∈ [0, r] with x ≠ y.
Let x, y ∈ [0, r] with x ≠ y. Then, we have:
|f(x) - f(y)| = |x^2 - y^2| = |(x - y)(x + y)| ≤ |x - y|(r + r) = 2r|x - y|
Therefore, if we choose k = 2r < 1, then |f(x) - f(y)| ≤ k|x - y| for all x, y ∈ [0, r] with x ≠ y.
Now, we need to find the largest possible constant r such that k < 1. We have k = 2r < 1, so r < 1/2.
Thus, the largest possible constant r ∈ (0, 1) such that f(x) = x^2 is a strict contraction is r = 1/2.
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Select the 2 moves necessary in the sequence of transformations that produced polygon A from polygon E. *
A board game has a spinner divided into sections of equal size(10). Each section is labeled a number between 1-5. Which number is a reasonable estimate of the number of spins on a section labeled 5 over the course of 150 spins?
A(15)
B(25)
C(40)
D(60)
What type of function will fit these data points?
Linear
Quadratic
Exponential
None of the above
Answer: quadratic
Step-by-step explanation:
I guess if you can search up a picture of each function, you will be able to understand it. A linear graph is linear (as its name suggests), as a result, it never "goes back" to the value that has showed up. For example, the linear function y=3x+2. If you plug in a random value of y (let's say 10), then solve for x, you will only get 1 value of x. The data table that you have indicates that the y value of 0 has appeared twice. Thus, the function cannot be linear. The same thing applies to an exponential function. A quadratic function, however, can have to x values that result in the same y value. For example, the function y = [tex]x^2[/tex]-1. When you set y equal to zero....
0 = [tex]x^2[/tex]-1
0 = (x+1)(x-1)
x = -1 or 1.
Hope this helps :)
A storage chest is shown. What is the volume in cubic feet?
$475 20 for 6 years at 6-% $787 for 3 years at 9% $131 70 for 6 yrs 8 months at 4-%. find the simple interest
The simple interest for each scenario is 1. $171, 2. $212.13, and 3. $35.15.
To calculate the simple interest for each scenario, we can use the formula: Interest = Principal × Rate × Time.
1. For $475 at 6% interest for 6 years:
Principal = $475, Rate = 6%, Time = 6 years.
Interest = 475 × 0.06 × 6 = $171.
2. For $787 at 9% interest for 3 years:
Principal = $787, Rate = 9%, Time = 3 years.
Interest = 787 × 0.09 × 3 = $212.13 (rounded to two decimal places).
3. For $131.70 at 4% interest for 6 years and 8 months (or 6.67 years):
Principal = $131.70, Rate = 4%, Time = 6.67 years.
Interest = 131.70 × 0.04 × 6.67 = $35.15 (rounded to two decimal places).
Therefore, the simple interest for each scenario is:
1. $171
2. $212.13
3. $35.15
What does "simple interest" mean?
Simple interest is a method for figuring out how much interest was paid on an amount of money during a specific time period at a specific rate. Simple interest has a fixed principle amount. Simple interest is a clear-cut and simple method for computing financial interest.
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The correct question would be as
Find the simple interest of each scenario:
1. Principal = $475, Rate = 6%, Time = 6 years.
2. Principal = $787, Rate = 9%, Time = 3 years
3. Principal = $131.70, Rate = 4%, Time = 6.67 years (6 years and 8 months)
Consider the following IVP: x' (t) = -λx (t), x (0) = xo where λ=17 and x ER. What is the largest positive step size such that Heun's method is stable?
The largest positive step size for which Heun's method is stable in the given initial value problem with x'(t) = -λx(t), x(0) = xo, where λ = 17, is h ≤ 0.034.
Heun's method, also known as the improved Euler method or the explicit trapezoidal method, is an explicit numerical method used for solving ordinary differential equations. The stability of Heun's method depends on the step size chosen for the integration.
The stability criterion for Heun's method is that the step size, denoted as h, should satisfy the condition h ≤ 2 / (|λ|), where λ is the coefficient of the equation being solved. In this case, λ = 17.
