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The figure above shows the paths of two stars of equal mass as they orbit their common center of mass. The
positions of the stars at four different times are labeled in the figure. At which of the positions do the stars have their
greatest speed?
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(A) Position 2 only
(B) Position 4 only
(C) Positions I and 3 only
(D) All of the positions, since the stars move with constant speed
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11.252#The Figure Above Shows The Paths Of Two Stars Of Equal Mass As They Orbit Their Common Center

Answers

Answer 1

The stars have their highest speed at  Positions I and 3 only. Option C.

What happens to the stars system when they are closer to each other?

In a two-star system, both stars orbit around their common center of mass. When the stars are closer to each other, the gravitational force between them is stronger. This wil cause them to move at a great speed.

As the stars move away from each other, the gravitational force becomes weak, and their speed decreases.

Based on the information provided in the diagram, Positions 1 and 3 are the the points in the orbit where the stars are closest to each other.

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Related Questions

Bu lasarati pushes the trycicle with a force of 20 N so that it moves 10m in the direction of the force. The effort made by Mrs. Lasarati amounts to...

Answers

Answer:

200 J

Explanation:

Given that,

Force, F = 20 N

Distance covered in the direction of force, d = 10 m

We need to find the effort made by Mrs. Lasarati. It  will be given by :

W = Fd

W = 20 N × 10 m

W = 200 J

So, the required effort made by Mrs. Lasarati is 200 J.

If 6.0×105 J
J
of heat are added to the ice, what is the final temperature of the system?

Answers

The final temperature of the system is  63.33° C.

What is latent heat?

A body or thermodynamic system can release or absorb latent heat during a constant-temperature process, often a first-order phase transition.

Latent heat is energy that is provided or removed in a concealed form to alter the state of a substance without altering its temperature.

The applied heat = 6.0 × 10⁵ Joule

Mass of the ice = 1 kg

Latent heat of ice fusion = 334 kJ/kg

Hence,

334000 × 1 + 1 × 4200× (t - 0) =  6.0 × 10⁵

4200 × t = 266000

t = 63.33° C

Hence, the final temperature of the system is  63.33° C.

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A bucket tied to a rope is moving at a constant speed of 5.0 m/s in a circle of radius
2.0 m. Calculate the approximate magnitude of the centripetal acceleration of the bucket.
The below answer choices are in m/s^2

A.) 2.5
B.) 6.2
C.) 12.5
D. None of these

Answers

Answer:

\(a=12.5\ m/s^2\)

Explanation:

Given that,

The speed of the bucket tied to a rope, v = 5 m/s

The radius of the circle, r =2 m

We need to find the magnitude of the centripetal acceleration of the bucket. The formula for the centripetal acceleration is given by :

\(a=\dfrac{v^2}{r}\\\\a=\dfrac{(5)^2}{2}\\\\a=12.5\ m/s^2\)

So, the centripetal acceleration of the bucket is \(12.5\ m/s^2\).

a sinusoidal wave is traveling along a rope. the oscillator that generates the wave completes 45.0 vibrations in 29.0 s. a given crest of the wave travels 400 cm along the rope in 12.0 s. what is the wavelength of the wave?

Answers

The wavelength of the sinusoidal wave traveling along a rope is calculated to be 21.5 cm.

The wavelength of a sinusoidal wave is defined as the distance between two consecutive crests or troughs. It can be started by finding the frequency of the oscillator that generates the wave:

frequency = number of vibrations / time

frequency = 45.0 / 29.0 s = 1.55 Hz

After this, we can find the speed of the wave:

speed = distance / time

speed = 400 cm / 12.0 s = 33.3 cm/s

The speed of a sinusoidal wave on a rope is related to its frequency and wavelength by the equation:

speed = frequency x wavelength

Therefore, we can rearrange the equation to solve for wavelength:

wavelength = speed / frequency

wavelength = 33.3 cm/s / 1.55 Hz

wavelength = 21.5 cm

Therefore, the wavelength of the wave is 21.5 cm.

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if the power of sound at the source outlet is 100 w, what is its intensity at 4 m away from the source?

Answers

The intensity of sound is inversely proportional to the square of the distance from the source. The intensity of sound at 4 m away from the source is approximately \(0.993W/m^{2}\) (watts per square meter).

