In a one-dimensional perfectly elastic collision, an object of mass m is traveling with speed v0 in the +x-direction when it strikes an object with mass 3m that is at rest. What are the objects' velocities following the collision?

The approximate angle of repose for average soils when using the sloping method for the prevention of cave-ins is option c.) 1.5:1.0. This means that for every 1.5 feet horizontally, the soil should slope down 1 foot vertically.

The angle of repose is the maximum angle at which a soil can remain stable without collapsing. Sloping the soil at this angle helps to prevent cave-ins by providing stability and support to the walls of the excavation.

It is important to note that the angle of repose may vary depending on the type and condition of the soil, so it is always best to consult with a qualified engineer or geotechnical expert for specific recommendations.

However, as a general rule of thumb, the slope angle is typically in the range of 1.5:1.0 to 2.0:1.0, which means for every foot of vertical depth, the slope should extend 1.5 to 2 feet horizontally.

This angle allows the soil to maintain its stability and prevent it from collapsing or sliding, providing a safe working environment. Therefore, the correct option would be (c) 1.5:1.0 to (d) 2.0:1.0.

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The given statement "Each FCC transition assembly shall incorporate means for facilitating the entry of the type FCC cable into the assembly; connecting the Type FCC cable to grounded conductors; and electrically connecting the assembly to the metal cable shields and grounding conductors" is true because it is taken from the Code of Federal Regulations (CFR) 47 Part 76.604(e)(4).

This statement is taken from the Code of Federal Regulations (CFR) 47 Part 76.604(e)(4), which outlines the requirements for FCC transition assemblies used in cable television systems.

The assembly must have features that make it easy to insert the type FCC cable, connect it to grounded conductors, and establish electrical connections between the assembly and the metal cable shields and grounding conductors. This is important to ensure that the assembly is properly grounded and shielded, which helps to prevent interference and signal loss in the cable system.

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The vertical distance an object dropped from rest on this distant planet covers in 1.3 seconds is 18.59 meters.

To calculate the vertical distance an object dropped from rest on this distant planet covers in 1.3 seconds, we can use the following equation of motion:
d = vi * t + 0.5 * a * t^{2}
where d is the vertical distance, vi is the initial velocity (0 m/s, since the object is dropped from rest), a is the acceleration (22 m/s^{2}), and t is the time (1.3 s).
Step 1: Substitute the given values into the equation:
d = 0 * 1.3 + 0.5 * 22 * (1.3)^{2}
Step 2: Perform the calculations:
d = 0 + 0.5 * 22 * 1.69
d = 11 * 1.69
Step 3: Calculate the final value:
d ≈ 18.59 m
So, the object dropped from rest on this planet with an acceleration of 22 m/s^{2} covers a vertical distance of approximately 18.59 meters in 1.3 seconds.

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The magnitude of the horizontal force acting on the sprinter is 56 N, the sprinter's power output at 2.0 s is 125.44 W, at 4.0 s is 251.68 W, and at 6.0 s is 376.32 W.

a. To find the magnitude of the horizontal force acting on the sprinter, we can use the following kinematic equation:

[tex]d = 0.5 * a * t^2[/tex]

where d is the distance traveled (50m), t is the time taken (7.0s), and a is the acceleration of the sprinter.

Solving for a, we get:

[tex]a = 2 * d / t^2[/tex]

[tex]= 2 * 50m / (7.0s)^2[/tex]

[tex]= 1.12 m/s^2[/tex]

Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration:

F_net = m * a

Substituting the values, we get:

[tex]F_net =[/tex][tex]50kg * 1.12 m/s^2[/tex]

= 56 N

Therefore, the magnitude of the horizontal force acting on the sprinter is 56 N.

b. The power output of the sprinter can be calculated using the following formula:

P = F * v

where P is the power, F is the force, and v is the velocity.

At 2.0 s:

The sprinter's velocity can be found using the following kinematic equation:

v = a * t

where a is the acceleration found earlier [tex](1.12 m/s^2)[/tex], and t is the time taken (2.0 s).

Substituting the values, we get:

[tex]v = 1.12 m/s^2 * 2.0 s= 2.24 m/s[/tex]

Using the formula for power, we get:

[tex]P = 56 N * 2.24 m/s= 125.44 W[/tex]

Therefore, the sprinter's power output at 2.0 s is 125.44 W.

At 4.0 s:

The sprinter's velocity can be found using the same kinematic equation as before:

v = a * t

Substituting the values, we get:

[tex]v = 1.12 m/s^2 * 4.0 s= 4.48 m/s[/tex]

Using the formula for power, we get:

[tex]P = 56 N * 4.48 m/s= 251.68 W[/tex]

Therefore, the sprinter's power output at 4.0 s is 251.68 W.

At 6.0 s:

The sprinter's velocity can be found using the same kinematic equation as before:

v = a * t

Substituting the values, we get:

[tex]v = 1.12 m/s^2 * 6.0 s= 6.72 m/s[/tex]

Using the formula for power, we get:

[tex]P = 56 N * 6.72 m/s= 376.32 W[/tex]

Therefore, the sprinter's power output at 6.0 s is 376.32 W.

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you will gain the same amount of potential energy regardless of the path you take

The potential energy gained depends on the height difference between the bottom and the top of the hill. Both paths will give you the same final potential energy, but the longer path will take more time and require more energy input to climb. Therefore, you will gain the same amount of potential energy regardless of the path you take. However, the longer path may require more physical effort and time to climb, even though it is less steep.

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For waves:

Match the wave to the description:

The wave with the smallest amplitude would produce the softest sound, B.

The wave with the largest amplitude would produce the loudest sound, D.

The wave with the highest frequency would produce the sound with the highest pitch, A.

The wave with the lowest frequency would produce the sound with the lowest pitch, C.

Waves only transfer energy.

The electromagnetic spectrum is made of: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

An acronym to help me remember this from longest to shortest wavelength: ROYGBIV (stands for red, orange, yellow, green, blue, indigo, violet - the colors of the visible light spectrum).

Uses for electromagnetic waves: radio and TV broadcasting, communication via mobile phones, heating food in a microwave oven, infrared cameras for night vision, medical imaging using X-rays, and cancer treatment using gamma rays.

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A sound can be altered in a recording studio through a variety of techniques and equipment by an audio technician. One commonly utilized method is equalization (EQ), where certain frequency ranges are boosted or reduced to amplify or decrease specific aspects of the sound.

An engineer could employ EQ techniques to heighten the bass frequencies in a bass guitar recording or diminish the treble frequencies in a vocal recording.

Audio engineers often apply compression to sound as a means of altering it. Audio engineers often incorporate various methods in their work, such as applying reverb, delay or modulation effects like chorus.

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Cannot provide an answer to this question as there is not enough information given to solve for the magnitude of the emf E induced in the loop. Please provide additional information or context. Please provide the missing information, and I can help you find the magnitude of the induced emf E.

We need more information about the loop and the rate at which its circumference is decreasing. However, I can help you set up the approach to find the magnitude of the induced emf E. Determine the initial circumference Coinitial of the loop. Calculate the final circumference C final after 3.00 s, given the rate of decrease. Calculate the initial and final magnetic flux using the formula BA, where B is the magnetic field and A is the loop area. Use Faraday's law to find the induced where final initial and 3.00 s. Express the induced emf E numerically in volts to three significant digits. Please provide the missing information, and I can help you find the magnitude of the induced emf E.

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The elastic potential energy stored in the pole of a pole vaulter is an important type of potential energy involved in pole-vaulting, but it is not the only one. There is also gravitational potential energy.

When a pole vaulter runs towards the pit, they have kinetic energy. As they plant the pole into the ground and start to bend it, this kinetic energy gets converted into elastic potential energy, which is stored in the pole. When the pole begins to straighten, the stored elastic potential energy is released and converted back into kinetic energy, propelling the vaulter upwards. At the peak of the vaulter's jump, their kinetic energy is momentarily zero, and their potential energy is at its maximum. This is gravitational potential energy, which depends on their height above the ground and their mass. As the vaulter descends, the gravitational potential energy is converted back into kinetic energy until they land on the mat. So, both elastic potential energy (stored in the pole) and gravitational potential energy (related to the vaulter's height) are involved in pole-vaulting.

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The twinkling of stars is caused by the motion of air in our atmosphere:

1) When light from a star enters the Earth's atmosphere, it encounters a layer of air molecules.

2) The air in our atmosphere is not uniform in temperature, pressure, or density. This means that the density of the air along the path of the star's light can vary.

3) As the star's light passes through these different densities of air, it is refracted, or bent, in different directions.

4) The bending of the light causes the apparent position of the star to change slightly, leading to the appearance of twinkling.

5) The degree of twinkling depends on the amount of atmospheric turbulence, which is caused by the motion of air in our atmosphere.

6) As air moves around in the atmosphere, it creates different pockets of air with different temperatures and densities, which can refract the star's light in different ways and cause it to appear to twinkle.

7) Variations in the wind speed and direction, as well as temperature and pressure changes, can all contribute to the amount of atmospheric turbulence and thus the degree of twinkling.

So in summary, the twinkling of stars is primarily caused by the motion of air in our atmosphere, which causes the light from the stars to be refracted in different directions, leading to the appearance of twinkling.

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The battery can deliver 122.4 milliwatt-hours of energy.

To find out how much charge the rechargeable flashlight battery can release at a rate of 85 mA for 12 hours, we can use the formula:

Charge = Current x Time

Charge = 85 mA x 12 hours

Charge = 1020 mAh

So the battery can release 1020 milliampere-hours of charge at that rate.

To find out how much energy the battery can deliver, we can use the formula:

Energy = Power x Time

Since Power = Voltage x Current, we can rewrite the formula as:

Energy = Voltage x Current x Time

Energy = 1.2 V x 85 mA x 12 hours

Energy = 122.4 mWh

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The angular displacement of the bicycle from its starting position is approximately 4.7 radians.

To calculate the angular displacement in radians of the bicycle from its starting position, we can use the formula:
Angular Displacement (θ) = Arc Length / Radius
Given:
Arc Length (s) = 141 m
Radius (r) = 30 m
Now, plug the given values into the formula:
θ = s / r
θ = 141 m / 30 m
θ ≈ 4.7 radians
So the angular displacement of the bicycle from its starting position is approximately 4.7 radians. Therefore, the correct answer is:
D) 4.7 rad

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Opacity adjusts the transparency or translucence of a shape or a layer. It is a measure of the degree to which light is allowed to pass through an object. Option B is correct.

The opacity setting is often used in graphic design and image editing software to control the visibility of layers, allowing designers to create interesting visual effects and overlays. When the opacity is set to 100%, the object is completely opaque and does not allow any light to pass through.

When the opacity is set to 0%, the object is completely transparent and allows all light to pass through. Intermediate values of opacity create varying degrees of transparency or translucence, allowing the underlying layers or background to show through to some extent.

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The specific heat of a substance is defined as the amount of heat energy required to raise the temperature of one unit of mass of the substance by one degree Celsius (or one Kelvin).

As a result, given the same level of energy input, the material with the smallest amount of specific warmth will experience the largest temperature change. We can see through the table of metal specific heats that copper, exhibiting a value of 0.385 J/g°C, is the metal with the smallest specific heat.

So, among the metals presented in the table, metal would experience the largest rise in temperature whether the same quantity of joule were put to the identical amount of each metal.

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Correct Question:

The specific heats of several metals are given in the table. if the same number of joules were applied to the same mass of each metal, which metal would show the greatest temperature change?

True. Clouds in the upper stratosphere, known as polar stratospheric clouds, can absorb some ultraviolet radiation.

These clouds are composed of tiny ice particles and form under specific meteorological conditions, typically occurring at high latitudes during the winter months.

The absorption of ultraviolet radiation by these clouds is important because high levels of ultraviolet radiation can be harmful to human health, leading to skin cancer and other health issues.

The presence of polar stratospheric clouds helps to reduce the amount of ultraviolet radiation that reaches the Earth's surface, providing some protection against its harmful effects.

However, the formation of these clouds is closely linked to the presence of ozone-depleting substances in the atmosphere, such as chlorofluorocarbons (CFCs).

These substances can destroy ozone molecules in the upper atmosphere, leading to a thinning of the ozone layer. The thinning of the ozone layer can increase the risk of harmful effects from ultraviolet radiation and other environmental impacts.

Efforts to reduce the production and use of ozone-depleting substances, such as the Montreal Protocol, have been successful in reducing the thinning of the ozone layer and the formation of polar stratospheric clouds.

Nevertheless, continued monitoring of these clouds is important to understand their effects on the Earth's atmosphere and the environment.

In addition to polar stratospheric clouds, other atmospheric particles and gases can also absorb ultraviolet radiation.

These include aerosols, dust, and water vapor, among others. Understanding the interactions between these atmospheric components and ultraviolet radiation is important for understanding the Earth's energy balance and for protecting human health and the environment.

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Flexible metallic tubing may be utilised as long as it is installed according to the manufacturer's instructions and is not subject to physical harm.

Flexible metal conduit (FMC), also known as flexible metallic tubing (FMT), may be used as long as it is installed in compliance with the manufacturer's instructions and all relevant laws and regulations. Due to its flexibility and ease of installation, FMC is frequently utilised as a wiring enclosure in places where typical rigid conduit may be challenging to install. FMC must not be used in locations where it is susceptible to physical harm, such as those that are impact or vibration-prone or where it could be crushed or abraded. It is not appropriate for all applications. In these situations, it is necessary to employ more robust conduit choices to guarantee the integrity and safety of the electrical wiring system.

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The speed of the cylinder at the bottom of the inclined plane is approximately 1.44 m/s.

To determine the speed of the cylinder at the bottom of the incline, we can use the conservation of energy principle, which states that the total mechanical energy of the system is conserved.

At the top of the incline, the cylinder has only potential energy, which is given by:

PE = mgh

where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the incline.

At the bottom of the incline, the cylinder has both kinetic energy due to its translational motion and rotational energy due to its spinning motion. The total kinetic energy is given by:

KE = (1/2)mv^2 + (1/2)Iw^2

where v is the linear speed of the cylinder, I is its moment of inertia, and w is its angular speed.

Since the cylinder rolls without slipping, we can relate v and w using the equation:

v = rw

where r is the radius of the cylinder.

The moment of inertia of a solid cylinder is given by:

I = (1/2)mr^2

Substituting these expressions for KE and I into the conservation of energy equation, we obtain:

mgh = (1/2)mv^2 + (1/2)(1/2)mr^2w^2

Simplifying and substituting v = rw, we get:

v = √(2gh/3)

Plugging in the given values, we get:

v = √(2 × 9.81 m/s^2 × 0.55 m/3)

≈ 1.44 m/s

Therefore, the speed of the cylinder at the bottom of the inclined plane is approximately 1.44 m/s.

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To calculate the speed of the disk in conceptual example 10-17 at the bottom of the inclined plane, we need to use the conservation of energy principle. The potential energy at the top of the incline is converted into kinetic energy at the bottom.

First, we need to calculate the potential energy at the top of the incline. The potential energy can be calculated using the formula:

PE = mgh

Where m is the mass of the disk, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the incline (0.55 m).

PE = (0.5 kg) x (9.81 m/s^2) x (0.55 m) = 2.7 J

This potential energy is converted into kinetic energy at the bottom of the incline, which can be calculated using the formula:

KE = 0.5mv^2

Where v is the speed of the disk at the bottom.

