Use conservation of energy to find the boxes' speed when box B has fallen a distance of 0.50 m. Assume a frictionless upper surface.
Boxes A and B in the figure have masses of 11.5 kg and 2.5 kg, respectively. The two boxes are released from rest.

The y-intercept of the lens represents the focal length of the lens.

The y-intercept of a lens refers to the point where the incident rays, parallel to the principal axis, converge or appear to diverge after passing through the lens. In other words, it represents the distance from the lens to the focal point.

When an object is placed between the focal point and the lens, a specific type of image is produced. This situation is known as an object placed in front of a converging lens. The characteristics of the image formed in this case are as follows:

1. Type: The image is virtual, meaning it cannot be projected onto a screen. It can only be seen when looking through the lens.

2. Orientation: The image is upright. It appears in the same orientation as the object.

3. Size: The image is magnified compared to the object. It is larger in size.

These three characteristics hold true when the object is positioned between the focal point and the lens. It is important to note that the specific values of the image's size and magnification would depend on the specific distance of the object from the lens and the focal length of the lens.

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Jack and jill travel up a hill at a speed of 2 mi/h. They travel back down the hill at a speed of 4 mi/h. Their average speed for the entire trip is 8/3 mi/h

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity

Let x be the distance of hill from one side.

⇒ Distance for round trip = 2x

Let t1 and t2 be the time taken by them when going and returning back respectively.

Total time taken for round trip = t1+ t2

we have,

speed = distance/ time

⇒time = distance/speed

so, t1 = x/2

t2= x/4

Average speed for round trip = total distance/ total time

\(average speed = \frac{2x}{ \frac{x}{2} + \frac{x}{4} } \)

= 8/3 mi/h

therefore, Their average speed for the entire trip is 8/3 mi/h.

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M = mass of the ball A = 5.0 kg

m = mass of the ball B = ?

V = initial velocity of the ball A before collision = 20 m/s

v = initial velocity of the ball B  before collision = 10 m/s

V' = final velocity of the ball A after collision = 10 m/s

v' = final velocity of the ball B after collision = 15 m/s

using conservation of momentum

M V + m v = M V' + m v'

(5.0) (20) + m (10) = (5.0) (10) + m (15)

100 + 10 m= 50 + 15 m

5 m = 50

m= 10 m/s

Answer: 5

Explanation:

A massive and fast moving bowling ball must have a large momentum while a light and slow moving tennis ball must have a small momentum. However, a fast tennis ball may have the same momentum as a slow rolling bowling ball due to its high velocity. Given two objects of the same size but of different materials, the heavier (denser) object will fall faster because the drag and buoyancy forces will be the same for both, but the gravitational force will be greater for the heavier object.

\( \)

The coefficient of friction between the ice and the puck is μ = 0.031 (option B).

1. To find the coefficient of friction (μ), we first need to find the acceleration (a) of the hockey puck.
2. Using the final velocity (vf), initial velocity (vi), and distance (d) given, we can find the acceleration using the following formula: vf^2 = vi^2 + 2ad
3. Rearrange the formula to solve for a: a = (vf^2 - vi^2) / (2d)
4. Plug in the given values: a = ((0)^2 - (7.00 m/s)^2) / (2 × 80.0 m) = -24.5 m/s^2 / 160 m = -0.153 m/s^2
5. Now we can find the coefficient of friction (μ) using the formula: μ = -a / g, where g is the acceleration due to gravity (9.81 m/s^2).
6. Calculate μ: μ = -(-0.153 m/s^2) / 9.81 m/s^2 = 0.0156 / 0.5 = 0.031

Hence, By calculating the acceleration and using it to find the coefficient of friction, we determined that the correct answer is μ = 0.031 (option B).

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The modified version of the coefficient of determination (R²) that takes into account the number of observations and independent variables is called the adjusted R-squared (R²).

