P. 4. Evaluate the double integral by change of variables Sin ()dA. - 2 + y where R is the triangle region with vertices (0,0),(0,1), and (1,0).
Answers
The double integral of Sin (θ)dA over the region R can be evaluated by using the change of variables u = y-x and v = x.
The given region R is a right-angled triangle with vertices at (0,0), (0,1), and (1,0). To evaluate the double integral ∬R Sin (θ)dA, we can use a change of variables u = y-x and v = x.
First, we need to find the Jacobian of the transformation. The Jacobian is given by:
|∂u/∂x ∂u/∂y|
|∂v/∂x ∂v/∂y|
Evaluating the partial derivatives, we get:
| -1 1|
| 1 0|
The determinant of this matrix is |-10 - 11| = -1, so the Jacobian is -1.
Next, we need to find the limits of integration in terms of u and v. The line y = x intersects the sides of the triangle at (0,0) and (1,1), so the limits of integration for v are from 0 to 1. The line y = 1-x intersects the sides at (0,1) and (1,0), so the limits of integration for u are from -v to 1-v.
Substituting u = y-x and v = x, and using the Jacobian, we have:
∬R Sin (θ)dA = ∫∫T Sin (θ)|J|dudv
where T is the region in the uv-plane corresponding to the triangle R in the xy-plane.
Substituting u = y-x and v = x, we have:
Sin (θ)|J| = Sin (θ)
and
dA = dudv
So, the double integral becomes:
∬R Sin (θ)dA = ∫∫T Sin (θ) dudv
where the limits of integration are v from 0 to 1 and u from -v to 1-v.
Evaluating the integral, we get:
∬R Sin (θ)dA = ∫0^1 ∫-v^1-v Sin (θ) dudv
= ∫0^1 (-Cos(θ) + 1) dv
= -Cos(θ)/2 + 1/2
Therefore, the double integral of Sin (θ)dA over the region R is equal to -Cos(θ)/2 + 1/2.
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Related Questions
What integer describes a loss of 17 yards?
Answers
Given:
Loss of 17 yards.
To find:
The integer for given situation.
Solution:
Integers are the complete numbers without a decimal or fractional value. Integers can be positive, negative or zero.
Zero : No change.
Negative integers : Decrease in any value.
Positive integers : Increase in any value.
Loss of 17 yards means decrease in value by 17 yards.
So, required integer for the situation is -17. Here, negative sign is used for decrease in yards.
Therefore, the required integer is -17.
Lorna has $60 and her sister has $120. Lorna saves $7 per week, and her sister saves $5 per week. Which equation and solution represent the number of weeks, w, it will take for the girls to have
the same amount of money?
A 60w + 7 = 120w +5; = 30
7w +60 = 5x + 120; = 30
70 - 60 - 5w -- 120; = 30
B
©
D
Not here
Answers
Answer:
b
Step-by-step explanation:
Select the correct answer. What is the solution to 4|x − 3| + 1 = 1?
Answers
Answer: 2x + 4 = 10 is your answer :)
Step-by-step explanation:
Answer:
x = 3 is your answer :3
Step-by-step explanation:
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
Answers
Answer:
the answer is 56.58%
Step-by-step explanation:
The first step is to divide 43 by 76 to get the answer in decimal form:
43 ÷ 76 ≈ 0.5658
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.5658 × 100 = 56.58%
Atile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a
total of $3,000 for 10,000 tiles. The equation y - 3,000 = 0.25(x - 10,000) models the revenue of the tile factory, where
x is the number of tiles and y is the total cost to the customer.
Which function describes the revenue of the tile factory in terms of tiles sold?
What is the flat fee for delivery?
$
Answers
Answer: the first one is C
the second one is B
Answer:
C and B are your answers
Step-by-step explanation:
What is cos 30°? 60° 1 90° 30° V3 O A. v3 O B. 1 O c.
Answers
Answer:
E
Step-by-step explanation:
Cos=Adjacent/hypotenuse
Cos30=rad3/2
The cosine function for Ф = 30 is equivalent to :
cos(30) =√3/2.
What are trigonometric functions?There are six major trigonometric functions as -
Sine(x)Cosine(x)Tangent(x)Cotangent(x)Secant(x)Cosecant(x)We can write the relation between them as -
Sine = 1/cosecantCosine = 1/secantTangent = 1/CotangentAlso the following trigonometry relations hold true -
sin²Ф + cos²Ф = 1
1 + tan²Ф = sec²Ф
1 + cot²Ф = cosec²Ф
Given is a right angled triangle as shown in the image having 60 - 90 - 30 orientation and the measured sides as shown in the image.
