The correct option is A which is x=-1/2 is the position of stable equilibrium.
Given in the question,
F=2x²−3x−2
dx/dF = 4x−3<0
x<3/4 for stable equilibrium
x>3/4 for unstable equilibrium
For stable F=0
2x²−3x−2=0
2x²−4x+x−2=0
2x(x−2)+1(x−2)=0
(2x+1)(x−2)=0
x=−1/2 ,x=+2
In the event that a system in equilibrium is disturbed marginally, in the event that it is steady it will in general re-visitation or waver about its unique equilibrium state. An unsteady system will in general keep on getting away from its unique equilibrium state when moved away by it. Consequently, on account of a stable equilibrium, there is a tendency for the item to return to its old position. In an unstable equilibrium again, the balance is temperamental when a slight unsettling influence inspires further unsettling influence, with the goal that the first position is rarely reestablished.
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A train passes through a 360 m long tunnel completely in 24 seconds. It passes through another tunnel 216 m long completely in 16 seconds at the same average speed. Find the length of the train.
The average speed of the train is 18m/sec and the length of the train is 72 m.
let x represent the length of the train.
and 'S' be the speed of the train.
Given, that the train passes through 360 m long tunnel completely in 24 sec.
⇒ 360+x/24 = s
⇒ 24s = 360+x ...eq(1)
And also given that it passes through another tunnel 216 m long completely in 16 sec.
⇒ 216+x/24 = s
⇒ 16s = 216 + x .... eq(2)
⇒ subtract eq(1) from eq(2)
⇒ 24s = 360 + x
16s = 216 + x
8s = 144
s = 18 m/sec
length of the train: 24s = 360+x
24(18) = 360+x
432 = 360+x
x = 432-360
x = 72m
Hence the length of the train is 72 m.
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Select the choice that represents the two-variable equation after it has been solved for y in terms of x.
3(y + 2) - 4x = 0
Answer:
Step-by-step explanation:
3y+6-4x=0
3y-4x=0-6
3y-4x=-6
y-4x=6/3
y-4x=2
y-x=2/4
y-x=0.5
For each equation, find y when x = -6. Then find x when y = 20.
y = 6x +8 solve for y and x
y = 2/3x solve for y and x
y = -x + 5 solve for y and x
y = 6.5x + 7 solve for y and x
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
What is Equation?Two or more expressions with an Equal sign is called as Equation.
For equation y = 6x +8
When x=-6
y=6(-6)+8=-36+8=-28
when y =20
20=6x+8
28=6x
x=28/6=14/3
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
For equation y = 2/3x
When x=-6, y=2/3(-6)=-4
y=20, 20=2/3x
60=2x
x=30
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
For equation y = -x + 5
When x=-6, y=6+5=11
When y=20,
20=-x+5
15=-x
x=-15
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
For equation y = 6.5x + 7
When x=-6
y=6.5(-6)+7
y=-39+7=-2
When y=20
20=6.5x+7
13=6.5x
2=x
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
Hence,
x=14/3 and y=-28 when x = -6. and y = 20 for equation y = 6x +8
x=30 and y=-4 for when x = -6. and y = 20 for equation y = 2/3x
x=-15 and y=11, when x = -6. and y = 20 for equation y = -x + 5
x=2 and y=-2 , when x = -6. and y = 20 for equation y = 6.5x + 7
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help please and thankyou
The ratio that can be used to find x is sin 21 = x/22.
What are the trigonometric ratios?The trigonometric ratios are the ratios that we can use to obtain the sides and the angles that are in a right angled triangle. The term right angled triangle has to do with a triangle that has one of its angles as 90 degrees.
Now;
Given that;
Sin θ = opposite/hypotenuse
opposite = x
hypotenuse = 22
θ = 21 degrees
It now follows that to obtain the side x we have to use;
sin 21 = x/22
Hence, in looking for the side x, we have to use sin 21 = x/22
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Fill in the table using this function rule.
y=-5x+1
X
-2
0
2
4
y
0
0
0
0
Start over
S
Answer:
x y
-2 -9
0 1
2 -9
4 -19
explanation:
you simply replace the x with the figure given in the x table or columns or rows
Answer:
so -2024y0000 division is s
A polygon has 7 sides. The interior angle measures are 130°, 118°, 135°, 128°, 126°, 134°, and x°. Find the value of x.
