select all that apply select all the stars that would have the same luminosity. (use the stefan-boltzmann law.) presented are the radii and temperatures of five stars compared to the sun.

Answer:

i got 6

Explanation:lmk if i’m wrong

The distance at which the music is just barely audible to a person with a normal threshold of hearing depends on the intensity level of the sound and the threshold of hearing.

The threshold of hearing is the lowest level of sound that can be heard by the human ear. It is typically measured in decibels (dB) and varies depending on the frequency of the sound.

The most common method for measuring the threshold of hearing is through audiometry, which involves presenting sounds of varying intensities and frequencies to the subject and determining the lowest level at which they can hear the sound.

Sound intensity level decreases with distance from the source according to the inverse square law, which states that the intensity of a sound wave decreases as the square of the distance from the source.

This means that if the distance from the source is doubled, the sound intensity level will decrease by a factor of four.

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The natural length of the spring is 5 cm.

Given dataThe amount of work done to stretch a spring from 7 cm to 9 cm is 6 J.The amount of work done to stretch a spring from 9 cm to 11 cm is 10 J.

The formula for potential energy stored in a spring is

    U=12kx2

Here,

U is potential energy stored in a spring

k is a spring constantx is the displacement of the spring from its natural length

U = 12kx2

Thus, U is proportional to x2

For the first stretching, we have

U1 = 12k(0.02)2

For the second stretching, we have

U2 = 12k(0.02)2

The difference in the amount of work done to stretch a spring is proportional to the difference in the potential energy stored in the spring.

So,U2 - U1 = 10 J - 6 J= 4 J= 12k(0.02)2 - 12k(0.02)2= 12k(0.04)k = 4/3

The natural length of the spring is given by x0 = U/k

Here, U is the potential energy stored in a spring when stretched by x So, the natural length of the spring is

x0 = 12kx02x0 = 12(4/3)(0.05)2x0 = 5 cm

Therefore, the natural length of the spring is 5 cm.

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The speed of sound in air is approximately the same for all wavelengths.

Step by step Explanation :

The evidence that this is true is the following:

The speed of sound in air is approximately the same for all wavelengths. This is proved by the fact that a sound wave is an atmospheric disturbance that propagates as a longitudinal wave through the air, travelling as a pressure wave that causes areas of compression and rarefaction.

The speed of sound in air is constant and is determined by the average kinetic energy of the air molecules. This is why the speed of sound is the same for all wavelengths.

When the temperature of air is held constant, the speed of sound in air is constant. This is the primary reason why the speed of sound in air is practically constant at a given temperature.

The wavelengths of sound range from about 17 meters for the lowest audible frequency (about 20 Hz) to about 17 millimeters for the highest audible frequency (about 20,000 Hz).

The speed of sound in dry air at room temperature is around 343 meters per second, but it may vary depending on a variety of factors, including humidity, temperature, and pressure.

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When a ball is shot straight up into the air from the ground with initial velocity of 49ft/sec. assuming that the air resistance can be ignored, the maximum height that the ball goes up will be 73.96 ft.

This can be determined by using the kinematic equations for constant acceleration. The kinematic equation that relates the displacement, initial velocity, acceleration, and time is given by:

S = ut + 1/2 at²

where, S is the maximum height the ball goes up, u is the initial velocity of the ball, a is the acceleration of the ball, t is the time taken by the ball to reach maximum height.

Now, the initial velocity of the ball is u = 49 ft/s (given). Since the ball is thrown upwards, the acceleration of the ball will be downwards, i.e., a = -32.2 ft/s² (taken as negative since it is in the opposite direction to the motion)

At maximum height, the final velocity of the ball will be zero. Hence, using the equation, v = u + at, at maximum height, v = 0 and u = 49 ft/s, a = -32.2 ft/s²

Substituting these values in the equation,

v = u + at0

= 49 - 32.2*t

t = 1.52 s.

Now, substituting u, a, and t in the equation,

S = ut + 1/2 at²

S = 49(1.52) + 1/2 (-32.2)(1.52)²

S = 73.96 ft

Therefore, the maximum height that the ball goes up is 73.96 ft.

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246.5ft.

The ball shot straight up into the air with an initial velocity of 49ft/sec will reach a maximum height, before it begins to fall back to the ground. Assuming no air resistance, the ball will reach a maximum height of 246.5ft.

To calculate this, use the formula h = (vi2) / (2g), where vi is the initial velocity and g is the acceleration due to gravity (g = 9.8m/s2).

