Find the complex zeros of the following polynomial function. Write fin factored form. f(x) = x^4 + 122x^2 + 121
Answers
To find the complex zeros of the polynomial function f(x) = x^4 + 122x^2 + 121, we can use the quadratic formula to solve for x^2:
x^2 = (-122 ± sqrt(122^2 - 4(1)(121))) / 2(1)
x^2 = (-122 ± 2) / 2
x^2 = -60 or -61
Since both solutions are negative, we know that the zeros are complex. We can express them in factored form using the quadratic formula for complex numbers:
x^2 = -60
x = ±sqrt(60)i
x^2 = -61
x = ±sqrt(61)i
Therefore, the complex zeros of f(x) are x = sqrt(60)i, x = -sqrt(60)i, x = sqrt(61)i, and x = -sqrt(61)i. We can express the factored form of the polynomial as:
f(x) = (x - sqrt(60)i)(x + sqrt(60)i)(x - sqrt(61)i)(x + sqrt(61)i)
To find the complex zeros of the polynomial function f(x) = x^4 + 122x^2 + 121, we can first rewrite it as a quadratic equation in terms of y = x^2. This gives us:
y^2 + 122y + 121 = 0
Now, we can solve for y using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 122, and c = 121. Plugging in the values, we get:
y = (-122 ± √(122^2 - 4(1)(121))) / 2(1)
y = (-122 ± √(14884 - 484)) / 2
y = (-122 ± √(14400)) / 2
y = (-122 ± 120) / 2
We get two real solutions for y: y1 = 1 and y2 = -121. Since y = x^2, we can now solve for x by taking the square root of each solution:
x1 = ±√1 = ±1
x2 = ±√(-121) = ±11i
Now, we have four complex zeros: x = 1, x = -1, x = 11i, and x = -11i. In factored form, the polynomial is:
f(x) = (x - 1)(x + 1)(x - 11i)(x + 11i)
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Related Questions
A cell phone company sells about 500 phones each week when it charges $75 per phone. It sells about 20 more phones per week for each$1 decrease in price. The company's revenue is the product of the number of phones sold and the price of each phone. What price should the company charge to maximize its revenue?
Answers
The company can maximize its revenue by charging the price of $73 per phone.
Changing the price and monitoring how many phones are sold in reaction to the price change allows for trial-and-error in determining accuracy.
With 520 phones sold each week at $73, the corporation will make a total of $38,160 in revenue. There are 20 more phones than when it was charging $75, thus the business will make an additional $1,500 every week.
Due to the increased number of phones sold, the corporation may increase revenue by merely $2 by lowering the price, leading to an increase in both total revenue and profit.
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How do you calculate the required sample size for a desired ME (margin of error)?
Answers
Answer: Calculate
Step-by-step explanation: How to calculate the margin of error?
1. Get the population standard deviation (σ) and sample size (n).
2. Take the square root of your sample size and divide it into your population standard deviation.
3. Multiply the result by the z-score consistent with your desired confidence interval according to the following table:
john has walked 15% of the way home from school. if he has walked 54 yards so far, how far does he walk home from school
Answers
Answer: John walks a total of 360 yards from school.
Step-by-step explanation:
Let's represent the total distance John walks from school as "x".
According to the problem, John has already walked 15% of the way, which can be written as:
0.15x
We also know that he has walked 54 yards so far, which means:
0.15x = 54
To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:
x = 54 ÷ 0.15
x = 360
Therefore, John walks a total of 360 yards from school.
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define a function similarity() to calculate the movie taste similarity between two users. similarity is calculated as the ratio
Answers
There is a 13.3% chance that they will both enjoy a randomly selected movie.
The function similarity() is used to calculate the similarity between two users' movie tastes. This similarity is typically measured as a probability, or the likelihood that the two users will both enjoy a particular movie.
To calculate similarity, we first need to define a set of criteria that we can use to compare the two users' movie preferences. This might include things like genre, rating, actor/actress, or director. Once we have our criteria, we can then compare the two users' movie lists and calculate the number of movies that they have in common.
The similarity function can then be defined as the ratio of shared movies to total movies watched by both users. This ratio represents the probability that the two users will have similar tastes in movies.