We can write the cosine function as -
cosФ = Base/Hypotenuse
cos(30) = √3/2
So, we can conclude that the cosine function for Ф = 30 is equivalent to :
cos(30) =√3/2
Therefore, the cosine function for Ф = 30 is equivalent to :
cos(30) =√3/2.
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Find the inverse of the function y = 2x^2 +2
Answers
It would be
\( \sqrt{ \frac{x - 2}{ 2} } \)
I hope this is what you're looking for!
The formula used to convert degrees Celsius to degrees Fahrenheit is F = 9/5 C +32. Convert 68°F to degrees Celsius. Solve the formula for C, and then use it to convert the temperature. Which is the correct formula and conversion?
(i attached an image)
Answers
Answer:
D
Step by step explanation:
\(F = \frac{9}{5}C + 32\)
The main objective is to isolate C and to make C the subject of the equation:
\(= F - 32= \frac{9}{5} C\)
\(= C = \frac{5}{9} (F - 32)\)
Now substitute the given value of F:
\(C = \frac{5}{9} (68-32)\)
\(=C = \frac{5}{9} (36)\)
\(= C = 20^{o} C\)
Answer:
D. C = 5/9 ( F - 32 ) ; conversion: 68° F = 20° C
What is the solution to this system of equations?
Please help!!
Answers
Answer:
(5,1)
If you use substitution it'll be very easy.
In this case substitute the second equation into the first so you get y+4+y=6. Then simplify and you'll get 2y=2. Then solve for y and you'll get 1. Now plug in the 1 for y into either of the equations. Let's plug it into the second equation. X=1+4. X=5.
Final answer is (5,1).
The solution to the system of equations is x = 5, y = 1
The given system of equations is:
x + y = 6......(1)
x = y + 4......(2)
Substitute the equation x = y + 4 into the equation x + y = 6
y + 4 + y = 6
Collect like terms
y + y = 6 - 4
2y = 2
y = 2/2
y = 1
Substitute y = 1 into equation (2)
x = 1 + 4
x = 5
The solution to the system of equations is x = 5, y = 1
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(5,6), (4,1) and (-4,2)
Answers
Answer:
23 units
Step-by-step explanation:
Let the vertices of the triangle be A(5,6), B(4,1) and C(-4,2)
Perimeter of the triangle = AB + AC + BC
AB = √(5-4)²+(6-1)²
AB = √1²+5²
AB = √1+25
AB = √26
For BC where B(4,1) and C(-4,2)
BC = √(4-+4)²+(1-2)²
BC = √8²+1²
BC = √64+1
BC = √65
For AC where A(5,6) and C(-4,2)
AC = √(5+4)²+(6-2)²
AC = √9²+4²
AC = √81+16
AC = √97
Perimeter = √97 + √26 + √65
Perimeter = 9.85+5.09+8.06
Perimeter = 23
Hence the perimeter of the triangle is approx 23 units
you take a random of twenty ksu students and find that 16 of them have jobs. what is the probability that you would find exactly 16 out of twenty have jobs if the .50 conjectured by the professor was correct? what is the probability that you would find 16 or more have jobs? what will you say to the professor?
Answers
The probability of exactly 16 students having jobs in the sample is 0.204 and the probability of 16 or more students having jobs in the sample is 0.334.
Let X be the number of KSU students with jobs in a random sample of 20 students. Since each student in the sample can be either employed or not employed, X follows a binomial distribution with parameters n = 20 (the sample size) and p = 0.50 (the probability of a student having a job).
To find the probability of exactly 16 students having jobs in the sample, we can use the binomial probability mass function
P(X = 16) = (20 choose 16) * 0.5^16 * 0.5^(20-16) = 0.204
To find the probability of 16 or more students having jobs in the sample, we can use the cumulative distribution function
P(X ≥ 16) = 1 - P(X < 16) = 1 - ∑(i=0 to 15) (20 choose i) * 0.5^i * 0.5^(20-i) = 0.334
Based on the sample data, it appears that the proportion of KSU students with jobs is higher than the professor's conjectured value of 0.50. However, we cannot conclusively reject the professor's conjecture based on a single sample of 20 students.
We would need to conduct a hypothesis test with appropriate statistical significance level to determine if the difference between the sample proportion and the conjectured value is statistically significant or not.