Plugging in the values given, we get: h = (49ft/sec)2 / (2 * 9.8m/s2) = 246.5ft.

Therefore, the ball will reach a maximum height of 246.5ft.

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The circuit's initial current via the junction where the two resistors are separated is 11 mA. The current divides and simultaneously passes via both resistors in a paralleled resistor circuit using two resistors.

A battery and many capacitors are linked in series. The capacitors have a comparable amount of charge.

A battery and many capacitors are linked in series. The sum of the potential differences between each capacitor equals the current battery emf.

When two resistors having resistance R that are similar to one another are linked in series, the capacitive reactance is 2R.

Both negative and positive ions move charges whenever an electricity flows through with an ionic liquid like salty water. Energy is measured in electron-volts.

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Not all comet nuclei become active, comets have highly elliptical orbits, and can be obscured by other celestial bodies.

Despite the fact that stargazers gauge that there might be a trillion comet cores circling past Pluto, we don't see more comets in that frame of mind because of different elements. To begin with, not all comet cores become dynamic and form into comets. Second, numerous comets have profoundly circular circles that benefit them from the inward planetary group, where they are not apparent from Earth. Third, comets can be darkened by other heavenly bodies, like planets or stars. At last, numerous comets have extremely lengthy orbital periods, requiring hundreds or even millennia to finish a solitary circle, and hence may not be apparent during a human lifetime. Furthermore, the brilliant comets that are noticeable from Earth are frequently generally uncommon and happen inconsistently, making them much more extraordinary and energizing to see when they do show up.

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To determine the temperature increase if a specific amount of heat energy is transferred to the gas at a constant volume, we will use the equation:

Q = nCvΔT,

where Q is the amount of heat energy transferred, n is the number of moles of gas, Cv is the heat capacity at a constant volume, and ΔT is the temperature change.

The expression to determine the temperature change is:

ΔT = Q / (nCv)

where ΔT is the change in temperature, Q is the amount of heat energy transferred, n is the number of moles of gas, Cv is the specific heat capacity at constant volume.

For this case, the formula to calculate the change in temperature if a certain amount of heat energy is transferred to the gas at constant volume is given by:

ΔT = Q / (nCv)

Where; ΔT = temperature change, n = number of moles of gas, Cv = specific heat capacity at constant volume, Q = amount of heat energy transferred.


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Approximately [tex]1.31 \times 10^{20}[/tex] electrons are transferred in a strong lightning bolt carrying an electric charge of 21 C.

The electric charge of one electron is equal to [tex]-1.602 \times 10^{-19}[/tex] Coulombs (C). Therefore, we can calculate the number of electrons transferred by dividing the total charge transferred by the charge of a single electron:

Number of electrons = Total charge transferred / Charge of a single electron

Number of electrons = [tex]\frac{21 C }{-1.602 \times 10^{-19} C}[/tex]

The number of electrons ≈ [tex]1.31 \times 10^{20} electrons[/tex]

Hence the number of electrons transferred during the lightning bolt is [tex]1.31 \times 10^{20}[/tex].

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The star might be quite large in size, with a much larger surface area than the sun. This would increase its luminosity despite its cooler temperature.

The star has a high luminosity (100,000 x the sun's) and a cool temperature (3500 K) because of its size.

A star's luminosity is proportional to its size, so if a star is very large, it can have a high luminosity even if it is relatively cool.

Another possibility is that the star is in a phase of its life cycle where it has expanded and cooled, such as a red giant or supergiant, but still retains a high luminosity due to its large size.

These stars have relatively low surface temperatures, but their large sizes give them very high luminosities.

Therefore, this star is likely very large and thus has a very high luminosity despite its low temperature.

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The direction the automobile should move to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom towards the east.

A magnetic field is an area surrounding a magnet or an electric current, characterized by the presence of a force that can attract or repel other magnetic materials. The concept of magnetic fields is significant in a variety of contexts, including electromagnetism, particle physics, and ferromagnetism.

According to Faraday's Law of Electromagnetic Induction, the emf generated in a conducting wire moving in a magnetic field is proportional to the strength of the magnetic field and the velocity of the conductor.

The magnitude of the emf is given by ε = Blv sinθ, where

- ε is the magnitude of the induced emf,

- B is the magnetic field strength,

- l is the length of the wire in the magnetic field,

- v is the speed of the conductor relative to the magnetic field, and

- θ is the angle between the velocity vector and the magnetic field vector.