Answer:
129 degrees.
Step-by-step explanation:
The Sum of all the interior angles of an a-sided polygon is always (n−2) × 180 degrees.
As this is a seven-sided polygon, the sum of its interior angles is (7−2) × 180 degrees = 5 × 180 degrees = 900 degrees.
Step 1: Find the sum of six of the angles is 130 degrees, 118 degrees, 135 degrees, 128 degrees, 126 degrees, and 134 = 771 degrees
Hence the seventh angle is x = 900 degrees − 771 degrees= 129 degrees.
The car makes one complete rotation about its circuit
every 36 minutes, at a fairly constant rate. Through how
many degrees would the car, which starts from its original
position, drives by the circuit from 8:00 AM to 3:00 PM,
on the same day.
8 AM to 3 PM is 7 hours = 420 mins
Find how many rotations:
420 / 36 = 11.66666 rotations
Using ratio
1 rotation : 360 degrees
11.66666 : x degrees
x = 11.66666 / 1 * 360 = 4200 degrees
Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplified expression to represent the number of members this year. Enter your answer in the box.
m
The simplified expression to represent the number of members this year is 1.15m
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, the membership in the volunteers Club increased by 15% from last year. If the number of members last year was m.
The number of members will be:
= Old members+ Increase in members
= m + (15% × m)
= m + 0.15m
= 1.15m
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Does the quadratic function
f(x) = 5x² + 5x + 21 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.
Answer:
No real zeros.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Discriminant of the Quadratic Formula}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\When $b^2-4ac > 0 \implies$ two real zeros.\\When $b^2-4ac=0 \implies$ one real zero.\\When $b^2-4ac < 0 \implies$ no real zeros.\\\end{minipage}}[/tex]
The value of the discriminant shows how many zeros the function has.
Given quadratic function:
[tex]f(x)=5x^2+5x+21[/tex]
Therefore:
a = 5b = 5c = 21Substitute the values into the discriminant and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(5)^2-4(5)(21)\\& = 25 - 20(21)\\&=25-420\\&=-395\end{aligned}[/tex]
Therefore, as -395 < 0, there are no real zeros.
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer and Explanation:
m∠1 = 43° because opposite angles are congruent
m∠2 = 137° because ∠2 and 43° are supplementary, so m∠2 + 43° = 180°
m∠3 = 137° because opposite angles are congruent, so m∠3 = m∠2
m∠5 = 43° because alternate angles are congruent
m∠6 = 137° because ∠5 and ∠6 are supplementary, so 43° + m∠6 = 180°
m∠7 = 137° because alternate exterior angles are congruent, so m∠7 = m∠2
m∠8 = 43° because alternate exterior angles are congruent, so m∠8 = m∠1
Answer:
angle 1: 43
angle 2: 137
Step-by-step explanation:
Lets find angle 1 first :)
Since oposite diagonal angles are the same, this will make angle 1 43 degrees :)
Now lets find angle 2!
Since 1 was 43 degrees, and a flat line is 180 degrees we must subtract!
Lets do that now!
180 - 43 = 137
Angle 2 will be 137 degrees!
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Can someone tell me the answer piz •_•
The function f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex] end behavior is As, x → infinity , f(x) → - infinity ; as x → - infinity , f(x) → infinity .
Given,
The function is given as:
f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex]
To find the bend behavior of f(x)
Now, According to the question:
Based on the given condition:
Analyze the end behavior of
f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex]
As, x → infinity , f(x) → - infinity ;
as x → - infinity , f(x) → infinity .
Hence, The function f(x) = -[tex]5x^5 -5760-2880x+520x^2+260x^3-10x^4[/tex] end behavior is As, x → infinity , f(x) → - infinity ; as x → - infinity , f(x) → infinity .
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60 POINTS FOR FULL CORRECT ANSWER!!!!! I NEED IT NOW!!!!!