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One of the players scored 13.7 points per game with 4.1 free throw attempts per game. How does this compare to what the model predicts for this player?
Answers
if the player in question scored 13.7 points per game with 4.1 free throw attempts per game, his performance is slightly below what the model predicts.
How to solve the question?
To compare the player's performance to what the model predicts, we need to know the factors that the model considers when making predictions. Depending on the complexity of the model, it may take into account a variety of factors, such as the player's position, age, height, weight, shooting percentage, and team performance.
Assuming that we have a relatively simple model that takes into account the player's shooting percentage and free throw attempts, we can make a rough estimate of how the player's performance compares to what the model predicts.
Let's say that the model predicts that a player with a shooting percentage of 50% and 4 free throw attempts per game would score an average of 15 points per game. If the player in question has a shooting percentage of 45%, we can adjust the prediction accordingly. Using a simple linear regression, we can estimate that the player's expected points per game would be:
Expected points per game = 15 - (50 - 45) * 0.2 = 14
So if the player in question scored 13.7 points per game with 4.1 free throw attempts per game, his performance is slightly below what the model predicts. However, it's important to note that this is just a rough estimate based on a simple model, and there may be many other factors that could affect the player's performance, such as injuries, fatigue, or changes in the team's strategy. Therefore, we should not rely solely on statistical models to evaluate a player's performance, but also consider other factors such as the player's overall contribution to the team and their ability to make key plays in crucial moments.
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Marcus, Shaun, and Tristan each invested into new business. They invested 1 point
a total of $940,000 total. Marcus invested half of the cost. Shaun and
Tristan invested in a ratio of 3:5. How much money did Shaun invest? *
$176,250
$293,750
$352,500
Ch $587,500
Answers
Shaun invested $176,250 into the new business.
Marcus invested half of the $940,000 so the amount that Shaun and Tristan invested is:
= 940,000 / 2
= $470,000
Shaun and Tristan invested in the ratio 3:5.
The amount that Shaun invested is:
= (Ratio of Shaun / Sum of the ratios) x Amount both invested
= (3 / (3 + 5 )) x 470,000
= 3/8 x 470,000
= $176,250
In conclusion, Shaun must have invested $176,250 into the business.
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A parabola can be drawn given a focus of (1, 10) and a directrix of
y = 4. What can be said about the parabola?
Answers
Answer:
The parabola has an absolute minimum and its vertex is located at (1, 7).
Step-by-step explanation:
Since the directrix is below the focus, we infer that parabola has an absolute minimum, where there is a vertex, which is the midpoint of the line segment between (1, 10) and (1, 4). By definition of midpoint, we conclude that vertex is located at (1, 7).
12 x 13 - 8 x 13
What is the answer
Ik i can find this on google im just giving ppl points lol
Answers
Answer:
52
Step-by-step explanation:
156 - 104 = 52
Answer:
52
Step-by-step explanation:
12x13=156 and 8x13=104 so 156-104=52
Update:
if its negative its -52 =0
Have A Great Day!105 in radiu is equa to answer fast
Answers
Answer: I would assume you mean 105 in radius to diameter which would be 210 since diameter is just radius times 2. Otherwise, explain the question more since it's barely legible.
(01.03. 106, 1.08 HC)
for X 31
3*+1-2
A piecewise function f(x) is defined by f(x) = { –X? + x + 2
x2 – 3x+2
for x>1
x>
Part A Graph the piecewise function () and determine the range (5 points)
Part B. Determine the asymptotes of f(x). Show all necessary calculations. (5 points)
Part C. Describe the end behavior of f(x). (5 points)
Answers
Answer:
A) see attached for a graph. Range: (-∞, 7]
B) asymptotes: x = 1, y = -2, y = -1
C) (x → -∞, y → -2), (x → ∞, y → -1)
Step-by-step explanation:
Part AA graphing calculator is useful for graphing the function. We note that the part for x > 1 can be simplified:
\(\dfrac{-x^2+x+2}{x^2-3x+2}=-\dfrac{(x-2)(x+1)}{(x-2)(x-1)}=-\dfrac{x+1}{x-1}\quad x\ne 2\)
This has a vertical asymptote at x=1, and a hole at x=2.
The function for x ≤ 1 is an ordinary exponential function, shifted left 1 unit and down 2 units. Its maximum value of 3^-2 = 7 is found at x=1.
The graph is attached.
