The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.
What is the equation of the line tangent to a given curve?
Herein we have a rational function, of which we must derive the equation of the line tangent to the curve at a given point. First, find the first derivative of the function by derivative rules:
f'(x) = [(6 · x + 6) - 6 · (x - 9)] / (6 · x + 6)²
f'(x) = 60 / (6 · x + 6)²
Second, evaluate the first derivative of the function:
f'(11) = 60 / (6 · 11 + 6)²
f'(11) = 5 / 432
This value represents the slope of the tangent line.
Third, calculate the y-value of the curve:
f(11) = (11 - 9) / (6 · 11 + 6)
f(11) = 1 / 36
Fourth, determine the intercept of the tangent line:
b = 1 / 36 - (5 / 432) · (11)
b = - 43 / 432
The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.
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Person A leaves his home to visit his cousin, person B, who lives 78 miles away. He travels at an average rate of 50 miles per hour. One half-hour later, person B leaves her house to visit person A, traveling at a
average rate of 56 miles per hour. How long after person B leaves will it be before they meet?
Answer:
[tex]\frac{1}{2}[/tex] hour later
Step-by-step explanation:
Since Mr.A has already traveled 25 miles there are 53 miles left to person B's house. In half an hour, Mr. A will have traveled 25 miles, while person b will have traveled 28. 25 + 28 = 53.
When six times a number is decreased by 8
the result is 16. What is the number?
Answer: 24
Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16
Kiki And her friends want to go bowling on Friday night but can't decided where to go.Main event charges $3 for bowling shoe rental and $10 per bowling.MaxBowl charges $6 to run bowling shoes and $9 per bowling game.Write and solve an equation that shows how many games can be played for about places to cost the same.
The games that can be played for about places to cost the same is 3 games.
How to calculate the equation?Let the number of games be represented by b.
The event charges $3 for bowling shoe rental and $10 per bowling. This can be represented as:
= 3 + 10b
MaxBowl charges $6 to run bowling shoes and $9 per bowling game. This will be:
= 6 + 9b
We will equate them together:
3 + 10b = 6 + 9b
Collect like terms
10b - 9b = 6 - 3
b = 3
Therefore, the games that can be played for about places to cost the same is 3 games.
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Which equation represents the ellipse with vertices located at (3,-3) and (3,-13) and foci at (3,-5) and (3,-11)?
The equation of the ellipse in standard form is equal to (y + 8)² / 25 + (x - 3)² / 16 = 1. (Correct choice: D)
How to derive the equation of an ellipseIn this problem we find the case of an ellipse whose center is located at a point distinct of the origin and whose major semiaxis is parallel to the y-axis. The standard form of the equation of the ellipse is:
(y - k)² / a² + (x - h)² / b² = 1
Where:
(h, k) - Center of the ellipse.a - Length of the major semiaxis.b - Length of the minor semiaxis.First, determine the coordinates of the center:
(h, k) = 0.5 · (3, - 3) + 0.5 · (3, - 13)
(h, k) = (3, - 8)
Second, calculate the length of the minor semiaxis:
a = 0.5 · [- 3 - (- 13)]
a = 5
c = 0.5 · [- 5 - (- 11)]
c = 3
b = √(a² - c²)
b = 4
Third, substitute all the parameters in the standard formula:
(y + 8)² / 25 + (x - 3)² / 16 = 1
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SUBTRACT
5 2/5 - (-2 4/15)
Answer:
7.66666666667
Step-by-step explanation:
I looked it up
If your total from grocery shopping is 36.73 what would be the final cost with sales tax (3.5%)?
Answer:
$38.02
Step-by-step explanation:
$36.73 × 1.035 = $38.02 (after rounding to two decimal places)
A laptop has a listed price of $885.98 before tax. If the sales tax rate is 7.5%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
The total cost of the laptop including tax will be $952.43.
Step-by-step explanation:
885.98 x 7.5%= $66.45
885.98 + 66.45= $952.43
Hope this helps!
