If we place it charge q° at the centre of two same charges which are 2a distance apart so what will be the value of third charge so that the system comes in equilibrium?

The potential difference between the plates is 22.47 x 10² V.

Distance between the plates of the capacitor, d = 6.33 x 10⁻³m

Energy density of the capacitor, u = 0.37 J/m³

u = 1/2ε₀E²

where E is the electric field.

So,

E² = 2u/ε₀ = 2 x 0.37/(8.85 x 10⁻¹²)

E² = 12.65 x 10¹⁰

E = 3.55 x 10⁵ V/m

Therefore, the potential difference between the plates,

V = Ed

V = 3.55 x 10⁵ x 6.33 x 10⁻³

V = 22.47 x 10² Volt

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Answer:

A. The property of sound waves that is related to pitch is its frequency. Higher frequency sound waves create higher-pitched sounds, while lower frequency sound waves create lower-pitched sounds.

B. The property of sound waves that is related to volume is its amplitude. Larger amplitude sound waves create louder sounds, while smaller amplitude sound waves create softer sounds.

C. The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed in sound waves, such as the change in pitch of a siren as an ambulance passes by. The Doppler effect occurs because the relative motion between the wave source and the observer causes a change in the effective distance that the wave travels, resulting in a change in its frequency.

D. The speed of sound varies depending on the state of matter it is traveling through. In general, sound travels fastest through solids, slower through liquids, and slowest through gases. In air at room temperature and pressure, sound travels at a speed of approximately 343 meters per second (1,125 feet per second), while in water, sound travels at a speed of about 1,480 meters per second (4,850 feet per second). In solids such as steel, sound can travel at speeds up to 5,960 meters per second (19,550 feet per second)

The force produced by the car engine is what causes the car to accelerate. The greater the force, the greater the acceleration, provided there are no other opposing forces (like friction or air resistance). In this case, the car engine produces a force of 2940 N, which results in an acceleration of 1.9342 m/s^2, assuming no other forces are acting on the car.

We need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Mathematically, this can be expressed as:

a = F/m

where a is the acceleration of the car, F is the force applied by the engine, and m is the mass of the car.

Substituting the given values, we get:

a = 2940 N / 1520 kg

a = 1.9342 m/s^2

Therefore, the acceleration of the car is 1.9342 m/s^2.

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The type of radiation emitted in the given nuclear reaction is beta radiation or beta decay.Option (a)

The nuclear reaction given can be written as follows:

234/90 Th → 0/-1 e + 234/91 Pa

In this reaction, a nucleus of Thorium-234 emits a beta particle, which is an electron. The beta particle has a negative charge and a negligible mass. The emission of a beta particle from the nucleus of an atom results in the conversion of a neutron to a proton, with the emission of an electron and an antineutrino.

Therefore, the type of radiation emitted in the given nuclear reaction is beta radiation or beta decay.

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Yes, that is correct. The negative sign in momentum indicates direction.

Momentum is a vector quantity, meaning it has both magnitude and direction. The equation for momentum is:

Momentum (p) = mass (m) * velocity (v)

The negative sign in momentum signifies that the object is moving in the opposite direction from the reference point or coordinate system. In a one-dimensional system, a positive momentum value usually indicates movement to the right, while a negative momentum value indicates movement to the left. In a multi-dimensional system, the negative sign could represent movement in the opposite direction along any axis, such as left, down, or backward, depending on the coordinate system being used.

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The wavelength of the 512-hertz sound wave that travels 100 meters to an observer through air at STP is approximately 0.67 meters.

To find the wavelength of the sound wave, we can use the formula:
wavelength = speed of sound wave / frequency of sound wave
At standard temperature and pressure (STP), the speed of sound in air is approximately 343 meters per second. So, plugging in the given frequency of 512 hertz, we get:
wavelength = 343 m/s / 512 Hz
wavelength = 0.67 meters
Therefore, the wavelength of the 512-hertz sound wave that travels 100 meters to an observer through air at STP is approximately 0.67 meters.

