The velocity and acceleration vectors and the equation of the tangent line for the curve = 3i+4tj
What is Velocity?
When an item is moving, its velocity is the rate at which it is changing position as seen from a certain point of view and as measured by a specific unit of time.
What is Acceleartion?
Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.
r(t) = 3cos(t)+sin4(t)j
velocity,V(t) = dr(t)/dt
=3sin(t)i + 4cos4(t)j
and acceleration a(t) = dv(t)/dt
= [tex]d^{2}r(t)/dt^{2}[/tex]
i.e a(t) = -3cos(t)i - 16sin(4t)j
v(0) = 0.i + 4j =4j
and a(0) = -3i -0j
=-3i
now we find the equation of the tangent line for the curve (t) at t=0
r(0) = 3i
r(t) = -3sin(t)i +4 cos 4(t)j
r (0) = 4j
equation target to the curve r(t) at t=0 is
1(t) = r (0) + (t)r(0)
= -3i+(t).4j
= -3i+4tj
The curve's tangent line equation, velocity and acceleration vectors, is -3i+4tj
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determine where the absolute extrema of f(x)=4xx2 1 on the interval [−4,0] occur.
The absolute maximum and minimum of f(x) = [tex]\frac{4x}{x^2+1}[/tex] on the interval [−4,0] are at x = 0 and -1, respectively.
The function is f(x) = [tex]\frac{4x}{x^2+1}[/tex] .
The interval is [−4,0].
To find the value of x we differentiate the function using the u/v formula.
[tex]\frac{d}{dx}\frac{u}{v}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]
According to formula
f'(x) = [tex]\frac{(x^2+1)\frac{d}{dx}4x-4x\frac{d}{dx}(x^2+1)}{(x^2+1)^2}[/tex]
f'(x) = [tex]\frac{4(x^2+1)-4x(2x)}{(x^2+1)^2}[/tex]
f'(x) = [tex]\frac{4(x^2+1)-8x^2}{(x^2+1)^2}[/tex]
To determine the value of x equating f'(x) = 0
[tex]\frac{4(x^2+1)-8x^2}{(x^2+1)^2}[/tex] = 0
4(x^2 + 1) - 8x^2 = 0
4x^2 + 4 - 8x^2 = 0
4 - 4x^2 = 0
Add 4x^2 on both side, we get
4x^2 = 4
Divide by 4 on both side, we get
x^2 = 1
Taking square root on both side, we get
x = -1, 1
The value of x = 1 doesn't lie between the interval [-4, 0]. So we cannot consider 1.
Now evaluating the value of f(x) at -4,-1,0.
At x= -4, f(x) = -16/17
At x = -1, f(x) = -2
At x = 0, f(x) = 0
Therefore, the absolute maximum and minimum are at x = 0 and -1, respectively.
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The complete question is:
Determine where the absolute extrema of f(x) = [tex]\frac{4x}{x^2+1}[/tex] on the interval [−4,0] occur.
Last questions on circle 3 please. Points at 50 and I’ll give brainly.
[tex]-9^2=-(9^2)=-81[/tex], whereas [tex](-9)^2=9^2=81[/tex].
This is because of the order of operations.
Help me understand how to do it so I can pass?
Answer: Hi there! X = 7 would be your answer
Step-by-step explanation:
Simplify both sides of the equation.
2(3x − 6) = 3(x + 3)
(2) (3x) + (2) (−6)= (3) (x) + (3) (3)
6x + −12 = 3x + 9
6x − 12 = 3x + 9
Subtract 3x from both sides.
6x − 12−3x = 3x + 9−3x
3x − 12 = 9
Add 12 to both sides.
3x − 12+12 = 9+12
3x=21
Divide both sides by 3.
3x/3=21/3
x=7
I hope this helps!!
[tex] \: [/tex]
[tex] \frak{6x - 12 = 3x + 9}[/tex][tex] \: [/tex]
[tex] \frak{6x - 3x = 9 + 12}[/tex][tex] \: [/tex]
[tex] \frak{3x = 21}[/tex][tex] \: [/tex]
[tex] \frak{x = \cancel\frac{21}{3} }[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \bold{ \frak{{ \red{x = 7}}}} }}[/tex][tex] \: [/tex]
hope it helps!:)
Solutions to Systems of Linear Inequalities in Two Variables
A ordered pair that satisfies the inequality statement serves as the solution for linear inequalities involving two variables.
