refer to question 12 on page 6/7: a type ii cepheid has an apparent magnitude of 12 and a pulsation period of 3 days. what is the approximate distance to this cepheid variable star?

If sand can fall through a hole in the bottom of the trolley, its acceleration will increase since the applied force is constant.

The motion of the trolley can be described based on the acceleration of the trolley.

The acceleration of the trolley is determined by applying Newton's second law of motion as follows;

F = ma

where;

a = F / m

Thus, from the equation above, as the total mass of the trolley decreases as the sand falls through the hole, the acceleration of the trolley will increase provided the constant force applied to the trolley is maintained.

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It reduces the moment of inertia denoted by (I). This moment of inertia is directly proportional to (MR)² Where M = mass & R = distance from the rotational axis. Since the net external torque is absent, angular momentum (L) remains unchanged as L= I.W, and Kinetic energy or angular speed increases.

The amount that is expressed by a body's ability to resist angular acceleration is calculated as the product of each particle's mass and the square of its distance from the rotational axis.

The rotational counterpart of linear force is torque. The moment of force is another name for it. It illustrates how a force can cause a change in the body's rotational motion.

Hence, the net external torque is absent, angular momentum (L) remains unchanged as L= I.W, and Kinetic energy or angular speed increases.

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The next solar maximus which will be visible with 157 or close to 157 sunspots will be visible after 11 years. which is 2000.

Sunspots are formed in region of higher magnetic field, they appear dark on the surface of the Sun.

Solar maximus is nothing but the regular amount of period of the greatest solar activity during the sun's 11 year solar cycle.

It was not exactly 157 but 140 sunspots were seen in 2000.

As the year follows, the sunspots are becoming lesser and lesser.

This data is yearly created by NASA.

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The scale factor of dilation from center point is found by conjugating the equation.

Dilation is a transform used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image that is identical to the original shape.

However, there is a difference in the size of the shape. Dilation should stretch or shrink the original shape. This transformation is denoted by the term "scaling factor".

[tex]\alpha +mR+\beta \pi R^2=0\\\\dw^2.dt^2+M=0---(center)[/tex]

Enlarging an image by dilation is called enlargement.

When dilation creates a smaller image, it is called contraction.

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The gravitational force exerted on the moon while it is in orbit around the planet is 1 × 10¹⁹ N.

Given:

Mass of the moon (m) = 1 × 10²² kg

Gravitational field strength (g) = 0.001 N/kg

The gravitational force is given by:

Gravitational force (F) = mass of the moon (m) ×  gravitational field strength (g)

F = 1 × 10²²  ×  0.001

F = 1 × 10²² ×  0.001

F = 1 × 10¹⁹ N

Hence, The gravitational force exerted on the moon while it is in orbit around the planet is 1 × 10¹⁹ N.

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A. The graph provided is a Displacement-Time Graph. The x-axis provides the displacement made by the object and the y-axis gives the time taken by the object to travel.

The amplitude of an object is defined as the maximum displacement made by the object. From the graph provided, the maximum displacement made by the object is 2cm.

Hence, as per the definition of Amplitude, the Amplitude of the object is 2cm.

The Amplitude of the object depends on the displacement made by the object. The maximum displacement is made when the object moves to an extreme position in an oscillation.

B. The object in a Simple Harmonic Motion moves from mean position to extreme positions. As the object moves from mean position to extreme position and reaches back to mean position, one oscillation or one cycle is said to be completed.

The graph represents the positive displacement when it moves to extreme position and the negative displacement as it returns from the extreme position.

The graph provided shows that for a complete one cycle or oscillation, the time taken is 4seconds.

Hence, as per the definition of Time period, the time period is 4 seconds. Therefore, the time period as ω = 2[tex]\pi[/tex]/T.

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Rock expands and contracts as a result of temperature variations (with cold). The rock's structure deteriorates as this keeps happening over and over. It disintegrates with time.