Since energy is conserved, we can set PE equal to KE:

PE = KE

2.7 J = 0.5(0.5 kg)v^2

Solving for v, we get:

v = sqrt(2.7 J / 0.25 kg)

v = 3.3 m/s

Therefore, the speed of the disk in conceptual example 10-17 at the bottom of the inclined plane is 3.3 m/s.
In the conceptual example 10-17, a disk rolls down an inclined plane. To calculate the speed of the disk at the bottom of the inclined plane with a height of 0.55 meters, we can use the conservation of mechanical energy principle. This principle states that the total mechanical energy (potential energy + kinetic energy) of the disk remains constant if no external forces are acting on it.

At the top of the incline, the disk has only potential energy (PE) due to its height, and no kinetic energy (KE) since it is not moving. As it rolls down, the potential energy is converted into kinetic energy (both translational and rotational).

The potential energy at the top is given by PE = m * g * h, where m is the mass of the disk, g is the acceleration due to gravity (approximately 9.81 m/s^2), and h is the height of the incline (0.55 m).

At the bottom of the incline, the disk has no potential energy, and its kinetic energy is a combination of translational (KE_t) and rotational (KE_r) components. The total kinetic energy is given by KE = (1/2) * m * v^2 + (1/2) * I * ω^2, where v is the linear velocity, I is the moment of inertia of the disk, and ω is the angular velocity.

Since the total mechanical energy is conserved, we can set the potential energy at the top equal to the kinetic energy at the bottom:

m * g * h = (1/2) * m * v^2 + (1/2) * I * ω^2

To solve for the linear velocity (v) at the bottom of the incline, we also need to know the mass of the disk, the moment of inertia, and the angular velocity. These values are not provided in your question. However, once you have this information, you can use the conservation of mechanical energy equation to find the speed of the disk at the bottom of the inclined plane.

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The apple falls approximately 7.07 meters before it hits the ground.

To calculate how far the apple falls, we can use the equation for the distance fallen under the influence of gravity:

Gravity is a fundamental principle of physics which states that all objects in the Universe are attracted to each other through the gravitational force
distance = 0.5 * g * t^{2}
where g is the acceleration due to gravity (approximately 9.81 m/s^{2}) and t is the time it takes for the apple to fall (1.2 s).
Step 1: Square the time (t^{2})
t^{2} = 1.2 * 1.2 = 1.44
Step 2: Multiply 0.5 * g * t^{2}
distance = 0.5 * 9.81 * 1.44
Step 3: Calculate the distance
distance ≈ 7.07 meters

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The consumer product most significant in terms of radiation exposure is cigarettes.

Therefore the answer is d. cigarettes.

While all of the listed products can potentially expose consumers to radiation, cigarettes are the most significant in terms of radiation exposure.

This is because tobacco leaves naturally contain small amounts of radioactive isotopes, such as polonium-210 and lead-210, which can release radiation when they decay. These isotopes can accumulate in tobacco leaves and in the lungs of smokers, and can contribute to increased radiation exposure.

In fact, studies have estimated that smoking a pack of cigarettes per day can result in an effective dose of radiation to the lungs that is equivalent to the exposure from 250 chest x-rays per year. While the radiation exposure from other consumer products (such as wrist watch dials and TV receivers) is generally very low and not considered to be a significant health risk, the exposure from smoking cigarettes is a major contributor to the overall radiation exposure of the general population.

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There are a few reasons why certain areas in cities may have zero wind speed. One possible explanation is the presence of tall buildings or other structures that create a wind shadow.

This occurs when the buildings obstruct the flow of air, causing it to slow down or stop entirely in the space behind the structure. Another factor that can contribute to zero wind speed is topography. If an area is situated in a valley or other low-lying area, it may be shielded from the wind by the surrounding terrain. Additionally, weather conditions can affect wind speed, so it's possible that certain areas experience calm conditions due to a lack of wind at the time.
In cities, some areas may experience zero wind speed due to factors such as tall buildings, urban structures, and topography. These elements can obstruct and disrupt wind flow, creating areas of calm or stagnant air. This phenomenon is known as wind shadow or wind sheltering.