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The uncertainty of the focal length determined by measuring the maximum changes in the image distance which produce no apparent change in the clarity of the image is typically smaller than the error due to the object distance being less than infinite.

This is because the uncertainty in the focal length measurement is related to the precision of the measurement, while the error due to the object distance being less than infinite is a systematic error that cannot be eliminated by improving the precision of the measurement.

However, both sources of error should be considered when determining the overall uncertainty in the measurement of the focal length.

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Skeletal muscle fatigue refers to the decline in muscle force or power output during prolonged or repetitive muscle contractions. Several proposed causes contribute to muscle fatigue, including neural, metabolic, and mechanical factors.

Neural factors involve the nervous system's role in muscle contraction. Reduced motor neuron firing or synaptic transmission can lead to decreased muscle fiber recruitment, impacting the force generated by the muscle. Additionally, inhibitory neurotransmitters, such as gamma-aminobutyric acid (GABA), may play a role in fatigue by reducing motor neuron excitability.

Metabolic factors include the accumulation of metabolites and depletion of energy resources within muscle cells. During muscle contractions, adenosine triphosphate (ATP) is consumed to provide energy, and its depletion leads to reduced force production. Lactic acid, a byproduct of anaerobic glycolysis, accumulates in the muscle during intense exercise, causing a drop in pH and interfering with muscle contractile proteins. The build-up of inorganic phosphate (Pi), resulting from the breakdown of ATP, can also impair muscle contractile function.

Mechanical factors refer to physical changes within muscle fibers that affect their ability to generate force. Repeated muscle contractions can lead to the disruption of the actin-myosin cross-bridge cycling, which is essential for muscle contraction. Additionally, damage to the sarcomere structure or altered calcium (Ca2+) handling in the sarcoplasmic reticulum can impair muscle contraction and relaxation processes.

In summary, skeletal muscle fatigue arises from a combination of neural, metabolic, and mechanical factors that impact muscle force generation and contraction efficiency. Understanding these causes can help develop strategies to prevent or manage muscle fatigue during exercise and daily activities.

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"All other things being equal, decreasing the contribution margin per unit will increase the number of units that must be sold to earn a desired profit."

To answer this, let's break it down step-by-step:

1. The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit. It represents the amount that each unit contributes to covering fixed costs and generating profit.

2. The desired profit is the amount a business aims to achieve after covering all its costs (fixed and variable).

3. If the contribution margin per unit decreases, it means that each unit contributes less to covering the fixed costs and generating profit.

4. In order to achieve the desired profit, the business will now need to sell more units, because each unit is contributing less towards covering the fixed costs and generating profit.

Therefore, all other things being equal, decreasing the contribution margin per unit will indeed increase the number of units that must be sold to earn a desired profit.

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The intensity of the sound waves at a distance of 2 m from the source is 10 W/m^2.

The intensity of a sound wave is defined as the power transmitted per unit area perpendicular to the direction of propagation. According to the inverse square law, the intensity of a sound wave at a distance r from the source is inversely proportional to the square of the distance:

I(r) = I(r0) * (r0/r[tex])^2[/tex]

where I(r0) is the intensity of the sound wave at a reference distance r0.

In this problem, we are given that the intensity of the sound waves at a distance of 1 m from the source is 40 W/[tex]m^2[/tex]. Let's assume that this is the reference distance r0. We want to find the intensity of the sound waves at a distance of 2 m from the source. Using the inverse square law equation, we have:

I(2) = I(1) * (1/2[tex])^2[/tex]

I(2) = 40 * (1/4)

I(2) = 10 W/[tex]m^2[/tex]

Therefore, the intensity of the sound waves at a distance of 2 m from the source is 10 W/[tex]m^2[/tex].

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The height of the cliff is 144 ft, if it hits the ground with a speed of 96 ft/sec.

To determine the height of the cliff, we can use the equation of motion, v² = u² + 2as. Here, v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and s is the distance (height of the cliff in this case).

Given that the stone is dropped off the cliff, the initial velocity (u) is 0 ft/sec. The acceleration due to gravity (a) is -32 ft/sec² (the negative sign indicates downward acceleration). The final velocity (v) is -96 ft/sec (the negative sign indicates downward motion).