Heat is the energy that moves from one thing to another when temperatures are different. Heat passes from the hotter to the colder body when two bodies with differing temperatures are brought together. Usually, but not always, this energy transfer results in a rise in the heat of the colder body and a fall in the temperature of the hotter body.

By switching from one physical situation (or phase) to the other, such as melting from a solid to a liquid, sublimation from a solid to a vapor, boiling from a liquid to a vapor, or changing through one stable state to another, a substance can absorb heat without increasing in temperature.

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The distance when location of image is -27.8cm is 248.21 cm behind the lens and when location of image is -23.6 cm it is 421.43 cm front of lens.

The Lens formula in optics describes the relationship between the distance of an object (o), the distance of an image I and the focal length (f) of the lens. Both convex and concave lenses may be made with the same lens formula. These lenses are really thin. For a spherical mirror, the focal length, image distance, and object distance are all related by the lens equation, often known as the lens formula.

Using lens formula we know that  

v = uf/u + f

f = 25 cm

a) given u = -27.8

Thus v = -27.8 x 25/ 25+ (-27.8) =  248.21 from lens behind the lens.

The image will be real, inverted and large.

b) given u =  -23.6

Thus v =  -23.6 x 25/ 25+ ( -23.6) =  421.43 from lens front the lens.

The image will be virtual,upright and enlarge.

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Complete question is:

A thin lens has a focal length of 25.0 cm (a) Find the location of the image (in cm from the lens) formed by the lens when an object is placed p1 27.8 cm in front of the lens. (Enter a negative distance if the image is in front of the lens.) cm from the lens Choose the correct description of the image. (Select all that apply.) inverted reduced virtual enlarged upright (b) Find the location of the image (in cm from the lens) formed by the lens when an object is placed p2-23.6 cm in front of the lens. (Enter a negative distance if the image is in front of the lens.) cm from the lens Choose the correct description of the image.

A gas does 30.8 j of work after absorbing 0.0 j of heat. the gas's internal energy changed by -30.8 j.

E=change in internal energy and E=q + w

A greater q causes the system to heat up more. When q is negative, the system loses heat.

It is possible to improve the system when w (work completed) is positive. When w is zero, the system executes the operation.

Therefore, if the gas increases heat while losing 0.0 J of heat, q is positive 0.0 J.

The end result is negative, -30.8 J, as a result of the system performing 30.8 J of created labor.

The total of +0.0 J + +0.0 J is equivalent to - 30.8 J. (-30.8 J).

so that internal energy change =-30.8j

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Specific energy at this condition = 19699.34 ft

Altitude of the airplane = h = 15000ft

Velocity of the airplane = V = 375mi/h

Now total energy of a plane at height h is,

E = Potential energy + Kinetic energy

E = mgh + 1/2 m[tex]v^{2}[/tex]

Now, Specific energy is the energy per unit weight,

So, Specific energy = mgh + 1/2m[tex]v^{2}[/tex] /  mg

Specific energy = h + [tex]v^{2}[/tex]/2g

Now, using h = 15000ft, V = 375 mi/h

V = 375 × 1.467

V = 550.125ft/sec

g = 32.2 ft/sec²

So,  Specific energy = 15000 + 550.125²/65

Specific energy = 19699.34 ft

Energy per mass is also referred to as specific or massic energy. When compared to energy density, which is defined as the amount of energy in a given volume, gravimetric energy density is another name for it. It is used to quantify things like heat that has been trapped in a substance and other thermodynamic characteristics of that substance like particular internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. A body's kinetic or potential energy might also be considered when using this term. When compared to energy and mass, specific energy is an intensive attribute.

J/kg, or joule per kilogram, is the SI unit for specific energy. Kilocalories per gram (Cal/g or kcal/g), most commonly used in food-related contexts, are another unit that is still used in some situations

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A) The rock moves at 2.1 m/s when the string passes through the vertical position. (B) 0.83 N of string tension is present when the angle is 45 degrees. (c), the string is under 1.867 N of tension as it passes through the vertical position.

