Four positive point charges are arranged as shown in the accompanying diagram. The force between charges 1 and 3 is 6.0 N; the force between charges 2 and 3 is 5.0 N; and the force between charges 3 and 4 is 3.0 N. The magnitude of the total force on charge 3 is most nearly
(A) 6.3 N
(B) 8.0 N
(C) 10 N
(D) 11 N
(E) 14 N

The average tangential speed of the valve stem is approximately 0.945 m/s.

The circumference of the bicycle tire can be found by multiplying its diameter by pi:

C = πd = π(0.4 m) = 1.26 m

The number of revolutions per second can be found by dividing the total number of revolutions by the total time:

n = 600 rev / 800 s = 0.75 rev/s

The average tangential speed of the valve stem is equal to the product of the circumference and the number of revolutions per second:

v = Cn = (1.26 m)(0.75 rev/s) = 0.945 m/s

Therefore, the average tangential speed of the valve stem is approximately 0.945 m/s.

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Wavelength and frequency of light are related in an inverse manner.

Wavelength and frequency are inversely related to each other. This means that as the wavelength of light increases, the frequency of light decreases, and vice versa. Mathematically, this can be represented by the formula c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This formula shows that the product of wavelength and frequency is a constant (the speed of light). Therefore, if the wavelength of light increases, the frequency must decrease in order to keep the product constant. Conversely, if the frequency of light increases, the wavelength must decrease.

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The orbital period of the rocket is approximately 1.48 hours.

To determine the orbital period of the rocket, we need to use Kepler's third law which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit.

The semi-major axis of the orbit is the distance between the center of the Earth and the center of the rocket.

First, we need to find the altitude of the rocket from the surface of the Earth.

We can use the formula for the gravitational force between two objects:

F = [tex]G(M_1M_2)/r^2[/tex]

where G is the gravitational constant, [tex]M_1[/tex] is the mass of the Earth, [tex]M_2[/tex] is the mass of the rocket, and r is the distance between the center of the Earth and the center of the rocket.

We can solve for r and get

[tex]r = ((G(M_1+M_2))/(v^2))^{(1/3)} - R[/tex]

where R is the radius of the Earth.
Plugging in the given values, we get r = [tex]2.15\times10^7[/tex] meters.

The semi-major axis is half of the distance between the highest and lowest points in the elliptical orbit, which is equal to the altitude plus the radius of the Earth.

Thus, the semi-major axis is

a = r + R

a = [tex]2.15 \times 10^7 + 6.371 \timess 10^6[/tex]

a = [tex]2.787\times10^7[/tex] meters.
Now, we can use Kepler's third law to find the orbital period T.

[tex]T^2 = (4\pi^2/G(M_1+M_2)) \times a^3[/tex]

Plugging in the given values, we get T = 5318 seconds or about 1.48 hours.
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The lateral magnification of a plane mirror is always positive, meaning that the image appears the same size as the object and is not inverted.  The correct option is (a) it is positive.

The lateral magnification can be calculated by dividing the height of the image by the height of the object, and the value is always positive for a plane mirror. It does not depend on the distance of the object from the mirror, as the image is always the same distance behind the mirror as the object is in front of it. This property of a plane mirror makes it useful for applications such as reflecting light in optical instruments and for personal grooming.

The correct option is (a).

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angular acceleration, axis of rotation, acceleration.

Answer:

To find the magnitude of the total acceleration (a) at a point on a rotating platform with an angular speed (ω) of 3.00 rad/s and an angular acceleration (α) of 11.0 rad/s², located 1.75 m from the axis of rotation, follow these steps:

1. Calculate the centripetal acceleration (ac) using the formula: ac = ω² * r, where r is the distance from the axis of rotation (1.75 m).
  ac = (3.00 rad/s)² * 1.75 m
  ac = 9.00 * 1.75 m
  ac = 15.75 m/s²

2. Calculate the tangential acceleration (at) using the formula: at = α * r, where α is the angular acceleration (11.0 rad/s²).
  at = 11.0 rad/s² * 1.75 m
  at = 19.25 m/s²

3. Find the total acceleration (a) by combining the centripetal and tangential accelerations using the Pythagorean theorem: a = √(ac² + at²).
  a = √(15.75² + 19.25²) m/s²
  a ≈ 24.96 m/s²

The magnitude of the total acceleration at a point 1.75 m from the axis of rotation on the platform is approximately 24.96 m/s².