How many possible solutions does a two-variable linear inequality have? A ordered pair that satisfies the inequality statement serves as the solution for linear inequalities involving two variables.For example, if the linear inequality Ax + By > C has two variables, x and y, then the needed solution will be an ordered pair (x, y) that satisfies the statement.Several options infinity.A single linear inequality has an unlimited number of solutions since the solution set is always a half-plane.The number of solutions to a linear inequality in two variables is hence limitless.The area of the plane where all of the individual lines' shading overlaps is the area where the linear inequality system's solutions can be found.To learn more about linear inequalities refer
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Given f(x) = x/(x-6), and f(g(x)) = 2x, find g(x).
Please help.
The composite function g(x) is g(x) = 12x/(2x - 1)
How to determine the function g(x)From the question, we have the following parameters that can be used in our computation:
f(x) = x/(x - 6)
f(g(x)) = 2x
This means that
f(g(x)) = g(x)/(g(x) - 6)
So, we have
g(x)/(g(x) - 6) = 2x
Rewrite as
y/(y - 6) = 2x
This gives
y = 2x(y - 6)
Open brackets
y - 2xy = -12x
This gives
y = -12x/(1 - 2x)
So, we have
y = 12x/(2x - 1)
Hence, the function g(x) = 12x/(2x - 1)
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A hore heart beat 440 time in 10 minute. A cow heart beat 390 time in 6 minute. Which animal ha a greater heart rate?
A horse has a greater heart rate.
Heart Rate Comparison AnimalsTo compare the heart rate of two animals, we need to convert the number of beats per minute (bpm).
A horse's heart beats 440 times in 10 minutes, which is equivalent to 44 bpm (440 beats / 10 minutes).
A cow's heart beats 390 times in 6 minutes, which is equivalent to 65 bpm (390 beats / 6 minutes).
So, we can see that a horse has a heart rate of 44 bpm, while a cow has a heart rate of 65 bpm. Hence, a cow has a greater heart rate compared to a horse.
Generally, ini animal subject, not always calculate like this. This comparison is specific to horses and cows. The heart rate of different species of animals can vary significantly, and it is not possible to make a general statement about the heart rate of all animals based on the comparison of just two species. Additionally, the heart rate of animals can vary based on factors such as age, weight, stress, and activity level, among others.
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Write and exponential function in the form y=ab^x that goes through points (0,15) and (2,240)
Answer:
One possible exponential function that goes through points (0, 15) and (2, 240) is y = 15 * (2^x)
Another possible exponential function that goes through the points (0,15) and (2,240) is y= 15*(5^x)
Step-by-step explanation:
Triangle def contains right angle e. if angle d measures 40° and its adjacent side measures 7.6 units, what is the measure of side ef? round your answer to the nearest hundredth. 4.89 units 5.34 units 6.38 units 9.06 units
The measure of side EF in triangle DEF is 5.34 units when angle D measures 40° and its adjacent side measures 7.6 units.
To get this answer, use the Pythagorean Theorem:
a2 + b2 = c2,
where a and b are the lengths of the sides adjacent to the right angle, and c is the length of the hypotenuse.
In this case, a = 7.6 and b = 5.34, so c = 8.93. Round this to the nearest hundredth and you get 5.34.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides adjacent to the right angle is equal to the square of the hypotenuse.
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what is 40% as a decimal
In baseball, a player's slugging ratio is (s + 2d + 3t + 4h)/b, where:s = number of singlesd = number of doublest = number of triplesh = number of home runsb = times at batLucase came to bat 35 times during the season and hit 18 singles, 2 doubles, 0 triples, and 1 home run. What is Lucas's slugging ratio, rounded to the nearest thousandth?: *A) 0.714B) 0.829C) 0.629D) 0.743
Lucas's slugging ratio, rounded to the nearest thousandth is 0.743.
Therefore the answer is D) 0.743.
To find Lucas's slugging ratio, we first need to calculate the numerator of the equation:
number of singles, s = 18 singles
number of doubles, d = 2 doubles
number of triples, t = 0 triples
number of home runs, h = 1 home run
numerator = (s + 2d + 3t + 4h) = (18 + 2 * 2 + 3 * 0 + 4 * 1) = 26
denominator = b = 35 times at bat
Lucas's slugging ratio is numerator / b
= 26 / 35
= 0.743
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Dustin and his friends each have a step counter, and they competed today to see who could
walk the farthest. At the end of the day, Dustin's StepPro step counter says he walked 2;
3
miles. His friends, Bobby and Marco, both have StepperPlus step counters. Bobby's step
counter says he walked 2.3 miles, while Marco's says he walked 2.5 miles.