Now, we can substitute these values into the equation:

(-96 ft/sec)² = (0 ft/sec)² + 2(-32 ft/sec²)(s)

9216 ft²/sec² = 0 + (-64 ft/sec²)(s)

To solve for the height (s), we can rearrange the equation and divide both sides by -64 ft/sec²:

s = 9216 ft²/sec² / -64 ft/sec²

s = -144 ft (the negative sign indicates a downward distance)

However, since we're looking for the height of the cliff, we'll consider the absolute value of the distance, which is 144 ft. Therefore, the height of the cliff is 144 ft.

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A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision, both the momentum and kinetic energy are conserved due to the frictionless surface and elastic nature of the impact, leading to the puck and stick interacting without any energy loss.

When the hocket puck collides elastically with the end of the straight stick on the essentially frictionless ice, the momentum of the hocket puck is transferred to the stick. This transfer of momentum causes the stick to move in the opposite direction of the hocket puck's initial path. If the collision is perfectly elastic, there will be no loss of kinetic energy during the collision, and the hocket puck and stick will both continue to move at their respective speeds after the collision.

However, if there is any loss of kinetic energy during the collision, the speed of both the hocket puck and the stick will decrease slightly. Overall, the outcome of the collision will depend on the mass and velocity of the hocket puck and the stick, as well as the angle and position of the collision.
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We may observe from a straightforward harmonic system that the amount of time has grown by a factor of 4 = 2. As a result, simple harmonic system decreasing by a value of 2 is the right response.

The correct answer is B

In physics, simple harmonic motion is a steady rotation through an equilibrium position, or the position's centre point, where the largest displacement on either side of the position correlates to the largest motion on the other. There is a fixed interval of time between each complete vibration.

A body is considered to be in simple harmonic motion (S.H.M.) if its acceleration acts in opposition to the direction of a fixed point and is directly proportionate to its displacement. Examples: 1) Projecting a circular motion at a constant speed

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A white-hot metal object emits the full range of wavelengths, producing a continuous spectrum of light.

This means that all the colors of the rainbow are present in the emitted light, from red to violet. Unlike a discrete spectrum, where only specific wavelengths are present, a continuous spectrum contains all wavelengths in a smooth distribution. This phenomenon is commonly observed in high-temperature objects, such as stars and incandescent light bulbs. A white-hot metal object emits the full range of wavelengths, producing a continuous spectrum. This emission of various wavelengths is a result of the object's high temperature, which causes it to radiate energy across the entire electromagnetic spectrum, including visible light.

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When the car hits the bumper at F, its kinetic energy is transformed into gravitational potential energy and sound energy.

Energy transformation, also called energy conversion, is the process of converting energy from one form to another. In physics, energy is the quantity that provides the ability to do work, move (such as lift an object), or provide heat. In addition to transformation, energy can be transferred to another place or object according to the law of conservation of energy, but it cannot be created or destroyed.

Energy can be used in many ways in natural processes or to provide services to society, such as heating, cooling, lighting, and machine work to power machines. For example, a furnace burns fuel to heat a house. The chemical potential energy of this fuel is converted into thermal energy, which is transferred to the air inside the house to raise its temperature.

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Explanation:

The three rays used to locate images formed by lenses are the principal rays, the marginal rays, and the focal rays. The principal rays are the two rays that pass through the center of the lens. The marginal rays are the two rays that pass through the edge of the lens. The focal rays are the two rays that pass through the focal points of the lens.

A 1.6-kg grindstone in the shape of a uniform cylinder of radius 0.2m acquires a rotational rate of 180 rev/s from rest over a 6.0 s interval at constant angular acceleration. then the torque delivered by the motor.

