find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 9 cos(t)i 8 sin(t)j
Answers
The velocity, acceleration, and speed of the particle with position function \($r(t) = \begin{pmatrix} 9\cos(t) \ 8\sin(t) \ -150 \end{pmatrix}$\) are \($v(t) = \begin{pmatrix} -9\sin(t) \ 8\cos(t) \ 0 \end{pmatrix} a(t) = \begin{pmatrix} -9\cos(t) \ -8\sin(t) \ 0 \end{pmatrix}$\), and speed = \($|\mathbf{v}(t)| = \sqrt{(-9\sin(t))^2 + (8\cos(t))^2 + 0^2} = \sqrt{81\sin^2(t) + 64\cos^2(t)}$\).
To find the velocity, acceleration, and speed of a particle with the given position function, we need to differentiate the position function with respect to time, t.
The position function is given as \($r(t) = 9\cos(t)\mathbf{i} + 8\sin(t)\mathbf{j} - 150$\), where i and j are the unit vectors in the x and y directions, respectively.
To find the velocity, we differentiate the position function with respect to time, t:
\($v(t) = \dfrac{d\mathbf{r}}{dt} = -9\sin(t)\mathbf{i} + 8\cos(t)\mathbf{j}$\)
The velocity vector is a vector that shows the particle's direction of motion and its speed. The speed of the particle is the magnitude of the velocity vector, which is given by:
speed \($|\mathbf{v}(t)| = \sqrt{(-9\sin(t))^2 + (8\cos(t))^2} = \sqrt{81\sin^2(t) + 64\cos^2(t)}$\)
To find the acceleration, we differentiate the velocity function with respect to time, t:
\($a(t) = \dfrac{d\mathbf{v}}{dt} = -9\cos(t)\mathbf{i} - 8\sin(t)\mathbf{j}$\)
The acceleration vector is a vector that shows how the particle's velocity changes with time. The magnitude of the acceleration vector is given by:
\($|\mathbf{a}(t)| = \sqrt{(-9\cos(t))^2 + (-8\sin(t))^2} = \sqrt{81\cos^2(t) + 64\sin^2(t)}$\)
Therefore, the velocity of the particle is \($\mathbf{v}(t) = -9\sin(t)\mathbf{i} + 8\cos(t)\mathbf{j}$\), the acceleration of the particle is \($\mathbf{a}(t) = -9\cos(t)\mathbf{i} - 8\sin(t)\mathbf{j}$\), and the speed of the particle is given by speed \($|\mathbf{v}(t)| = \sqrt{81\sin^2(t) + 64\cos^2(t)}$\).
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Related Questions
please help with these tysm
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A body on the surface of the earth weichs 400 Ib. The radius of the earth is about 4,000 miles. If this same body were placed on a 4,000 mile high tower, its weight would be a. 100 lbs b. 200 lbs c. 400 lbs d. 800 lbs e. 16,000 lbs
Answers
Option a is correct.
F=GMm/R²
where F is the gravitational force or weight
G is the universal constant of gravitation
M is the mass of Earth
m is the mass of the object
R is the distance between the center of the earth and the object
Given,
initial distance R =4000miles
weight at surface of the earth F=400lb
Let the force be F' for a distance R' from earth's center.
Here R' = radius+ height of the tower = R+4000 miles = 4000 + 4000 = 8000 miles.
Since the other terms in the formula remain constant, the new weight F' can be calculated as follows:
F'/F = R²/R'(otherwise the inverse square law in gravitation)
F'/400=(4000)²/(8000)²
F' = 100 lb
Thus option a is correct.
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The weight of the body on a 4000-mile high tower would still be 400 lbs.
Explanation:The weight of an object depends on the gravitational acceleration at its location. On the surface of the Earth, the gravitational acceleration is approximately 32 ft/s2. Therefore, a 400 lb body on the Earth's surface would weigh 400 lbs. If the body were placed on a 4000-mile high tower, it would be much farther from the center of the Earth and experience a weaker gravitational pull. The weight of the body would decrease as the square of the ratio of the radii of the tower and the Earth. So, the weight on the tower would be:
Weight on the tower = (400 lb) * (4000 mi/4000 mi)2 = 400 lb * 1 = 400 lb
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A 500-N block, on a 30.0° incline, is being held motionless by friction. The coefficient of static friction between the block and the plane is 0.63. The force due to friction is:A. 0 N.B. 433 N.C. 250 N.D. 500 N.E. 354 N.
Answers
The force due to friction is B. 433 N.
1. First, find the gravitational force component acting parallel to the incline (F_parallel). This can be found using the formula F_parallel = F_gravity × sin(angle), where F_gravity is the gravitational force (500 N) and angle is the incline angle (30°).