We are given that,

Mass = m = 0.12kg

String length = l = 0.80m

The maximum angle = θ = 45°

a) To determine the rock's speed when the string is in the vertical position, we have

using the first principle of thermodynamics

Kinetic energy = potential energy

1/2×m×v² = m×g×l×(1-cosθ)

v² = 2×g×l×(1-cosθ)

v²  = 2×9.81×0.8×(1-cos45) = 4.597

v = √4.597 = 2.1 m/s

(b) The tension in the string at a 45° angle to the vertical is determined by in order to maintain equilibrium between tension and rock mass, ∑Forces = 0,

T - m×g×cosθ = 0

T =  m×g×cosθ

T = 0.12×9.81×cos45

T = 0.83 N

(c) The string's tension as it crosses the vertical as we cross the vertical,

T = m×g + (m×v²)/r

T = mg(1+2(1-cosθ))

T =0.981 × 0.12 (1+ 2(1-cos45))

T=1.867 N

The given question is incomplete , complete question is given below,

A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 ∘ with the vertical. Air resistance is negligible. (A). What is the speed of the rock when the string passes through the vertical position? Express your answer using two significant figures. (B) What is the tension in the string when it makes an angle of 45∘ with the vertical?(C). What is the tension in the string as it passes through the vertical?

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The bullet's undetermined mass is m1 = 1.458 x 103. Mass, in physics, quantitative measure of inertia, a fundamental property of all matter.

Newton's equations of motion state that when a body of mass m is subject to a net external force, the body's momentum changes and is represented by:

f = p/dt

Where:

P is the body's linear momentum.

m2 = m3 = 4.5 x 10-3 kg

v2 = v3 =  575 m/s

The equal masses must move at angles of to each other in order for momentum to be zero in the y-direction.

θ1=180°, θ2=60°, θ3=-60°

m₁ ₓ v₁ ₓ cos180° + m₂ ₓ v₂ ₓ cos60° + m₃ ₓ v₃ ₓ cos(-60°) = 0

m₁ ₓ 575m/s ₓ cos180° + 4.5 x 10-3 kg ₓ 324 m/s ₓ cos60° + 4.5 x 10-3 kg ₓ 324 m/s ₓ cos(-60°) = 0

-m1 ₓ 575m/s + 1.458 ₓ 0.5 + 1.458 ₓ 0.5 = 0

-m1 ₓ 575m/s + 0.729 + 0.729 = 0

-m1 ₓ 575m/s + 1.458 = 0

m1 = 1.458 ₓ 10⁻³

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A material with a mass of 2.0 g when placed in a graduated cylinder the volume changed from 70 ml to 75 ml has a density of 0.4 g/mL.

How do I calculate the substance's density?

We'll start by getting the substance's volume. This is attainable as follows:

Water volume: 70 mL

75 mL = volume of material + water.

Substance volume =?

Substance volume equals (substance volume plus water) - (Volume of water)

Substance volume = 75 - 70

5 mL is the substance's volume.

Finally, we will calculate the substance's density. Below is an example to help:

2.0 g is the substance's mass.

5 mL is the substance's volume.

Substance density =?

Mass / volume equals density.

Substance density = 2/5

0.4 g/mL is the substance's density.

The density is therefore 0.4 g/mL.

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1/4 of the old gravity influence would remain.

Newton's universal principle of gravitation states that the attracting force among any two components is equal to the square of the length that separates them and equal to the ratio of their masses.

Gravitational pull is the term for something like the pressure which the planet exerts upon the object. Illustrations of movement caused by gravitational influence include the downward force of flow of water, the downward movement liquid flowing water, and the upward motion of a ball when it is tossed. Every two mass-containing items are attracted to one another by the gravitational force.

Since the force of gravity rarely aims to push masses apart, it is referred to as appealing since it constantly seeks to draw them towards.

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The tension on the wire is 52.02 N.

