Answers
Answer:
Explanation:
Given that:
Mass of block M
Mass of penny m
spring stiffness constant k
The frequency of oscillation of the block \(f=\frac{1}{2\pi}\sqrt{\frac{k}{m} }\)
The angular velocity is \(\omega =2\pi f\)
\(=\sqrt{k/m}\)
when the penny is resting on the block
The acceleration of the penny = acceleration of the block
If R is the reaction of the block on the penny
\(R-mg=a_{max}m\\\\=-\omega^2A_{max}m\\\\R=mg-\omega^2A_{max}m\)
The penny will leave the block if R = 0
\(mg=\omega^2A_{max}m\\\\g=\omega^2A_{max}\\\\A_{max}=\frac{g}{\omega^2} \\\\=\frac{g}{(k/M)} \\\\A_{max}=gM/k\)
Therefore the amplitude \(A_{max}<gM/k\) for the penny to remain on the block
Related Questions
An invading barbarian whirls a stone in a leather sling. If the sling is 90 cm
long, and the velocity of the stone is 90 m/s, what is the centripetal
acceleration of the stone?
Answers
Answer:
56,643.36m/s²Explanation:
Centripetal acceleration is expressed as shown:
a = v²/r
v is the velocity
r is the radius
If the length of the sling is 90cm, hence the circumference of the circular path is 90cm
Since C = 2πr
0.9 = 2πr
r = 0.9/2π
r = 0.9/2(3.14)
r = 0.9/6.28
r = 0.143m
Get the centripetal acceleration:
a = 90²/0.143
a = 56,643.36m/s²
Hence the the centripetal acceleration of the stone is 56,643.36m/s²
Place a small object on the number line below at the position marked zero. Draw a circle around the object. Mark the center of this circle with the symbol for “initial position”. Move the object 5.0cm to the right and stop. Label this circle with the correct symbol for “final position.”

(A) What was the initial position of the object?
(B) What is the final position of the object?
(C) What is the distance traveled by the object?
(D) What is the displacement of the object?
(E) Of the three underlined quantities, which are numerically equal?
Answers
7. [Honors] A turn of radius 100 m is being designed for a speed of 25 m/s. At what angle should the turn be banked?
Answers
Answer:
The angle at which a turn should be banked depends on the speed of the vehicle, the radius of the turn, and the acceleration due to gravity. To calculate the angle, we can use the following formula:
tanθ = v^2 / (g * r)
where
θ is the angle at which the turn should be banked (in radians)
v is the speed of the vehicle (in m/s)
g is the acceleration due to gravity (approximately 9.81 m/s^2)
r is the radius of the turn (in meters)
Plugging in the values given in the problem, we get:
tanθ = (25 m/s)^2 / (9.81 m/s^2 * 100 m)
tanθ = 6.44
Taking the inverse tangent of both sides, we get:
θ = tan^-1(6.44)
θ ≈ 80.5 degrees
Therefore, the turn should be banked at an angle of approximately 80.5 degrees.
A 250 kg cart is traveling at 8 m/s when it strikes a 100 kg cart at rest. After the elastic collision, the 250 kg cart continues to travel forward but at a lower velocity of 3 m/s. Determine the velocity of the 100 kg cart after the elastic collision.
Answers
Answer: In this scenario, we have two carts colliding with each other. One cart weighs 250 kg and is moving at a speed of 8 m/s, while the other cart weighs 100 kg and is initially at rest.
After the collision, the 250 kg cart continues moving forward, but at a slower speed of 3 m/s. We want to find out the speed at which the 100 kg cart moves after the collision.
To solve this, we use the principle that the total "push" or momentum before the collision should be the same as the total momentum after the collision.
Since the 100 kg cart is initially at rest, its momentum is zero. The momentum of the 250 kg cart before the collision is 250 kg * 8 m/s = 2000 kg·m/s.
After the collision, the momentum of the 250 kg cart becomes 250 kg * 3 m/s = 750 kg·m/s.