F_parallel = 500 N × sin(30°) = 500 N × 0.5 = 250 N
2. Next, find the maximum static friction force (F_max) using the formula F_max = µ × F_normal, where µ is the coefficient of static friction (0.63) and F_normal is the normal force. Since the block is motionless, the normal force equals the gravitational force component acting perpendicular to the incline. We can find this using the formula F_normal = F_gravity × cos(angle).
F_normal = 500 N × cos(30°) = 500 N × 0.866 = 433 N
3. Now, find the maximum static friction force (F_max):
F_max = 0.63 × 433 N ≈ 273 N
4. Since the block is held motionless by friction, the force due to friction equals the gravitational force component acting parallel to the incline (F_parallel). Thus, the force due to friction is:
F_friction = F_parallel = 250 N
However, the given options do not include 250 N as an answer. The closest option to the calculated value is B. 433 N, which is the normal force, not the frictional force. Due to the absence of the correct answer in the given options, we select the closest option.
Conclusion: The force due to friction is B. 433 N, considering the given options. However, the correct answer should be 250 N.
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How is communication important in a science experiment?
(simple but detailed answer)
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In order to ensure that everyone on the team is aware of the goals, rules, and steps involved in the science experiment, communication is crucial. It permits the transparent exchange of information and thoughts.
Why is dialogue crucial in experiments?The chance to get input from stakeholders, experts, and other people with a professional or academic interest in the topic is provided by the presentation of your research findings.
Why is dialogue a crucial component of the science process?Science gains support, understanding of its broader relevance to society is promoted, and it encourages more informed decision-making at all levels, from government to communities to individuals, when scientists are able to effectively communicate outside of their peer group.
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What is the 3rd Law of coilation?
1. Bounce
2. Gravity
3. Re-flux
Answers
Answer:
Re-flux
Explanation:
Does visible have more energy than infrared radiation?
Answers
what is the minimum angular velocity (in rpm ) for swinging a bucket of water in a vertical circle without spilling any? the distance from the handle to the bottom of the bucket is 35 cm . express your answer in revolutions per minute.
Answers
The minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any is 5.56 rpm.
The minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any is given by the formula; Vmin=√g/R
where:
Vmin = minimum angular velocity (in rpm)g = acceleration due to gravity (9.81 m/s²)R = radius of the circular path or distance from the handle to the bottom of the bucket (35 cm)To express the answer in revolutions per minute, the radius of the circle must be converted to meters;R = 35 cm = 0.35 m
Substituting the values given above into the formula;
Vmin=√g/R Vmin=√9.81/0.35 Vmin = 5.56 rpmTherefore, the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any is 5.56 rpm.
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If you pull on a car with 200N of force, what does Newton’s 3rd Law says will happen?
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Weight lifiter raise 18 kg stone to heights 20m what is increase the potential energy
Answers
The increase in potential energy when a weight lifter raises an 18 kg stone to a height of 20m is 3,528 joules.
To calculate the increase in potential energy, we use the formula: Potential Energy = mass * gravity * height. In this case, the mass of the stone is 18 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is 20m.
Therefore, the potential energy = 18 kg * 9.8 m/s^2 * 20m = 3,528 joules.
Potential energy is the energy an object possesses due to its position in a gravitational field. When the stone is lifted to a higher height, its potential energy increases because it now has the potential to do work if released or if converted into another form of energy, such as kinetic energy. The increase in potential energy is directly proportional to the mass of the object, the acceleration due to gravity, and the height it is lifted.
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An electron is accelerated from rest by an electric potential difference of 437 V, and then enters a region of uniform magnetic field. The magnetic field is oriented perpendicular to the velocity with a magnitude of 42.8 mT. What will the radius of the electron's path be once it enters the magnetic field
Answers
The radius of the electron's path is once it enters the magnetic field 3.16*10^-4 m.
The electric capacity difference, additionally called voltage, is the outside work needed to bring a rate from one region to some other area in an electric discipline. The electric powered capacity distinction is the change of potential electricity skilled by way of a test rate that has a fee of +1.
The distinction in ability among two points represents the paintings worried or the electricity released in the switch of a unit amount of power from one factor to the other.
Electric ability is the work executed in step with unit fee in bringing the fee from infinity to that factor against electrostatic pressure. In a conductor, electrons float simplest when there is a difference in electric stress at its ends. This is additionally known as the capacity distinction.
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What is the main function (job) of the immune system?
A. to produce hormones for growth and development
B. to protect you from illness and disease
C. to get rid of waste in the body
Answers
To protect you from illness and disease.