The intensity of sound is defined as the power per unit area. According to the inverse square law for sound propagation, the intensity of sound is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as

\(I=P/(4\pi r^{2})\)

where I is the intensity, P is the power, and r is the distance from the source.

Given that the power of sound at the source outlet is 100 W and the distance from the source is 4 m, we can substitute these values into the formula. Thus, we have

\(I = 100 W / (4\pi (4 m)^2)\)

Simplifying this expression, we find that the intensity of sound at 4 m away from the source is approximately \(0.993W/m^{2}\) (watts per square meter).

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HELP PLS
Explain what happens when two light waves travelling from the same direction of displacement meet.

Answers

Answer:

When two light waves traveling from opposite directions meet they experience wave interference. This happens when they are traveling along the same medium!

Explanation:

Hope it help! (Please mark brainliest!)

Several students are riding in bumper cars at an amusement park, the combined mass of a car A and its occupants is 250 kg. The combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B and moving to the right at 2 m/s when the driver decides to bump into car B. which is at rest. Car A accelerates at 1.5 m/s² to a speed of 5 m/s and then continues at constant velocity until it strikes car B.a. Calculate the total time for car A to travel the 15 m.After the collision car B moves to the right at a speed of 4.8 m/s.b. Calculate the speed of car A after the collision. After the collision did car A move to the left, right, or is at rest? Is this an elastic collision?

Answers

The car A is moving to the right at 3.36 m/s after the collision.

Why is carA still moving after collision?

After the collision, car A is still moving to the right, but at a slower speed than before. This is because some of its kinetic energy was transferred to car B during the collision, causing it to move to the right. Since some kinetic energy was lost, this is not an elastic collision.

a. To calculate the total time for car A to travel the 15 m, we need to use the equation:

s = ut + \1/2at²

where s is the distance traveled (15 m), u is the initial velocity (2 m/s), a is the acceleration (1.5 m/s²), and t is the time we want to find.We can reformat this equation to find t:

t = √{2s}/{a} + {u²}{a²}

Plugging in the values, we get:

t = √{2}¹⁵/{1.5} + {2²}{1.5²}  = 6.24 s

Therefore, it takes about 6.24 seconds for car A to travel the 15 m.

b. To calculate the speed of car A after the collision, we can use the principle of conservation of momentum:

m_Au_A + m_Bu_B = m_Av_A + m_Bv_B

where m is the mass of the car and occupants, u is the initial velocity, and v is the final velocity. We know that car B is initially at rest, so u_B = 0. We also know the masses and initial velocities of the two cars, so we can plug in the values and solve for v_A:

(250 { kg})(2{m/s}) + (200 { kg})(0{m/s}) = (250 {kg})v_A + (200 {kg})(4.8{m/s})

Solving for v_A, we get:

v_A = {(250{ kg})/(2{ m/s}) + (200{ kg})(4.8 m/s})}{250{kg}} = 3.36 m/s

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a rock with mass of 7.45 kg is thrown straight up with a force of 497 n gravity is 9.81 what is the net acceleration of the rock

Answers

The net acceleration working on the rock is 56.9 m/s² in upward direction, if the mass of the rock is 7.45 kg and the force applied on it is 497 N.

The upward force applied on the rock, F = 497 N

Mass of the rock, M = 7.45 kg

Acceleration due to gravity, g = 9.81 m/s²

We know force = Mass × Acceleration

Acceleration produced in the rock due to the force applied, a = 497/7.45

= 66.71 m/s²

Acceleration due to gravity is working downward, so net acceleration working on the rock, = 66.71 - 9.81 = 56.9 m/s²

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How
did the solar system begin? ( use complete sentences ) will mark b

Answers

Our solar system formed about 4.5 billion years ago from a dense cloud of interstellar gas and dust. The cloud collapsed, possibly due to the shockwave of a nearby exploding star, called a supernova. When this dust cloud collapsed, it formed a solar nebula—a spinning, swirling disk of material.

At the center, gravity pulled more and more material in. Eventually the pressure in the core was so great that hydrogen atoms began to combine and form helium, releasing a tremendous amount of energy. With that, our Sun was born, and it eventually amassed more than 99 percent of the available matter.