From the question, we have

Density of aluminum = 2700 kg/m3

Area,

A = πd²/4

A = π x (4.6 x 10⁻³)²/4

A = 1.66 x 10⁻⁵ m²

μ = Mass per unit length of the wire

μ = ρA

μ = 2700 kg/m³ x 1.66 x 10⁻⁵ m²

μ = 0.045 kg/m

Tension on the wire = √T/μ

34 = √T/0.045

34² = T/0.045

T = 52.02 N

The tension on the wire is 52.02 N.

Complete question:

The density of aluminum is 2700 kg/m3. If transverse waves propagate at 34 m/s in a 4.6-mm diameter aluminum wire, what is the tension on the wire.

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The ratio of the orbital radii of the planets is  4:1.

The ratio of their periods is 8:1.

Planetary bodies circle the Sun according to Kepler's three laws. They explain how planets orbit the Sun in elliptical fashion, how they traverse the same amount of space in a given length of time regardless of where they are in their orbit, and how their orbital periods are related to the size of their orbits (its semi-major axis).

An object's orbital radius is the typical distance it travels around a bigger object. An illustration would be that the Sun and Earth are typically 150 million kilometres apart. The orbital radius is also this.

Let the mass of the planet be m and the mass of the star be M.

r = radius of ordit

v = speed

We know that

gravitational attraction = centripital force

GMm/r^2 = mv^2/r

[tex]v = \sqrt{GM/r}[/tex]

Hence

v  ∝ 1/[tex]\sqrt{r}[/tex]

a) Here v₁/v₂ = v/2v = [tex]\sqrt{\frac{r2}{r1\\\ }[/tex]  

squuaring both sides

1/4 = r2/r1

Thus r1/r2 = 4/1

Hence ratio of orbital radii is 4:1.

b) As per keplers law of planetary motion,

T^2 ∝ r^3

[tex]\frac{T_{v} ^{2} }{T_{2v} ^{2} } = \frac{r_{v} ^{3} }{r_{2v} ^{3} }[/tex]

[tex]\frac{r_{v} ^{3} }{r_{2v} ^{3} } = 4^{3} = 64[/tex]

[tex]\frac{T_{v} }{T_{2v}} = \sqrt{64} = 8[/tex]

Thus ratio of time periods is 8:1.

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The change in internal energy when work is done on system is 9J.

In thermodynamics, the ideal gas concept is often used. This is an approximation of a real system used for educational purposes.

An ideal gas is a gas made up of particles that appear as point objects that interact only by elastic collisions. Here the kinetic energy consists only of the translational energies of the individual atoms.

Therefore, the change in the internal energy of an ideal gas is due only to the change in its kinetic energy. In this case the energy depends only on pressure, volume and thermodynamic temperature. Values ​​are proportional to the mass (in moles), temperature, and specific heat of a given volume of gas.

Q=U+W

U=Q-W

U=150-159=9J

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This feature of a comet develops when the celestial body passes close to a star such as the sun. The ice around the nucleus of the comet sublimates forming the coma around the comment (when hit by light photons as observed from the earth). The tails are also formed by the ice being pushed a bit behind the comet by light pressure.

When the comets gets near the sun, they get heated up. The white fumes seen on the comet are actually the burning sensations of the sun. When the comet gets near to the sun, the hot fire catches up the comet and the fumes are born on it.

The same happens when a meteor or a comet enters the surface of the earth.

Therefore, when they enter the surface of the earth, they tend to come in contact with the gases present in the atmosphere with great speed which makes those astronomical bodies turn into a globe of fire.

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The band gap energy in kilojoules per mole is 1.73×105J.

The band gap is the distance between the valence band and the conduction band of an electron. Essentially, the bandgap represents the minimum energy required to excite an electron to a state in the conduction band where it can participate in conduction. Higher frequencies and lower wavelengths of light are absorbed.