To find the momentum of the 100 kg cart after the collision, we subtract the momentum of the 250 kg cart after the collision from the total momentum before the collision: 2000 kg·m/s - 750 kg·m/s = 1250 kg·m/s.
Now, we divide this momentum by the mass of the 100 kg cart to find its velocity: 1250 kg·m/s / 100 kg = 12.5 m/s.
Therefore, the 100 kg cart moves at a velocity of 12.5 m/s after the collision, in the opposite direction of the 250 kg cart's motion.
If you pour liquid into a tall, narrow glass, you may hear sound with a steadily rising pitch. What is the source of the sound
Answers
Answer:
the vibration of the glass tube creating sound waves within itself. reason is the rising pitch is that the liquid rise shortens the length of the vibrating area within the tube.
Explanation:
2. Gerard is riding his bicycle directly east. His maximum
instantaneous velocity was 8 meters per second and his
minimum instantaneous velocity was 0 meters per second. He
covered 7.20 kilometers in 20.0 minutes. What is his average
velocity for the ride?
Answers
Gerard's average velocity for the ride is 6 meters per second.
To find Gerard's average velocity for the ride, we can use the formula:
Average velocity = Total displacement / Total time
First, we need to convert the distance traveled from kilometers to meters:
7.20 kilometers * 1000 = 7200 meters
Next, we convert the time from minutes to seconds:
20.0 minutes * 60 = 1200 seconds
Now, we can calculate the total displacement by subtracting the initial position from the final position. Since Gerard is riding directly east, there is no change in the east-west direction, so the displacement is equal to the distance traveled:
Total displacement = 7200 meters
Finally, we substitute the values into the average velocity formula:
Average velocity = 7200 meters / 1200 seconds
Average velocity = 6 meters per second
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7. Which of the following is true about Earth's gravity?
A. Gravity does not act on objects that are at rest or not moving.
B. Gravity only acts on oljects that are accelerating,
C. Gravity only acts on objects that are falling down.
D. Gravity acts on all objects on Earth, whether it is at rest or moving.
Answers
Answer:
D
Explanation:
Gravity is always having an effect on every object on earth, whether or not its moving.
If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 41 N · m, what minimum force must be exerted by the mechanic at the end of a 24 cm-long wrench to loosen the nut?Answer in units of N.
Answers
We have that the Force is mathematically given as
F=170.833N
ForceQuestion Parameters:
The torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 41 N · m,the end of a 24 cm-long wrench to loosen the nutGenerally the equation for the Force is mathematically given as
\(F=\frac{T}{d}\)
Therefore
F=41/0.24
F=170.833N
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ayuden ha resolver este ejercicio porfa
Answers
Answer:
un café y a seguir pensando porque no se la respuesta xd
Does fire get rid of waste
Answers
Answer:
Backyard burning of trash in a barrel, pile or outdoor boiler releases smoke into the air. ... Trash fires in burn barrels can smolder and as a result produce greater amounts of harmful chemicals in the smoke. Harmful chemicals can also be present in the ash.Explanation:
A 0.1 kg toy train car moving at 1.0 m/s runs into a stationary car with a mass of 0.15 kg. At what speed do they move off together?
Answers
We can use the conservation of momentum principle to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system. In this case, we can assume that there are no external forces acting on the two cars after they collide, so the total momentum of the system before the collision must be equal to the total momentum of the system after the collision.
The momentum of an object is defined as its mass multiplied by its velocity:
momentum = mass * velocity
Before the collision, the momentum of the first car (m1) is:
p1 = m1 * v1 = (0.1 kg) * (1.0 m/s) = 0.1 kg⋅m/s
Since the second car is stationary, its momentum before the collision is zero:
p2 = m2 * v2 = (0.15 kg) * (0 m/s) = 0 kg⋅m/s
The total momentum of the system before the collision is:
p1 + p2 = 0.1 kg⋅m/s + 0 kg⋅m/s = 0.1 kg⋅m/s
After the collision, the two cars move together with a common velocity (v), so the momentum of the system is:
p = (m1 + m2) * v
We can set the total momentum before the collision equal to the total momentum after the collision:
p1 + p2 = p
0.1 kg⋅m/s + 0 kg⋅m/s = (0.1 kg + 0.15 kg) * v
0.1 kg⋅m/s = 0.25 kg * v
v = 0.1 kg⋅m/s ÷ 0.25 kg
v = 0.4 m/s
Therefore, the two cars move off together at a speed of 0.4 m/s after the collision.
question is below............