Matter farther out in the disk was also clumping together. These clumps smashed into one another, forming larger and larger objects. Some of them grew big enough for their gravity to shape them into spheres, becoming planets, dwarf planets and large moons. In other cases, planets did not form: the asteroid belt is made of bits and pieces of the early solar system that could never quite come together into a planet. Other smaller leftover pieces became asteroids, comets, meteoroids, and small, irregular moons.

A rocket burns fuel at a rate of 269 kg/s and
exhausts the gas at a relative speed of 3 km/s.
Find the thrust of the rocket.
Answer in units of MN.

Answers

The thrust of the rocket is 0.807 MN.

What is the thrust of the rocket?

The thrust of the rocket is calculated by applying Newton's second law of motion as shown below.

F = ma

where;

a is the acceleration of the rocketm is the mass of the rocket

F = m (v/t)

F = m (x/t²)

F = ( m/t) (x / t)

F = ( m/t ) ( v )

where;

m/t is the mass flow rate of the rocketv is the speed of the rocket

F = ( 269 kg/s ) ( 3,000 m/s )

F = 807,000 N

F = 0.807 MN

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Complete the following statement: The magnetic field around a current-carrying, circular loop ismost like that of(a) the earth.(b) a short bar magnet.(c) a current-carrying, rectangular loop.(d) a long straight wire that carries a current.(e) two long straight wires that carry currents in opposite directions.

Answers

The correct answer is (b) a short bar magnet because the circular loop of current creates a magnetic field that looks similar to the field created by a bar magnet.

The magnetic field around a current-carrying, circular loop is similar to that of a bar magnet because the circular loop acts as a magnetic dipole, with a north and south pole, just like a bar magnet. The magnetic field lines around the circular loop are also circular, just like the field lines around a bar magnet.

    The other options, such as a current-carrying, rectangular loop or long straight wire, do not produce a magnetic field that is similar to a bar magnet. Additionally, the strength of the magnetic field is greatest at the center of the circular loop and decreases with distance. This is similar to the field of a bar magnet, where the field is strongest at the poles and diminishes with distance.

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Certain family dynamics, such as abusive parenting, can increase the susceptibility of someone developing a(n) __________ disorder.

Answers

Answer:

personality disorder

Explanation:

Certain family dynamics, such as abusive parenting, can increase the susceptibility of someone developing a(n) personality disorder.

How does a person with personality disorder behave?

A disorder is diagnosed when these personality traits are significantly “deviated” from others and are very inflexible, impairing a person's adaptation to everyday situations and causing distress and discomfort in their personal relationships and other areas of life.

Personality disorders are generally pervasive and persistent patterns of thinking, perceiving, reacting, and relating that cause significant distress or functional impairment.

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the average human body contains approximately 5 liters of blood. if the blood has a density of 1060 kg/m3, what is the total mass of blood in the average human? (note: 1 l

Answers

The total mass of blood in the average human is approximately 5.3 kilograms.

To find the total mass of blood in the average human, we need to multiply the volume of blood by its density.

Given that the average human body contains approximately 5 liters of blood and the density of blood is 1060 kg/m^3, we can proceed as follows:

1. Convert 5 liters to cubic meters:
1 liter = 1/1000 cubic meters
So, 5 liters = 5/1000 = 0.005 cubic meters

2. Multiply the volume of blood by its density:
Mass = Volume × Density
Mass = 0.005 cubic meters × 1060 kg/m^3

3. Calculate the total mass of blood:
Mass = 5.3 kg

Therefore, the total mass of blood in the average human is approximately 5.3 kilograms.

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define liquid in matter

Answers

Answer:

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds.

A liquid is nearly incomprehensible fluid that conforms to the shape of its container but retains a constant volume independent of pressure.

Describe what will happen to mass and weight when you go to the moon and why would this happen

Answers

When you go to the moon, your mass remains the same, but your weight decreases significantly. This is because weight is the force exerted by gravity on an object, and the moon's gravitational pull is much weaker than that of Earth.

Mass is a fundamental property of an object and remains constant regardless of the location. Therefore, when you go to the moon, your mass remains the same as it was on Earth. Mass is a measure of the amount of matter in an object and is independent of gravitational forces.

Weight, on the other hand, is the force exerted by gravity on an object. It depends on the mass of the object and the strength of the gravitational field it is in. The moon has a much weaker gravitational field compared to Earth. The moon's gravity is about 1/6th of Earth's gravity. As a result, when you go to the moon, the force of gravity acting on your body decreases significantly, leading to a decrease in your weight.