For example, if User A has watched 50 movies and User B has watched 100 movies, and they both have watched 20 movies in common, then their similarity score would be 20/(50+100) = 0.133. This means there is a 13.3% chance that they will both enjoy a randomly selected movie.
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Find the value of x in the triangle shown below
Answers
Answer:
x = 50
Step-by-step explanation:
Since the 2 legs are congruent, both 7, then the triangle is isosceles and the 2 base angles are congruent, then
x = \(\frac{180-80}{2}\) = \(\frac{100}{2}\) = 50
\(-2\sqrt{50x^5} +5\sqrt{18x^5}\)
Answers
Answer:
234.98
Step-by-step explanation:
in class notes
Find the measure of x.
40
45°
X
x = [?]
X
Round to the nearest tenth.
![Find the measure of x.4045Xx = [?]XRound to the nearest tenth.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/4Ouvx9vQXZc4He557KA2qVtebCwcWIwK.png)
Answers
Answer:
x ≈ 28.3
Step-by-step explanation:
using the cosine ratio in the right triangle
cos45°= \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )
40 × cos45° = x , then
x ≈ 28.3 ( to the nearest tenth )
Given that the sum of squares for treatments (SST) for an ANOVA F-test is 9,000 and there are four total treatments, find the mean square for treatments (MST).
OA. 1,500
OB. 1,800
OC. 3,000
OD. 2,250
Answers
The mean square fοr treatments is 3,000, which cοrrespοnds tο οptiοn OC.
How to find the mean square fοr treatments ?Tο find the mean square fοr treatments (MST), we need tο divide the sum οf squares fοr treatments (SST) by the degrees οf freedοm fοr treatments (dfT).
In this case, the given SST is 9,000 and there are fοur tοtal treatments.
The degrees οf freedοm fοr treatments (dfT) is equal tο the number οf treatments minus 1. Since there are fοur treatments, dfT = 4 - 1 = 3.
Nοw we can calculate the MST:
MST = SST / dfT
= 9,000 / 3
= 3,000.
Therefοre, the mean square fοr treatments (MST) is 3,000.
The mean square fοr treatments is 3,000, which cοrrespοnds tο οptiοn OC.
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A company wants to evaluate the effects of a reduction in material cost of 3 percent and an increase in sales of 15 percent on a product with the following current characteristics: labor costs of $1,250,000, material costs of $5,000,000, overhead of $710,000, and sales of $8,000,000. What are the effects on net income with a 3 percent reduction in material costs? What is the effect with a 15 percent increase in sales?
Answers
The effect on net income with a 3 percent reduction in material costs is a decrease of $150,000. The effect on net income with a 15 percent increase in sales is an increase of $1,200,000.
To calculate the effects on net income, we need to consider the impact of the changes in material costs and sales on the company's financials.
First, let's calculate the effect of a 3 percent reduction in material costs. The current material costs are $5,000,000, so a 3 percent reduction would be 0.03 * $5,000,000 = $150,000. Since material costs are an expense, a reduction in material costs would lead to a decrease in expenses, which in turn would increase net income by the same amount.
Next, let's calculate the effect of a 15 percent increase in sales. The current sales are $8,000,000, so a 15 percent increase would be 0.15 * $8,000,000 = $1,200,000. An increase in sales would directly increase revenue, leading to an increase in net income.
Therefore, the effects on net income with a 3 percent reduction in material costs is a decrease of $150,000, and the effect with a 15 percent increase in sales is an increase of $1,200,000.
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A company estimates that its sales will grow continuously at a rate given by the function s(t) = 11. Where S' (t) is the rate at which sales are increasing, in dollars per day, on dayt a) Find the accumulated sales for the first 6 days, b) Find the sales from the 2nd day through the 5th day. (This is the integral from 1 to 5. ) a) The accumulated sales for the first 6 days is $ (Round to the nearest cent as needed. ) b) The sales from the 2nd day through the 5th day is $ (Round to the nearest cent as needed. )
Answers
din textul 1.
In redactarea compunerii:
vei menţiona două trăsături ale personajului;
4 puncte
6 puncte
vei ilustra două modalități de caracterizare diferite, prin câte o secvență comentată;
vei corela o valoare transmisă prin acest personaj cu una importantă pentru tine, justificându-ți
2 puncte
răspunsul.
