How many days makes 20 years (show all workings).​

The total mass of water vapor in the air in the apartment can be calculated using the formula for absolute humidity. The total mass is approximately 5.04 kg.

To calculate the total mass of water vapor in the air, we need to determine the volume of the apartment and then use the formula for absolute humidity.

Calculate the volume of the apartment: The volume of the apartment can be calculated by multiplying its dimensions: Volume = length x width x height = 18 m x 9 m x 6 m = 972 cubic meters.

Determine the vapor pressure: The relative humidity of 59 percent indicates that the air is holding 59 percent of the maximum amount of water vapor it can hold at the given temperature.

Find the saturation vapor pressure: The saturation vapor pressure is the maximum pressure of water vapor that air can hold at a given temperature. At 25°C, the saturation vapor pressure is approximately 3.17 kPa.

Calculate the actual vapor pressure: The actual vapor pressure can be calculated by multiplying the saturation vapor pressure by the relative humidity: Actual vapor pressure = Relative humidity x Saturation vapor pressure = 0.59 x 3.17 kPa = 1.867 kPa.

Calculate the mass of water vapour: The mass of water vapor can be determined using the formula for absolute humidity: Mass = Absolute humidity x Volume = (Actual vapor pressure / (0.287 kJ/(kg·K) x Temperature)) x Volume. In this case, the temperature is 25°C, which is 298 K.

Mass = (1.867 kPa / (0.287 kJ/(kg·K) x 298 K)) x 972 m^3 = 5.04 kg.

Therefore, the total mass of water vapor in the air in the apartment is approximately 5.04 kg.

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Answer:800 Joules

Explanation: Energy = Power × Time = 100∗8100∗8 = 800 joules

orbital decay causes the ISS to get closer to Earth, resulting in an increase in its velocity but not affecting its orbital velocity. The increase in velocity helps the ISS maintain its orbital stability despite the decrease in altitude.

Orbital decay of the International Space Station (ISS) leads to a decrease in its altitude, causing it to get closer to Earth.

This decrease in altitude affects the velocity and orbital velocity of the ISS.

As the ISS gets closer to Earth, the gravitational pull becomes stronger, resulting in an increase in its velocity.

This increase in velocity is a consequence of the conservation of angular momentum.

According to this principle, as the orbiting object gets closer to the central body (in this case, Earth), its velocity must increase to maintain the balance between gravitational pull and centrifugal force.

However, it's important to note that the increase in velocity due to orbital decay does not affect the orbital velocity of the ISS.

Orbital velocity is the minimum velocity required to maintain a stable orbit at a given altitude.

Even though the ISS experiences orbital decay, its orbital velocity remains constant because the decrease in altitude compensates for the increase in velocity, ensuring that the ISS continues to maintain a stable orbit.

In summary, orbital decay causes the ISS to get closer to Earth, resulting in an increase in its velocity but not affecting its orbital velocity. The increase in velocity helps the ISS maintain its orbital stability despite the decrease in altitude.

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If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The

wavelength of the wave is 1.69m.

The wavelength of a wave can be determined using the equation:

Wavelength = velocity / frequency

To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.

frequency = 1 / time

frequency = 1 / 0.230

frequency ≈ 4.35 Hz

Substitute the values into the wavelength equation:

wavelength = velocity / frequency

wavelength = 7.33 / 4.35

wavelength ≈ 1.69m

Therefore the wavelength of the wave is approximately 1.69 meters.

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(a) The work done by the donkey on the cart is 59,721.9 J.

(b) The work done by the force of gravity on the cart is -48,434.87 J.

(c) The work done on the cart by friction during this time is 11,315.12 J.

(a) The work done by the donkey on the cart is calculated as follows;

Wd = Fd cosθ

where;

Wd = 375 N x 163 m x cos(12.3)

Wd = 59,721.9 J

(b) The work done by the force of gravity on the cart is calculated as;

Wg =  Fg x d x cosθ

Where;

θ = 90⁰ + 4.03⁰ = 94.03⁰

Wg = (431 kg x 9.81 m/s²) x 163 m x cos (94.03)

Wg = -48,434.87 J

(c) The work done on the cart by friction during this time is calculated as;

Wf = Ff x d x cosθ

where;

Ff = μmg cosθ

Ff = 0.0165 x 431 kg x 9.81 x cos (4.03)

Ff = 69.59 N

Wf = 69.59 x 163 x cos (4.03)

Wf = 11,315.12 J

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The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.