Due to the given conditions in the question, we can use the above formula for calculating the maximum emf. To generate the maximum motional emf in the antenna, the automobile should move in a direction perpendicular to both the antenna and the Earth's magnetic field. The angle between the velocity vector and the magnetic field vector should be 90°.

1: Identify the direction of the magnetic field. In this case, the magnetic field is directed toward the north and downward at an angle of 65.0° below the horizontal.

2: Determine the direction perpendicular to both the antenna and the magnetic field. This can be done by using the right-hand rule. Point your right thumb in the direction of the magnetic field (north and downward at 65.0° below the horizontal) and your right index finger in the direction of the antenna (vertical). Your right middle finger will then point in the direction of the motion required to generate the maximum emf (perpendicular to both the magnetic field and the antenna).

The direction the automobile should move to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom, is to the east.

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The terminal speed of the skydiver as he falls feet first would be  54.9 m/s.

To find the terminal velocity of the skydiver, we need to balance the forces acting on him. At terminal velocity, the force of air resistance (also known as drag) is equal and opposite to the force of gravity. This means that the net force on the skydiver is zero and his velocity remains constant.

The force of air resistance is given by:

F_drag = (1/2) * rho * v^2 * C_d * A

where:

rho is the density of air (about 1.2 kg/m^3 at sea level)

v is the velocity of the skydiver

C_d is the drag coefficient (0.6 in this case)

A is the cross-sectional area of the skydiver

The force of gravity on the skydiver is given by:

F_gravity = m * g

where:

m is the mass of the skydiver (75 kg in this case)

g is the acceleration due to gravity (9.81 m/s^2)

At terminal velocity, F_drag = F_gravity, so we can set the two equations equal to each other:

(1/2) * rho * v^2 * C_d * A = m * g

Solving for v, we get:

v = sqrt((2 * m * g) / (rho * C_d * A))

Substituting in the values given, we get:

v = sqrt((2 * 75 kg * 9.81 m/s^2) / (1.2 kg/m^3 * 0.6 * 1.5 m^2))

v = 54.9 m/s

Therefore, the terminal speed of the skydiver is about 54.9 m/s when falling feet first with a drag coefficient of 0.6.

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The strobe light's flashes occur at a 70 Hz frequency.

The frequency of a sound pressure wave, also known as pitch, is the quantity of times every second that it repeats. A bullfrog cry is far downward communication than a whistle, while a cricket is much downward communication than a drum beat.

T is the amount of time between flashes in seconds, and f is the frequency expressed in Hertz (Hz).We obtain the following value by inserting the given value: f = 1 / (1/70) f = 70 Hz.

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The speed of the cart is 4.0 m/s.

step by step explanation:

Force F is 10-N,

Distance d is 8.0-m, and

Mass m is 20-kg,

A constant 10-N horizontal force is applied to a 20-kg cart at rest on a level floor.

If friction is negligible, then the speed of the cart when it has been pushed 8.0 m can be calculated using the equation v = Fd/m,

where v is the speed of the cart,

F is the applied force,

d is the distance, and

m is the mass of the cart.

so the speed of the cart is v = (10 N × 8.0 m) / 20 kg = 4.0 m/s.

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"  deep currents circulate seawater around the globe due to differences in the density of water at different locations. two factors that can alter the density of water are salinity and temperature. " The correct Answers are option : A & D.

The density of seawater depends on various factors, including salinity and temperature. Salinity is the measure of  amount of dissolved salts in seawater, and affect the density of water because saltwater is denser than freshwater. Temperature plays a crucial role in density of seawater, as cold water is denser than warm water. These factors can lead to  formation of currents circulate seawater around  globe, transferring heat and nutrients across vast distances in the ocean. Hence option A & D are correct.

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Wavelength of light = 5 x 10^-7 m = 500 nm.Using Young's experiment formula, we can find the wavelength of the light.