Punctajul pentru compunere se acordă astfel:
conținutul compunerii - 12 puncte
redactarea compunerii-8 puncte (marcarea corectă a paragrafelor-1 punct; coerenta textului-1 punct
proprietatea termenilor folosiți-1 punct; corectitudine gramaticalà - 1 punct; claritatea exprimării ideilor -
1 punct; respectarea normelor de ortografie - 1 punct; respectarea normelor de punctuație - 1 punct;
lizibilitate-1 punct).
Notă! Punctajul pentru redactare se acordă doar in cazul în care compunerea are minimum 150 de cuvinte
şi dezvoltă subiectul propus.
5(x+1)-x=x-1 pls help
Answers
Answer:
x=-2
Step-by-step explanation:
5(x+1)-x=x-1
5x+5-x=x-1
4x+5=x-1
3x+5=-1
3x=-6
x=-2
find the multiplier for the rate of exponential growth or decay.
1) 1% growth
Answers
1% growth has a multiplier 1+0.01=1.01
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
The exponential function which models the exponential growth has a form
\(y= C(1+r)^x\)
where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1+r is a multiplier.
The exponential function which models the exponential decay has a form
\(y= C(1-r)^x\)
where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1-r is a multiplier.
Thus,
1. 1% growth has a multiplier 1+0.01=1.01;
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find a 3×3 matrix a whose −2-eigenspace is v={(x,y,z) in r3∣−2x 12y−2z=0} and whose 2-eigenspace is w=span{[30−1]}. a= [
Answers
The desired 3x3 matrix A is:
[ 6, 5, 3],
[ 1, 0, 0],
[ 0, 1, -1]
To find a 3x3 matrix A with the given eigenspaces, we'll first determine eigenvectors for each eigenspace and then construct matrix A using these eigenvectors as columns.
For the -2-eigenspace with equation -2x + 12y - 2z = 0, we can rewrite it as x = 6y - z. Let y = 1 and z = 0, we have the eigenvector v1 = (6, 1, 0). Similarly, let y = 0 and z = 1, we get the eigenvector v2 = (5, 0, 1).
For the 2-eigenspace, we are given w = span{[3, 0, -1]}. This vector is already an eigenvector for the 2-eigenspace, so v3 = (3, 0, -1).
Now, we construct the matrix A using these eigenvectors as columns:
A = [v1 v2 v3] = [(6, 1, 0), (5, 0, 1), (3, 0, -1)]
A = [
[ 6, 5, 3],
[ 1, 0, 0],
[ 0, 1, -1]
]
So, the desired 3x3 matrix A is:
[
[ 6, 5, 3],
[ 1, 0, 0],
[ 0, 1, -1]
]
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Reduce the third order ordinary differential equation y-y"-4y +4y=0 in the companion system of linear equations and hence solve Completely. [20 marks]
Answers
To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:
Let u = y,
v = y',
w = y".
Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:
du/dx = y' = v,
dv/dx = y" = w,
dw/dx = y"'.
Now we can rewrite the given differential equation in terms of u, v, and w:
u - w - 4u + 4u = 0.
Simplifying the equation, we get:
-3u - w = 0.
This equation can be expressed as a system of first-order linear differential equations as follows:
du/dx = v,
dv/dx = w,
dw/dx = -3u - w.
Now we have a companion system of linear equations:
du/dx = v,
dv/dx = w,
dw/dx = -3u - w.
To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.
The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.
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Which of the following best describes the possible values for a chi-square statistic?
a. Chi-square is always a positive whole numbers.
b. Chi-squarc is always positive but can contain fractions or decimal values.
c. Chi-square can be either positive or negative but always is a whole number.
d. Chi-square can be either positive or negative and can contain fractions or
decimals.
Answers
Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.
However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.
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Evaluate 4(a2+2b)-2 when a = 2 and b =-2
Answers
Answer: -2
Explanation 》》》》》》》》》》
4×(2×2+2×-2)-2
=4×(4-4) -2
=4×0 -2
= -2
geometry help please!!