Answer:
B. to protect you from illness and disease
Explanation:
The immune system protects your body from outside invaders, such as bacteria, viruses, fungi, and toxins . It is made up of different organs, cells, and proteins that work together.
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A 2.90-kg block is released from rest and allowed to slide down a frictionless surface and into a spring. The far end of the spring is attached to a wall, as shown. The initial height of the block is 0.500 m above the lowest part of the slide and the spring constant is 443 N/m. A. What is the maximum compression of the spring?B. The spring sends the block back to the left. How high does the block rise?
Answers
Part (a)
The potential energy of the block due to its height can be given as,
\(U=\text{mgh}\)The potential energy due to presence of spring can be expressed as,
\(U=\frac{1}{2}kx^2\)Equating both the values,
\(\begin{gathered} \text{mgh}=\frac{1}{2}kx^2 \\ x^2=\frac{2mgh}{k} \\ x=\sqrt[]{\frac{2mgh}{k}} \end{gathered}\)Substitute the known values,
\(\begin{gathered} x=\sqrt[]{\frac{2(2.90kg)(9.8m/s^2)(0.500\text{ m)}}{(443\text{ N/m)}}(\frac{1\text{ N}}{1kgm/s^2})} \\ \approx0.253\text{ m} \end{gathered}\)Thus, the maximum compression of the spring is 0.253 m.
Part (b)
Since the slide is frictionless, therefore no energy loss happened during the sliding of block. Therefore, the block will rise up to the same initial height which is 0.500 m.
Which type of telescope is known to be difficult to keep aligned Compound Refracting Reflecting Radio
Answers
The refracting telescope uses large lenses. The larger lenses increase the weight of the telescope. The weight of the refracting telescopes makes it difficult for the observer to keep them aligned.
Thus the correct answer is option b, refracting telescopes.
Answer:
Is Reflecting telescope
Explanation:
I took the test
A two-resistor series circuit has an applied voltage of 100 V. The voltage across one of the resistors is 40 V. The voltage across the other resistor is _____.
Answers
Given that you have a two-resistor series circuit with an applied voltage of 100 V, we can use the principle of voltage distribution in a series circuit to determine the voltage across the second resistor.
In a series circuit, the total applied voltage is distributed across all the resistors. The voltage across each resistor is directly proportional to its resistance. In this case, we know the voltage across one resistor is 40 V.
Using the principle of voltage distribution, we can calculate the voltage across the other resistor as follows:
Total applied voltage = Voltage across resistor 1 + Voltage across resistor 2
100 V = 40 V + Voltage across resistor 2
Now, we can solve for the voltage across resistor 2:
Voltage across resistor 2 = Total applied voltage - Voltage across resistor 1
Voltage across resistor 2 = 100 V - 40 V
Voltage across resistor 2 = 60 V
So, the voltage across the other resistor in the series circuit is 60 V.
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Explain what happens to an atom when the number of protons neutrons or electrons changes while the number of the other two particles remain the same
Answers
Answer: oxidizes or reduces
Explanation: When you change the number of protons in an atom, you will change the atom from one element to a different element.
A boy hears an echo of his voice from a hill after 0.1 sec. The velocity of sound in air is 340 m/s. Calculate the distance between the boy and the hill.the answer is 17m (i just need the process)
Answers
The distance between the boy and the hill is 17 metersTo calculate the distance between the boy and the hill, we can use the formula: distance = (velocity × time) / 2.
Given that the velocity of sound in air is 340 m/s and the time taken for the echo to reach the boy is 0.1 seconds, we can substitute these values into the formula:
distance = (340 m/s × 0.1 s) / 2 = 34 m · s / 2 = 17 m.
This calculation is based on the assumption that the sound traveled from the boy to the hill and back, so the total distance traveled by the sound is twice the distance between the boy and the hill
. By dividing the total distance by 2, we can determine the actual distance between the boy and the hill, which in this case is 17 meters.
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3 strings are attached to a small metal ring,2 of the strings make an angle of 30° with the vertical and each is pulled with a force of 10 newton what force must be applied to the third string to keep the string stationery
Answers
Answer:
Tension force.
Explanation:
Because to exert force from each other.
You have an oxygen atom that is looking to bond. How many atoms of one element from column 1 would need to bond with that oxygen to form an ionic bond? Why?
Answers
A 2-kg mass placed 30-cm to the left of the fulcrum is balanced by a 2-kg mass placed ______ cm to the right of the fulcrum.
Answers
Answer:
30 cm
Explanation:
0.06 or \(\frac{1}{15}\)
What is the effort and load arm?The lever has two “arms”:
The load arm is the portion of the lever directly connected to the load.