Whose sequence proves trapezoid PQRS is similar to trapezoid KLMN? Why?
THE ACTIVITY IS : Unit Activity: Transformations
What is the answer
The question is what is the equation of line a and then b
Find the angle x using circle theorem
Hey there! I explained and wrote everything on paper since it's hard to type so you can view the pic uploaded! Hope it helps, if you have any doubts, please feel free to ask :)
The equation of a line is y = -3x – 2. What are the slope and the y-intercept of the line?
A.
slope = -3 and y-intercept = 2
B.
slope = 3 and y-intercept = -2
C.
slope = 3 and y-intercept = 2
D.
slope = -3 and y-intercept = -2
Answer:
D
Step-by-step explanation:
The slope if before the x so in this case it's -3.
The y-intercept is at the end so it's -2.
Answer:
D. slope = -3 and y-intercept = -2
Step-by-step explanation:
Slope Intercept Form:
y - y₁ = m(x - x₁) (original version)y = mx + b (simplified version)The variables:
m ⇒ represents slopeb ⇒ represents the y-intercepty = -3x -2
m = -3b = -2which of the following can be classified as data reduction techniques? a. cluster analysis b. sampling c. data visualization d. none of the above
The answer of the question is A. Cluster Analysis
Data reduction is a stage of qualitative data analysis techniques. Data reduction is simplification, classification, and unnecessary hoarding of data in such a way that the data can produce meaningful information and facilitate drawing conclusions.
Data reduction is done to provide more specific representation and make it easier for researchers to collect data then look for additional data if needed.
Various dimension reduction methods are used to reduce the complexity of data before further processing. One of data reduction techniques is Cluster Analysis. Cluster analysis is used to group or classify data with various types, for example in types according to the concept, and certain categories according to the research being conducted.
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Given the ordered pair (-5, 4), name the coordinates after a rotation of 90° counter-clockwise.
Answer:
(-5,-4)
as 90 degree rotation counter clockwise would land in the third quaderant where both x and y are negative
Which graph shows the solution to the system of linear inequalities?
y < 2x – 5
y > –3x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
The graph of the system of inequalities can be seen in the image at the end.
How to get the graph of the system of inequalities?
Here we have the following system of inequalities:
y < 2x - 5
y > -3x + 1
So first we need to graph the two lines:
y = 2x - 5
y = -3x + 1
With dashed lines (because the symbols < and > are used).
And then we shade all the region below the line:
y = 2x - 5
And we shade the region above the line:
y = -3x + 1
So we will get the graph below:
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what is the probability of rolling a small straight on the first round? round your answer to have three decimal places. enter your solution into variable
Answer:it depends on how many sides their are
Step-by-step explanation:
just factual
what does correlation investigate? select one: a. linear association between two numeric variables b. variances between two numeric variables c. association between two categorical variables d. differences of means between two numeric variables
Correlation is a bi-variate analysis that measures the strength of association between two variables and the direction of the relationship.
What is bi-variate analysis?
Bivariate analysis is one in every of the only kinds of quantitative (statistical) analysis. It involves the analysis of 2 variables (often denoted as X, Y), for the aim of deciding the empirical relationship between them.
Main Body:
The correlation coefficient's value ranges from +1 to -1. the entire degree of correlation between the 2 variables is indicated by a worth of one. The association between the 2 variables are weaker because the parametric statistic price approaches zero.
Hence correlation investigate linear association between two variables.
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an airplane is travelling down a runway at a speed of 66 feet per second, when it begins to slow down. the airplane decelerates at a constant rate of 6 feet per square second. how many feet does the airplane travel before it stops? (do not include units in your answer.
With deceleration of 6 ft/s² and initial speed of 66 ft/s, the airplane will stop after travelling 363 ft.
Use the equation of motion:
v² = u² + 2 · a · s
Where:
v = final velocity
a = acceleration
u = initial velocity
s = distance
Deceleration is a negative acceleration.
Parameters given from the problem:
u = 66 ft/s
a = - 6 ft/s²
v = 0 since the airplane stops.
Plug these parameters into the formula:
v² = u² + 2 · a · s
0 = 66² + 2 · (-6)· s
s = 66² / 12
s = 363 ft.