The work-energy theorem states that "the work done on an object is the change in its kinetic energy".

Hence;

Kinetic energy = work done

Note that: work-done is expressed as:

Work done = f × d

Where f is force applied and d is distance traveled.

Given that:

Force applied f = 5 newton

Distance d = 2 meters

Work done = ?

Plug these values into the above formula and solve for the workdone.

Work done = f × d

Work done = 5N × 2m

Work done = 10Nm

Work done = 10 Joules

Therefore, the kinetic energy is 10 Joules.

Option B) 10 J is the correct answer.

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The reactive force when a fish swims through water is the force of the water on the fish. This is an example of Newton’s third law of motion which states that for every action, there is an equal and opposite reaction. The active force is the fish pushing against the water, so the reactive force would be the reverse, the equal force of the water pushing back on the fish.

In any given week, I think I am exposed to sounds loud enough to cause hearing damage about 2-3 times. I am not using hearing protection at those times. I do not think I have already experienced hearing loss, but I am not sure.

Hearing loss refers to a partial or total inability to hear sounds in one or both ears. It can vary in severity, from mild to profound, and can affect people of all ages.

I think there are a few reasons why people don't use hearing protection more often. One reason is that they may not be aware of the risks of noise-induced hearing loss. Another reason is that they may not think the risks are high enough to warrant using hearing protection. Finally, some people may find hearing protection uncomfortable or inconvenient to use.

Here are some things that could be done to encourage people to protect their hearing:

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Answer: B) remain same

If a substance is at its triple point and we increase the pressure, then the triple point will remain the same.

A triple point is a condition in which a substance exists in a state of equilibrium between three phases, typically solid, liquid, and gas. The triple point is a unique point on a phase diagram that represents the temperature and pressure at which all three phases of the substance can coexist in equilibrium.

If the pressure is increased at the triple point, the temperature will remain the same because it is the temperature at which all three phases of the substance can coexist. The triple point will remain the same because it is a unique point on a phase diagram and is independent of external conditions such as pressure.

Therefore, the correct answer is b) remain the same.

The ranking of the blocks in order of total mechanical energy, from most positive to most negative is as follows: D > A > C > B. Note that the total mechanical energy of blocks A and C is the same (83.8 J + 7.1 J = 90)

Let us first find the total mechanical energy of each block using the formula: Total mechanical energy = Kinetic energy + Potential energy.

Kinetic energy = 0.5mv², where m is the mass of the block and v is its velocity.

Potential energy = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block above the ground.

We are given the mass, velocity, and height of each block.

Let us substitute these values in the formulas for kinetic energy and potential energy and find the total mechanical energy of each block.

The units of kinetic energy, potential energy, and total mechanical energy are joules (J).

Ranking of blocks A, B, C, and D in order of total mechanical energy, from most positive to most negative is as follows:Block D: Total mechanical energy of block D is the most positive, hence it ranks first.

The velocity of block D is the highest among all the blocks, and its height below the ground level contributes to its potential energy, making it the highest among all the blocks.

Total mechanical energy of block D = Kinetic energy + Potential energyKinetic energy = 0.5mv² = 0.5 × 4 × (10.0)² = 200 J Potential energy = mgh = 4 × 9.80 × (-2.00) = -78.4 J

Total mechanical energy = 200 + (-78.4) = 121.6 JBlock A: Total mechanical energy of block A is the second most positive.

The velocity of block A is the second highest among all the blocks, and its height above the ground level contributes to its potential energy.

Total mechanical energy of block A = Kinetic energy + Potential energy Kinetic energy = 0.5mv² = 0.5 × 2 × (5.00)² = 25.0 JPotential energy = mgh = 2 × 9.80 × (3.00) = 58.8 JTotal mechanical energy = 25.0 + 58.8 = 83.8 J Block C: Total mechanical energy of block C is the third most positive. The velocity of block C is the same as that of block A, but its height above the ground level is greater than that of block A, contributing to its potential energy.

Total mechanical energy of block C = Kinetic energy + Potential energyKinetic energy = 0.5mv² = 0.5 × 1 × (5.00)² = 12.5 JPotential energy = mgh = 1 × 9.80 × (8.00) = 78.4 J

Total mechanical energy = 12.5 + 78.4 = 90.9 JBlock B: Total mechanical energy of block B is the most negative, hence it ranks last.