Answers
The total distance traveled by the gardener is 8 meters. the magnitude of total displacement is approximately 7 meters.
Total distance covered by gardener = 2 + 1 +2 + 3= 8 meters
For the magnitude of displacement, we will take the shortest path for the gardener movement.
for displacement-
\(=\sqrt{( 0-4^{2}) +( 6-0^{2} )}\\=\sqrt{52} \\=7\)(approximately)
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Suppose you have 4 bulbs in a parallel circuit. If you were to add 2 more bulbs in
parallel with these 4, what would happen to the brightness of all the bulbs.
Answers
The correct answer is that the bulb will glow brighter when more bulbs are added in parallel.
How do the current and resistance alter as the number of circuits (bulbs) increases in parallel?The voltage across the paralleled lights will be equal to the battery's voltage, and the current through the light will be determined by V=IR, where R is the filament resistance. The parallel circuit will appear brighter because more current will be taken from a battery into it than a series one would.
When the brightness of the bulb rises, an increase in current can be seen. More light is produced in parallel circuit than by series of lights. Each bulb in a parallel circuit has the same voltage as the whole circuit . The other bulb is unaffected when the first bulb is unscrewed.
Each bulb has its own circuit in a parallel circuit. The circuit's resistance increases when more lights are added. Since each additional circuit provides an additional route for electrons to travel from one end of the circuit to the other, the resistance in the circuit reduces as more bulbs are added.
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A projectile is launched at an angle of 60° from the horizontal and at a velocity of
12.0 m/s. What is the horizontal velocity of the projectile? *
Answers
Answer:
60*12.0= 720 = v/60 * 12.0 squared which is 1,728
Explanation:
Horizontal velocity component: Vx = V * cos(α)
The horizontal velocity of the projectile is 6.0m/s
If a projectile is launched at an angle from the horizontal and at a velocity v, the horizontal velocity of the projectile is expressed as:
\(v_x =vcos \theta\)
Given the following parameters
v = 12.0m/s
\(\theta=60^0\)
Substitute the given parameters into the formula to have:
\(v_x=12.0cos60\\v_x=12.0(0.5)\\v_x=6.0m/s\\\)
Hence the horizontal velocity of the projectile is 6.0m/s
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1. express the following in proper SI form using the appropriate prefixes. a. 52500000 m b. 1000 g c. 2435200000
Answers
Answer:
a
\(L = 5.25*10^{7} \ m\)
b
\(m = 1 \ kg\)
c
\(t = 1.46112000000 *10^{11} \ s\)
Explanation:
From the question we are told that
Length is L = 52500000 m
Mass is
Time is 2435200000 minutes
Generally the proper SI for length is meters ,
Now converting the given length to proper SI form using the appropriate prefixes we have that
\(L = 5.25*10^{7} \ m\)
Generally the proper SI for mass is kilograms
converting grams to kilograms , we have
\(m =\frac{1000}{1000 }\)
=> \(m = 1 \ kg\)
Generally the proper SI for time is seconds
converting minutes to seconds , we have
\(t = 24352000000* 60\)
=> \(t = 146112000000 \ s\)
Now converting to the proper SI form using the appropriate prefixes
\(t = 1.46112000000 *10^{11} \ s\)
Air at 80 kPa and 400 K enters an adiabatic diffuser steadily at a rate of 6000 kg/h and leaves at 100 kPa. The velocity of the airstream is decreased from 230 to 30 m/s as it passes through the diffuser. Find (a) the exit temperature of the air and (b) the exit area of the diffuser.