Torque is defined as force times perpendicular distance from axis of rotation to the point at which force is applied. Torque is denoted by τ and its SI unit is Nm. i.e Torque is given by, τ = F×d sinθ. Torque is vector quantity. Torque is analogous to force in rotational motion. like there angular velocity ω is analogous linear velocity v. means Torque is a force in rotational motion.

in this problem,

Given,

m = 1.6 Kg

radius r =0.2m

Rotational velocity ω = 180 rev/s = 1130 rad/s.

time t = 6 s

the Force applied by the motor is,

F = m.dv/dt

velocity v  = rω = 0.2×1130 = 226 m/s

dv/dt = 226/6 = 37.6 m/s²

F = 1.6×37.6 = 60.2 N

Torque applied by the motor is,

τ = Fr = 60.2N × 0.20m = 12.04 Nm.

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A. Radio waves from an AM radio station broadcasting at 680 kHz have the longest wavelength among the options given.

Radio waves have the longest wavelengths in the electromagnetic spectrum. They can have wavelengths ranging from about 1 millimeter to 100 kilometers. This makes them useful for long-range communication, as they can travel long distances without being absorbed by the atmosphere. Radio waves are used in various applications such as radio and television broadcasting, cell phone communication, GPS navigation, and satellite communication.

Radio waves have the longest wavelengths in the electromagnetic spectrum, ranging from about 1 millimeter to 100 kilometers. The radio waves from an AM radio station have a frequency of about 680 kHz, corresponding to a wavelength of about 440 meters.

Infrared radiation has wavelengths ranging from about 1 micrometer to 1 millimeter, while microwaves have wavelengths ranging from about 1 millimeter to 1 meter.

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A pendulum has a bob with a mass of 25.0kg and a length of 0.750m. It is pulled back a distance of 0.250m then angular frequency of the pendulum is 3.61 rad/s

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string. The mean position of a simple pendulum is shown by a vertical line flowing through a fixed support. The length of the simple pendulum, abbreviated L, is the vertical distance between the point of suspension and the suspended body's centre of mass (when it is in mean position). The resonant mechanism supporting this type of pendulum has a single resonant frequency.

Period of the simple pendulum is given by,

T = 2π√L/g

∵ T = 2π/ω

Where ω = Angular frequency of pendulum,

2π/ω = 2π√L/g

ω  = √g/L

Given,

m = 25 kg

l = 0.75m

x = 0.25 m

g = 9.8 m/s² ( acceleration due to gravity)

putting values in the equation,

ω  = √g/L

ω  = √(9.8/0.75)

ω  = 3.61 rad/s

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The quantity "stress" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to [tex]ML^{-1}T^{-2}[/tex]. Therefore, option b. is correct.

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation.

In physics, stress is the force acting on the unit area of a material.

The effect of stress on a body is named as strain. Stress can deform the body.

Stress is defined as force per unit area.

Force has units of mass (M) times acceleration, which is length (L) divided by time squared (T²).

Area has units of length squared (L²).

So, when we divide force by area, we get:

(M * (L / T²)) / (L²)

By simplifying this expression, we arrive at:
[tex]ML^{-1}T^{-2}[/tex]

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The correct option is B, The voltage per individual light bulb in Circuit II is smaller than the voltage per individual light bulb in Circuit I.

voltage is a measure of the electric potential difference between two points in an electric circuit. It is commonly referred to as electric potential or electric potential difference. Voltage is measured in units of volts (V), which is equivalent to joules per coulomb. Voltage is a fundamental concept in electrical engineering and physics, and it is essential in understanding the behavior of electric circuits.

When an electric charge moves from one point to another in a circuit, it experiences a change in electric potential energy due to the voltage difference between the two points. The voltage in a circuit is determined by the source of electric power, such as a battery or generator. The voltage can be increased or decreased using various components in the circuit, such as resistors and capacitors.

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The final image is located 32.0 cm from the converging lens, it is virtual, upright, and magnified by a factor of 2.0.

Step 1: Find the location of the image formed by the converging lens using the thin lens equation:

1/f = 1/do + 1/di

where f is the focal length of the converging lens, do is the object distance, and di is the image distance from the converging lens.

1/6.0 cm = 1/4.0 cm + 1/di

di = 12.0 cm

Step 2: Find the location of the image formed by the diverging lens using the thin lens equation:

1/f = 1/do + 1/di'

where f is the focal length of the diverging lens, do is the distance from the diverging lens to the object, and di' is the distance from the diverging lens to the image.