Answers
Answer: 13
Step-by-step explanation:
Equilateral triangle means that all sides are equal
Soo
3x + 1 must be equal to 5x - 9
3x + 1 = 5x - 9
-2x = -10
x = 5
Substitute x as 5 into either side value
3(5) + 1 = 15 + 1 = 16
So, all sides equal 16
Which means that y + 3 also equals 16
y + 3 = 16
y = 13
The shaded area in the distribution below represents approximately 95% of the data. Use the diagram to find the mean and the standard deviation.
Answers
Answer:
85 i guess
Step-by-step explanation:
The mean of the distribution is 70 and the standard deviation of the distribution is 4.
The shaded area in the distribution below represents approximately 95% of the data. This means that the shaded area is equal to 1.96 standard deviations from the mean.
The 68-95-99.7 rule states that 95% of the data in a normal distribution falls within 2 standard deviations of the mean. So, the shaded area in the distribution below represents the area between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.
The mean of the distribution is the center of the shaded area. The standard deviation of the distribution is the distance from the mean to the edge of the shaded area.
In this case, the mean of the distribution is approximately 70. The standard deviation of the distribution is approximately 4.
Here is a step-by-step explanation of how to find the mean and the standard deviation:
Identify the shaded area in the distribution.
Remember that the shaded area represents 95% of the data.
Use the 68-95-99.7 rule to determine that the shaded area is between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.
Find the mean by averaging the two points on the distribution that are 1.96 standard deviations from the mean.
Find the standard deviation by subtracting the mean from one of the points on the distribution that is 1.96 standard deviations from the mean.
Therefore, the mean of the distribution is approximately 70 and the standard deviation of the distribution is approximately 4.
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Anne goes out to lunch every Friday. On average she spends around
$18 each time, How much money can she save in one year if she
stops going out for lunch each week?
Answers
Answer:
$936
Step-by-step explanation:
there are about 52 weeks in a year
18*52=936
Hope this helps!
What is the remainder when f(x) is divided by x-2 given that f(x)=4x^3-2x^2+x-13?
Answers
Answer:
13
Step-by-step explanation:
pick me as the brainliest. thx
Multiply. Write your answer as a fraction or as a whole or mixed number.5710×416=
Answers
Answer:
2,375,360
Step-by-step explanation:
A box with a square base of side \( y \) is five times higher than it is wide. Express the volume \( V \) of the box as a function of \( y \). \[ V(y)= \]
Answers
The volume V of a box having a square base of side y and five times as high as it is wide is to be expressed in terms of y. Now let's see how to express the volume as a function of y.
Most important point to remember while solving the question is that the box has a square base of side y and the height of the box is 5 times the width of the base. The height is, therefore, 5y. So,Volume of the box = (Area of the square base)*(Height of the box) Area of the square base = y^2Height of the box = 5y.
Putting these values in the formula for the volume of the box, we have, Volume of the box, V = (y^2)*(5y) Hence, the required function is: V(y) = 5y^3 The box has a square base of side y. Let the height of the box be h. Then, according to the question: Height of the box, h = 5(width of the box)We know that the base of the box is a square, therefore, Therefore, Volume of the box, V = Area of the square base * Height of the box Area of the square base, A = y^2 Hence, the required function is:V(y) = 5y^3
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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day. Determine the mass of the radioactive sample at the beginning of the 13th day of the experiment. Round to the nearest tenth (if necessary).
Answers
Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.
What is an exponential function?A decaying exponential function is modeled by:
\(A(t) = A(0)(1 - r)^t\)
In which:
A(0) is the initial value.r is the decay rate, as a decimal.At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:
\(A(t) = A(0)(1 - r)^t\)
\(A(t) = 500(1 - 0.08)^t\)
\(A(t) = 500(0.92)^t\)
At the 13th day, the mass is given by:
\(A(13) = 500(0.92)^{13} = 169.1\)
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Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 14 centimeters. The base is half as long as the height.
What area of the notebook does the sticker cover?
Answers
Answer:
The answer is 98 square cm
Step-by-step explanation:
14/2=7
14*7=98
edge lengths are given in units. Find the surface area of each prism in square units
Answers
To find the surface area of a prism, we need to add up the areas of all the faces. For a rectangular prism, we have two congruent rectangular faces and four congruent rectangular faces. The area of each rectangular face is simply length times width, so for a rectangular prism with edge lengths a, b, and c, the surface area is 2ab + 2bc + 2ac.