Please help with the math problem
Answer:
C
Step-by-step explanation:
For this problem you use the distributive property
the first expression should match the second
Write the five smallest integers that are greater than the number -3.1
Which are numbers are rational?
Answer: D, E, A
Step-by-step explanation: By friend got rejected by them hopefully you don't.
Answer:
F, C, and D
Step-by-step explanation:
PLEASE PLEASE HELP Explain how to find the average value of a function and contrast this with finding the average rate of change
The average value of function can be calculated using the formula →
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex] and to find average rate of change of function can be calculated using → f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex].
We have a function (say f(x)).
We have to find the average value of a function and the average rate of change of function.
What is a function in Mathematics?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question -
PART - A → Finding the Average value of a function.
The average (or the mean) value of f (x) on [a, b] is defined by -
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]
PART - B → Finding the Average Rate of Change of a function.
The average rate of change of function f(x) is found out as follows -
f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex]
Hence, to find the average value of function -
[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]
and to find average rate of change of function -
f '(x) = [tex]$\frac{f(b)-f(a)}{b-a}[/tex].
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Diberi jumlah nilai bagi empat nombor genap berturut-turut ialah 60,cari nombor terbesar.
A.18
B.20
C.22
D.24
Answer:
A
Step-by-step explanation:
Answer: A. 18
Step-by-step explanation:
Let the smallest number be x
Hence,
x+(x+2)+(x+4)+(x+6)=60
x+x+2+x+4+x+6=60
4x+12=60
4x+12-12=60-12
4x=48
Divide both parts of the equation by 4:
x=12
x+6=
12+6=
18
FUNDRAISING The sophomore class is making blakets for the local animal shelter. The cost to make the blakets can be modeled by 0. 2x^2 + 7.2x + 78 where represents the number of blankets. Find how many blankets the sophomore class can make if they have $663 to spend on supplies.
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
How to illustrate the information?It should be noted that from the information, tje sophomore class is making blakets for the local animal shelter and the cost to make the blakets can be modeled by 0.2x² + 7.2x + 78.
Therefore, the number of blankets the sophomore class can make if they have $663 to spend on supplies will be illustrated as:
C = 0.2x² + 7.2x + 78.
0.2x² + 7.2x + 78 = 663
0.2x² + 7.2x = 663 - 78
0.2x² + 7.2x - 585 = 0
Using almighty formula, it should be noted that x will be 69.
The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.
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What is the slope of the line that passes through the points (6, -5) and (-6, -5)? What is the simplest form
The slope of the line for which the line passes through the points (6, -5) and (-6, -5) is zero .
The slope of a line is outlined because the amendment in y coordinate with relation to the amendment in x coordinate of that line. net amendment in y coordinate is Δy, whereas net amendment within the x coordinate is Δx. The slope of a line will be calculated victimisation 2 points lying on the line. Given the coordinates of the 2 points, we will apply the slope of line formula m = y₂ - y₁ / x₂ - x₁ where (x₁ , y₁) are the coordinate of the first point and (x₂ , y₂) are the coordinate of the second point .We have given two points (6, -5) and (-6, -5) .
Using slope formula , we get
m = - 5 - (-5) / - 6 - 6
m = - 5 + 5 / -12
m = 0 / 12
m = 0
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Are 1/2 and 9/3 integers, rationals or irrational numbers
The number 1/2 is a rational number and the number 9/3 is an integer rational number.
What is a rational number?They are referred to as rational numbers if the value of a numerical expression terminates, in which case they are a rational number, and as irrational numbers if the value of the expression does not terminate.
The numbers are given below.
1/2 and 9/3
The fraction numbers are converted into decimal numbers. Then we have
1/2 = 0.5
9/3 = 3
The number 1/2 is a rational number and the number 9/3 is an integer rational number.
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10. Trent earns scores of and on three chapter tests for a certain class. His homework grade is and his grade for a class project is. The overall average for the course is computed as follows: the average of the three chapter tests makes up of the course grade; homework accounts for the grade; the project accounts for, and the final exam accounts for. What scores can Trent earn on the final exam to pass the course if he needs a "C" or better? A "C" or better requires an overall score of or better and is the highest score that can be earned on the final exam. Assume that only whole-number scores are given.
Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.
What is the missing information?The complete problem is given as follows:
"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.
His homework grade is 68 and his grade for a class project is 64.
The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.
What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?
A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."
What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
For this problem, we have that:
The average of the three chapters is of (62 + 86 + 80)/3 = 76, with a weight of 0.5.Homework grade of 68, with a weight of 0.1.Class project grade of 64, with a weight of 0.2.Final exam grade of x, with a weight of 0.2.Hence his weighted mean is given by:
76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.
For a grade C, he needs a score of at least 70, hence:
57.6 + 0.2x ≥ 70.
0.2x ≥ 12.4
x ≥ 12.4/0.2
x ≥ 62.
Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.
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In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 6000 students
participated in the poll, how many chose Red?
Green 11%
Orange
7%
Blue
11%
Red
36%
Purple
23%
Pink
12%
What company has the absolute advantage when it comes to producing phones?
a. Gonzalez and Bros. Inc
b. The G company Inc
c. they both do
d. neither
The company which has the absolute advantage when it comes to producing phones is: a. Gonzalez and Bros. Inc.
What is a comparative advantage?A comparative advantage can be defined as the ability of a business firm or country to produce goods and services at a lower opportunity cost than their rivals (competitors) or trade partners.
What is an absolute advantage?An absolute advantage can be defined as a measure of the ability of an individual or a business firm (manufacturer) to perform a specific economic activity such as the production of goods and services, more efficiently than another individual or business firm.
In this scenario, we can reasonably infer and logically deduce that the company which has the absolute advantage when it comes to producing phones is Gonzalez and Bros. Inc because it can produce 300 phones in comparison with the G company Inc.
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A football is punted from a starting height of 3ft. With an initial upward velocity of 40 ft/sec. Will the football ever reach a height of 30ft? please explain step by step
Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
How to determine if the ball will ever reach a height of 30 ft?To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.
What is the maximum height of the ball?Using the equation of motion, v² = u² - 2gh where
v = speed of ball at maximum height = 0 ft/s(since it stops momentarily), u = initial vertical velocity of ball = 40 ft/s, g = acceleration due to gravity = 32 ft/s² and h = maximum height of ball from starting point.So, making h subject of the formula, we have
h = (v² - u²)/-2g
Substituting the values of the variables into the equation, we have
h = (v² - u²)/-2g
h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)
h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)
h = - 1600 ft²/s²/-64 ft/s²
h = 25 ft
Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h
= 3f + 25 ft
= 28 ft
So, we see that H = 28 ft < 30 ft.
Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.
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Diego makes an open-top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard is 15 inches by 15 inches. The volumeV(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts.
The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
and side of length x in inches of the square cutouts is
V(1) = 15 - 2 = 13
x ∠ 7.5
The vertical sides were 15 inches before we cut out the corners.
The horizontal sides were 15 inches before we cut out the corners.
So now, if you fold all of the "tabs" up, you get a box that has a height of "x".
The sides are now each missing a length of "x" from each end.
So the longer edges of the box are now (15 - 2x) long.
The shorter edges of the box are now (15 - 2x)
The volume of a box is given by V = (length)(width)(height)
length = 15 - 2x
width and height of the box are equal to x in so
Multiply these together and get:
V(x) = (15 - 2x)(x)(x)
V (x) = (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
let x = 1
V (x) = (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
V(1) = 15 - 2 = 13
First x must be greater than 0,
then, we have 2x ∠ 15
x ∠ 7.5
therefore, The volume V(x) in cubic inches of the open-top box is (15[tex]x^{2}[/tex] - 2[tex]x^{3}[/tex])
side of length x in inches of the square cutouts is
V(1) = 15 - 2 = 13
x ∠ 7.5
This unit has two parts:
The surface area of a box, and its volume
The length of the diagonal of a box
Each student should bring an empty cereal box (or some other box) to work on. (The length, width, and height of the box should all be different.)