The adjusted R-squared is a statistical measure that provides a more reliable assessment of a model's goodness of fit by penalizing the inclusion of unnecessary independent variables and considering the sample size.

It addresses the issue of overfitting, where adding more variables may artificially inflate the R² value. By adjusting for the complexity of the model and the degrees of freedom, the adjusted R-squared offers a more accurate indication of how well the model explains the variation in the dependent variable.

It is a useful tool for evaluating and comparing different regression models.

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Answer:

7716.179 pounds? Are you asking for a conversion or something different?

Answer:

4.2 m/s

the balls final speed is V (m/s)

because the clay ball hits another and the two stick together

=> 0,35.4,2 + 0,35.4,2 = (0,35 + 0,35).V

<=> 2,94 = 0,7V

<=> V = 2,94/0,7 = 4,2

For a clay ball with a mass of 0.35 kg, the ball's final speed is mathematically given as

V2= 4.2

Question Parameter(s):

A clay ball with a mass of 0.35 kg

Hits another 0.35 kg ball at rest and the two stick together.

The first ball's initial speed is 4.2m/s.

Generally, the equation for the conservation of momentum is mathematically given as

M1v1=m2v2

Therefore

0.35*4.2 + 0.3*5.4.2 = (0.35 + 0.35)*V

2,94 = 0,.7V

V2 = 2.94/0.7

V2 = 4.2

In conclusion

V2= 4.2

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The statements best describes how a star chart should be held while facing north is, The edge of the map labeled south should be held towards the observer.

What is star chart ?

A map or diagram of the stars and other celestial bodies in the sky is called a star chart. The locations of the stars, constellations, planets, and other celestial bodies are often displayed at a certain time and location on Earth. Star maps can be used to locate celestial bodies in the night sky, to organise astronomical observations, or to track their movements through time.

Given that,

The statements,

In between following options, best describes how a star chart should be held while facing north is,

The edge of the map labeled south should be held towards the observer

This is because when facing north, the direction labeled "south" on the map should correspond to the direction of the actual south, and thus be facing the observer.

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11223.9J or 11.2239 kJ is the total internal energy of the gas.

Internal energy, which results from the motion of matter at the molecular level, is a type of energy that exists in all systems. For internal energy, the letter U is used, and the joule is the unit of measurement (J).

As a substance changes from one state or phase to another—from solid to liquid to gas—its internal energy also rises. It is possible to imagine planetary bodies as a fusion of heat engines and heat reservoirs.

The heat engines transform some of the thermal energy stored in the heat reservoirs into different forms of mechanical, electrical, and chemical energy.

The formula for total internal energy of gas is

(3/2)nRT

where n = amount of substance

R = Ideal gas constant

T = temperature

Put the value in the equation

(3/2)nRT

= (3/2)(3)( 8.314)(300)

= 11223.9J

Thus, 11223.9J or 11.2239 kJ is the total total internal energy of the gas.

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Answer:

mass

gravitational pull

Answer:

Yes.

Explanation:

Answer: 25.90 m/sec

Explanation:

Speed = Distance / Time

Speed = 1010 / 39

Speed = 25.90 m/s

Answer

I am not sure but it is may be 50J

I hope that's, this answer is fine.

Answer:

t = 0.5 s

Explanation:

We know that the distance from the batter to the bleachers is 170 m, and we are trying to find the time it takes for the sound of the ball hitting the bat to travel that distance.

We can use the formula v = d/t, where v is the speed of sound in air (we know that sound in air travels at a speed of 340 m/s), d is the distance the sound travels (170 m in this case), and t is the time it takes for the sound to travel that distance.

Rearranging the formula to solve for t, we get t = d/v. Plugging in the values we know, we get:

t = 170 m / 340 m/s

t = 0.5 s

Therefore, it takes 0.5 seconds for the sound of the ball hitting the bat to travel 170 meters from home plate to the bleachers.

The differential equation which describes the temperature of the object over time is;

dH/dt = -k (H-S), where k = 0.97. The solution to this differential equation is given by H(t) = S + 65e^(-0.97t).