1/-6.0 cm = 1/12.0 cm + 1/di'

di' = -24.0 cm

Step 3: Find the location of the final image relative to the converging lens:

The final image is formed by the diverging lens, which is located 8.0 cm behind the converging lens.

The distance between the converging lens and the final image is the sum of the distance between the converging lens and the diverging lens (8.0 cm) and the distance between the diverging lens and the final image (-24.0 cm):

di(final) = di(diverging lens) - d(diverging lens to converging lens)

= -24.0 cm - 8.0 cm = -32.0 cm

Therefore, the final image is located 32.0 cm from the converging lens.

Step 4: Determine whether the image is virtual or real:

Since the final image is formed by a diverging lens, which always produces virtual images, the final image is virtual.

Step 5: Determine the magnification and orientation of the final image:

[tex]m (converging) = -di/do = -12.0 cm/4.0 cm = -3.0\\m (diverging) = -di'/d = -24.0 cm/8.0 cm = -3.0\\m (final) = m (converging) * m (diverging) = (-3.0) * (-0.67) = 2.0[/tex]

Since the magnification is positive, the final image is upright.

Therefore, the final image is virtual, upright, and magnified by a factor of 2.0.

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The parent isotope is 222/88Ra.

The nuclear reaction given is a form of alpha decay, which involves the emission of an alpha particle from the nucleus. In this case, the parent isotope is 222/88Ra, which undergoes alpha decay to form the daughter isotope 218/86Rn and an alpha particle with a mass of 4 and atomic number of 2.

The notation for a nuclear reaction includes the symbol of the parent isotope on the left side of the arrow, followed by the symbol of the daughter isotope on the right side, along with any emitted particles. In this case, the alpha particle (4/2He) is emitted from the parent isotope, resulting in the formation of the daughter isotope.

Radioactive decay occurs when a nucleus is unstable and spontaneously emits radiation in the form of particles or electromagnetic waves in order to achieve a more stable state. In the case of alpha decay, the emission of an alpha particle reduces the mass and atomic number of the parent isotope, resulting in the formation of a new, more stable nucleus as the daughter isotope.

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Answer:

c

Explanation:

To double the wave speed of a wave traveling in a string, the tension needs to be increased by a factor of four. This is because the wave speed is directly proportional to the square root of the tension according to the wave equation.

The speed of a wave traveling in a string is dependent on the tension and the linear density of the string. According to the wave equation, v = √(T/μ), where v is the wave speed, T is the tension, and μ is the linear density. From this equation, we can see that the wave speed is directly proportional to the square root of the tension.

Therefore, to double the wave speed, we need to increase the tension by a factor of four. This is because if we double the tension, we will get a square root of two in the numerator, which will increase the wave speed by a factor of approximately 1.41.

To double the wave speed, we need to double it again, which means increasing the tension by a factor of 1.41^2 or 2.

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According to the question the magnitude of the resultant force is approximately 22.47 lb.

Magnitude is a measure of the size or intensity of something. It is most commonly used to describe the size of earthquakes, but can also be used to describe the size of other phenomena such as storms, winds, and floods. Magnitude can also refer to the size of a star or other celestial body. Magnitude is expressed as a number on a logarithmic scale, with larger numbers representing larger magnitudes.

We can use the Law of Cosines to calculate the magnitude of the resultant force. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following formula holds:

c2 = a2 + b2 - 2abcos(C)

In this case, a is 18 lb, b is 12 lb, and C is the angle between the two forces, 25 degrees. We can substitute these values into the formula and solve for c, the magnitude of the resultant force:

c2 = (18 lb)2 + (12 lb)2 - 2(18 lb)(12 lb)cos(25 degrees)

c2 = 324 + 144 - 432cos(25 degrees)

c2 = 324 + 144 - 216cos(25 degrees)

c2 = 468 - 216cos(25 degrees)

Now we can solve for c:

c = √(468 - 216cos(25 degrees))

c ≈ 22.47 lb

Therefore, the magnitude of the resultant force is approximately 22.47 lb.