Formula for the area of the surface
(a) If l, w, and h are the length, width, and height of a box, its surface area is given by surface area = 2*(l*w + l*h + w*h). (Do you see it?)
(b) Measurements
Measurements are made in inches and sixteenths of an inch, but they are recorded as decimals.
1/8 inch = .125 inch, ¼ inch = .25 inch, 3/8 inch = .375 inch, ½ inch = .5 inch, and so on.
Example:
length l = 8.375 inches
width w = 6.125 inches
height = 2.25 inches
(c) How to enter these measurements into a TI-108 calculator to get the surface area:
8.375*6.125 M+ 51.29…
8.375*2.25 M+ 18.84…
6.125*2.25 M+ 13.78…
MRC * 2 = 167.84… square inches
We round this to 168 square inches (more or less)
Part 1b. We can also find the volume of the box:
volume = l*w*h = 8.375*6.125*2.25 = 115.4… cubic inches
If this were a hands-on unit, we would paper the box with square inch paper and fill the box with cubic inch blocks to see whether our computations are confirmed.
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what is 5 4/5 as in improper fraction
Answer:
29/5
Step-by-step explanation:
5 x 5 +4 = 29
now in fraction form it is 29/5.
Can someone help me with this question? It's due tomorrow :(
The measures of the angles D, F and B are 43°, 105° and 32°, respectively. (Correct choice: C)
What are the values of the missing angles?
Herein we find a geometric system generated by two parallel lines and two lines that pass through the two lines. The values of the missing angles by using triangle properties and concepts of alternating internal angles, supplementary angles and vertical angles. Now we proceed to find the measures of the missing angles:
m ∠ C + m ∠ F + m ∠ D = 180° Sum of the measures of internal angles in a trianglem ∠ D = 180° - 137° = 43° Supplementary anglesm ∠ F = 180° - 32° - 43° = 105° Step 1 / Algebram ∠ F' = 105° Step 3 / Vertical anglesm ∠ B = m ∠ C = 32° Internal alternating anglesTo learn more on angles: https://brainly.com/question/14954407
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Solve the system of equations. Remember: systems with one solution will have an answer in the form of an ordered triplet.
Example: (3, -4, 10)
For systems with infinite solutions or no solutions, write the words ‘infinite solutions’ or ‘no solutions’.
x + 2y -z = 2
2x - 7y + 5z = 3
-4x + y + 2z = 4
The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)
System of Linear EquationsFrom the question, we are to solve the given system of linear equations
The given system of linear equation is
x + 2y - z = 2 ----------- (1)
2x - 7y + 5z = 3 ----------- (2)
-4x + y + 2z = 4 ----------- (3)
From equations (1) and (2), eliminate z
5 × ( x + 2y - z = 2
1 × ( 2x - 7y + 5z = 3
---------------------------------------
5x + 10y -5z = 10
2x -7y + 5z = 3
Add the resulting equations
7x + 3y = 13 ----------- (4)
From equations (2) and (3), eliminate z
2 × ( 2x - 7y + 5z = 3
5 × ( -4x + y + 2z = 4
-----------------------------------
4x - 14y + 10z = 6
-20x + 5y + 10z = 20
Subtract the resulting equations
24x - 19y = -14 ---------- (5)
Now, solve equations (4) and (5) simultaneously
7x + 3y = 13
24x - 19y = -14
Eliminate y
19 × ( 7x + 3y = 13
3 × ( 24x - 19y = -14
---------------------------------
133x + 57y = 247
72x - 57y = -42
Add the resulting equations
205x = 205
x = 205/205
x = 1
Substitute the value of x into equation (4)
7x + 3y = 13
7(1) + 3y = 13
7 + 3y = 13
3y = 13 - 7
3y = 6
c = 6/3
y = 2
Substitute the values of x and y into equation (1)
x + 2y - z = 2
1 + 2(2) - z = 2
1 + 4 - z = 2
1 + 4 - 2 = z
3 = z
z =3
The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)
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identify the postulate or theorem that proves j∥k.