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The magnitude of the total acceleration at the point on the platform is [tex]25.0 m/s^2.[/tex]

The total acceleration a at a point on the platform is the vector sum of the tangential acceleration and the radial acceleration:

[tex]a = sqrt(at^2 + ar^2)[/tex]

where at is the tangential acceleration and ar is the radial acceleration.

The tangential acceleration is given by:

at = r * alpha

where r is the distance from the axis of rotation to the point on the platform and alpha is the angular acceleration.

Substituting the given values, we get:

at = [tex](1.75 m) * (11.0 rad/s^2) = 19.25 m/s^2[/tex]

The radial acceleration is given by:

ar = r * omega^2

where omega is the angular speed.

Substituting the given values, we get:

[tex]ar = (1.75 m) * (3.00 rad/s)^2 = 15.75 m/s^2[/tex]

Therefore, the magnitude of the total acceleration is:

[tex]a = sqrt((19.25 m/s^2)^2 + (15.75 m/s^2)^2) = 25.0 m/s^2[/tex]

Therefore, the magnitude of the total acceleration at the point on the platform is [tex]25.0 m/s^2.[/tex]

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During the open-die forging process, the friction between the dies and the part can have a significant impact on the final product.

The frictional force can cause surface defects on the part due to the high pressure applied during the forging process. The friction can also lead to uneven deformation, which can cause dimensional inaccuracies and inconsistent mechanical properties across the part.

However, a certain degree of friction is necessary for the forging process, as it helps to control the flow of the metal and prevent cracking or other defects. Therefore, it is important to carefully control the amount of friction during the forging process to achieve the desired outcome. This can be achieved through proper lubrication of the dies and careful control of the process parameters such as temperature, speed, and pressure.

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if the object is speeding up, the acceleration must be positive.

Acceleration is a measure of how quickly the velocity of an object changes. When an object is speeding up, its velocity is increasing, and therefore its acceleration is positive.

However, if an object were to have a negative acceleration, it means that its velocity is decreasing. In other words, the object is slowing down.

Therefore, it is physically impossible for an object to have a negative acceleration and yet be speeding up.

This is because the object's velocity cannot be increasing while its acceleration is decreasing. It is important to note that the direction of the acceleration and the velocity can be opposite if the object is slowing down.

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The probable question may be:

Can an object have a negative acceleration and speed up? Could you explain why?

The electric motor must supply a torque of approximately 0.0606 N m to take the disk from 0 to 2000 rpm in 4.4 s.

To find the torque required by the electric motor, we'll first need to determine the angular acceleration of the disk. Here are the steps:

1. Convert 2000 rpm to radians per second:
(2000 revolutions/min) * (2π radians/revolution) * (1 min/60 s) ≈ 209.44 radians/s

2. Find the angular acceleration (α):
α = (ω_final - ω_initial) / time
α = (209.44 radians/s - 0) / 4.4 s ≈ 47.6 radians/s²

3. Calculate the moment of inertia (I) for the disk:
I = 1/2 * m * r^2
I = 1/2 * 0.23 kg * (0.105 m)^2 ≈ 0.00127225 kg m²

4. Determine the torque (τ) using the formula:
τ = I * α
τ ≈ 0.00127225 kg m² * 47.6 radians/s² ≈ 0.0606 N m

The electric motor must supply a torque of approximately 0.0606 N m to take the disk from 0 to 2000 rpm in 4.4 s.

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During LASIK eye surgery, if it is performed to correct for nearsightedness, the cornea needs to be reshaped in such a way that it becomes flatter.

This is because in nearsightedness, the cornea is too steeply curved, which causes light to focus in front of the retina instead of directly on it. By flattening the cornea through the removal of tissue, the light is able to focus directly on the retina, correcting the nearsightedness.

LASIK eye surgery is the best known and most commonly performed laser refractive surgery to correct vision problems. Laser-assisted in situ keratomileusis (LASIK) can be an alternative to glasses or contact lenses.

During LASIK surgery, a special type of cutting laser is used to precisely change the shape of the dome-shaped clear tissue at the front of your eye (cornea) to improve vision.

In eyes with normal vision, the cornea bends (refracts) light precisely onto the retina at the back of the eye. But with nearsightedness (myopia), farsightedness (hyperopia) or astigmatism, the light is bent incorrectly, resulting in blurred vision.

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Matter in motion possesses energy in various forms such as kinetic energy and potential energy.  The right option is B and C.

Kinetic energy is the energy possessed by an object in motion.

Potential energy, on the other hand, is the energy possessed by an object due to its position or configuration.

Heat flow is the transfer of thermal energy from a body at a higher temperature to one at a lower temperature.

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This law implies that the total amount of energy in a system remains constant.