Who walked the farthest?
Dustin
Submit
Bobby
Marco
Answer:
Step-by-step explanation:
Factor each Polynomial:
1. 2b^2+10b+12
2. 4x^2+4x-3
3. 6m^2+7m-3
4. 10x^2-9x+6
5. 18h^2+15h-18
QUICK PLEASE!!!!!!!
Answer:
2b^2+10b+12 = 2(b^2+5b+6) = 2(b+3)(b+2)
4x^2+4x-3 = 4(x^2+x-3/4) = 4(x+3/2)(x-1/2)
6m^2+7m-3 = 6(m^2+m-1/2) = 6(m+1/2)(m-1/2)
10x^2-9x+6 = 10(x^2-x+6/10) = 10(x-1/2)(x-3/2)
18h^2+15h-18 = 18(h^2+5/6h-1) = 18(h+3)(h-2)
Provide the answer to question number 5
The function value that us greater is with estimated value of 96
How to find the estimated value?The estimated value is the value read from the graph which gives the accumulated value for each of the line
The first line gives an estimated value of
10+14+18+19+28 = 89
The second graph gives gives an estimated value of
17+18+19+20+22 = 96
Therefore comparing the two graphs, the one with 96 has the greater value
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2. Find the distance between (-4, -8) and (-4, 0). Round to the nearest tenth if needed.
A.-2
B. 2
C.-8
D. 8
-8
it is -8 because it is 8 blocks away, but since it os - it will be -8 your welcome
A thin wire of linear charge density ????λ is bent in the form of a triangle "ABC" and an imaginary cube of side 'a' is taken with vertex "A" at the centre of the top face and vetices B, C at the opposite edge centre of the bottom face.The total electric flux linked with the cube is
The total electric flux linked with the cube is .
Electric flux is a characteristic of an electric field and refers to the quantity of electric lines of force (or electric field lines) that span a given area. This hypothesis states that electric field lines have positive electric charges at the beginning and negative electric charges at the end. Field lines pointing toward a closed surface are deemed negative, whereas those pointing away from it are deemed positive.
The electric field inside a charged conductor is zero, and since the wire is a conductor, the electric field inside the cube is zero.
Hence, the total electric flux linked with the cube is also zero.
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“Exchange rate is the value of a country's _______ in terms of another _______ currency.”
The exchange rate is the value of a country's currency in terms of another country's currency.
What is the exchange rate?The exchange rate is the cost of a country's currency in respect to another currency. If the exchange rate between the U.S. dollar (USD) and the Japanese yen (JPY) is 120 yen for every dollar, then one dollar may be exchanged for 120 yen in the foreign exchange market.
From the above definition, it is clear that the complete definition of the exchange rate is given as the exchange rate is the value of a country's currency in terms of another country's currency.
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{x is greater than or equal to 3, y is less than or equal to 2. Graph the solution of the system of linear inequalities. (and fill in)
The solution to the system of linear inequalities x ≥ 3 and y≤ 2.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
This is represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x= 2 and above the line y= 3 .
x ≥ 3
y ≤ 2.
It can be represented on a coordinate plane as a region that satisfies both inequalities.
To graph the solution, we first plot the line x = 2 on the coordinate plane. Since x <= 2, this line represents the boundary of the solution. Everything to the left of the line x = 2 is included in the solution.
Next, we plot the line y = 3. Since y less than 3, everything above the line y = 3 is included in the solution.
The solution set is x ≥ 3 and y≤ 2
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The student council at
Lonestar High School is selling tickets to prom. They are selling senior tickets for $20 and junior tickets for $30. So far they have sold 426 tickets and have made $10,390. Write a system of equations that represents this scenario and choose the best method for solving based on how the equations are set up.
HELP!!!
Answer:
number of senior tickets = 239
number of junior tickets = 187
Step-by-step explanation:
let 's' = number of senior tickets
let 'j' = number of junior tickets
20s + 30j = 10390
s + j = 426
we could use the substitution method to solve the system by making
s = 426-j
we can substitute '426-j' in for 's' in the first equation to get:
20(426-j) + 30j = 10390
8520 - 20j + 30j = 10390
8520 + 10j = 10390
10j = 1870
j = 187
s + 187 = 426
s = 239
Based on the national food survey called What We Eat in America, about 75% of the United States population has an eating pattern that is low in which of the following?
Fruits
Answer: Fruits
Step-by-step explanation:
Fruits!