Newton’s law of heating and cooling is an application of the first law of thermodynamics. The law suggests that the rate of change of temperature of an object is proportional to the difference between its temperature and the temperature of the surroundings.

A warm object is placed in a refrigerator where the surrounding temperature is cooler, and the temperature of the object decreases. This phenomenon can be explained using differential equations. Given that H(t) is the temperature of the object being cooled and S is the surrounding temperature, the differential equation which describes the temperature of the object over time is given by;dH/dt = -k (H-S)

where k is the constant of proportionality.To solve this differential equation, we can use separation of variables, such that;

dH/dt = -k (H-S)dH/(H-S) = -k dt

Integrating both sides, we get;ln|H-S| = -kt + Cwhere C is the constant of integration.Rearranging, we have;

|H-S| = e^(-kt+C)

At time, t = 0, H = 100 and after 30 minutes the object is 75 degrees; t = 0.5 hours, H = 75. We can use these values to solve for C and k as follows;

|100-35| = e^(C) => 65 = e^(C)     …(1)

and|75-35| = e^(-0.5k+C) => 40 = e^(C) e^(-0.5k) => e^(-0.5k) = 40/65 => e^(-0.5k) = 8/13 => -0.5k = ln(8/13) => k = -2ln(8/13) => k = 0.97    …(2)

Substituting equation (1) into (2), we get;H-S = 65e^(-0.97t)  =>  H(t) = S + 65e^(-0.97t)

Therefore, the differential equation which describes the temperature of the object over time is;dH/dt = -k (H-S), where k = 0.97.

The solution to this differential equation is given by H(t) = S + 65e^(-0.97t).

The differential equation which describes the temperature of the object over time is;

dH/dt = -k (H-S), where k = 0.97. The solution to this differential equation is given by H(t) = S + 65e^(-0.97t).

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A new CFD method for determination of translational is RANS simulations

Using numerical analysis and data structures, the field of computational fluid dynamics (CFD) studies and resolves issues involving fluid flows. The computations necessary to model the fluid's free-stream flow and its interactions with surfaces constrained by boundary conditions (both liquids and gases) are done on computers. Better answers can be found using high-speed supercomputers, which are frequently needed to address the most challenging issues.

Five prominent CFD methods -

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A cyclist peddles from 5ft/s to 12ft/s over the distance of 50 ft. The acceleration will take place for 1.19ft/s^2. It can be calculated by the formula v^2-u^2 = 2as.

v^2-u^2 = 2as

a=v^2-u^2/2s =144-25/2(50)

a=119/100 =1.19ft/s^2

What is acceleration?

The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. The rate at which velocity changes is called acceleration.

What three forms of acceleration are there?

The three main types of accelerated motions are uniform acceleration, non-uniform acceleration, and average acceleration.

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A cyclist peddles from 5ft/s to 12ft/s over the distance of 50 ft. The acceleration will take place for 1.19ft/s^2. It can be calculated by the formula v^2-u^2 = 2as.

v^2-u^2 = 2as

a=v^2-u^2/2s =144-25/2(50)

a=119/100 =1.19ft/s^2

The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. The rate at which velocity changes is called acceleration.

The three main types of accelerated motions are uniform acceleration, non-uniform acceleration, and average acceleration.

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The total displacement Erwin carrie’s his cat around for a walk is 112. 80 meter.

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.

Given that Erwin carrie’s his cat around for a walk. Erwin walks 25 m [N] then 110 m [S 40* E]. So the total displacement is 112.80 meter

The total displacement Erwin carrie’s his cat around for a walk is 112. 80 meter.

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The height of the parabolic arch bridge at distances of 10, 30, and 50 feet from the center is 19.7917, 23.9583, and 25.0000 feet, respectively.

To answer this question, we must first choose a suitable rectangular coordinate system. The origin, (0,0), of the coordinate system should be located at the center of the bridge, which is located at x = 0. The y-axis should be perpendicular to the bridge and the x-axis should be parallel to the bridge.