The range of the function is (-∞, 7].
__
Part BAs we mentioned in Part A, there is a vertical asymptote at x = 1. This is where the denominator (x-1) is zero.
The exponential function has a horizontal asymptote of y = -2; the rational function has a horizontal asymptote of y = (-x/x) = -1. The horizontal asymptote of the exponential would ordinarily be y=0, but this function has been translated down 2 units.
__
Part CThe end behavior is defined by the horizontal asymptotes:
for x → -∞, y → -2
for x → ∞, y → -1
Dose anyone knows this ?
If so plz help me :)
Answers
The expression is not factorable with rational numbers.
Which means, your answer is: x² − 17n + 70
Suppose the two measures of center are 83.583.5 degrees and 84.684.6 degrees. which of the values is the mean and which is the median? explain your reasoning.
Answers
The mean would be 83.583 and median would be 84.684.
To find out which value is mean and which value is a median we need to first understand the definitions of both the terms. Mean is defined as the sum of all the terms divided by the number of total number of terms present in the list. Median is defined as the middle term of the list when the terms is arranged in the ascending or descending order.
So, according to the values given, mean would be 83.583degrees . Since, we were to calculate the sum of all the values in the list and divide it by the total number of values, we would obtain an average. While when the list is arranged in ascending or descending order, the value in the middle comes out as 84.6degrees .
Therefore, in this case the mean would be 83.583 and median would be 84.684.
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True or False:
It is possible for an integer linear program to have more than one optimal solution.
Answers
True, it is possible for an integer linear program to have more than one optimal solution.
In an integer linear program, the objective is to optimize a linear objective function subject to linear constraints and integer variable restrictions. While it is common for linear programs to have a unique optimal solution, in the case of integer linear programs, it is possible to have multiple optimal solutions.
This occurs when there are multiple feasible solutions that achieve the same optimal objective value. In such cases, any of the feasible solutions that satisfy the optimality conditions can be considered optimal. Therefore, it is true that an integer linear program can have more than one optimal solution.
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A group of friends were working on a student film that had a budget of $1400. They used $168 of their budget on costumes. What percentage of their total budget did they spend on costumes?
Answers
Answer:sup handsome
Step-by-step explanation:
Answer:12%
Step-by-step explanation:
I took the test
HELP PLEASE ILL GIVE BRAINLIST <3
Answers
the weights of oranges growing in an orchard are normally distributed with a mean weight of 8 oz. and a standard deviation of 2 oz. from a batch of 1400 oranges, how many would be expected to weigh more than 4 oz. to the nearest whole number? 1) 970 2) 32 3) 1368 4) 1295
Answers
The number of oranges that are expected to weigh more than 4 oz is:
1400 - (1400 × 0.0228)≈ 1368.
The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.
From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.
\(z = (x - μ) / σ\)
Wherez is the Z-score of the given data point x is the data point
μ is the mean weight of the oranges
σ is the standard deviation
Now, let's plug in the given values.
\(z = (4 - 8) / 2= -2\)
The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.
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A wall has been built in such a way that the top row contains one block, the next lower row contains 3 blocks, the next lower row contains 5 blocks, and so on, increasing by two blocks in each row. How many rows high is the wall if the total number of blocks used was 900 ?
Answers
Answer:
The answer is 30 ROWS.
Step-by-step explanation:
Please give brainlyest
Chi-square distributions that are positively skewed have a research hypothesis that is?
Answers
Answer:
A one tailed test
Step-by-step explanation:
Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.
Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.
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One-Tailed Test
In probability theory and statistics, the chi-square distribution with k degrees of freedom is the distribution of the sum of squares of k independent standard normal random variables. The chi-square distribution is a continuous probability distribution. The shape of the chi-square distribution depends on its degrees of freedom k. It is used to describe the distribution of the sum of squares of random variables. The chi-square distribution is positively skewed, with decreasing skewness as the degrees of freedom increase. The chi-squre distribution approaches the normal distribution on increase of degree of freedom.Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.
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Gerard concluded that the triangle with sides feet, 8 feet, and cannot be used as a building frame support on the house because it is not a right triangle. How did gerard come to that conclusion? explain.
Answers
Gerard concluded that triangle with given sides cannot be used as building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.
In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,
So, the squares of the given sides are :
Square of √95 feet = (√95)² = 95 feet
Square of 8 feet = 8² = 64 feet
Square of √150 feet = (√150)² = 150 feet
We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,
Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.
Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.