The decrease in weight on the moon is due to the inverse square law of gravitational attraction. The gravitational force between two objects decreases with the square of the distance between them. Since the distance between you and the moon is greater than the distance between you and Earth, the gravitational force on you is much weaker on the moon. Therefore, you will feel lighter and experience a significant decrease in weight when you go to the moon.

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The potential energy, at x =8 m is -2000 V and at x = 2 m is +400 V. What is the magnitude and direction of the electric field? A) 200 V/m directed parallel to the +x-axis B) 300 V/m directed parallel to the +x-axis C) 400 V/m directed parallel to the +x-axis D) 500 V/m directed parallel to the +-x-axis E) 600 V/m directed parallel to the +x- axis

Answers

The correct answer is option B) 300 V/m directed parallel to the +x-axis. The electric field is given by the negative gradient of the potential energy.

Explanation:

The electric field is given by the negative gradient of the potential energy. Using the formula E = -dV/dx, we can calculate the electric field at any point.

In this case, the potential energy changes from -2000 V to +400 V over a distance of 8 m - 2 m = 6 m.

Therefore, the magnitude of the electric field is:

|E| = |-dV/dx| = |(400 V - (-2000 V))/(8 m - 2 m)| = 300 V/m

The electric field is directed parallel to the +x-axis, because the potential energy is decreasing in the +x direction, which means the electric field is pointing in the opposite direction.

Hence, the correct answer is B) 300 V/m directed parallel to the +x-axis.

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Penetration capabilities in...
- Radio Waves
- Microwaves
- Infrared
- Visible light
- Ultraviolet
- X-rays
- Gamma rays

Answers

Ultra = X-ray

Explanation:

how are things going to paint the roof for beginners painting and decorating the whole house so I'm going away with a few sports mates for a couple nights for beginners but will have a look painting at a time and see what is going to be Strong enough

What is the speed of a bird of mass 8kg which has kinetic energy of 8836J?

Answers

Answer:

For the bird moving in a straight line, the kinetic energy is one-half the product of the mass and the square of the speed: Ek=12mu2.

Two hockey pucks with mass 0.1 kg slide across the ice and collide. Before the collision, puck 1 is going 15 m/s to the east and puck 2 is going 12 m/s the west. After the collision, puck 2 is going 15 m/s to the east. What is the velocity of puck 1?

Answers

The velocity of puck 1 after the collision is 15 m/s to the east.

Conservation of momentum principle to solve this problem

The total momentum of the system before the collision is equal to the total momentum of the system after the collision.

The momentum of each puck can be calculated as:

p = m * v

where

p is the momentum (in kg*m/s)

m is the mass (in kg)

v is the velocity (in m/s)

The total momentum of the system before the collision is:

p_total_before = p1_before + p2_before = m1 * v1_before + m2 * v2_before

where subscripts 1 and 2 refer to pucks 1 and 2, respectively, and "before" refers to the velocity before the collision.

Substituting the given values, we get:

p_total_before = (0.1 kg) * (15 m/s) + (0.1 kg) * (-12 m/s) = 0.3 kg*m/s

The total momentum of the system after the collision is:

p_total_after = p1_after + p2_after = m1 * v1_after + m2 * v2_after

where "after" refers to the velocity after the collision. We are given that puck 2 is going 15 m/s to the east, so the velocity of puck 2 before the collision is -12 m/s to the west, and the change in velocity is:

Delta_v2 = v2_after - v2_before = 15 m/s - (-12 m/s) = 27 m/s

The momentum of puck 2 is conserved during the collision, so we have:

p2_before = p2_after

m2 * v2_before = m2 * v2_after

v2_after = v2_before = -12 m/s

Substituting the given values and solving for the velocity of puck 1 after the collision, we get:

p_total_after = m1 * v1_after + m2 * v2_after

0.3 kg*m/s = (0.1 kg) * v1_after + (0.1 kg) * (-12 m/s)

v1_after = (0.3 kgm/s + 1.2 kgm/s) / (0.1 kg)

v1_after = 15 m/s

Therefore, the velocity of puck 1 after the collision is 15 m/s to the east.

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Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank you!

Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank
Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank
Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank
Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank
Hi! I have answered them but can someone review them and tell me if I am correct plssssssss and thank

Answers

Explanation:

yes, you are correct in both cases.

this is in one hand exactly the definition of science (science tries to find out how the natural world works and hence how we can use that in our favor), and on the other hand exactly the problem when dealing not just with general behavior but exact results in natural systems.

mother nature "hates" exact results. it works by chance and by the law of big numbers and tendencies (only with many, many comparable events can you see a tendency of the system). when you observe the behavior of one horse in a situation, you still know nothing about how horses behave. only after observing many horses in the same situation can you see a pattern emerging.

flipping a coin 4 times will usually not show the expected 50/50 pattern of heads and tails. but 100 or 1000 flips will start to show the tendency. but they will still not have an exact and as such repeatable result and will almost never produce the limit of the tendency of a 50/50 split of results.

What is the difference between epicenter and focus?

Answers

Answer:

The hypocenter is the point within the earth where an earthquake rupture starts. The epicenter is the point directly above it at the surface of the Earth. Also commonly termed the focus.

Explanation:

An antibaryon composed of two antiup quarks and one antidown quark would have a charge of:.

Answers

A charge of -1e would be present in an antibaryon made up of two antiup quarks and one anti-down quark. Option 2 is correct.

What is the charge?

When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.

The complete question is

"An antibaryon composed of two antiup quarks and one anti down quark would have a charge of

(1) +1e

(2) −1e

(3) 0e

(4) −3e"

An antibaryon composed of two antiup quarks and one anti-down quark would have a charge of  −1e.

Hence,option 2 is correct.

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all of the following statements about power are true except: select one: a. power is known as a single-dimension concept. b power is always present c. power can be positive or negative d dower is context specific

Answers

All of the following statements about power are true except power is known as a single-dimension concept. Hence, Option(A) is correct.

What is power?

Power is often characterized in terms of two characteristics: (1) the capacity to influence one's own and other people's actions, and (2) the freedom to do so. Status, authority, and dominance are all aspects of power, but they are not the same thing.

Status is the result of a social judgement that results in variations in prominence and respect, which add to a person's power within a group. It is possible to have status without relative power and power without status (such as the corrupt politician) (e.g., a religious leader in line at the Department of Motor Vehicles).

Power that comes from institutionalized roles or arrangements is known as authority. However, even in the lack of official responsibilities, power might still exist (e.g., within informal groups).

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Two men, Joel and Jerry, each pushes an object that are identical on a horizontal frictionless floor starting from rest. Joel and Jerry are using the same force F. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

Answers

Answer:

The work done by Joel is greater than the work done by Jerry.

Explanation:

Let suppose that forces are parallel or antiparallel to the direction of motion. Given that Joel and Jerry exert constant forces on the object, the definition of work can be simplified as:

\(W = F\cdot \Delta s\)

Where:

\(W\) - Work, measured in joules.

\(F\) - Force exerted on the object, measured in newtons.

\(\Delta s\) - Travelled distance by the object, measured in meters.

During the first 10 minutes, the net work exerted on the object is zero. That is:

\(W_{net} = W_{Joel} - W_{Jerry}\)

\(W_{net} = F\cdot \Delta s - F\cdot \Delta s\)

\(W_{net} = (F-F)\cdot \Delta s\)

\(W_{net} = 0\cdot \Delta s\)

\(W_{net} = 0\,J\)

In exchange, the net work in the next 5 minutes is the work done by Joel on the object:

\(W_{net} = W_{Joel}\)

\(W_{net} = F\cdot \Delta s\)

Hence, the work done by Joel is greater than the work done by Jerry.

A rose plant inherited two alleles for white flower petals.

Which conclusion is best supported by the given information?

Answers

Answer:

a

Explanation:

Answer:

A or each parent had at least one allele for white pedals

Explanation:

why does a lake freeze from the top down instead of from the bottom up?

Answers

A lake freezes from the top down because ice is less dense than liquid water.

Water is an exceptional substance because it expands when it freezes. As a result, the density of ice is lower than that of liquid water. As the temperature drops, the surface water begins to cool down and eventually freezes.

When the water freezes, it expands and becomes less dense. Therefore, the ice floats on top of the water, and the water below the ice stays liquid.