Youthful's trial is an exemplary examination in material science that exhibits the wave-like nature of light. In this trial, light is gone through two cuts and the subsequent impedance design is seen on a screen. The distance between the cuts is known as the cut partition, indicated by "d", and the separation from the cuts to the screen is known as the screen distance, signified by "D".The distance between the focal most extreme and the third dim band is known as the third-request dim periphery, indicated by "x". We are given that the cut partition, d, is 1.5 x 10^-4 m, the screen distance, D, is 1.0 m, and the third-request dim periphery, x, is 1 cm (or 0.01 m).To decide the frequency of the light, indicated by λ, we can utilize the accompanying recipe:

λ = (xd)/D

Subbing the given qualities, we get:

λ = (0.01 m)(1.5 x 10^-4 m)/(1.0 m) = 1.5 x 10^-7 m = 150 nm

Accordingly, the frequency of the light is 150 nanometers. This is inside the scope of apparent light, which has frequencies between roughly 400 nm (violet) and 700 nm (red). The exactness of this computation is subject to the accuracy of the estimation of the distances in question.

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The tension in the wire created by the bird landing on it is calculated by using the equation T= (mgh)/d, where m is the mass of the bird, g is the acceleration due to gravity, h is the amount the wire sags and d is the distance between the two telephone poles.

In this case, with m = 1.02 kg, g = 9.81 m/s2, h = 0.212 m and d = 49.5 m, the tension in the wire is calculated as T = (1.02 kg x 9.81 m/s2 x 0.212 m)/49.5 m = 4.299 N.

This means that the bird produces a tension of 4.299 N in the telephone wire when it lands on it midway between the two poles. This amount of tension is relatively small, but enough to cause the wire to sag slightly. The tension in the wire will increase if the bird moves further along it, as the distance d between the poles will decrease.

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The apparent weight of a person with a mass of 78 kg in an elevator accelerating upward at 1.80 m/s2 is 91.2 kg.

This is calculated using the equation: apparent weight = mass x acceleration due to gravity + acceleration of elevator, which equals 78 kg x 9.81 m/s2 + 1.80 m/s2 = 91.2 kg.

Steps:

Therefore, the apparent weight of the person is 767.78 N + 140.4 N = 908.18 N.

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Yes, sometimes even if all the trackers are green, they might produce the wrong camera solve/calibration.

The green tracker status indicates that the tracker is properly tracked, but it does not guarantee the accuracy of the camera solve. Various factors could lead to an incorrect camera solve.

One of the primary factors is improper tracking. In some cases, a tracker may seem to be in the right position, but the camera solver could generate an inaccurate camera solve if the tracker is not in the appropriate location on the image. To get accurate camera solves/calibration, you should place trackers in areas of high contrast, where the tracker can be tracked consistently throughout the sequence. If the trackers are placed in low-contrast regions, the tracker might not be tracked accurately, resulting in a poor camera solve. Therefore, it's critical to double-check the tracker placement for each frame to ensure that the tracking is accurate.

Other factors that could lead to an incorrect camera solve include incorrect lens distortion measurements, incorrect focal length measurements, improper image sequence alignment, incorrect image resolution, and other variables.

Hence, it is essential to monitor and inspect the solver settings to ensure accurate camera solve/calibration.

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The damping ratio of the system can be calculated as 0.13.

What is displacement?

Displacement at resonance, Xn = 0.6 inches

Displacement at very high RPM, Xv = 0.15 inches

Natural frequency of a system is:

f = (1/2π) * √(k/m)

where k is the stiffness of the system and m is its mass.

Let's assume the mass of the system as m and k is the stiffness of the system.

When the motor is at resonance, the frequency of the system is: n = f

where n is the frequency of the system.

When the motor is running at very high rpm, the frequency of the system is given as:v = f

where v is the frequency of the system.

Now, let's assume the damping coefficient of the system as c.

The displacement of the system:

X = [Xn * exp(-ζωnt)] * sin(ωdt)

where X is the displacement of the system, ζ is the damping ratio of the system, ωn is the natural frequency of the system and ωd is the frequency of the applied force.

The maximum value of the displacement is:

Xmax = Xn / (2ζ * √(1 - ζ²))

Here, Xmax = 0.6 inches when the motor is at resonance Xmax = 0.15 inches

when the motor is running at very high RPM, putting the given values of Xmax in the above equation, we can find the value of the damping ratio, ζ.

For resonance:0.6 = Xn / (2ζ * √(1 - ζ²))

=> 2ζ * √(1 - ζ²)

= Xn / 0.6=> 4ζ² * (1 - ζ²)

= Xn² / 0.36=> 4ζ⁴ - 4ζ² + 0.26244

= 0

Solving this quadratic equation gives us the value of ζ as 0.32.