Answers
Answer:
a) 425.6 K = 152.6 degree Celsius
b) 678.6 square centimeter
Explanation:
Initial enthalpy = Final enthalpy
m(h1 + v1^2/2) = m(h2 + v2^2/2)
(h1 + v1^2/2) = (h2 + v2^2/2)
h 2 = (h1 + v1^2/2) - (v2^2/2)
h 2 = 400.98 + (230^2 – 30^2)/2 * 10^-3
= 426.98 KJ/Kg
T2 = T1’ + (T2’ -T1’)(h2-h1’)/( h2’-h1’)
T2 = 420 + (430-420)(431.43-421.26)(426.98-421.26)/(431.43 – 421.26)
T2 = 425.6 K = 152.6 degree Celsius
Area = mRT2/P2V2
Area = (600/60*60*1) *0.287*425.6/(100*30) *10^4
Area = 678.6 square centimeter
You jog at 9.5 km/h for 8.00 km; then you jump into a car and ride an additional 16.0 km. What average speed must the car have for the average speed for the entire 24.0-km trip to be 20 km/h
Answers
Average speed must the car have for the average speed for the entire 24.0 km trip 67.039 km/hr.
Equation :Average speed for entire journey (jogging + drive) = 20 km/hr
total distance traveled = 24 km
total time spent (on jog + drive) = total distance/average speed
total time spent (on jog + drive) = 24/20
total time spent (on jog + drive) = 1.2 hr
Jogging:
Speed = 9.5 km/hr
Distance = 8.0 km
Time spent jogging = Distance/Speed
= 8.0 / 9.5 = 0.842 hr
Driving car :
Speed = ?
Distance = 24 km
time spent driving = total time spent on journey - time spent jogging
time spent driving = 1.2 - 0.842 = 0.358 hr
average speed for driving = distance / time
average speed for driving = 24/0.358
average speed for driving = 67.039 km/hr
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Scientists monitor the ozone layer by taking air samples by airplane or weather balloons. What atmospheric layer do the scientists collect the ozone samples from?
Answers
Scientists typically collect ozone samples from the stratosphere, which is the atmospheric layer located between about 10 and 50 kilometers (6 to 30 miles) above the Earth's surface.
What is the stratosphere?The stratosphere is the layer of the Earth's atmosphere located above the troposphere and below the mesosphere. It extends from about 10 kilometers (6 miles) to about 50 kilometers (30 miles) above the Earth's surface.
The stratosphere is characterized by a gradual increase in temperature with altitude, due to the absorption of ultraviolet radiation by ozone in the stratosphere.
This is where most of the Earth's ozone is found and where the ozone layer is located. The ozone layer absorbs harmful ultraviolet (UV) radiation from the sun, protecting life on Earth from its harmful effects. Scientists collect air samples from this layer using airplanes or weather balloons equipped with specialized instruments.
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Kindly please tell me the answer to this question...
Answers
Following are the answers:
Pressure = \(force/area = 1.92 N/0.196 m^2 = 9.79 N/m^2\) or 9.79 PaDensity = Pressure/ (acceleration due to gravity x height) =\(9.79 N/m^2 / (9.8 m/s^2 x 0.92 m)\) = 1060 kg/m^3.What is the pressure and density?1. To calculate the pressure exerted by the water column on the surface of the mercury, we can use the formula:
Pressure = force/area
The force is the weight of the water column and the area is the cross-sectional area of the container.
The weight of the water column is given by the mass of the water times the acceleration due to gravity:
mass = density x volume
volume = area x height
So, mass = density x area x height = 1000 kg/m^3 x pi x (0.025 m)^2 x 0.25 m = 0.196 kg
Weight = mass x acceleration due to gravity =\(0.196 kg * 9.8 m/s^2\) = 1.92 N
The cross-sectional area of the container is pi x (0.025 m)^2 =\(0.196 m^2.\)
So, Pressure = force/area = \(1.92 N/0.196 m^2 = 9.79 N/m^2\) or 9.79 Pa
2. To calculate the density of the oil, we can use the formula:
density = mass/volume
Since the height of the oil column is 0.92 m and the cross-sectional area of the container is 0.196 m^2, the volume of the oil column is 0.196 m^2 x 0.92 m = 0.18012 m^3.