This process continues until the whole lake is frozen. If water were to freeze from the bottom up, the ice would sink to the bottom, and the process would continue until the entire body of water became ice, which would have catastrophic consequences for aquatic life.

However, because of the unique properties of water, lakes and other bodies of water freeze from the top down, allowing life in the water to survive beneath the ice.

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helllllllppppp
Question 7 of 10 Here is a model of the Sun-Earth system at a certain point in Earth's orbit around the Sun. Axis 对联 Rotation axis Arctic Trop of Cancer C Sunlighet Equator Trople of Capricom D netic Circle B 1 Perpendicular to orbit According to the model, which two places on Earth are experiencing summer? AC B. A D C D 0 DB​

helllllllpppppQuestion 7 of 10 Here is a model of the Sun-Earth system at a certain point in Earth's

Answers

Answer: c and a

Explanation:

Following a lecture on transverse and longitudinal waves, four students make venn diagrams to characterize these waves. which venn diagram is correct? a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string, created by a disturbance and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, all parts of the electromagnetic spectrum, vibrating string, medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and can travel through a vacuum. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, all parts of the electromagnetic spectrum and travel faster in a denser medium. the overlapping region has entries, created by a disturban

Answers

Venn diagram B is correct. A Venn diagram is a type of graph that uses circles to depict connections between objects or fixed groups of entities.

What Is a Venn Diagram and how does It Work?

A Venn diagram is a diagram that uses circles to depict relationships between objects or finite groups of objects. Circles that overlap share characteristics, whereas circles that do not overlap do not.

A Venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular.

The circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium.

The overlapping region has entries, created by a disturbance, has speed, and travels through solids.

Hence Venn diagram B is correct

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a car has acceleration given by a(t) = −8e0.2tm/s2 and initial velocity 15 m/s. (a) how much time does it take the car to stop? (b) how far does the car travel in this time?

Answers

If a car has acceleration given by a(t) = −8e0.2t m/s² and initial velocity 15 m/s then it takes the car about 3.86 seconds to stop and the car travels about 43.6 meters before coming to a stop.

(a) To find the time it takes the car to stop, we need to find when its velocity becomes zero. We can use the kinematic equation:

v = u + at

where v is the final velocity (zero in this case), u is the initial velocity (15 m/s), a is the acceleration (-8e0.2t m/s²), and t is the time we are looking for. Substituting these values, we get:

0 = 15 - 8e0.2t

Solving for t, we get:

t = (1/0.2) ln(15/8) ≈ 3.86 seconds

Therefore, it takes the car about 3.86 seconds to stop.

(b) To find how far the car travels in this time, we can use the kinematic equation:

s = ut + (1/2)at²

where s is the distance traveled. Substituting the values we know, we get:

s = 15(3.86) + (1/2)(-8e0.2)(3.86)²≈ 43.6 meters

Therefore, the car travels about 43.6 meters before coming to a stop.

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a coin of 3 cm diameter is placed 3 m in front of a parallel wall on which is hung a circular flat mirror. a person stands 9 m from the wall. what is the smallest- diameter mirror in which the observer can just see the reflected edge of the coin (i.e., the image of the coin just fills the mirror)?

Answers

Using mirror's equation, The smallest diameter mirror in which the observer can just see the reflected edge of the coin is 6 cm.

We must compute the size of the mirror's produced image in order to identify the lowest diameter mirror that would allow the spectator to just view the coin's reflected edge.

We must first determine how far the picture is from the mirror. In order to compute this, use the mirror equation:

\(\frac{1}{f} = \frac{1}{d} + \frac{1}{d'}\)

where f is the mirror's focal length, d and d' are the object's and image's distances from the mirror, respectively.

Since the mirror is flat, the focal length is determined by dividing the radius in half. Therefore, we may apply the formula:

\(f = \frac{R}{2}\)

This results from substituting it into the mirror equation:

\(\frac{2}{R} = \frac{1}{3} + \frac{1}{d'}\)

Calculating d':

\(d' = \frac{3R}{ (R-6) (R-6)}\)

The mirror's diameter, D, is equal to 2R. As a result, the minimal diameter of the mirror, at which the spectator can only see the coin's edge reflected, can be calculated as follows:

\(D = 2R = \frac{2d' (R - 6)}{ 3}\)

d' = 9, thus we can condense it to:

D = 18 / 3 = 6 cm

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