This formula gives the total surface area of the prism in square units. Make sure to substitute the given edge lengths into the formula and simplify the expression to get your final answer in square units. To find the surface area of a prism with given edge lengths in units, you need to first identify the type of prism (e.g., rectangular, triangular, etc.).
Then, determine the areas of each face by multiplying the edge lengths corresponding to each face. Finally, add the areas of all the faces together to find the total surface area in square units. Remember, the surface area will be expressed in square units.
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since r is so widely used, it is appropriate to calculate r for nonlinear data.true/false
Answers
since r is so widely used, it is appropriate to calculate r for nonlinear data: False.
The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.
In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.
n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.
When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.
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Consider the function f (x) = 2000 (1.10), which models the amount of money in your bank account after investing some money. Part a) Is the money growing or decaying? How do you know? Part b) What is the rate of growth or decay? Part c) What does the 2000 represent?
Answers
The answer of the given question based on the function is , Part(a) The money is growing , Part(b) The rate of growth is 10% per year , Part(c) The 2000 represents the initial investment or starting amount of money.
What is Function?A function is a mathematical concept that describes the relationship between two sets of numbers or variables, called the domain and the range. A function maps each element in the domain to a unique element in the range. In other words, for every input value in the domain, there is only one output value in the range.
Part a) The money is growing because the value of the function f(x) is increasing with respect to x.
Part b) The rate of growth is 10% per year, as indicated by the 1.10 multiplier in the function. This means that for every year that passes, the value of the function will increase by 10% of its current value.
Part c) The 2000 represents the initial investment or starting amount of money that was invested in the account. In other words, if x=0 (i.e., the initial time of investment), then f(0) = 2000, which means the initial amount invested was $2000.
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Which ordered pair is a solution to the following:
Y= -2x + 5
Choose 1 answer:
A: Only (2,-9)
B: Only (-2,9)
C: both
D: neither
Answers
Answer:
Option B: Only (-2, 9)
Step-by-step explanation:
Given the linear equation, y = -2x + 5:
We'll plug in the given options to see which of the ordered pairs will satisfy the equation:
Substitute option A: (2, -9) into the equation:
y = -2x + 5
-9 = -2(2) + 5
-9 = -4 + 5
-9 = 1 (False statement). Therefore, (2, -9) is not a solution.
Substitute option B: (-2, 9) into the equation:
y = -2x + 5
9 = -2(-2) + 5
9 = 4 + 5
9 = 9 (True statement). Therefore, the ordered pair, (-2, 9) is a solution.
The other two options are irrelevant at this point since we've proven that option B is the correct answer.
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Which of the following could be the first sentence in a paragraph proof of the statement below?
If 2x + 5 = 11, then x = 3
(point)
A.The solution of the given statement is 2 = 3.
.BThe solution of the given statement is 23 + 5 = 11.
C.The given statement is x = 3.
D.The given statement is 2x + 5 = 11.
Can someone help me with this asap
Answers
Answer:
D(may not be D for everyone)
Step-by-step explanation:
The given statement is 2x + 5 = 11 :)
A sector with an angle 110° at the centre of a circle is cut away from a circular piece of paper of radius 7cm. the remaining part is folded to forming a cone
1; find the vertical angle
2:the angle of sector
Answers
The required vertical angle and angle of the sector is 110° and the arc length of the sector is 11 cm.
Given that the central angle of the sector is 110° and the radius of the circle is 7 cm.
To find the arc length when central angle (a) and radius (r) of the circle is given by using the formula,
Arc length (A) = a/360 × 2× \(\pi\)× r
The vertical angle is same as the central angle of the sector is 110°.
By using the given data and formula of arc length of the sector gives,
A = 110/360 × 2 × \(\pi\) × 7
By using the value of \(\pi\) = 22/7 in the above equation gives,
A = 11/36 × 2× 22/7 × 7
On simplifying gives,
A = 11/9 × 11
A = 121 / 9 = 13.44.
Therefore, the arc length of the sector is 13.44 cm.
Hence, the required vertical angle and angle of the sector is 110° and the arc length of the sector is 11 cm.
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