The second law of thermodynamics states that in any energy transfer or transformation, the total amount of usable energy in a system decreases. This law implies that energy tends to flow from a higher state of order to a lower state of order.

Therefore, it is difficult to achieve 100% efficiency in any energy transfer process.

In conclusion, matter in motion possesses energy in different forms, and the laws of thermodynamics govern energy transfer and transformation processes.

Understanding these laws is crucial in various fields, including engineering, physics, and chemistry. Therefore, the correct option is B and C.

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The primary force that causes the vocal folds to vibrate is the airflow from the lungs. The energy for this vibration is supplied by the air pressure created when we exhale. Here's a step-by-step explanation:

1. When we exhale, air pressure builds up below the closed vocal folds.
2. This air pressure pushes the vocal folds apart, allowing the air to pass through.
3. As the air passes, the vocal folds are drawn back together due to their elasticity and the Bernoulli effect (a principle in fluid dynamics).
4. This cycle of opening and closing repeats rapidly, causing the vocal folds to vibrate and produce sound.

So, the airflow from the lungs is the primary force causing the vocal folds to vibrate, and the energy is supplied by the air pressure created during exhalation.

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In a real pulley system, the work input must be greater than the work output.

In an ideal or theoretical pulley system, the work input would equal the work output because there would be no energy loss due to friction or other inefficiencies. However, in real-world pulley systems, some of the energy is lost as heat due to friction, which means that the actual work output is less than the work input. Therefore, in a real pulley system, the work input must be greater than the work output to compensate for these energy losses and still achieve the desired work output.

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For force 1, the straight-line distance r1 is equal to the magnitude of the force F1, which is 1.0 N, and the angle ϕ1 between an extension of that straight line and the direction of the force is 0 degrees. The torque due to force 1 is equal to r1 x F1 x sin(ϕ1), which is 0 Nm.

The torque produced by a force is determined by multiplying the force's magnitude by the lever arm's length and then by the sine of the angle formed by the force's line of action and the lever arm.

In this case, force 1 has a magnitude of 1.0 N, a straight-line distance of 1.0 N, and an angle between the extension of that straight line and the direction of the force of 0 degrees.

Therefore, the torque due to force 1 is equal to r1 x F1 x sin(ϕ1), which is equal to 1.0 N x 1.0 N x sin(0), which is equal to 0 Nm.

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Based on the laws of physics, we can predict that if we increase the mass of the ball but allow it to collide with the same velocity (drops it from the same height), the maximum force of the collision will also increase. This is because the force of impact is directly proportional to the mass and velocity of an object.

If the mass of the ball is increased, it will have greater inertia, meaning it will resist changes in motion more strongly. This means that the ball will collide with greater force when it hits the ground.

However, it's worth noting that the maximum force of the collision may not increase in direct proportion to the increase in mass.

Other factors, such as the elasticity of the ball and the surface it's colliding with, can also affect the force of impact.

Additionally, if the ball is very heavy, it may also start to deform upon impact, which can affect the force of the collision.

Overall, while we can make predictions about how increasing the mass of the ball will affect the force of impact, the actual force will depend on a number of factors and may be difficult to predict precisely.

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Yes, that is correct. The effective force and its impact on kinetic and potential energy:

The effective force will change the kinetic energy, but not the potential energy, of the system. This is because the effective force, which is the net force acting on an object, can cause the object to accelerate or decelerate. As a result, this change in motion directly affects the kinetic energy (KE = 1/2 * m * v^2), where m is the mass of the object and v is its velocity.

However, the potential energy (PE = m * g * h) of the system remains unchanged because it is only affected by the height (h) of the object above a reference point, its mass (m), and the acceleration due to gravity (g). Since the effective force does not influence these factors, the potential energy of the system remains constant.

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When a nucleus emits a gamma ray, it does not change its atomic number or mass number.

Gamma rays are emitted by a nucleus that is in an excited state, and the emission of a gamma ray allows the nucleus to return to its ground state.

The emission of a gamma ray does not change the identity of the nucleus.

Therefore, the resulting nucleus after the emission of a gamma ray is still 22890Th, with 90 protons and 138 neutrons.

None of the other answer choices in the question have the same atomic number and mass number as 22890Th, so the correct answer is (a) 22890Th.

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Based on the information provided, the best speed for the vehicle would be around 30 mph. So, correct option is B.

Given the scenario, it is clear that traffic is heavy, and the speed of the vehicles is considerably less than the posted speed limit. It is important to maintain a safe and efficient speed to avoid accidents and to ensure smooth traffic flow.