In physics, especially for solids, the band gap is also called the energy gap. It is the range of energies that exist in solids where no other electronic state can exist. In the diagram of the electronic band structure of solids, the bandgap is commonly called the energy difference.

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The period of this pendulum if its mass is doubled. The required analysis involves thinking about ratios is The period is 8 s when the pendulum's mass is doubled.

When a weight is shifted sideways from its equilibrium position, gravity acts as a restoring force on it, causing it to accelerate back toward the equilibrium position. This is what is meant by the term "pendulum," which refers to a weight that is hanging from a pivot so that it can swing freely. The restoring force acting on the mass of the pendulum once it is released causes it to oscillate, swinging back and forth about its equilibrium point. The duration, or the time required for a left swing and a right swing, is the period. The length of the pendulum and, to a lesser extent, the width of the amplitude, or swing, affect the period. Since Galileo Galilei's early scientific investigations of it in 1602, pendulums have been employed for timekeeping, and they remained the most precise timekeeping technology until the 1930s. For 270 years, households and offices utilized the pendulum clock invented by Christiaan Huygens in 1658 as the world's primary timekeeper before the quartz clock took its place.

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The type of electromagnetic radiation whose wavelength is efficiently observed using ground based telescopes simply is radio.

The correct answer choice is option a.

A wave can simply be defined as a disturbance which travels through a medium transferring energy from one point to another point.

However, from the context of the task given above, the simple reason why the wavelength of radio waves efficiently observed using ground based telescopes is simply because radio waves can penetrate the Earth's atmosphere.

In addition to the explanation above, there are different types of waves including transverse waves, mechanical waves, sound waves and so on and so forth.

In conclusion, we can now confirm and deduce from the explanation given above that radio waves are a form of electromagnetic radiation.

Complete question:

Which electromagnetic radiation wavelength is efficiently observed using ground based telescopes?

a. radio

b. infrared

c. visible

d. X-rays.

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If the number of particles twice, the average kinetic energy of molecules in an ideal gas also doubles.

Energy is referred to by scientists as the capacity for work. People have figured out how to transform energy from one form to another and then use it to accomplish tasks, making modern civilization possible.

Everything we eat, drink, or use has energy. The inherent physiological processes of the body are fueled and controlled by energy. The more abrasive the environment, the more energy is required to maintain homeostasis, which is critical for cell and body tissue repair, muscle growth, and other functions.

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A standing wave with one antinode in a string means fundamental mode of vibration  being formed at the lowest frequency.

Frequency = f

String length = l

We need to drive a formula of the speed of the wave

Using formula of fundamental frequency

f = v / λ

We know that,

λ = 2L

f = v / 2L

Where, v = speed of wave

λ = wavelength of the wave

f = frequency

The frequency of the wave is v / 2L

Therefore, the lowest frequency at which a standing wave is possible because standing can occur only at a fundamental frequency and at odd harmonics --> the lowest frequency.

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Katie exerts a force on Arman's shoulder and Arman exerts a force on Katie's hand. It's the third law of motion, of equal and opposite reaction.

If object A applies a force to object B, then object B must apply a force to object A in the opposite direction and of equal strength. This law illustrates a symmetry in nature whereby forces always occur in pairs and whereby no, body can exert a force without also being subjected to one.

Motion is the shift in an object's location in relation to its environment over a specific amount of time.

An influence that can alter an object's motion is known as a force. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe forces.

Hence, Katie exerts a force on Arman's shoulder and Arman exerts a force on Katie's hand. It's the third law of motion, of equal and opposite reaction.

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A student pulls a box of books on a smooth horizontal floor with acceleration of the box will be 1.99 m/s.

When we apply a horizontal force on a body kept on horizontal floor, a horizontal force starts opposing the net applied force. This force is called frictional force and is always tangential to the contact surface.

We can also find the normal force on the horizontal surface using the coefficient of friction. The basic formula of friction is f =mu N; from this, we get N = f/mu. mu is the coefficient of friction which tells the measure of friction acting between the surface.