The velocity of block B is the lowest among all the blocks, and its height above the ground level contributes to its potential energy, but to a lesser extent than that of block C.

Total mechanical energy of block B = Kinetic energy + Potential energyKinetic energy = 0.5mv² = 0.5 × 3 × (4.00)² = 24.0 JPotential energy = mgh = 3 × 9.80 × (1.00) = 29.4 J

Total mechanical energy = 24.0 + 29.4 = 53.4 J

Therefore, the ranking of the blocks in order of total mechanical energy, from most positive to most negative is as follows: D > A > C > B. Note that the total mechanical energy of blocks A and C is the same (83.8 J + 7.1 J = 90.9 J).

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The cannon will completely stop when it collides with the barrier.

To calculate the speed at which the cannon collides with the barrier, we can follow these step-by-step calculations:

Determine the initial momentum of the system.

Since the cannon is initially stationary, the initial momentum is zero.

Apply the conservation of linear momentum.

According to the principle of conservation of linear momentum, the initial momentum of the system (zero) is equal to the final momentum of the system. The final momentum is the momentum of the cannon after firing.

Calculate the final momentum of the system.

Let's assume the mass of the cannon is represented by 'm' and the final velocity of the cannon is represented by 'v'. The final momentum of the system is given by: final momentum = m × v.

Set up the equation.

Since the initial momentum is zero, we have: 0 = m × v.

Solve for the final velocity of the cannon.

Dividing both sides of the equation by 'm', we get: v = 0.

Interpret the result.

The calculation shows that the final velocity of the cannon is zero. This means that the cannon comes to a complete stop when it collides with the barrier.

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The crate moves this time because the applied force of 150 N is greater than the maximum static friction force that opposes the motion of the crate. Static friction is a force that opposes the relative motion between two objects in contact. The maximum static friction force is determined by the normal force and the coefficient of static friction between the two surfaces in contact. The harder the surfaces are pushed together, the more force is needed to move them. When the applied force exceeds the maximum static friction force, the crate will start to move. Once in motion, it is easier to keep it in motion than it was to get it started because the kinetic friction force is less than the static friction force.

There are 630,720,000 seconds in 20 years.

To calculate the number of seconds in 20 years, we need to consider the number of seconds in a minute, minutes in an hour, hours in a day, and days in a year.

1 minute consists of 60 seconds.

1 hour contains 60 minutes (60 minutes × 60 seconds = 3600 seconds).

1 day consists of 24 hours (24 hours × 3600 seconds = 86,400 seconds).

1 year typically consists of 365 days (365 days × 86,400 seconds = 31,536,000 seconds).

To find the number of seconds in 20 years, we multiply the number of seconds in one year by 20:

20 years × 31,536,000 seconds = 630,720,000 seconds.

Therefore, there are 630,720,000 seconds in 20 years.

This calculation assumes a non-leap year with 365 days.

If the 20 years span a leap year, the total number of seconds would be slightly higher, accounting for the extra day in the leap year.

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Carl Rogers, along with Abraham Maslowsignificantly contributed to the humanistic psychology movement through his development of the person-centered approach and his emphasis on the individual's subjective experience and potential for personal growth.

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The total distance is 105 kilometers and the total displacement is 15 kilometers east. Option C

To calculate the total distance, we add the distances traveled in each leg of the journey: 60 kilometers (from A to B) + 45 kilometers (from B back to A) = 105 kilometers.

However, displacement refers to the change in position of an object in a straight line from its starting point to its ending point. In this case, since the boat starts and ends at the same point (A), the total displacement is zero.

Hence The total distance is 105 kilometers and the total displacement is 15 kilometers east.

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The magnitude of the force on the tooth is approximately 0.022 N.

To find the magnitude and direction of the force on the tooth, we can use Hooke's Law, which states that the force exerted on an object is directly proportional to the change in length of a material when it is stretched or compressed.

First, we need to calculate the strain (ε) of the stainless-steel wire.

Strain is defined as the change in length divided by the original length:

ε = ΔL / L₀

Given that the change in length (ΔL) is 0.10 mm [tex](0.10 \times 10^{-3} m)[/tex] and the unstretched length (L₀) is 3.1 cm [tex](3.1 \times 10^{-2} m)[/tex], we can calculate the strain:

[tex]\epsilon=(0.10 \times 10^{-3} m)/(3.1 \times 10^{-2} m)=0.003225[/tex]

Next, we can use Young's modulus (E) to calculate the stress (σ) in the wire.