This speed is a balance between moving too slowly and causing traffic disruptions and moving too fast, which can lead to unsafe conditions.

Driving at 25 mph may cause disruptions in traffic flow, and driving too slowly can be dangerous, especially on a busy freeway. On the other hand, driving at 35 mph may be too fast for the surrounding vehicles, leading to unsafe conditions and an increased risk of accidents.

Overall, the best course of action is to maintain a speed of around 30 mph, which allows for efficient traffic flow and minimizes the risk of accidents.

So, correct option is B.

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Yes, during engine run-up, if you cause rocks, debris, and propeller blast to be directed toward another aircraft or person, it could be considered careless or reckless operation of an aircraft.

This could be considered careless or reckless operation of an aircraft as it poses a safety risk to other aircraft or people on the ground. Pilots should always be aware of their surroundings during engine run-up and take precautions to avoid directing debris or propeller blast towards others. It is important to follow proper procedures and guidelines to ensure the safety of all involved. It is essential to maintain proper safety precautions and be aware of your surroundings to prevent potential harm or damage.

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The width of the slit is approximately 75.54 μm.

d = mλ/sin(θ)

For the first minimum, m = 1 and sin(θ) = 2.6 mm / 350 mm = 0.0074

Plugging in the values, we get:

d = (1)(0.559 μm) / (0.0074) = 75.54 μm

Diffraction is a fundamental concept in physics that refers to the bending and spreading of waves as they encounter an obstacle or aperture. When a wave, such as light or sound, encounters an obstacle or aperture that is comparable in size to its wavelength, the wave will bend around the obstacle or spread out after passing through the aperture. This phenomenon is known as diffraction and is a result of interference between the different parts of the wavefront.

The diffraction of waves has many important applications in physics, including the study of the structure of materials, the measurement of atomic and molecular structures, and the design of optical instruments such as telescopes and microscopes. Diffraction is also responsible for many everyday phenomena, such as the blurring of images through small apertures and the colorful patterns seen in soap bubbles and peacock feathers.

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b) Red color

The use of a red filter will better help resolve the stars in a binary star system because red light has a longer wavelength than blue light. Longer wavelengths of light are less affected by atmospheric turbulence, which can cause the images to appear blurry and affect the resolution of the stars. Therefore, using a red filter can reduce the effect of atmospheric turbulence and help to better resolve the two stars in the binary star system.

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a) The minimum necessary power output rating of the water pump is approximately 273.06 watts.

b) The minimum necessary power output rating of the water pump in horsepower is approximately 0.366 hp.

a) To find the minimum necessary power output rating of the water pump in watts, we can use the formula for power: P = mgh/t, where P is power, m is mass, g is the acceleration due to gravity (9.81 m/s²), h is height, and t is time.

Given the values, m = 200 kg, h = 5.0 m, and t = 1 hour (which is equivalent to 3600 seconds), we can calculate the power as follows:

P = (200 kg)(9.81 m/s²)(5.0 m) / (3600 s)
P ≈ 273.06 W

So, the water pump's minimum required power output rating is roughly 273.06 watts.

b) To convert the power output from watts to horsepower, we can use the conversion factor 1 hp = 746 W:

P_hp = 273.06 W / 746 W/hp
P_hp ≈ 0.366 hp

Therefore, the water pump's minimum required horsepower power output rating is roughly 0.366 hp.

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The relationship between force, linear momentum, and time.

Force is equal to the change in linear momentum over the change in time. To explain this relationship, we can use the equation:

Force (F) = Δ(linear momentum) / Δ(time)

Where:
- Force (F) is measured in newtons (N)
- Linear momentum is the product of an object's mass (m) and velocity (v), represented as p = m*v
- Δ(linear momentum) represents the change in linear momentum
- Δ(time) represents the change in time

According to Newton's second law of motion, force is directly proportional to the rate of change of linear momentum with respect to time. This means that when a force is applied to an object, its linear momentum changes over time, causing it to accelerate or decelerate.

1. Determine the initial and final linear momentum (p_initial and p_final) of the object by calculating the product of its mass (m) and its initial and final velocities (v_initial and v_final) respectively.
2. Calculate the change in linear momentum (Δp) by subtracting p_initial from p_final (Δp = p_final - p_initial).
3. Determine the change in time (Δt) during which the force was applied.
4. Divide the change in linear momentum (Δp) by the change in time (Δt) to find the force (F).

Force (F) = Δ(linear momentum) / Δ(time)

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A battery gets warm while in use because of the chemical reactions happening inside it.