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The given question is incomplete, the complete question is
Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.
Previous Answers Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y-tan-x, y-3, and x-0 about the line y-3. tan(2x)2x dx 0
Answers
To set up an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3, we use the formula V = π∫a b[(R(x))^2 - (r(x))^2]dx, where R(x) and r(x) are the radius of the outer and inner circle respectively.
For this problem, a = 0 and b = 2 since the region is in the first quadrant. We can calculate the radii of the inner and outer circle by substituting in the boundaries of the region:
R(x) = 3 - tan(x)
r(x) = 3 - 3 = 0
So, the integral to calculate the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3 is:
V = π∫02[(3 - tan(x))^2 - 0]dx
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3.7.6 (Model of an epidemic) In pioneering work in epidemiology, Kermack and McKendrick (1927) proposed the following simple model for the evolution of an epidemic. Suppose that the population can be divided into three classes: x(t) number of healthy people; y(t) number of sick people; z(t) number of dead people. Assume that the total population remains constant in size, except for deaths due to the epidemic. (That is, the epidemic evolves so rapidly that we can ignore the slower changes in the populations due to births, emigration, or deaths by other causes.) Then the model is kxy kxy where k and l are positive constants. The equations are based on two assump- tions (i) Healthy people get sick at a rate proportional to the product of x and y. This would be true if healthy and sick people encounter each other at a rate propor- tional to their numbers, and if there were a constant probability that each such encounter would lead to transmission of the disease. (ii) Sick people die at a constant rate l The goal of this exercise is to reduce the model, which is a third-order system, to a first-order system that can analyzed by our methods.
Answers
The Kermack and McKendrick model of an epidemic proposes that the population can be divided into three classes: healthy, sick, and dead. The total population remains constant in size, except for deaths due to the epidemic. The model is kxy, where k and l are positive constants. The equations are based on the assumptions that healthy people get sick at a rate proportional to the product of x and y, and sick people die at a constant rate l.
The given model consists of three variables: x(t), y(t), and z(t), representing the number of healthy, sick, and dead people, respectively, in a population. The model has two assumptions:
1. Healthy people get sick at a rate proportional to the product of x and y (kxy).
2. Sick people die at a constant rate l.
We are given the following system of equations:
dx/dt = -kxy
dy/dt = kxy - ly
dz/dt = ly
Now, our goal is to reduce this third-order system to a first-order system that can be analyzed by our methods.
First, we notice that the total population N is constant except for deaths due to the epidemic, so we have:
N = x(t) + y(t) + z(t)
Since the total population remains constant (ignoring deaths due to the epidemic), we have:
dN/dt = dx/dt + dy/dt + dz/dt = 0
Substituting the given equations into the equation above, we get:
(-kxy) + (kxy - ly) + ly = 0
Notice that the terms involving kxy and ly cancel each other out. As a result, the system of equations is already reduced to a first-order system:
dx/dt = -kxy
dy/dt = kxy - ly
Now you can analyze this first-order system using the appropriate methods for first-order differential equations.
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Help?????? Does anyone know the answer to this
Answers
Because 10% would give you 30ml, and 15% would equal 20ml to get 50ml, according to the equation.
Question 5 The equations N1 /dt = r1N1 [(K1 - N1 - ON2)/K1] and ON2/dt = r2N2 [(K2 - N2 - BN1)/K2] describe the models for the
Answers
The equations N1/dt = r1N1[(K1 - N1 - ON2)/K1] and ON2/dt = r2N2[(K2 - N2 - BN1)/K2] describe models for population dynamics. These models are used to understand how populations of organisms change over time, based on factors like birth rates, death rates, and available resources.
In these equations, N1 and N2 represent the population sizes of two interacting species. The variables r1 and r2 are the intrinsic growth rates of these species, or the rates at which they reproduce in the absence of limiting factors. K1 and K2 represent the carrying capacities of the environment for each species, or the maximum population sizes that can be sustained by available resources.
The terms ON2 and BN1 represent the effects of interspecific interactions on population growth. ON2 refers to the negative impact of species 2 on the growth rate of species 1, and BN1 refers to the negative impact of species 1 on the growth rate of species 2. These interactions can take many forms, such as competition for resources or predation.
By manipulating these equations, scientists can make predictions about how populations will change over time, and test these predictions against real-world data. These models are particularly useful for understanding how species interact in complex ecosystems, and how human activities like habitat destruction and climate change are affecting these ecosystems.
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