We do not know the mass of the oil, but we can calculate it using the pressure exerted by the oil column on the surface of the mercury:
Pressure = force/area = density x acceleration due to gravity x height
So, density = Pressure/ (acceleration due to gravity x height) = 9.79 N/m^2 / (9.8 m/s^2 x 0.92 m) = 1060 kg/m^3.
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Why are the orbits of planets only nearly circular and not perfectly circular?
PLEASE HELP!!!!!!!!!!!!!
Answers
Explanation:
this is my answer this is helpful for you
How do you add sound waves?
Answers
The addition of two sound waves produces a new wave of higher amplitude if their compressions and refractions line up. It is also known as constructive interference.
What is interference?Interference can be described as a phenomenon in which two waves combine by adding at every single point in space and time, to form a resultant wave of greater or lower amplitude.
Constructive and destructive interference occurs in the interaction of waves that are correlated with each other because they come from the same source.
When two sound waves propagate in the same direction in phase with each other, their amplitude gets added, and the resultant wave is produced from constructive interference.
When two waves interfere with each other and have a displacement in the opposite direction. When a crest of a wave meets the trough of another wave, the waves undergo destructive interference.
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which is a property of bases?
Answers
Answer:
to turn red litmus blue and react with acid to form salt
How do I find the mass in kg
Answers
To find the mass in kilograms, you need to know the object's weight in newtons and the acceleration due to gravity. The formula for finding mass is mass = weight / acceleration due to gravity. So if you have an object with a weight of 100 N and the acceleration due to gravity is 9.8 m/s^2, the mass would be 10.204 kg.
The mass of the block is 0.025 kg or 25 g, when the spring has k = 28 N/m, and compresses 0.11 m before bringing the block to rest.
When a block is dropped onto a spring with k=28 N/m, the block has a speed of 3.2 m/s just before it strikes the spring. If the spring compresses an amount of 0.11 m before bringing the block to rest, what is the mass of the block?The formula for the spring potential energy is given as follows; PE = (1/2) kx² where k is the spring constant and x is the amount of deformation of the spring. Substituting the values given;PE = (1/2) 28 (0.11)²PE = 0.16972 J. According to the law of conservation of energy, the potential energy stored in the spring at maximum compression is equal to the kinetic energy the block had before it struck the spring;KE = (1/2) mv²where m is the mass of the block and v is its velocity.Substituting the values;0.16972 = (1/2) m (3.2)²m = 0.025 kg or 25 gTherefore, the mass of the block is 0.025 kg or 25 g.For more questions on mass
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A block of wood weighing 55.0 N is sliding on a surface. If a force of 37.1 N is necessary to keep it sliding at a constant velocity, what is the coefficient of kinetic friction of the wood on the surface?
Answers
The coefficient of kinetic friction of the wood on the surface is 0.675.
Kinetic friction:This is the force that acts between two moving surfaces. The magnitude of the force depends on the coefficient of kinetic friction.
To calculate the coefficient of kinetic friction of the wood on the surface, we use the formula below.
⇒ Formula:
F = Wμ................ Equation 1⇒ Where:
F = Force needed to keep the block sliding at a constant velocity.W = Weight of the woodμ = coefficient of kinetic friction of the wood on the surface⇒ Make μ the subject of the equation
μ = F/W............... Equation 2From the question,
⇒ Given:
F = 37.1 NW = 55.0 N⇒ Substitute these values into equation 2
μ = 37.1/55μ = 0.675.Hence, the coefficient of kinetic friction of the wood on the surface is 0.675.
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can someone help with me 1,2,3 please I will mark brainless .
Answers
Answer:
1) A. .33 hr
2) B. 6ft
3) A. 58mi/hr
2 An electric kettle is marked "230V, 1.5 kW.
a Explain what these numbers mean.
b Calculate the correct fuse that should be used.
c Explain why a 230V, 100 W bulb glows more brightly than a 230 V, 60 W
bulb when both are connected to the mains supply.