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For a 65-kg swimmer to push against the pool wall, there is a force of 490N applied, and the swimmer accelerates at a speed of 6 m/s2. The swimmer encounters 100 n of friction.

According to Newton's second law,

sum Force = mass × acceleration

Fm - Ff = ma

Fm is the moving force

If s the frictional force = 100N

mass = 65kg

acceleration = 6m/s²

Required

Moving force Fm

Substitute the given force into the expression and get Fm

Fm -100 = 65(6)

Fm -100 = 390

Fm = 390+100

Fm = 490N

Hence the force that will cause two carts to move is 490N.

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Option-1,3 1. Not monochromatic sources. - interference is due to two monochromatic sources,3. observed from a distance similar to or smaller than the separation between the sources. -

Monochromatic radiation is electromagnetic radiation having a single, fixed frequency in physics. The term monochromatic light is frequently used when that frequency is a component of (or close to) the visible spectrum. The human eye recognizes spectral color in monochromatic light.

Monochromatic radiation has a single wavelength that never changes when it moves through a vacuum or a uniform transparent medium.

Because of the Fourier transform's localization property, no radiation can be completely monochromatic because that would need a wave with an endless length (cf. spectral coherence). Even from lasers or spectral lines, "monochromatic" radiation in reality always consists of components with a range of frequencies of non-zero breadth.

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When a balloon is released, its buoyant force is 0.0316 N, and its net vertical force is 0.0096 N.

a) volume of balloon = 2.5 litre = 0.0025 m3

Buoyant force = Density of air * g * Volume of displaced air

At STP, the density of air is approximately 1.29 kg/m3

Buoyant force = 1.29 * 9.8 * 0.0025 = 0.0316 N

b) Net vertical force = Buoyant force – Weight

density of helium = 0.1786 kg/m3

Weight of rubber + helium = [0.0018 + (0.1786*0.0025)] * 9.8 = 0.0220 N

Net vertical force = 0.0316 – 0.0220 = 0.0096 N

A fully or partially submerged object is subject to an upward force known as the buoyant force. Upthrust is another name for this thrust upward. A body that is partially or completely submerged in a fluid gives the impression of losing weight because of the buoyant force, or that it is lighter.

The tendency for an object to sink is when its density exceeds that of the liquid it is submerged in. The object may be kept afloat by force if it is either less dense than the liquid or is shaped properly (like a boat). It floats in water if its relative density is less than one, and it sinks in water if its relative density is more than one.

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The formula for wave speed is - wave speed=frequency of wave × wavelength of wave.

Wave speed is the distance the wave goes in a given measure of time, for example, the quantity of meters it voyages each second. The condition that addresses the wave speed is given as follows:

On the off chance that a sea wave peak ventures a distance of 30 m in 10 seconds, then, at that point, the speed of the sea wave is 3 m/s. Then again, in the event that the peak of the sea wave covers a distance of 40 m while is 10 seconds, then, at that point, the speed of this sea wave is 4 m/s. From this, we can reason that the quicker wave covers a bigger distance in a similar measure of time.

In mathematical terms ,formula of wave speed is

c=ν × λ

where c is the defined as the speed of wave  in any medium,

ν is  defined as the frequency of the wave and

λ is defined as the  wavelength of the wave.

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Answer:

Most stars take millions of years to die. When a star like the Sun has used up all its hydrogen fuel, it expands into a red giant. It may be millions of kilometers in diameter, being large enough to engulf the planets Mercury and Venus.

After shedding its outer layers, the star collapses into a very dense white dwarf. A teaspoon of matter from a white dwarf would weigh up to 100 tons. Over trillions of years, the white dwarf cools and becomes invisible.

Stars heavier than eight times the mass of the Sun end their lives very suddenly. When they run out of fuel, they expand into red supergiants. They try to stay alive by consuming different fuels, but this only works for a few million years. After that, they produce a huge supernova explosion.

Explanation: