Saturn takes 29.5 Earth-years to revolve around the Sun. In one century (100 years), both Saturn and Earth will complete several revolutions of the Sun. Which of the following correctly compares the number of revolutions that the two planets will complete?

The current in amperes going through this resistor is 0.005208 Amperes or 5.208 mA.

Ohm's law is one of the most fundamental laws of electrical engineering. It states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. Mathematically, the relationship is given by the equation: I = V / R, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms.

In our example, we are given a resistor with a resistance of 960 ohms and a potential difference (voltage) of 4.98 volts across its two terminals. We need to divide the voltage by the resistance to find the current flowing through the resistor. Using the equation I = V / R, we have: I = 4.98 volts / 960 ohms = 0.005208 Amperes or 5.208 milliamperes.

So, the current flowing through the 960-ohm resistor is 5.208 milliamperes.

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The velocity of the ball just before it hits the ground is 35 m/s.

What is velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in a specific direction. It is defined as the derivative of an object's position with respect to time. Mathematically, velocity is expressed as:

v = Δx / Δt

The velocity of the ball just before it hits the ground can be calculated using the concept of projectile motion. In this case, we have two components of motion: horizontal and vertical. The horizontal component is constant and equal to the initial velocity, while the vertical component is affected by gravity and follows a parabolic path.

We can use the following equation to find the time it takes for the ball to fall from the roof to the ground:

h = vi * t + 0.5 * g * t²

where h is the height of the building (45 m), vi is the initial velocity (which we are trying to find), g is the acceleration due to gravity (9.8 m/s²), and t is the time it takes for the ball to fall.

Since the ball lands 105 m from the base of the building, we can also use the horizontal component of the motion to find the time:

d = vi * t

where d is the horizontal distance traveled by the ball (105 m).

We can equate these two equations to eliminate time and find the velocity of the ball:

h = vi * (d/vi) + 0.5 * g * (d/vi)²

45 = 105 + 0.5 * 9.8 * (d/vi)²

(d/vi)² = 2 * h / g = 2 * 45 / 9.8 = 9.18

d/vi = 3

vi = d / 3 = 105 / 3 = 35 m/s

So, the velocity of the ball just before it hits the ground is 35 m/s.

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The orbital period of the asteroid to the nearest hundredth of a year is 34.43 years.

The orbital period of an asteroid is given by the formula T = 2 × pi × (a³ / G × M)^(1/2). To find the orbital period, we need to calculate T using the given values for a, G, and M.

a = 5.07 a.u.

G = 6.67 x 10⁻¹¹ N × m² / kg²

M = 1.989 x 10^30 kg

T = 2 × pi × (a³ / G × M)^(1/2)

T = 2 × pi × (5.07³ / 6.67 x 10⁻¹¹ × 1.989 x 10³⁰)^(1/2)

T = 2 × pi × (156.9837 / 6.67 x 10⁻¹¹ × 1.989 x 10³⁰)^(1/2)

T = 2 × pi × (1.8048 x 10¹² / 6.67 x 10⁻¹¹ × 1.989 x 10³⁰)^(1/2)

T = 2 × pi × (1.8048 x 10¹² / 1.38 x 10⁻²³)^(1/2)

T = 2 × pi × (1.30 x 10³⁵)^(1/2)

T = 2 × pi × (3.66 x 10¹⁷)^(1/2)

T = 2 × pi × 1.91 x 10⁹

T = 12.57 x 10⁹

T = 12.57 / 365.25

T = 34.43 years

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The spheres are now 6.08 cm apart. The force between two charged spheres is proportional to the product of their charges and inversely proportional to the square of the distance between them.

This means that if the force is tripled, the distance between the spheres must have been reduced by a factor of the square root of 3. To find the new distance, we can use the formula:

d_new = d_old / √3

Where d_old is the original distance of 10.68 cm and d_new is the new distance. Plugging in the values, we get:

d_new = 10.68 cm / √3 = 6.08 cm

So, the spheres are now 6.08 cm apart.

In this case, F_old / F_new = 1/3, since the force has been tripled. Plugging in the original distance of 10.68 cm and the value for F_old / F_new, we can calculate the new distance. The final result shows that the spheres are now 6.08 cm apart.

This result shows how the force between charged spheres is directly influenced by the distance between them. Understanding this relationship is important in many fields, including physics, electrical engineering, and materials science.

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The increase in surface area when the temperature rises from 20 to 75 degrees Celsius.  =  11cm².

Heat waves will probably occur more frequently and persist longer as a result of the higher temperatures. Heat waves can be deadly, leading to conditions like heat cramps and heat stroke as well as actual mortality. Additionally, warmer temperatures have the potential to trigger a variety of other changes all around the world.

A fever is defined as a rise in body temperature above what is regarded as normal. It's also known as a high temperature, hyperthermia, or pyrexia, and it typically indicates that your body is attempting to protect you from an infection.

The increase in the surface area of the brass cube (which has six faces), which had side length L at 20 o, is

Δ A - 6(L - ΔL)² - 6L²

12LΔL = 12abL²ΔT

= 12(19 x 10⁻⁶/c)(30cm)²

=(75c - 20c)

= 11cm²

The increase in surface area when the temperature rises from 20 to 75 degrees Celsius.  =  11cm².

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[tex]T_{1}+\sqrt{2 }T_{1}[/tex]  is the time (in terms of [tex]T_{1}[/tex]) does it take the ladybug to get back to its starting point from the place where it reverses its acceleration

The following is a roughly formula-free, Physics-focused solution. The velocity continues to move incorrectly even when the acceleration  [tex]T_{1}[/tex]changes. By symmetry, the ladybug is at rest after an additional period  and is twice as far from its starting point as it was before it applied the brakes.

As a result, it must now go twice as far. Under constant acceleration, the distance traveled is proportional to the square of the time. Consequently, the amount of time needed to return to the starting location from the farthest point reached is 2–[tex]\sqrt{T_{1} }[/tex]. Total time from the time the acceleration reversed is therefore [tex]T_{1}+\sqrt{2 }T_{1}[/tex].

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The one and only way to ensure that power off in a system, circuit, or piece of equipment is to measure the voltage with a known working meter.

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The average kinetic energy is increased by 4 times when the average velocity of the molecules is increased by a factor of 2.

It is given that the average velocity that is average velocity is increased by a factor of 2, so it is increased by 2 x times.

Another formula to calculate kinetic energy,

[tex]\dfrac{1}{2} \times m \times v^2[/tex]

Kinetic energy will also increase by, 4 times as it is proportional to the square of velocity.

Average kinetic energy is a function of gas molecule speed, increasing temperature causes the gas molecules to move more quickly, which raises the average kinetic energy of the gas molecule.

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To burn a hole in a piece of paper with sunlight using your father's 1.80 D reading glasses, you must hold the glasses about 6 cm away from the paper.

This is because the glasses will act as a magnifying lens, and the focal length of the lens is determined by the diopter number (1.80 in this case). The focal length of a 1.80 D lens is approximately 6 cm.

The focal length of a lens is the distance between the lens and the image sensor when the subject is in focus, usually stated in millimeters (e.g., 28 mm, 50 mm). The focal length determines the angle of view of the lens, and thus how much of the scene will be captured when the image is taken.

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The magnitude of the centripetal acceleration at the tip of a 3.20 m long helicopter blade that rotates at 205 rev/min is 1,474.7 m/s2

The acceleration that a body experiences when moving around in a circle is known as centripetal acceleration. Since velocity is a vector quantity (that is, it possesses both a magnitude, which is the speed, and a direction), when a body travels on a circular path, its direction is constantly changing, and as a result, its velocity is changing as well, which results in an acceleration. The acceleration is exerted in a radial direction that is directed toward the center of the circle. To calculate the centripetal acceleration, we can use this following formula:

                                                   Ac = v² ÷ r  

V = ωr

Ac = (ωr)² ÷ r

                                                    Ac = ω²r

ω = 205 rev/min = 21.47 rad/s

r = 3.20 m

Next, we can substitute the required values to find the centripetal acceleration:

Ac = (21.47 rad/s)²  × 3.20 m

Ac = 1,474.7 m/s²

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The surface pressure is higher or lower than the SLP (Sea Level Pressure) of your location depending on the altitude at which it was measured. At Falcon Field, the surface pressure was measured at 245 meters above sea level.

This means that the pressure is lower than the SLP because the higher the altitude, the lower the atmospheric pressure. The atmospheric pressure decreases with an increase in altitude due to the decrease in the air density at higher elevations.

Surface pressure, also known as atmospheric pressure, is the pressure that the air exerts on the surface of the Earth.

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Northern American Emergency Response Guide.The main goal of the ERG Handbook is to help first responders immediately identify any unique or general risks associated with the material(s) at issue.

There is also Guide 111, which is for "hazardous" materials.When using generic information, make sure to replace it with more detailed instructions as soon as new information becomes available.