About 75% of the United States population has an eating pattern that is low in fruits.
What is percent?A percent(%) is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
Approximately 75% of the US population has a low-fruit eating trend.
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Here is a list of numbers: -45,-21,-16,12,33,40
C) work out the sum off all numbers in the list
Answer:
To find the sum of all the numbers in the list, we can add each number together:
-45 + -21 + -16 + 12 + 33 + 40 = 59
So the sum of all the numbers in the list is 59.
What is the purpose of converting a random variable to a z-value? Select all that apply.
O To compare a normal distribution to a standard normal distribution.
O To convert a normal distribution to a uniform distribution
O To standardize the random variable so that the sum of the probabilities is one.
O To express the distance from the mean in terms of the standard deviation.
The purpose of converting a random variable to a z-value is to Compare a normal distribution to a standard normal distribution and Express the distance from the mean in terms of the standard deviation.
The purpose of converting a random variable to a z-value is to:
Compare a normal distribution to a standard normal distribution: By converting a random variable to a z-value, it can be compared to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. This allows for the calculation of probabilities and the interpretation of the results in a standard way.
Express the distance from the mean in terms of the standard deviation: The z-value expresses the distance of the random variable from the mean in terms of the standard deviation. This standardization makes it easier to compare values and to perform statistical analysis.
Converting a normal distribution to a z-value does not convert it to a uniform distribution or ensure that the sum of the probabilities is one. The sum of the probabilities in a normal distribution does not equal one, but rather approaches one as the values approach infinity.
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the average temperatures recorded over a five-day period last winter in salt lake city is: 12 , 18 , 19, 22 , 25 formulas: the standard deviation of these temperatures is . a) the median m is [ select ] b) the variance is [ select ]
The standard deviation of the given data is 4.35.
The standard deviation of data is the calculation of the dispersion/ spreading of the data value about its mean. It can be mathematically defined as the square root of the variance of the data.Here we have, X = 12, 18, 19, 22, 25 N=5The variance of data can be expressed as the expectation of as
σ²[tex]= E(X^{2} ) - (E(X))^{2}[/tex]
[tex]E(X) = \frac{12 +18+ 19 + 22 + 25}{5}[/tex] [tex]= \frac{96}{5} = 19.2[/tex] ⇒ [tex](E(X))^{2} = 368.64[/tex]
Now we have,
[tex]E(X)^{2} = \frac{12^{2} +18^{2} +19^{2} + 22^{2} +25^{2} }{5}[/tex] = 387.6
From the above values we get the variance,
σ² = 387.6 - 368.64 = 18.96
σ = 4.35
Hence, the standard deviation of the given data is 4.35.
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Can someone please please help mke i was suppose to finnish this at least 4 weeks ago please can someone answer these 3 question for at leat 150 or 200 points.
Answer:
1/6, 6, 10, and then 8:1/3, 4:1/6, 6:1/4, 10:5/12
Step-by-step explanation:
1) From 8 meters to 4 meters is 8 multiplying 1/2=4, so 1/3 multiplying 1/2 is 1/6; or 8 multiplying x=4, x=1/2, so 1/3 multiplying 1/2=1/6
2) 1/3 multiplying x= 1/4, so x=3/4
8 multiplying 3/4=6
3) 1/3 multiplying x=5/12, so x=5/4
8 multiplying 4/5=10
Equivalent ration:
8:1/3, 4:1/6, 6:1/4, 10:5/12
in class 12A there are 40 students, 12 have blue eyes, 4 have green and 24 have brown in class 12B there are 50 students, 21 have blue eyes, 2 have green and 27 have brown one person is chosen at random from each class to represent the sixth form what is the probability of:
P(different colours)
P(both blue)
P(one brown)
Answer: P(different colours) = 1 - P(same colours) = 1 - (3/10 * 42/100) - (1/10 * 4/100) - (6/10 * 54/100) = 1 - (3/25) - (1/250) - (27/25) = 1- 61/250 = 189/250
P(both blue) = (3/10) * (42/100) = 3/25
P(one brown) = (6/10) + (54/100) - (6/10) * (54/100) = (6/10) + (54/100) - (27/250) = (24/25) - (27/250) = 973/1000
Step-by-step explanation:
To find the probability of different colours, we need to find the probability that the student chosen from class 12A has a different eye color than the student chosen from class 12B.
The probability of the student from class 12A having blue eyes is 12/40 = 3/10.
The probability of the student from class 12A having green eyes is 4/40 = 1/10.
The probability of the student from class 12A having brown eyes is 24/40 = 6/10.