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A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is.
The standard error of the mean is 11.99
Given,
In the question :
No. of observation is 100
The sample mean is = 1234
Standard Deviation is = 120
To find the standard error of the mean.
Noe, According to the question:
No. of observation:
N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2
Where,
∈ = allowance % error of mean
[tex]C_{v}[/tex] = coefficient of variation
[tex]C_{v} =[/tex] σ / x bar × 100
σ = standard deviation and x bar = mean
x bar = 1234 , σ = 120 and N = 100
[tex]C_{v} = \frac{120}{1234}[/tex] × 100
[tex]C_{v}[/tex] = 9.72%
N = [tex](C_{v}[/tex] / ∈[tex])[/tex] ^2
100 = (9.72/∈)^2
100∈^2 = (9.72)^2
∈^2 = 0.944784
∈ = 0.972%
The standard error of mean = mean x percentage of absolute mean error
= 1234 x 0.972/100
= 11.99
Hence, The standard error of the mean is 11.99
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insert 10, 15, 20, 40, 60, 80, 90, 100, 30, 70, and 50 into a 2-3-4 tree and select the correct answer
The numbers are inserted into the tree and shown in the below diagrams.
Given that,
Put these numbers into a 2-3-4 tree: 10, 15, 20, 40, 60, 80, 90, 100, 30, 70, and 50.
Binary Tree Data Structure: What is it?
A Binary Tree is a Tree data structure with two children or less. We typically refer to them as the left and right child since each element in a binary tree can only have two children.
Representation of a Binary Tree
A pointer to the topmost node of a binary tree serves as its representation. The root's value is NULL if the tree is empty.
The following components are found in a binary tree node:
Data
Pointer to left child in data
Pointer to the right-hand child
Thereforer, The numbers are inserted into the tree
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The question was incomplete. Check below the complete question.
insert 10, 15, 20, 40, 60, 80, 90, 100, 30, 70, and 50 into a 2-3-4 tree and select the correct answer
The distance of a golf ball from the hole can be represented by the right side of a parabola with vertex (−1, 8). The ball reaches the hole 1 second after it is hit. What is the equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit?.
The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
Define quadratic equation.ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given,
Assume for the moment that the hole is located at y = 0m, where x represents the time variable.
We are aware of:
The vertices are (-1s, 8m).
x in seconds and y in meters, I presume
The ball enters the hole at time x = 1s, hence we also have the following point:
(1s, 0m).
The vertex of the quadratic equation y = ax2 + bx + c is located at:
x = -b/2a,
Next, we have:
-1 = -b/2a.
Next, we have equations for trees:
8m = a(-1s)2, b(-1s), and c
0m = (a(1s)2) + (b(1s)2) + (c)
-1s = -b/2a.
The third equation should have one variable isolated first, and then it should be substituted in one of the other two:
1s2a = b.
Therefore, we can change b to bi 1s2a in the first two equations.
8m = 1s×2a×1s - a×1s2a1s + c
0m = 1s×2a×1s + a×1s×2a + c
We can combine the two equations to get:
8m is equal to a(1s2 - 2s2) + c, or a×1s2 - c.
0m is equal to a(1s2 + 2s2) + c, or a×3s2 + c.
We may quickly remove c from the second equation and then substitute it in the first equation:
c = -a3s^2
The initial equation is now:
8m is equal to -a×1s2 - a×3s2 - a×4s2.
a = 8m/-4s^2 = -2m/s^2.
We can now determine the values of c and b using a.
c = -(-(-2m/s2)*3s2)*3s2 = 6m.
B is equal to 1s*2a = 1s*(-2m/s2) = -2m/s.
The equation is then:
y = (-2m/s^2)t^2 + (-2m/s)t + 6m
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PLEASE ANSWER I WILL MARK BRAINLYEST
Factor −6x2 + 18x.