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When capacitors are connected in parallel, they have the same voltage across them, but the charges on each capacitor can be different.

In the case of capacitors with different capacitances, the capacitor with the larger capacitance will have the greatest charge. This is because capacitance is a measure of a capacitor's ability to store charge. Capacitors with larger capacitances can store more charge than capacitors with smaller capacitances. Therefore, the capacitor with the largest capacitance will have the greatest charge. This can be explained by the fact that the larger capacitance provides more surface area for the accumulation of charge, which results in a greater amount of charge being stored.

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The angular velocity of the disk remains constant as it rolls on the horizontal surface. However, the spring will introduce vibrations to the system.

The amplitude of these vibrations will depend on the spring constant and the radius of the disk. Without knowing these values, it is impossible to determine the amplitude of the resulting vibrations of the center of the disk.

To find the amplitude of the resulting vibrations of the center of the disk, we need to consider the system's properties: constant, velocity, and vibrations. Given the disk has a constant clockwise angular velocity of 2 rad/s,

we can calculate the linear velocity (v) of the disk using the formula v = rω, where r is the radius of the disk, and ω is the angular velocity. However, the radius is not provided in the question. Once we have the linear velocity, we can examine the spring and its spring constant (k).

Unfortunately, the spring constant value is also missing in the question. With both the linear velocity and the spring constant, we can then use the equations of motion for a simple harmonic oscillator to determine the amplitude (A) of the resulting vibrations.

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Answer:

Explanation:

Friction is a force that opposes the motion or potential motion of two items that come into contact. The word "relative motion" emphasizes that friction resists the motion of the objects with respect to one other, and it emphasizes that friction specifically operates against the motion or potential motion between two objects in contact.

Any two objects dropped from the same height will land at the same time only if there is no air resistance.

When objects fall through a fluid medium, such as air or water, they experience a force known as air resistance or drag, which opposes their motion. This force depends on the shape, size, and velocity of the object, as well as the properties of the fluid it is falling through. In the absence of air resistance, the only force acting on an object is its weight, which is proportional to its mass. According to the law of universal gravitation, all objects near the surface of the Earth experience a gravitational force towards the center of the Earth, which is also proportional to their mass.

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the total amount of thermal energy required 389232 J.

calculate the amount of thermal energy required to raise the temperature of the water to boiling point:

Q1 = m * c * ΔT

where m is the mass of water, c is the specific heat of water, and ΔT is the temperature change needed.

Here, m = 0.15 kg, c = 4186 J/(kg·K), and ΔT = 100°C - 20°C = 80°C.

Q1 = 0.15 kg * 4186 J/(kg·K) * 80°C

Q1 = 50232 J

Therefore, 50 kJ of thermal energy is required to boil the water after it reaches the boiling point.

Now we can calculate the total amount of thermal energy required to boil the water:

Q2 = m * L

where L is the latent heat of vaporization of water.

Q2 = 0.15 kg * 2260 kJ/kg

Q2 = 339 kJ

Adding Q1 and Q2, we get the total amount of thermal energy required:

Q = Q1 + Q2

Q = 50232 J + 339 kJ

Q = 389232 J

Comparing this to the 500 kJ of thermal energy given off by the stove, we see that there is enough energy to boil all the water.

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The value of the inductance in this circuit  is  E) 19.7 mH.

We can use the following formula to calculate the phase angle of an LRC circuit:

tan(φ) = (Xc - XL) / R

where φ is the phase angle, Xc is the capacitive reactance, XL is the inductive reactance, and R is the resistance.