Answers
The power needed to boil the water is divided by the element's power output, and the result is multiplied by 100 to get the efficiency of the kettle as a percentage. The answer is 79 %.
To Find the efficiency of electric kettle ?We are informed that
Electric kettle power is 1 kW.
Electric kettle voltage is 230 V.
The time it takes the kettle to bring the water to boiling point is 7.5 minutes.
1 kg = mass of water.
Heat generated equals V x I x t + Pt.
generated heat = 1000 W x 7.5 x 60
Heat absorbed equals (100 - 15) x 1 x 4200 = 4200 x 85
Efficiency is determined by multiplying the heat produced by the heat absorbed by 100.
= 4.2 x 85 x 10^3 / 4.5 x 10^5 x 100
= 357 / 4.5 = 79 %
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Part C Now, grab Tracker’s protractor tool (the green angle in the video frame) and measure the angle of incidence and the angle of refraction for the frame numbers specified in the table below. Hints: To advance the video a frame at a time, use the step buttons on the right. Position the vertex of the protractor exactly at the origin of the coordinate axis. Move the arms of the protractor so that one arm is on the vertical axis (above or below, as appropriate) and the other on the light ray.
Answers
In order to measure the angle of incidence and the angle of refraction using Tracker's protractor tool (the green angle in the video frame), the following steps should be followed:
Step 1: Open the video in Tracker software.
Step 2: Click on the "Measure" button on the toolbar at the top of the software.
Step 3: From the dropdown menu, select "Angle".
Step 4: Click on the "protractor tool" icon (the green angle in the video frame).
Step 5: Position the vertex of the protractor exactly at the origin of the coordinate axis and move the arms of the protractor so that one arm is on the vertical axis (above or below, as appropriate) and the other on the light ray.
Step 6: Measure the angle of incidence and the angle of refraction for the frame numbers specified in the table below by using the step buttons on the right to advance the video a frame at a time.
Step 7: Record the measured angles in the table below. Note that the angle of incidence should be measured on the incident ray (the ray that is coming from the left), and the angle of refraction should be measured on the refracted ray (the ray that is coming from the right).In conclusion, by following these steps, one can measure the angle of incidence and the angle of refraction using Tracker's protractor tool.
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There are two seemingly inconsistent models of light. One model suggest light ispure energy wave and the other suggests that light is made up of particles orphotons. How would you explain the results when white light passes through a prismand is split into different colors?White light is made up of waves that can transform themselves.White light is made of particle and white particle are blocked by the prism.White light is made up of waves of different frequencies.White light is made up of particles of many colors.
Answers
We have that the white light is a mixture of many different colors each with a different frequency. White light can be sipe into a spectrum of these colors
Therefore the correct choice is
White light is made up of waves of different frequencies
A __________is a large cool star located in the top right of the HR diagram.
Answers
Answer:
Vermeer star is located at the top of large Venus
A 12 volt power supply is connected
to two 30 Ohm resistors in parallel.
What is the voltage drop across the
resistors?
12 V
30 Ω
30 Ω
[?] volts
Answers
24 volts is the voltage drop across each of the resistors in the parallel configuration.
When resistors are connected in parallel, they share the same voltage across them. Therefore, the voltage drop across each resistor in this scenario would be the same.
Given:
Power supply voltage (V) = 12 V
Resistance of each resistor (R) = 30 Ω
Since the resistors are in parallel, the total resistance (R_total) can be calculated using the formula:
1/R_total = 1/R1 + 1/R2
Substituting the values:
1/R_total = 1/30 Ω + 1/30 Ω
1/R_total = 2/30 Ω
R_total = 15 Ω
Now, we can find the current flowing through the resistors (I) using Ohm's Law:
I = V / R_total
I = 12 V / 15 Ω
I = 0.8 A
Since the voltage drop across each resistor is the same, we can find it using Ohm's Law:
V_drop = I * R
V_drop = 0.8 A * 30 Ω
V_drop = 24 V
Therefore, the voltage drop across each of the resistors in the parallel configuration is 24 volts.
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