For high RPM:

0.15 = Xn / (2ζ * √(1 - ζ²))

=> 2ζ * √(1 - ζ²)

= Xn / 0.15=> 4ζ² * (1 - ζ²)

= Xn² / 0.0225

=> 4ζ⁴ - 4ζ² + 1.728 = 0

Solving this quadratic equation gives us the value of ζ as 0.13.

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The angular momentum of the Earth spinning on its axis is 7.1 × 10³⁰ kilogram meters squared per second.

Angular momentum is the quantity of rotation of a body that takes into account its mass and its rotational speed. Angular momentum = Moment of inertia × Angular velocity

where the moment of inertia is a measure of how an object's mass is distributed around its centre of rotation.

The moment of inertia of the Earth:

moment of inertia = 2/5 × mass × radius²

where the mass of the Earth is 5.97 × 10²⁴ kg and its radius is 6.38 × 10⁶ m.

Therefore, moment of inertia = 2/5 × 5.97 × 10²⁴ kg × (6.38 × 10⁶ m)²

                                                = 9.83 × 10³⁷ kg m²

Using the fact that the Earth completes one rotation every 24 hours, or 86400 seconds,

the angular velocity of the Earth:

angular velocity = 2π / time taken for one rotation

                           = 2π / 86400 seconds

                           = 7.27 × 10⁻⁵ radians per second

Finally, the angular momentum of the Earth spinning on its axis:

angular momentum = Moment of inertia × Angular velocity

                                 =9.83 × 10³⁷ kg m² × 7.27 × 10⁻⁵ radians per second

                                 = 7.1 × 10³⁰ kg m²/s

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As a percentage of their total volumes, the cores of Uranus and Neptune are smaller than the cores of Saturn and Jupiter.

Uranus, Neptune, Saturn, and Jupiter are all gas giant planets with a layered structure consisting of a core, mantle, and atmosphere. The size of the core relative to the rest of the planet is determined by the planet's formation and evolution history.

Jupiter and Saturn are known to have relatively large cores compared to their overall size, while Uranus and Neptune are believed to have smaller cores.

However, the exact sizes and compositions of the cores of these planets are still a subject of research and debate. As a result, it is difficult to provide a precise comparison of the sizes of the cores of these planets as a percentage of their total volumes.

Based on current knowledge, it is generally accepted that the cores of Uranus and Neptune are smaller than the cores of Saturn and Jupiter as a percentage of their total volumes.

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The problem involved calculating the speed of an airplane using the change in wavelength of radio waves it emits. By using the formula and substituting the given values, we found that the speed of the airplane is 2.5 x 10^5 m/s.

The given information can be summarized as:

The wavelength of the radio wave emitted by the airplane = λ_emitted = 1.2 m

The wavelength of the radio wave received at the airport = λ_received = λ_emitted + 1.1 x 10^-6 m

The speed of the radio wave = v_wave = 3.0 x 10^8 m/s

We can use the formula given in the problem to find the speed of the airplane:

change of wavelength = speed of airplane x wavelength / speed of radio wave

Substituting the given values, we get:

λ_received - λ_emitted = speed of airplane x λ_emitted / v_wave

Simplifying and solving for the speed of the airplane, we get:

speed of airplane = (λ_received - λ_emitted) x v_wave / λ_emitted

Plugging in the values, we get:

speed of airplane = (1.2 + 1.1 x 10^-6 - 1.2) x 3.0 x 10^8 / 1.2

speed of airplane = 2.5 x 10^5 m/s

Therefore, the speed of the airplane is 2.5 x 10^5 m/s.

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The boat will bob up and down on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s once every 7.50 seconds.

To solve the given question, we must use the formula:

n= v/f

Where: v is the velocity of the wave (in m/s)f is the frequency of the wave (in Hz)n is the number of cycles per second

Therefore, the frequency of the wave (in Hz) can be calculated by using the formula:

f= v/λ

where: v is the velocity of the wave (in m/s)λ is the wavelength of the wave (in m)

The frequency of the wave is 0.1333 Hz (approx).

Now, the number of cycles per second (n) is: n = v/λ

We can solve for n by dividing the velocity of the wave by the wavelength of the wave.

Therefore,

n= v/λ= (4.80 m/s) / (36.0 m)= 0.1333 Hz

So, the boat bob up and down 0.1333 times a minute on ocean waves that have a wavelength of 36.0 m and a propagation speed of 4.80 m/s.

1 Hz = 60 seconds,

0.1333 Hz = 7.50 seconds.

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The current that would pass through the body is 0.92 A.