The orange panel next to the diamond-shaped sign or on the extremities and sides of the a cargo tank, vehicle, or rail car may also display the 4-digit ID Number.

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During 0.004s to 0.006s interval of time does the magnitude of the momentum of cart y change the most.

Momentum (more particularly linear momentum , translational momentum) is defined in Newtonian physics as the product of an object's mass and velocity. It consists of a vector quantity with magnitude and direction. If an object's mass is m and its velocity is v (also a vector quantity).

The kilogram metre per second (kgm/s) is the unit of momentum measurement in the International System of Units (SI), which really is equivalent to the newton-second. During 0.004s to 0.006s interval of time does the magnitude of the momentum of cart y change the most.

Therefore,  during 0.004s to 0.006s  interval of time does the magnitude of the momentum of cart y change the most.

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The velocity of the koala at the bottom of the circle is 2.23 m/s.

The velocity of the koala at the bottom of the circle can be determined by considering the concepts of centripetal force and centripetal acceleration. Centripetal force is the force that acts towards the center of the circle and is responsible for keeping the object moving in a circular path. Centripetal acceleration is defined as the acceleration of an object moving in a circular path, and it can be calculated as follows: a = [tex]v^{2}[/tex] / r, where v is the velocity of the object and r is the radius of the circle.

v = [tex]\sqrt{g\times r}[/tex], where v is the velocity, g is the acceleration due to gravity (9.8 m/[tex]s^{2}[/tex]), and r is the radius of the circular path.

Since the speed of the koala is constant at 2 m/s, we can use this value to find the radius of the circular path:

r = [tex]v^{2}[/tex] / g

r = [tex](2 m/s)^2[/tex] / (9.8 m/[tex]s^{2}[/tex])

r = 0.408 m

Now that we have the radius, we can use the equation for centripetal velocity to find the velocity of the koala at the bottom of the circle:

v = [tex]\sqrt{g\times r}[/tex]

v = √(9.8 m/[tex]s^{2}[/tex] × 0.408 m)

v = 2.23 m/s

Since the speed of the koala is constant, its velocity at the bottom of the circle will be equal to its speed, which is 2.23 m/s.. Hence, the velocity of the koala at the bottom of the circle is 2.23 m/s.

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It is widely believed that an asteroid impact was responsible for the extinction of the dinosaurs and many other species, which took place approximately 65 million years ago.

The exact effects of this collision would have been massive, including:

These events likely had a significant and long-lasting impact on the Earth's environment and ecology, and led to one of the largest mass extinctions in Earth's history.

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The magnitude of the electric field between the oppositely charged parallel plates is 100,336 N/C.

The electric field (E) between the parallel plates can be calculated using the following formula:

E = V / d

where V is the potential difference between the plates and d is the separation distance between the plates.

In this case, the potential difference is 600 V and the separation distance is 5.96 mm = 0.00596 m.

So, the magnitude of the electric field between the plates can be calculated as:

E = 600 V / 0.00596 m = 100,336 N/C

Therefore, the magnitude of the electric field between the oppositely charged parallel plates is 100,336 N/C.

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The difference in point of view that occurs when the lens (or other device) through which the eye views a scene is separate from the lens that exposes the film is called the parallax effect.

Parallax effect is an interactive technique used by web developers to create a visually engaging experience for users. It works by having the background move at a slower speed than the foreground when the user scrolls down the page. This creates an illusion of depth, as if the user is looking into the scene from different angles. The effect is especially popular for creating immersive experiences such as 3D games, virtual tours, and interactive storytelling. Parallax effect can be used to bring websites to life, offering users an engaging and dynamic experience. It is also a great tool for storytelling, helping to convey emotion and create a unique visual experience.

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The rate of diffusion is directly related to concentration, temperature, and pressure meaning that an increase in concentration, temperature, or pressure results in an increase in the rate of diffusion.

This is because diffusion is a process where particles move from an area of high concentration to an area of low concentration, driven by a concentration gradient. As the concentration gradient increases, more particles move from the high concentration area to the low concentration area, resulting in a faster rate of diffusion.

Temperature also affects the rate of diffusion because it affects the kinetic energy of the particles. At higher temperatures, particles have more kinetic energy and move faster, leading to a higher rate of diffusion.

Pressure affects the rate of diffusion because it affects the concentration gradient. An increase in pressure can compress the gas and increase the concentration gradient, resulting in a higher rate of diffusion.

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If the car is initially moving at a speed of 45 mi/h and it takes 300 ft to stop with uniform acceleration after its brakes are applied, it will take 600 ft to stop under the same conditions.