The effort arm is the portion of the lever to which we apply the effort, or input force.
The formula of the mechanical advantage(MA) of a lever is given as
MA = load/effort.
Given,
load = 2kg , effort = 30cm
MA = \(\frac{2}{30}\) = \(\frac{1}{15}\)
MA = 0.06 cm
Therefore,
A 2-kg mass placed 30-cm to the left of the fulcrum is balanced by a 2-kg mass placed 0.06 cm to the right of the fulcrum.
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What is the estimated density of the table tennis ball?
Answers
Answer:
tennis ball 0.07, Golf ball 1.37
Answer: step 6 answer is 0.07 g/cm3 and golf ball is 1.15 g/cm3
Explanation: doing lab.. step 6 answer on Edg
what is the momentum of tectonic plate if its kinetic energy is zero?
Answers
Answer: It is zero
Explanation: Without kinetic energy a plate cannot move. It is impossible.
A 24 resistor, an inductor with a reactance of 12 , and a capacitor with a reactance of 10 are in series across a 60 V 50 Hz source. Calculate the voltage across the inductor.
Answers
Answer:
A⋅24=24A
12=24A
10=24A
a⋅(60V)⋅(50Hz)=3000aVHz
Explanation:
because the bead is immersed in a fluid, we have to consider the upward buoyant force of the fluid on the bead, which acts whether the bead is moving or not through the fluid. in general, then, we can replace the combined weight of an object ( ) with the buoyant force acting on the object, which equals the weight of the fluid the object displaces ( ), with an effective downward gravitational force. in terms of the density of the object , the density of the fluid , and the volume of the object , what is the effective weight of an object immersed in a fluid? group of answer choices
Answers
The buoyant force on an object is equal to the weight of the fluid it is displacing, according to Archimedes' principle.
Why does a submerged object experience an upward push from buoyancy?The pressure gradient from the top to the bottom of a submerged object causes the buoyant force to act upward on it. The variation of the vertical distance or the depth within a liquid affects the pressure therein.
What determines the buoyant force acting on an item submerged in liquid?The weight of the fluid that the submerged object has displaced determines the buoyant force acting on it. There is a situation where an object's buoyant force and weight don't match.
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QUESTION 1
Describe the motion of the car in the following picture.
The car is slowing down.
The car is not moving.
The car is speeding up
The car is moving at a constant velocity
Answers
Answer:the car is speeding up
Explanation:
Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position a. Assuming the spring obeys Hooke's law, find the spring constant k b. How much work is required to compress the spring 0.5 m from its equlibrium position? c. How much work is required to stretch the spring 0.4 m from its equilibrium position? d. How much addisional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from is equilibrium? a, k = 600 (Type an integer or a decimal) b. Set up the integral that glives the work done in compressing the spring 0 5 m from its equilibrium position. Use decreasing limits of integration -05 (600x) dx (Type exact answers) Find the work done in compressing the spring The work is 75J (Type an integer or a decimal) c. Set up the integral that gives the work done in stretching the spring 04 m from its equilibrium position. Use increasing limits of integration (600x) dx Type exact answers) Find the work done in stretching the spring The work is 48J (Type an integer or a decimal) d. Set up the integral that gives the work done to stretch the spring 0.1 m if it has already been stretched 0.1m from its equilibrium. Use increasing limits of integration 0 2 600x) dx 0.1
Answers
Given that the force required to stretch and hold the spring 0.1m from its equilibrium position a is 60N.Force, F = 60 NDistance, x = 0.1mSpring constant, k = ?. According to Hooke's Law,F = kx60 = k × 0.1k = 60/0.1k = 600.
Therefore, the spring constant is k = 600
b) Work done in compressing the spring 0.5m from its equilibrium position can be calculated as: Work done, W = (1/2)kx².
Limits of integration: -0.5 to 0, Work done, W = ∫(-0.5 to 0) 600x² dx= 75 Joules.
Therefore, the work done in compressing the spring is 75 J.
c) Work done in stretching the spring 0.4m from its equilibrium position can be calculated as: Work done, W = (1/2)kx²Limits of integration: 0 to 0.4, Work done, W = ∫(0 to 0.4) 600x² dx= 48 Joules.
Therefore, the work done in stretching the spring is 48 J.
d) To stretch the spring 0.1m further from its position (already stretched by 0.1m from its equilibrium position), the spring is being stretched by a distance of 0.1 m. Distance stretched, x = 0.1m.
Therefore, the work done is, Work done, W = (1/2)kx²Limits of integration: 0.1 to 0.2Work done, W = ∫(0.1 to 0.2) 600x² dx= 6 Joules.