1. 6x(−x + 3)
2. −6x(x + 3)
3. x(6x + 18)
4. 6(−x2 + 18x)
Answer: 6x(-x+3)
Step-by-step explanation:
You can factor out the 6 and x. -6x^2 divided by 6x = -x, and 18x divided by 6x = 3. So the answer is 1. 6x(-x+3)
Answer:
-6x^2+18x
-6x^2-18x
6x^2+18x
-6x^2+108x
Step-by-step explanation:
1.
6x(-x+3)
6x(-x)+6x(3)
-6x^2+18x
2.
-6x(X+3)
-6x(X)+-6x(3)
-6x^2-18x
3.
x(6x+18)
x(6x)+x(18)
6x^2+18x
4.
6(-x^2+18x)
6(-x^2)+6(18x)
-6x^2+108x
Hopes this helps please mark brainliest
You invet $892 at the end of each year in an invetment with annual rate of return 6%. How much will the invetment be worth after 15 year?
You invest $892 at the end of each year in an investment with annual rate of return 6%. Then the investment worth after 15 year will be 14182.8 dollar
we know that
SI = prt
where
SI= simple interest
A= amount
P= principal
r= rate
t= number of year
according to the question
SI= 892* 0.06*1
= 53.52
A = 892+53.52
= 945.52
after 15 years amount will be
A= 945.52*15
= 14182.8
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Ken hikes a trail at a constant rate of 4/5 of a mile of a mile every 2/5 if an hour.he stops for a 3/4 hour lunch.he wants to hike at least 20 miles
Answer:
below
Step-by-step explanation:
Rate = 4/5 mi / 2/5 hr = 2 mi /hr
3/4 hr for lunch
20 miles / 2 miles/hr + 3/4 hr = 10 3/4 hr to hike 20 miles with a lunch
through (-3,-1) perp to y=-1/2x=5
PLease ANSWER HURRY
The equation of line passing through the point (-3, -1) and is perpendicular to the line y = -x/2 - 5 is y = 2x + 5
What are perpendicular lines?perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).
In such lines the product of their gradients is -1.
if y = -x/2 - 5
then comparing the equation with y = mx + c
it means slope(m) = -1/2
so the slope(p) of the second line perpendicular to the above line will be
p x m = -1
p = -1/m
p = -1 ÷ -1/2
p = 2
so if x = -3, y = -1 and substituting these values into the equation of line , y = mx + c becomes
-1 = 2 x (-3) + c
-1 = -6 + c
collect like terms
c= 6 - 1
c = 5
Equation of the second line becomes,
y = 2x + 5
In conclusion, the equation of the lines passing through point(-3, -1) is y = 2x + 5
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Which equation represents the line that is perpendicular to y = 4 5 x + 23 and passes through (-40,20)? A. y = - 5 4 x − 15 B. y = - 5 4 x − 30 C. y = 4 5 x + 52 D. y = 4 5 x − 56
The equation of the required perpendicular line is y = (-5/4)x - 30.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation of the given straight line is y = (4/5)x + 23. We need to find the equation of the straight line that is perpendicular to the given line and passes through the point that has coordinates (-40, 20).
The slope of the given line is 45. Let the slope of the required perpendicular line be represented by the variable "m". The slope of the perpendicular line must be the negative reciprocal of the slope of the given line.
m = -1/(4/5)
m = -5/4
The equation of the required line is of the form y = mx + c.
y = (-5/4)x + c
We know that this line passes the point (-40, 20).
20 = (-5/4)(-40) + c
20 = 50 + c
c = -30
Hence, the equation of the required line is y = (-5/4)x - 30.
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Kirk has just moved to Vindale and wants to check out some nearby restaurants. Starting from home, he drives 15 kilometers west, 45 kilometers east, and 75 kilometers west. Which direction must Kirk go to get back to his home?
Kirk will drive 15 kilometer east to get back to his home
How to determine the amount Kirk has to drive to get homeThe problem will be solved using basic addition operator and subtraction
Let the given information be represented as follows
he drives 15 kilometers west = 15 W
45 kilometers east = 45 E
75 kilometers west = 75 W
Kirk will drive East to get home = ?
since the distances are all in the horizontal direction we add up the west directions and subtract the east direction
15 W + 75 W = 45 E + ?
90 W = 45 E + ?
? = 90 - 45
? = 45 E
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