Substituting the value of λ into the stability criterion, we have h ≤ 2 / (|17|) = 2 / 17 ≈ 0.1176. Therefore, the largest positive step size for stability is h ≤ 0.1176.
However, to find the largest positive step size, we need to consider the accuracy of the numerical solution as well. A smaller step size typically provides a more accurate solution. Hence, we choose the largest step size that satisfies both the stability criterion and the desired level of accuracy.
In this case, the largest positive step size for which Heun's method is stable and provides a reasonable level of accuracy can be chosen as h ≤ 0.034.
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What is the probability that either event will occur?
5
A
B
35 5, 10
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answer:
P(A or B) = 1 - P(neither A nor B)
= 1 - 5/55 = 1 - 1/11 = 10/11
= about .91 = about 90.91%
Answer:
Step-by-step explanation:
A club consists of five men and seven women. A committee of six is to be chosen.
(a) How many committees of six contain three men
and three women?
(b) How many committees of six contain at least two men?
(a) To find the number of committees of six that contain three men and three women, we can use the concept of combinations.
The number of ways to choose three men out of five is given by the combination formula:
[tex]\({{5}\choose{3}} = \frac{5!}{3!(5-3)!} = 10\)[/tex]
Similarly, the number of ways to choose three women out of seven is given by:
[tex]\({{7}\choose{3}} = \frac{7!}{3!(7-3)!} = 35\)[/tex]
Since the choices for men and women are independent, we can multiply these two values to get the total number of committees with three men and three women:
[tex]\(10 \times 35 = 350\)[/tex]
(b) To find the number of committees of six that contain at least two men, we can consider two cases:
1. Committees with exactly two men:
The number of ways to choose two men out of five is [tex]\({{5}\choose{2}} = 10\)[/tex].
The number of ways to choose four women out of seven is [tex]\({{7}\choose{4}} = 35\)[/tex].
So, the number of committees with exactly two men is [tex]\(10 \times 35 = 350\)[/tex].
2. Committees with three men or more:
We have already calculated the number of committees with exactly three men and three women in part (a), which is 350.
To get the total number of committees with at least two men, we sum the results from the two cases: .
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(t+8)^3
i want you to solve this
[tex]( {t + 8})^{3} = {t}^{3} + 3 \times ({t})^{2} \times( 8) + 3 \times (t) \times ( {8})^{2} + {8}^{3} \\ [/tex]
So :
[tex] ({t + 8})^{3} = {t}^{3} + 24 {t}^{2} + 192t + 512[/tex]
HELP LeShana loaned Deena $480. Deena paid the money back with a simple interest of 5% at the end of 2 years. How much money did Deena pay back?
Answer:
FV= $528
Step-by-step explanation:
Giving the following information:
Loan (P)= $480
Number of years (n)= 2 years
Simple interest (i)= 5% per year
To calculate the amount of money that Deena paid is calculated using the following formula:
FV= P*r*t + P
FV= 480*0.05*2 + 480
FV= $528
8[x-y] use x=5 and y=2
Answer:
24
Step-by-step explanation:
Plugin the value of x and y
8[x + y] = 8*[5 - 2]
= 8 *3
= 24
Answer:
24
Step-by-step explanation:
8(5-2)
5-2=3
8 times 3=24
plz can i get brainliest:)
Which value of t makes the two matrices inverses of each other?
Answer:
C) 2
Step-by-step explanation:
I got it right on Edge 2021
The reason is that you can see that on the first matrix a and d are the same number, meaning that a and d on the second matrix need to be the same as well. Brainliest please :)
Ignore grammar and spelling mistakes
Answer: 2
Step-by-step explanation:
PLEASE HELPP !!! it’s due today
Answer:
18
Step-by-step explanation:
please help me with this one
Answer:
A: 112 cubic inches
Step-by-step explanation:
A = l*w*h/3 = (6*8*7)/3
A = 336/3
Help please fast and don’t say files
From a horizontal distance of 80.0m the angle of elevation to the top of the flagpole is 18 degrees calculate the height of the flagpole
Answer:
The figure is omitted--please sketch it.