Therefore, the additional work done to stretch the spring by 0.1m if it has already been stretched by 0.1m from its equilibrium position is 6 J.
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the difference between the time an operation actually takes place and the time it would have taken under uncongested conditions without interference from other aircraft?
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The difference between the actual time an operation takes place and the time it would have taken under uncongested conditions without interference from other aircraft is known as the operational delay.
Operational delay refers to the discrepancy between the actual time it takes for an operation to occur and the time it would have taken if there were no congestion or interference from other aircraft. In an ideal scenario with uncongested conditions, operations can proceed smoothly and efficiently, adhering to their scheduled timelines. However, in reality, various factors can contribute to delays in the aviation industry.
Operational delays can occur at different stages of an operation, including taxiing, takeoff, en route navigation, and landing. These delays are often caused by congestion in airspace or on the ground, traffic flow management issues, adverse weather conditions, or unexpected events such as equipment malfunctions or air traffic control restrictions. When these factors impede the normal flow of operations, the actual time it takes for an operation to be completed extends beyond what it would have taken under uncongested conditions.
Reducing operational delays is a significant focus for air traffic management systems and aviation stakeholders. Efforts are made to optimize airspace utilization, enhance communication and collaboration between aircraft and air traffic control, improve routing and navigation procedures, and implement advanced technologies to mitigate congestion and interference. By minimizing operational delays, the aviation industry can enhance efficiency, punctuality, and overall customer satisfaction.
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Draw a stationary wave and show the position of node and antinode
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I hope that the attachment helps you..
25 points! Will give brainliest!
1. Draw the diagram
2. List the Givens
3. Select the correct equation to solve for and manipulate the equation
4. Substitute the given values
A ball is thrown horizontally from the roof of a building 60 m tall with a speed of 6.9 m/s.
a.How much later does the ball hit the ground?
b. How far from the building will it land?
c. What is the velocity of the ball just before it hits the ground?
Answers
Answer:
B my brother say that it was
For the permanent magnet/ compass experiment, you have measured the magnetic field B at several distances r from the center of the permanent magnet. You plotted the natural log of the magnetic field In(B) versus the natural log of the distance In(r) and found a straight line with a slope of -2.9. The intercept was 15, what is the magnetic dipole moment of the magnet?
a. 1.5 Am2
b. 2.9 Am2
c. 5.2Am2
d. 7.5 Am2
e. 15 Am2
Answers
The intercept was 15, what is the magnetic dipole moment of the magnet is e. 15\(Am^{2}\)
In the given scenario, the natural logarithm of the magnetic field (In(B)) is plotted against the natural logarithm of the distance (In(r)). If the resulting plot is a straight line with a slope of -2.9 and an intercept of 15, we can use this information to determine the magnetic dipole moment of the magnet.
The equation that relates the magnetic field, distance, and magnetic dipole moment is:
In(B) = -2.9 * In(r) + C
where C is the intercept of the line (15 in this case). Comparing this equation with the standard form y = mx + b, we can see that the slope (-2.9) corresponds to the coefficient of In(r), and the intercept (15) corresponds to the constant term.
The magnetic dipole moment (μ) is related to the slope of the line by the equation:
μ = -4πk * slope
where k is a constant. In this case, since the slope is -2.9, we can substitute it into the equation to find the magnetic dipole moment:
μ = -4πk * (-2.9)
The value of the constant k depends on the units used for magnetic field and distance. Since the answer options are given in \(Am^{2}\)(Ampere meter squared), we can assume that k = 1.
μ = 4π * 2.9
μ ≈ 36.26 \(Am^{2}\)
None of the given answer options match exactly with this value. However, the closest option is 15 \(Am^{2}\). Therefore, Option e is correct.
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The sports car is traveling along a 30∘ banked road having a radius of curvature of rho = 500 ftIf the coefficient of static friction between the tires and the road is μs = 0.1, determine the maximum safe speed so no slipping occurs. Neglect the size of the car.Note: μs = 0.1 NOT 0.2
Answers
The maximum safe speed of the sports car on the banked road is 31.3 mph.
The maximum safe speed of the car can be calculated using the formula V = sqrt(μs * g * rho * tan(theta)), where V is the maximum safe speed, μs is the coefficient of static friction between the tires and the road, g is the acceleration due to gravity, rho is the radius of curvature of the road, and theta is the angle of inclination of the banked road. Substituting the given values, we get V = sqrt(0.1 * 32.2 ft/s^2 * 500 ft * tan(30 deg)) = 31.3 mph, where acceleration due to gravity is taken 32.2ft/s^2.
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