Current is a measure of the rate of flow of electric charge in a circuit and is measured in amperes (A). Ohm's law describes the relationship between voltage, current, and resistance in an electrical circuit.

Using Ohm's Law, the current that would pass through the body can be calculated as:

I = V/R, where V is the voltage and R is the resistance.

In this scenario,

V = 120 V

R = 130,000 ohms

Substituting these values in the formula, we get:

I = 120 V / 130,000 ohms = 0.92 A.

Therefore, approximately 0.92 amperes (or 920 milliamperes) of current would pass through the body.

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The Neocrystallization topic of the Metamorphic Change Animation options are A (Neocrystalline garnets form), B(Existing minerals become elongated and take on a foliation), and D. (Existing minerals undergo plastic deformation. E. Neocrystalline garnets are compressed.)

Based on the information provided, during the transition of mudstone to schist through neocrystallization:
A. Neocrystalline garnets form - This occurs as new minerals, like garnets, form during the metamorphic process.
B. Existing minerals become elongated and take on a foliation - As the mudstone undergoes metamorphism, the existing minerals align and elongate, developing a foliation.
D. Existing minerals undergo plastic deformation - During metamorphism, pressure and temperature changes cause the minerals to undergo plastic deformation, changing their shape and size.
Based on the Neocrystallization topic of the Metamorphic Change Animation, the following occur during the transition of mudstone to schist: - Existing minerals become elongated and take on a foliation - Neocrystalline garnets form Therefore, options A and B are the correct answers.
So, the correct options are A, B, and D.

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The field strength on the loop axis at 10.0 cm from the loop center is 0.01 microtesla.

The field strength on the loop axis at 10.0 cm from the loop center can be calculated using Ampere's law, which states that the integral of the magnetic field around a closed loop is equal to the total current passing through the loop. The field strength at a distance from the loop center is inversely proportional to the square of the distance from the loop center. Thus, the field strength on the loop axis at 10.0 cm from the loop center is inversely proportional to 10.0 cm^2 or 100 cm^2, which is equal to 0.01 microtesla.
To explain further, the magnetic field strength is the force per unit charge at a particular point in space. It is a vector quantity, and its direction is perpendicular to the loop plane. The strength of the magnetic field is affected by the radius of the loop, the number of turns in the loop, and the current passing through the loop. The magnetic field strength is inversely proportional to the square of the distance from the loop center, so the field strength on the loop axis at 10.0 cm from the loop center is 0.01 microtesla.

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In the inner solar system the largest surface fratures such as volacanos or valleys are found on the largest planets is a False  statement.

The largest planets in our solar system are gas giants, which do not have a solid surface. Therefore, they cannot have surface features like volcanoes or valleys.

In the inner solar system, the planet with the largest surface features is actually Mercury, which is the smallest planet. Mercury has a giant impact basin called the Caloris Basin, which is over 1,500 kilometers in diameter.

Lastly, Venus has large volcanic features, including its highest mountain, Maxwell Montes, which is over 11 kilometers tall.

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The given statement a constructor which has thrown an exception will also return a reference to its constructed object is false  because when an exception is thrown during the construction of an object, the constructor does not complete its initialization process.

As a result, the constructed object may be in an invalid or partially constructed state, which can lead to unexpected behavior if the object is used later in the program. A constructor cannot return a value, not even a reference to its constructed object. Instead, the constructor initializes the object's data members and sets up the object's state. If a constructor throws an exception, the object is not fully constructed and is therefore not valid. The exception can be caught and handled by the caller of the constructor.

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The speed of the water coming out of the nozzle is 19.2 m/s. The result is obtained by using the formula for volumetric flow rate.

The speed of the water coming out of the nozzle can be calculated using the flow rate equation. This equation states that the flow rate of a fluid passing through a constant cross-sectional area is constant, meaning that the water coming out of the nozzle must have the same flow rate as it did when it entered the hose.

Q₁ = Q₂

A₁v₁ = A₂v₂
We have

Determine v₂!

While A is the cross-sectional area of the hose and nozzle, it can be find by πr², where r = ½d.

Using the formula above, we get:

πr₁² × v₁ = πr₂² × v₂

(½(9.6))² × 1.3 = (½(2.5))² × v₂

23.04 × 1.3 = 1.562 × v₂

v₂ = 19.2 m/s

Hence, the speed of the water coming out of the nozzle is 19.2 m/s.

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