The probability of the student from class 12B having blue eyes is 21/50 = 42/100.
The probability of the student from class 12B having green eyes is 2/50 = 4/100.
The probability of the student from class 12B having brown eyes is 27/50 = 54/100.
To find the probability of different colours, we need to find the probability that the student chosen from class 12A has a different eye color than the student chosen from class 12B.
P(different colours) = 1 - P(same colours) = 1 - (3/10 * 42/100) - (1/10 * 4/100) - (6/10 * 54/100) = 1 - (3/25) - (1/250) - (27/25) = 1- 61/250 = 189/250
To find the probability of both blue eyes, we need to find the probability that the student chosen from class 12A has blue eyes and the student chosen from class 12B also has blue eyes.
P(both blue) = (3/10) * (42/100) = 3/25
To find the probability of one brown eye, we need to find the probability that either the student chosen from class 12A or the student chosen from class 12B have brown eyes.
P(one brown) = (6/10) + (54/100) - (6/10) * (54/100) = (6/10) + (54/100) - (27/250) = (24/25) - (27/250) = 973/1000
It's important to note that these probability calculations assume that the two students are chosen independently and at random, one from each class. And all the students are different from each other.
A book has a front and back and 400pages the front and back are 0.9mm thick to 1 decimal place and each page is 0.13mm thick to two decimal places calculate the minimum thickness of book
Answer:
To calculate the minimum thickness of the book, we need to add the thickness of the front and back covers to the thickness of all the pages.
Step 1: Calculate the thickness of the front and back covers:
2 * 0.9 mm = 1.8 mm
Step 2: Calculate the thickness of all the pages:
400 pages * 0.13 mm/page = 52.0 mm
Step 3: Add the thickness of the front and back covers to the thickness of all the pages:
1.8 mm + 52.0 mm = 53.8 mm
Answer:
The minimum thickness of the book is 53.8 mm.
a survey of 800 volunteers yielded the following information: 539 were tour guides, 430 were retirees, and 310 of the tour guides were retirees. how many of the 800 surveyed volunteers were tour guides or were retirees?
869 of the 800 surveyed volunteers were either tour guides or retirees. 539 were tour guides, and 430 were retirees, with 310 of the tour guides also being retirees.
Surveys are a type of data collection method in which individuals or organizations are asked to provide information about a particular topic or issue. Surveys can be used to collect information about people's opinions, behaviors, and preferences.
They can also be used to gather data on a particular population or group, such as demographics, employment, health, or other topics. Surveys are often used in research studies and can help to provide valuable insights into a variety of topics.
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Suppose that a colony of Jeevesium beetles grows exponentially with doubling time 9 years. How many years does it take for the colony to triple in size? (Give the answer as a decimal number with no units. Round to three decimal places.)
The population of Jeevesium beetles is tripled in a time of approximately 14.265 years.
How to predict the population of a colony of Jeevesium beetles
The statement indicated that a colony of Jeevesium beetles double its population every 9 years and we are required to find the number of years such that the population is tripled, the prediction model for population growth is shown below:
[tex]p(t) = p_{o}\cdot 2^{\frac{t}{9}}[/tex]
Where:
p₀ - Initial populationp(t) - Current populationt - Time, in yearsIf we know that p(t) / p₀ = 3, then the time needed for the colony of Jeeversium beetles is:
[tex]3 = 2^{t / 9}[/tex]
㏒₂ 3 = t / 9
t = 9 · ㏒₂ 3
t ≈ 14.265
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6. A roller rink floor is show below. Each end is a emicircle. What is its area? Use π = 3.14 7 m 20 m
Answer:
it is 27
Step-by-step explanation:
because we need to add 27 and the 7m
8.6 more than the product of 3 and a number y.
Write phrase as an expression
y = 24
The formula "3y + 8.6 = 24" can be expressed as "8.6 greater than for the combination of 3 and just a number y."
How should a phrase be written?Mathematical operators like addition, deletion, multiply, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.For instance, the mathematical equation for "4 increased to 2" will be 2+4.
What is a mathematical expression?A mathematical expression is formed of a statement, at least two integers or variables, and one or more arithmetic. This mathematical operation enables the multiple, division, modification, or subtraction of numbers. The the above is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
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i need help and i need it ASAP
The requried simplified value of the given exponential expression is 1.
what is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
F = [25x²y¹⁴w³]⁰
Since a⁰ = 1
F = 1
Thus, the requried simplified value of the given exponential expression is 1.
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