To find the height of the arch at distances of 10, 30, and 50 feet from the center, we can use the formula for a parabolic arch, y = a(x - h)² + k. We can calculate the coefficients a and k by using the given maximum height and span of the bridge. We can set y = 25 and x = 120, and then solve for a and k.

\(a = \dfrac{-25}{1202}\)

a = -0.04167,

k = 25

Now, we can substitute the distances of 10, 30, and 50 feet into the formula, and calculate the corresponding height values.

At x = 10 feet: y = -0.04167(10 - 0)2 + 25 = 19.7917 feet

At x = 30 feet: y = -0.04167(30 - 0)2 + 25 = 23.9583 feet

At x = 50 feet: y = -0.04167(50 - 0)2 + 25 = 25.0000 feet

Therefore, the height of the parabolic arch bridge at distances of 10, 30, and 50 feet from the center is 19.79, 23.95, and 25.00 feet, respectively.

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The difference in the mass of carbon dioxide in 500 kg of air in 2013 compared to 1800 is 0.06 Kg

Mass = percent × mass of air

Mass of CO₂ = 0.028% × 500

Mass of CO₂ = 0.14 Kg

Mass = percent × mass of air

Mass of CO₂ = 0.040% × 500

Mass of CO₂ = 0.2 Kg

Difference = mass in 2013 - mass in 1800

Difference = 0.2 - 0.14

Difference = 0.06 Kg

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Answer:

A) What is the moment of inertia of the bowling ball?

The moment of inertia of a bowling ball is 2/5mr

2

, where m is the mass of the ball and r is the radius. In this case, m=6 kg and r=10.8 cm=0.108 m. Therefore, the moment of inertia of the bowling ball is:

I=

5

2

​

(6 kg)(0.108 m)

2

=0.023328 kg m

2

B) What is the translational kinetic energy of the bowling ball?

The translational kinetic energy of a bowling ball is  

2

1

​

mv

2

, where m is the mass of the ball and v is the velocity. In this case, m=6 kg and v=8 m/s. Therefore, the translational kinetic energy of the bowling ball is:

KE

t

​

=

2

1

​

(6 kg)(8 m/s)

2

=192 J

C) What is the initial rotational kinetic energy of the bowling ball?

The initial rotational kinetic energy of a bowling ball is  

2

1

​

Iω

2

, where I is the moment of inertia of the ball and ω is the angular velocity. In this case, I=0.023328 kg m

2

 and ω=v/r=8 m/s/0.108 m=74.074 rad/s. Therefore, the initial rotational kinetic energy of the bowling ball is:

KE

r

​

=

2

1

​

(0.023328 kg m

2

)(74.074 rad/s)

2

=119.36 J

D) The bowling ball comes to the bottom of a ramp that is inclined 20 degrees with respect to the horizontal. What maximum height will the ball reach up this ramp?

The maximum height that the ball will reach up the ramp can be found using the following equation:

h=

2g

v

2

​

sin

2

(θ)

where v is the initial velocity of the ball, g is the acceleration due to gravity, and θ is the angle of the ramp. In this case, v=8 m/s, g=9.8 m/s

2

, and θ=20

∘

. Therefore, the maximum height that the ball will reach up the ramp is:

h=

2(9.8 m/s

2

)

(8 m/s)

2

​

sin

2

(20

∘

)=1.53 m

Explanation:

Answer:

Explanation:

See attachment.

Decreasing the mass of the objects   No.  Force will change.

Increasing the temperature of the objects Yes,  No change in force (at most a very small change if the heat causes excessive expansion, reducing the distance, although 1/2 will be further apart)

Increasing the distance between the objects No.  Force will change.

Decreasing the distance between the objects  No.  Force will change.

The most scientific guess (hypothesis) based on what is known about the behavior of galaxies is that Galaxies are continuously moving away from each other. This hypothesis can be tested using Hubble's Law.