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When you have a voltage difference between the two ends of the lamp, the lamp lights up because there is a voltage difference applied :

The correct answer is b) The lamp lights up because there is a voltage difference applied to it. This voltage difference causes an electric current to flow through the lamp, which in turn generates heat and light due to the resistance of the filament inside the lamp.

When there is a voltage difference between the two ends of the lamp, it creates an electric field that causes the electrons to flow through the lamp. This flow of electrons creates light and heats up the filament in the lamp, which causes it to glow. This process is known as the Joule heating effect, and it is the reason why lamps light up when a voltage difference is applied to them.
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The speed of the sand-filled balloon at the instant prior to the collision is 1 meter per second.

In order to calculate the speed of the sand-filled balloon at the instant prior to the collision, we need to use the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant if no external forces act on it.

Let's assume that the sand-filled balloon is moving with a velocity 'v' before the collision and that it collides with an object of mass 'm' at rest. After the collision, the sand-filled balloon and the object move together with a common velocity 'v'.

We can use the principle of conservation of momentum to calculate the velocity 'v'. The total momentum before the collision is:

P_before = m_sand * v

where 'm_sand' is the mass of the sand-filled balloon.

The total momentum after the collision is:

P_after = (m_sand + m) * v

where 'm' is the mass of the object.

According to the principle of conservation of momentum, P_before = P_after. Therefore:

m_sand * v = (m_sand + m) * v

Solving for 'v', we get:

v = (m_sand * v) / (m_sand + m)

We can now substitute the values of 'm_sand', 'm', and 'v' to get the speed in meters per second.

For example, if the sand-filled balloon has a mass of 0.5 kg, the object it collides with has a mass of 1 kg, and the balloon is moving with a velocity of 2 meters per second, then:

v = (0.5 * 2) / (0.5 + 1) = 1 m/s

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Option C is correct. The fundamental mechanism of formation for a comet tail artifact is refraction.

The refractive index, or index of refraction, is calculated as the difference between the speed of light in a vacuum and that in a material with a higher density. The refractive index variable is most usually represented by the letter n or n' in mathematical calculations and descriptive prose.

Higher index of refraction: mechanism as light moves more slowly at higher refractive indices, its orientation within the substance changes proportionately more. A substance with a higher refractive index can bend light more forcefully and allow for a lower lens profile, which has an effect on lenses.

The refractive index, or index of refraction, is calculated as the difference between the speed of light in a vacuum and that in a material with a higher density. The refractive index variable is most usually represented by the letter n or n' in mathematical calculations and descriptive prose.

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Answer:

To find the top speed and total time of the run, we can use the equations of motion. We'll start with finding the velocity of the car after 4.48 seconds of acceleration.

Using the equation:

v = u + at

where v is the final velocity, u is the initial velocity (which is 0 m/s as the car is starting from rest), a is the acceleration, and t is the time:

v = 0 + (7.20 m/s/s)(4.48 s)

v = 32.256 m/s

So the top speed of the car is 32.256 m/s.

To find the total time of the run, we need to calculate how long it takes to cover the remaining distance of 400 - (0.5 x 7.20 x 4.48^2) meters (i.e. the distance covered during the acceleration phase).

Using the equation:

s = ut + 0.5at^2

where s is the distance, u is the initial velocity, a is the acceleration, and t is the time:

s = (32.256 m/s)(t) + 0.5(0 m/s/s)(t^2)

s = 400 - (0.5 x 7.20 x 4.48^2)

Substituting s and solving for t:

(32.256 m/s)(t) = 272.672 m

t = 8.444 s

Therefore, the total time of the run is 8.444 seconds.

The reason a low mass star can live so long is that it fuses its hydrogen fuel slowly and the region outside the core is convective, so the fuel can make it back to the core where it will eventually be used.

This process allows the star to maintain a steady energy output for a longer period of time compared to high mass stars, which fuse their fuel more quickly and exhaust it sooner.

Additionally, low mass stars do not mix very well, which means they only use a small fraction of their mass for fusion reactions.

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