Stress is defined as the force per unit area:

σ = E * ε

Given that Young's modulus (E) for stainless-steel is 18 × 10¹⁰ N/m², we can calculate the stress:

σ = (18 × 10¹⁰ N/m²) * 0.003225 = 5.805 × 10⁸ N/m²

Now, we can find the force (F) on the tooth by multiplying the stress by the cross-sectional area (A) of the wire:

F = σ * A

The cross-sectional area (A) can be calculated using the formula for the area of a circle:

A = π * (d/2)²

Given that the diameter (d) of the wire is 0.22 mm[tex](0.22 \times 10^{-3} m)[/tex], we can calculate the cross-sectional area:

[tex]A = \pi * (0.22 \times 10^-3 m / 2)^{2} = 3.802 \times 10^{-8} m^2[/tex]

Finally, we can calculate the force:

[tex]F = (5.805 \times 10^{8} N/m^{2}) * (3.802 \times 10^-8 m^{2}) \approx 2.206 \times 10^{-2} N[/tex]

Therefore, the magnitude of the force on the tooth is approximately 0.022 N.

Since the wire is stretched, the force is pulling the tooth in the direction opposite to the stretching.

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The distance covered by a ball in the first second of free fall is approximately 4.9 meters.

When an object falls freely under the influence of gravity, it experiences constant acceleration. In the case of Earth's gravity, the acceleration due to gravity is approximately 9.8 m/s². This means that the velocity of the falling object increases by 9.8 meters per second every second.

To determine the distance covered by the ball in the first second, we can use the equations of motion for uniformly accelerated motion.

The equation that relates distance (d), initial velocity (u), acceleration (a), and time (t) is:

d = ut + (1/2)at²

In this case, the initial velocity is zero (as the ball starts from rest), the acceleration is 9.8 m/s², and we want to find the distance covered in the first second (t = 1 second).

Plugging in the values:

d = 0 * 1 + (1/2) * 9.8 * (1)^2

d = 0 + (1/2) * 9.8

d = 0 + 4.9

d = 4.9 meters

Therefore, the ball covers a distance of approximately 4.9 meters in the first second of free fall.

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The reaction equations for the steps involved in the decay of U-238 to Ra-226 are;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

The radioactive equation for the decay of U-238 to Ra-226 is calculated as follows;

First the uranium atom (U-238) will decay thorium by emitting alpha particle as shown in the equation below;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

The second stage is, the thorium will decay to radium by emitting alpha particles again as shown below;

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

The third, and final stage, the radium will decay to an isotope of radium again, by emitting alpha particle as shown below;

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

Thus, the reaction equations for the steps involved in the decay of U-238 to Ra-226 are;

[tex]^{238}_{92}U\ \rightarrow \ ^{234}_{90}Th \ + \ ^{4}_{2}He[/tex]

[tex]^{234}_{90}Th \ \rightarrow \ ^{230}_{88}Ra \ + \ ^{4}_{2}He[/tex]

[tex]^{230}_{88}Ra \ \rightarrow \ ^{226}_{86}Ra \ + \ ^{4}_{2}He[/tex]

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The correct answer is Option C. and D. The Earth consists of several layers, and the two layers that represent parts of Earth that are mostly iron and nickel are layers B and C.

The Earth's structure has been divided into several layers based on the physical and chemical properties of the materials that make up each layer.

The model is made up of four main layers: the crust, mantle, outer core, and inner core.

The outer core and inner core are the two layers that are primarily made up of iron and nickel.

Layer B, the mantle, is made up of magnesium, silicon, and iron.

Layer C, the outer core, is made up of molten iron and nickel, with some lighter elements such as sulfur and oxygen.

The inner core, layer D, is mostly composed of solid iron and nickel.

The outer core is a liquid layer located between the mantle and the inner core.

This layer is approximately 2,300 km thick and is composed primarily of iron and nickel, with some lighter elements such as sulfur and oxygen.

The outer core is responsible for generating the Earth's magnetic field.

It's also responsible for producing seismic waves that help scientists learn about the interior of the

Earth. The inner core is a solid layer located at the center of the Earth, approximately 6,371 km below the Earth's surface.

It is composed mainly of iron and nickel, with trace amounts of lighter elements such as sulfur and oxygen.

The pressure at the center of the Earth is so high that the iron and nickel in the inner core are solid, despite being at a temperature of over 5,500°C.

Therefore, The correct answer is Option C. and D.

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