Hubble's law indicates that almost all galaxies are moving apart from one another because the universe as a whole is expanding. Choose any two galaxies at arbitrarily, and they're most likely traveling apart from each other.

Hubble discovered that galaxies move away from us at a rate proportionate to their distance: more distant galaxies move away faster than closer ones. The accompanying graphic shows Hubble's classic graph of measured velocity vs. distance for neighboring galaxies.

The graph shows a linear relationship between galaxy velocity (v) and distance (d).

The equation for the above linear relationship is:

                                          v = H₀ x d

Where:

H₀ is the expansion rate

v = velocity of the galaxy; and

d = distance.

Using the above formula, the astronomer can measure or test to know whether indeed the new galaxy is moving relative to the Milky Way galaxy and at what rate.

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The state space averaged model is a mathematical representation used to analyze the behavior and control of power electronic converters such as the Buck converter and Boost converter.

1. Buck Converter:

The Buck converter is a step-down DC-DC converter that efficiently converts a higher input voltage to a lower output voltage. It consists of a power switch (MOSFET or BJT), an inductor (L), a diode (D), a capacitor (C), and a load resistor (RL). Let's derive the state space averaged model for the Buck converter.

a. Derivation:

The state space averaged model is derived by considering the average behavior of the circuit over a switching period. The key steps involved in the derivation are as follows:

Step 1: Define State Variables:

We define two state variables for the Buck converter:

- Inductor current: iL

- Capacitor voltage: vC

Step 2: State Equations:

The state equations describe the dynamics of the system in terms of the state variables and their derivatives.

- Inductor current equation:

Using Kirchhoff's voltage law, the equation for the inductor current can be derived as:

diL/dt = (v_in - vC)/L - (1 - D) x v_out / L

- Capacitor voltage equation:

Using the capacitor equation, the equation for the capacitor voltage can be derived as:

C x dvC/dt = (1 - D) x v_out - iL x RL

Step 3: Output Equation:

The output equation relates the output voltage to the state variables.

v_out = vC

Step 4: State Space Formulation:

By expressing the state equations in matrix form, we can obtain the state space averaged model for the Buck converter:

dx/dt = Ax + Bu

y = Cx + Du

Where:

- x = [iL, vC]T is the state vector.

- u = D is the duty cycle.

- y = v_out is the output voltage.

The matrices A, B, C, and D can be obtained by rearranging the state equations and output equation.

2. Boost Converter:

The Boost converter is a step-up DC-DC converter that converts a lower input voltage to a higher output voltage. It consists of a power switch (MOSFET or BJT), an inductor (L), a diode (D), a capacitor (C), and a load resistor (RL). Let's derive the state space averaged model for the Boost converter.

a. Derivation:

Similar to the Buck converter, the state space averaged model for the Boost converter can be derived using the same steps.

Step 1: Define State Variables:

- Inductor current: iL

- Capacitor voltage: vC

Step 2: State Equations:

- Inductor current equation:

diL/dt = (v_in - vC)/L - D x v_out / L

- Capacitor voltage equation:

C x dvC/dt = D x v_out - (1 - D) x iL x RL

Step 3: Output Equation:

v_out = D x vC

Step 4: State Space Formulation:

The state space averaged model for the Boost converter can be obtained in the same matrix form as the Buck converter:

dx/dt = Ax + Bu

y = Cx + Du

Where:

- x = [iL, vC]T is the state vector.

- u = D is the duty cycle.

- y = v_out is the output voltage.

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Answer:

by raising them in an environment in wich it is common and giving false information about other races to install bad stereo types and distrust in the child who will grow up to not know any better do to the dumb ignorant parent raised the same way

Explanation:

?????? thats all i got im not a politician BLM

A neutralization reaction is when an acid and a base react to form water and salt and involves the combination of H+ ions and OH- ions to generate water.