This is because the deceleration is the same, but the initial velocity is halved.

Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity which is defined as the rate of change of an object's velocity and is usually represented by the symbol a. Acceleration can be caused by a variety of factors, including external forces, changes in direction, or changes in speed. In physics, acceleration can be described as the rate of change of an object's velocity over a period of time.

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The required new magnification of the telescope when the focal lengths of objective lens and eye-piece are given is calculated to be four times that of original magnification.

We know the expression for magnification as, m = -fo/fe

where,

The objective lens's focal length is fo

fe is the focal length of eye piece

It is given that, focal length of the objective lens is doubled.

⇒ fo₂ = 2 fo

It is given that, focal length of the eye piece is doubled.

⇒ fe₂ = 1/2 fe

So, the new magnification is,

m' = -fo₂/fe₂ = - 2 fo/(1/2 fe) = -4 fo/fe = 4 m

Thus, the required new magnification is calculated to be four times that of the original magnification.

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The gauge pressure at point P, which has a zero-reference against the atmospheric pressure, is 3200 Pa. The needle meets the wider chamber of the syringe at the end of the needle.

Using Poiseuille's law, we can resolve the exercise. In a closed pipe, it states that for a fluid in laminar flow.

The equation:

ΔP = 8μLQ / 4r⁴

Where,

μ = viscosity of the fluid

L = length of the pipe

r = radius

Q = Av

= πr²v

= (3.14 x 10⁻³) (10)

= (3.14 x 10⁻⁵)

Hence, the gauge pressure:

ΔP = 8 (0.001) (4 cm) (3.14 x 10⁻⁵)) / 4 (0.001 m)⁴

= 3200 Pa

So, the gauge pressure of the water at point P is 3200 Pa.

And, the needle meets the wider chamber of the syringe at the end of the needle.

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The resultant displacement of the object is 45 m.

The resultant displacement of the object is calculated as follows;

Sum of the vertical displacement of the object is calculated as;

y = 27 m - 63 m = -36 m

Sum of the horizontal displacement of the object is calculated as;

x = 31 m - 58 m = -27 m

The resultant displacement of the object is calculated as follows;

d = √ [ ( -36² ) +  ( - 27² ) ]

d = 45 m

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The complete question is below;

2.4 Displacement of 27m north,31 m east,63m south and 58m west. Take east as the positive x-direction and north as the positive y-direction. 3. Check 2.4 with an accurate tail to head vector diagram​. Calculate the resultant displacement of the vector

a) Rocks reach height 26.4 times maximum height they could reach on Earth b) rocks will be 0.753 times duration they would be in the air on Earth

(a) Max height H reached by a projectile launched vertically upward on Earth is given by:

[tex]H = v^{2} / (2g),[/tex]

where v₀ : initial velocity and g: acceleration due to gravity on Earth. To find height reached by same projectile launched with same initial velocity on Mars, we can use same formula but with the value of g on Mars:

[tex]H = v^{2} / (2g),[/tex]

where gₘ is the acceleration due to gravity on Mars. We know that  initial velocity of the rocks is the same on both planets, so we can write:

[tex]H = H * g / g[/tex]

Put values:

[tex]H = H * 9.81 m/s^{2} / 3.71 m/s^{2} = 26.4 * H[/tex]

Therefore, the rocks ejected from the volcano on Mars would reach a height that is 26.4 times the maximum height they could reach on Earth.

(b) The time T for the rocks to be in the air on Earth can be found using the formula:

[tex]T = 2v / g[/tex].

To find time the rocks would be in air on Mars, we use same formula but with the value of g in terms of Mars:

[tex]T = 2v / g[/tex]

Put values:

[tex]T = 2v / 3.71 m/s^{2} = 2/ (9.81 m/s^{2} / 3.71 m/s^{2} ) * (2v / 9.81 m/s^{2} )[/tex]

[tex]Tm = (2/2.652)*T[/tex]

[tex]Tm = 0.753 * T[/tex]

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6 possible falls producing 6 wavelengths so the Correct option is C)

no. of radiation = [tex]^{4} C_2=\frac{4\times3}{2}[/tex] =6

a wave's wavelength is the separation between two adjacent waves' corresponding points. Two points or particles that are in the same phase—i.e., points that have completed identical fractions of their periodic motion—are referred to as "corresponding points." Wavelength is typically measured from crest to crest or from trough to trough in transverse waves (waves with points vibrating at right angles to the direction of their advance); from compression to compression or from rarefaction to rarefaction in longitudinal waves (waves with points vibrating in the same direction as their advance).