We know that Xc = 40 Ω, R = 100 Ω, and φ = 40.0°. We can rearrange the formula to solve for XL:

XL = (Xc - R tan(φ)) / tan(φ)

Substituting the values we have, we get:

XL = (40 Ω - 100 Ω tan(40.0°)) / tan(40.0°)

XL ≈ 59.55 Ω

Now we can use the formula for inductive reactance:

XL = 2πfL

where f is the frequency and L is the inductance. Rearranging the formula to solve for L:

L = XL / (2πf)

Substituting the values we have, we get:

L = 59.55 Ω / (2π x 1000 Hz)

L ≈ 9.47 mH

Therefore, the value of the inductance in this circuit is approximately 9.47 mH. None of the answer choices match this value exactly, but the closest one is E) 19.7 mH.

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Answer:

a) Alpha rays because an alpha ray involves a Helium nucleus - with an atomic number of two and a mass number of 4

Beta rays would be next which involve an electron which is thousands of times less massive than an alpha ray

The total intensity engulfing of sound produce by Music have loudness is 91.0 db is approximately 91.2 dB.

To find the total sound intensity, you need to combine the intensity levels of the music (91.0 dB) and the baby yelling (86.0 dB).

1. Convert the decibel levels to intensity values using the formula: I = 10^(dB/10), where I is the intensity and dB is the decibel level.

For the music:

[tex]I_{(music)} = 10^{(91.0/10)} = 10^{9}[/tex]

1 For the baby:[tex]I_{baby} = 10^{(86.0/10)} = 10^{8.62}[/tex]

Add the intensities together to get the total intensity:

[tex]I_{(total)} = I_{(music)} + I_{(baby)}[/tex]3. Convert the total intensity back to decibels using the formula:

[tex]dB = 10 * log10(I) dB_{total }[/tex]

[tex]= 10 * log10(I_{total})[/tex]

Following these

steps:1.[tex]I_{music} = 10^{9.1} = 1,258,925 I_{baby} = 10^{8.6} = 398,1072.[/tex]

[tex]I_{(total)} = 1,258,925 + 398,107 = 1,657,0323.[/tex]

[tex]dB_{total} = 10 * log10(1,657,032) =91.2 dB[/tex]

So, the total sound intensity engulfing you is approximately 91.2 dB.

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The badger's displacement from t=2s to t=3s is -5m.

Displacement is the change in position of an object. From t=0s to t=1s, the badger's velocity increases from 0 m/s to 5 m/s, so its displacement during this time interval is:

From t=1s to t=3s, the badger's velocity decreases from 5 m/s to -5 m/s. Its displacement during this time interval is:

From t=3s to t=6s, the badger's velocity remains constant at -5 m/s. Its displacement during this time interval is:

Therefore, the total displacement of the badger from t=0s to t=6s is

To find the displacement from t=2s to t=3s, we need to subtract the displacement from t=0s to t=2s from the displacement from t=0s to t=3s:

So the badger's displacement from t=2s to t=3s is -5 m.

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The complete question is:

A badger is trying to cross the street. Its velocity v as a function of time t is given in the graph below where rightwards is the positive velocity direction. A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,0) and (1,5). This first line is connected to a second line with endpoints (1,5) and (3,-5). This second line is then connected to a third line of endpoints (3,-5) and (6,-5). A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,0) and (1,5). This first line is connected to a second line with endpoints (1,5) and (3,-5). This second line is then connected to a third line of endpoints (3,-5) and (6,-5). What is the badger's displacement \Delta xΔxdelta, x from t=2\,\text st=2st, equals, 2, start text, s, end text to 3\,\text s3s3, start text, s, end text?

b. 1000-5000 cps.

Answer - Hi! Maximum sensitivity to sound for humans is in the range of 1000-5000 cps (cycles per second The cycle per second is a once-common English name for the unit of frequency now known as the hertz. Cycles per second may be denoted by c.p.s., c/s, or, ambiguously, just "cycles"). So, the correct answer is option b. 1000-5000 cps.Sound frequency is measured in terms of cycles per second (cps), or hertz (Hz), which is the standard unit for cps. The normal human ear can detect sounds that range in frequency from about 20 Hz to about 15,000 Hz.

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