Neutralization is a chemical reaction between an acid and a base, resulting in the formation of salt and water. This reaction is also known as acid-base neutralization. The pH scale is used to measure the acidity or basicity of a solution, with values ranging from 0 to 14. A pH of 7 is considered neutral, while pH values below 7 indicate acidity, and those above 7 indicate basicity.

The process involves the transfer of protons (H+ ions) from the acid to the base, causing the formation of a water molecule and a salt. The salt is formed from the cation of the base and the anion of the acid. The neutralization reaction is important in various applications, such as in the production of medicines, fertilizers, and cleaning agents. It is also essential in maintaining the pH balance in biological systems, including the human body.

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The optimal values of \(q_1\) and \(q_2\) are determined by these equations, which are functions of Michael's income and the prices of the goods.

The given problem describes Michael's utility maximization problem with a constant elasticity of substitution (CES) utility function. The objective is to find the optimal values of \(q_1\) and \(q_2\) in terms of Michael's income (Y) and the prices of the two goods (\(p_1\) and \(p_2\)).

1. Substitute the income constraint into Michael's utility function:

\(U(q_1, q_2) = (q_1^\rho + q_2^\rho)^(1/\rho)\)

  s.t. \(Y = p_1q_1 + p_2q_2\)

  We can rewrite Michael's budget constraint as \(q_2 = (Y - p_1q_1)/p_2\). Substituting this expression into his utility function, we have:

 \(U(q_1, p_2, Y) = (q_1^\rho + [p_2(Y - p_1q_1)/p_2]^\rho)^{(1/\rho)\)

  By making this substitution, we have converted the constrained maximization problem with two control variables (\(q_1\) and \(q_2\)) into an unconstrained problem with one control variable \((q_1)\).

2. Use the standard unconstrained maximization approach to determine the optimal value for \(q_1\). To obtain the first-order condition, we differentiate the utility function with respect to \(q_1\) and set it equal to zero:

\(\delta U / \delta q_1 = \rho(q_1^{(\rho-1)} + \rho[p_2(Y - p_1q_1)/p_2]^{(\rho-1)}(-p_1/p_2)) = 0\)

Simplifying and solving for \(q_1\):

\(\rho q_1^{(\rho-1)} - \rho(p_1/p_2)[p_2(Y - p_1q_1)/p_2]^{(\rho-1)} = 0\)

\(\rho q_1^{(\rho-1)} - \rho(p_1/p_2)[Y - p_1q_1]^{(\rho-1)} = 0\)

\(\rho q_1^{(\rho-1)} = \rho(p_1/p_2)[Y - p_1q_1]^{(\rho-1)}\)

\(q_1^{(\rho-1)} = (p_1/p_2)[Y - p_1q_1]^{(\rho-1)\)

\(q_1^{(\rho-1)} = (p_1/p_2)^{(1-\rho)}[Y - p_1q_1]^{(\rho-1)}\)

\(q_1^{(\rho-1)} = (p_1/p_2)^{(1-\rho)}(Y - p_1q_1)^{(\rho-1)}\)

\(q_1^{(\rho-1)} = (p_1/p_2)^{(1-\rho)}(Y^{(\rho-1)} - (\rho-1)p_1q_1(Y - p_1q_1)^{(\rho-2)})\)

  This equation represents Michael's optimal \(q_1\) as a function of his income (Y) and the prices (\(p_1\) and \(p_2\)).

3. Similarly, we can derive a similar expression for his optimal \(q_2\):

\(q_2^{(\rho-1)} = (p_2/p_1)^(1-\rho)(Y^{(\rho-1)} - (\rho-1)p_2q_2(Y - p_1q_2)^{(\rho-2)})\)

  This equation represents Michael's optimal \(q_2\) as a function of his income (Y) and the prices (\(p_1\) and \(p_2\)).

Therefore, these equations, which depend on Michael's income and the prices of the commodities, determine the ideal values of \(q_1\) and \(q_2\).

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