6 possible falls producing 6 wavelengths

4 → 3, 4→2 , 4→1

3→2,3→1

2→1

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The weight of the trunk is 735 N

The force of friction  is 147 N

The force exerted on the trunk is 882 N

The work done to move the trunk is 10,584 J

The power exerted  is  814 W

The weight of the trunk can be calculated as :

Weight = 75 kg * 9.8 m/s^2 = 735 N

The force of friction can be calculated as:

Friction = μ * N = 0.20 * 735 N = 147 N

The force exerted on the trunk can be calculated as :

Force = Weight + Friction = 735 N + 147 N = 882 N

The work done to move the trunk can be calculated as

Work = Force * Distance = 882 N * 12 m = 10,584 J

The power exerted can be calculated as :

Power = Work / Time = 10,584 J / 13 s = 814 W.

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In an isothermal expansion, the pressure of a monatomic ideal gas increases by a factor of 1/3 (or 2/3).

A collection of presumptions about a gas's behavior defines, it as an ideal gas in theory. These hypotheses, which are based on experimental observations of actual gases, are helpful for comprehending and forecasting the behavior of gases under diverse circumstances.

The temperature of the gas doesn't change during an isothermal expansion. In the equation of state for an ideal gas, PV = nRT, where n is the number of moles, R is the universal gas constant, and T is the temperature, pressure and volume are connected.

The pressure of a monatomic ideal gas will change by a factor of 1/3(2/3) if its volume triples. This can be obtained by maintaining a constant temperature and changing the equation of state to P = (nRT) / V.

Since the pressure and volume are inversely related, the pressure will fall by a factor of 1/3 (or 2/3) if the volume triples.

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A tentative explanation for a natural phenomenon describes hypothesis .

A straightforward hypothesis can indicate that there is a causal relationship—that is, that one variable affects the other—between two variables. Here's an illustration: Higher grades are the result of more time spent preparing for a test. The number of hours spent studying is the independent variable in this statement, and the result is the dependent variable. The independent variable is altered while the dependent variable is evaluated to ascertain how the dependent variable is impacted by the independent variable. Similar to a simple hypothesis, a complex hypothesis has two or more independent variables and/or two or more dependent variables.

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The pressure that a gas, at a constant temperature, exerts over a liquid surface is known as vapour pressure. Since the kinetic energy of molecules increases with temperature, vapour pressure likewise rises.

As a result, more molecules possess the necessary energy to transform from a liquid to a gas.

The pressure that a gas, at a constant temperature, exerts over a liquid surface is known as vapour pressure. Due to the fact that more molecules have adequate kinetic energy to transition from a liquid to a gas as the temperature rises, the vapour pressure likewise rises.

A liquid or solid's vapour pressure increases along with its temperature. On the other hand, when the temperature drops, the vapour pressure drops.

There are several techniques to calculate a liquid's vapour pressure. A little amount of the liquid is injected into a closed flask that is attached to a manometer for a straightforward measurement.

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It was discovered that the rate of desorption of a single molecular layer of n-butane from a single crystal of aluminum oxide was first order. constant of 0. 128/s at 150 K , Half life=[tex]\frac {ln(2)}{k}[/tex]=5.415 s

For first order desorption:

In([tex]\frac {N}{N_o}[/tex]) =-kt and [tex]\frac {N}{N_o}[/tex] = [tex]e^{(-kt)[/tex] where N is the number of molecules remaining at time t, No is initial number and k is rate constant

(A) Half life=[tex]\frac {ln(2)}{k}[/tex]=5.415 s

(B) 25% desorbs [tex]\rightarrow[/tex]  75% remains

⇒ [tex]\frac {N}{N_o}[/tex] x 100% = 75% => [tex]\frac {N}{N_o}[/tex]=0.75

In(0.75)=-0.128 x t

Time t = 2.25 s

(C) 50% desorbs ⇒ 50% remains

=> [tex]\frac {N}{N_o}[/tex] x 100% = 50% => [tex]\frac {N}{N_o}[/tex]= 0.50

In(0.50) = -0.128 x t

Time t = 5.42 S

(D) For t = 14 s

Fraction remaining= [tex]\frac {N}{N_o}[/tex] =[tex]e^{(-0.128 \times 14)[/tex]

Fraction remaining= -0.167 (approximately 0.17)

(E) For t = 20 s

Fraction remaining= [tex]\frac {N}{N_o}[/tex] = [tex]e^{(-0.128 \times 20)[/tex]

Fraction remaining=  -0.0773 (approximately 0.077)

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