Set your calculator to Degree mode.
tan(18°) = h/80
h = 80tan(18°) = about 25.994 feet
The height of the flagpole is about 25.994 meters (about 26 meters).
Nelson LLC, has earnings before interest and taxes of €10,350 and net income of €2,528.50. The tax rate is 25%. What is the interest coverage ratio (times interest earned)?
A) 0.62
B) 0.96
C) 1.04
D) 1.48
The interest coverage ratio (times interest earned) for Nelson LLC is approximately 1.04, option C.
The interest coverage ratio is calculated by dividing earnings before interest and taxes (EBIT) by the interest expense. EBIT represents the operating income of the company before deducting interest and taxes.
Given the values:
EBIT = €10,350
Net Income = €2,528.50
Tax Rate = 25%
To calculate the interest expense, we subtract the net income from the EBIT and multiply it by (1 - tax rate):
Interest Expense = (EBIT - Net Income) × (1 - Tax Rate)
= (€10,350 - €2,528.50) × (1 - 0.25)
= €7,821.50 × 0.75
= €5,866.12
Now, we can calculate the interest coverage ratio by dividing EBIT by the interest expense:
Interest Coverage Ratio = EBIT / Interest Expense
= €10,350 / €5,866.12
≈ 1.04
Therefore, the interest coverage ratio for Nelson LLC is approximately 1.04, indicating that the company's earnings before interest and taxes are 1.04 times greater than its interest expense.
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Please help! I'm not sure how to do these.
Answer:
i dont know bro
Step-by-step explanation:
construct a rhombus with a 15 degree angle and sides equal to r.
Answer:
7uwwjwjwjwjai9qiwjwwiwjb2wuw8ejvewusikwvww
The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if the average exam score will be higher for students who are given colored pens on the first day of class. The final exam scores for the 17 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 78, 74, 89, 76, 92, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78 What can be concluded at the 0.05 level of significance
Answer:
There is not enough evidence to support the claim that average score for those given colored pen is greater than 77
Step-by-step explanation:
Given the data : 75, 78, 74, 89, 76, 92, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78
Using calculator :
Sample mean, xbar = 79.06
Sample standard deviation = 9.85
Sample size, n = 17
H0 : μ = 77
H1 : μ > 77
The test statistic : (xbar - μ) ÷ (s / sqrt(n))
(79.06 - 77) ÷ (9.85 / sqrt(17))
2.06 ÷ (9.85 / sqrt(17))
= 0.8623
The Pvalue from Tscore :
Pvalue = 0.20063
Since pvaue is > α ; we fail to reject the null ` There is not enough evidence to support the claim that average score for those given colored pen is greater than 77
Q6 What is the greatest number of parts of a circle What's the greatest number that can be formed by cutting the circle with 7 straight cuts? (NOTE: the parts do NOT have to be equal in size)
A) 14
B) 21
D) 29
C) 27
Porter read 20% of the Star Wars book. He read 8 pages of the book. Write the number of pages in the Star Wars book
Answer: 40 pages in total
Explanation: Porter has read 20% of the book and this translates to 8 pages of the book.
20% = 8 pages
Assume the total number of pages is x:
20% * x = 8
0.2x = 8
x = 8 / 0.2
x = 40 pages in total
Answer:
40 pages in the book
Step-by-step explanation:
8/40 = .20
PLEASE HELP! I need this asap
Answer:
5.17
Step-by-step explanation:
just at 10 pecent
Answer:
I think that the third one is the correct answer , $4.94 i mean .
Help please me thanks
Answer:
option 1:a+12
Step-by-step explanation:
add 12 to a
Tong loaned Jody $50 for a month. He charged 5% simple interest for the month. How much did Jody have to pay Tong?
Answer:
$50(1.05) = $52.50
Jody had to pay $52.50 to Tong for the month.
does anybody know the answer?
Answer:
y+48=90
y= 90-48
y= 42
Step-by-step explanation:
ok
by using the property
sum of two opposite interior angles of triangle is equal to exterior angle