When a battery is being used, electrons are flowing from the negative terminal to the positive terminal, generating an electrical current. These reactions involve the transfer of electrons between the battery's electrodes (anode and cathode) through an electrolyte. As the electrons flow through the external circuit, they generate heat due to electrical resistance in the circuit and the battery itself. This heat causes the battery to get warm during use.

During this process, the electrolyte solution in the battery reacts with the electrodes, producing heat as a byproduct. This heat energy is dissipated into the surrounding environment, causing the battery to warm up. Additionally, if the battery is being used at a high rate or if it is being charged too quickly, it can generate more heat than it can dissipate, leading to further warming.

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To calculate the acoustic pressure (in micropascals) that produces a sound pressure level of 40 dB, you need to use the following formula:

Sound Pressure Level (SPL) = 20 * log10(P / P0)

where SPL is in decibels (dB), P is the acoustic pressure, and P0 is the reference pressure, which is usually 20 µPa.

To find the acoustic pressure P, you can rearrange the formula as follows:

1. Divide the SPL by 20: 40 dB / 20 = 2
2. Calculate 10 raised to the power of the result: 10^2 = 100
3. Multiply the result by the reference pressure P0: 100 * 20 µPa = 2000 µPa

So, the acoustic pressure that produces a sound pressure level of 40 dB is 2000 micro-pascals.

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As the temperature of a steel plate with a hole drilled through it increases, the size of the inside diameter of the hole:
B) increases.

When the steel plate is heated, its overall size expands due to thermal expansion.

As a result, both the outer dimensions of the plate and the inside diameter of the hole will increase.

The atoms in the steel have more energy when heated, causing them to vibrate more and move further apart from each other, leading to the expansion.

Therefore, the internal diameter of a hole that has been drilled through a steel plate grows as the temperature of the plate rises, as stated by B).

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The particle's momentum at t = 3.00 s is (-1.00 kg⋅m/s)i^.

Hi! To find the particle's momentum at t = 3.00 s, we will use the equation p(t) = p_initial + FΔt, where p(t) is the momentum at time t, p_initial is the initial momentum, F is the force, and Δt is the change in time.

Given values:
F = -2.00 N i^
p_initial = 5.00 kg⋅m/s i^
Δt = 3.00 s

Now, calculate the momentum at t = 3.00 s:
p(3) = p_initial + FΔt
p(3) = (5.00 kg⋅m/s)i^ + (-2.00 N)i^ × 3.00 s

p(3) = (5.00 kg⋅m/s)i^ + (-6.00 kg⋅m/s)i^
p(3) = (-1.00 kg⋅m/s)i^

The particle's momentum at t = 3.00 s is (-1.00 kg⋅m/s)i^.

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The answer is C) equal to the force of the hammer on the nail.

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that when a hammer hits a nail, the hammer exerts a force on the nail, and the nail exerts an equal and opposite force on the hammer.

Therefore, the force of the nail on the hammer is equal in magnitude but opposite in direction to the force of the hammer on the nail. This is because the two forces form an action-reaction pair, which means that they are equal in magnitude but opposite in direction.

In other words, if the hammer exerts a force of F on the nail, then the nail exerts a force of -F on the hammer. The negative sign indicates that the direction of the force of the nail is opposite to that of the force of the hammer.

So, the answer is C) equal to the force of the hammer on the nail.

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Reciprocal determinism is the concept that a person's behavior is influenced by their individual characteristics, the environment, and their behavior itself, which creates a feedback loop.

An example of its application to personality is that a person's personality traits can shape their behavior, which in turn can shape the environment they are in and create a feedback loop that reinforces or modifies their personality traits.

Reciprocal determinism is a key concept in cognitive psychology, developed by psychologist Albert Bandura. It suggests that a person's behavior is influenced by three factors: their individual characteristics, the environment they are in, and their behavior itself. These three factors create a feedback loop where each one influences the others, which in turn influences the person's behavior. This means that a person's behavior is not simply the result of their personality or the environment they are in, but rather the product of an ongoing interaction between the two.

An example of how reciprocal determinism can be applied to the analysis of personality is as follows:

Imagine a person who has the personality trait of being outgoing and sociable. This trait might lead them to seek out social situations and interact with others, which in turn creates a social environment that reinforces their outgoing and sociable behavior.

As they continue to behave in an outgoing and sociable manner, they may receive positive feedback from others and begin to view themselves as someone who is outgoing and sociable. This feedback loop can then reinforce and amplify their personality trait, leading to a stable pattern of behavior over time.

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Answer:

The answer is Igneous rocks