Given: ∠2 and ∠3 are supplementary.
Yes, ∠2 and ∠3 are postulate or theorem that proves the condition is identified as supplementary.
∠1 and ∠2 are supplementary (Linear Pair Theorem)
m∠1 + m∠2 = 180◦ (Definition of supplementary ∠s)
∠1 ≈ ∠3 (Given)
m∠1 = m∠3 (Definition of ≈)
m∠3 + m∠2 = 180◦( Subst . prop . of ≈)
∠2 and ∠3 are supplements (Definition of supplementary ∠s)
An unsubstantiated claim that is assumed to be true is referred to as a postulate. A provable true assertion is referred to as a theorem. A line has at least two points, according to postulate 1. A plane has at least three noncollinear points, according to postulate 2.
Hence, postulate or theorem that proves j∥k and also ∠2 and ∠3 are supplementary.
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What are the coordinates of G after it is REFLECTED OVER THE X-AXIS?
The coordinates of G after it is reflected over the x-axis are (4, -3)
How to determine what are the coordinates of G after it is reflected over the x-axis?The graph represents the given parameter
On the graph, we have the following point
G = (4, 3)
The rule of reflection across the x-axis is
(x, y) = (x, -y)
This means that
G' = (x, -y)
So, we have
G' = (4, -3)
Hence, the coordinates of G after it is reflected over the x-axis are (4, -3)
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Part 1 of 2
The length of a rectangular photograph is 9 in more than the width. If the area is 70 in², what are the dimensions of the photograph?
18
The dimensions of the photograph are the length= 14 in and the width= 5 in.
RectanglesThe rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).
The area of a rectangle is given by the multiplication between the base and the height.
The question gives:
length (base) = 9 + wwidth (height) = warea = 70 in²Thenm
A= b * h
70 = (9 +w) * w
70= 9w +w²
w²+9w-70=0
[tex]w_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \left(-70\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-9\pm \:19}{2\cdot \:1}[/tex]
Thus, [tex]w_{1}=\frac{-9-\:19}{2\cdot \:1}=\frac{-28}{2}=-14[/tex] and [tex]w_{2}=\frac{-9+\:19}{2\cdot \:1}=\frac{10}{2}=5[/tex]
The dimensions should have positive values, then w=5.
If w=5, the length will be 5+9 = 14. With these dimensions, the area will be 14 * 5 = 70.
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If a+2b=11 & a-b=-4 then what is a & b?
Answer:
a = 1
b = 5
Step-by-step explanation:
a + 2b = 11
(a - b = -4) × 2
2a - 2b = -8
------------------------
a + 2b = 11
2a - 2b = -8
-------------------
3a = 3
÷3 ÷3
-----------
a = 1
----------------------------------------------------------------------------------------------------------
a - b = -4
1 - b = -4
-1 -1
---------------
-b = -5
÷-1 ÷-1
-------------
b = 5
I hope this helps!
pless i really need help
Perimeter of the parallelogram = 210 in.
Area of parallelogram = 2,484 in.²
What are the Perimeter and Area of a Parallelogram?Perimeter of parallelogram = 2(a + b), where a and b are its sides.
Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.
Given:
a = 51 in.
b = 54 in.
h = 46 in.
Perimeter of the parallelogram = 2(54 + 51) = 210 in.
Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²
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7(4a-3)-3a{8-2a(1+2a)}
if its solve then we can do it like above
The table shows pricing information for two pizzas. How many toppings would make the cost the same for all pizza
number 13 only
Using linear functions, it is found that 5 toppings would make the cost the same for all pizza.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The cheese pizza price is the intercept.The price per topping is the slope.Hence the cost functions are given as follows:
A(x) = 10 + 1.5x.B(x) = 12.5 + x.The costs will be the same when:
A(x) = B(x)
10 + 1.5x = 12.5 + x
0.5x = 2.5
x = 2.5/0.5
x = 5.
5 toppings would make the cost the same for all pizza.
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