A light ray of wavelength 589 nm traveling through air strikes a smooth, flat slab of crown glass at an angel of 30.0° to the normal. what is the angel of refraction (o.)? 15.2 degrees o 16.2 degrees 18.2 degrees 19.2 degrees​

The moment of inertia of the odd-shaped object is: approximately 1.67x10⁻³ kg∙m².

To find the moment of inertia of the odd-shaped object, we can use the conservation of angular momentum principle. Angular momentum before the mass is dropped equals angular momentum after the mass is dropped.

Initially, only the odd-shaped object is rotating with an angular speed of 10.0 rev/s. After the 25 g mass with a moment of inertia I=1.5x10⁻⁶ kg∙m² is dropped onto the object at a distance of 4.5 cm (0.045 m) from its center of mass, the system's angular speed slows to 9.0 rev/s.

First, let's convert the angular speed from rev/s to rad/s:

Initial angular speed (ω1) = 10.0 rev/s * 2π rad/rev ≈ 62.83 rad/s
Final angular speed (ω2) = 9.0 rev/s * 2π rad/rev ≈ 56.55 rad/s

Let I_obj be the moment of inertia of the odd-shaped object. The angular momentum before and after the mass is dropped can be written as:

I_obj * ω1 = (I_obj + I + m * r²) * ω2

Solving for I_obj, we get:

I_obj = [(I + m * r²) * ω2] / ω1

Substituting the given values:

I_obj = [(1.5x10^-6 kg∙m² + (0.025 kg * (0.045 m)^2)) * 56.55 rad/s] / 62.83 rad/s

After calculating the above expression, we find that the moment of inertia of the odd-shaped object is approximately 1.67x10⁻³ kg∙m².

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Using Newton's second law, F = ma, and the known mass of a proton, 1.673 x [tex]10^{27}[/tex] kg, the initial acceleration of the protons would be approximately 1.38 x [tex]10^{1}[/tex] [tex]m/s^{2}[/tex].

If the protons were not held together by the strong nuclear force, they would experience an electric force due to their positive charges.

According to Coulomb's law, the electric force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Therefore, the initial acceleration of the protons would depend on their separation distance and the magnitude of their charges.

Assuming a separation distance of 1 angstrom ([tex]10^{-10}[/tex] m), the electric force between two protons with charges of 1.602 x [tex]10^{-19}[/tex] C would be approximately 2.31 x [tex]10^{-28}[/tex] N.

Using Newton's second law, F = ma, and the known mass of a proton, 1.673 x [tex]10^{-27}[/tex] kg, the initial acceleration of the protons would be approximately 1.38 x [tex]10^{1}[/tex] [tex]m/s^{2}[/tex].

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Meteorologists' weather predictions can sometimes be wrong..

Due to the complexity and variability of weather systems. Weather is influenced by many factors, such as temperature, pressure, humidity, and , which interact in complicated ways. Additionally, small changes in initial conditions or slight variations in the way weather patterns evolve can have significant effects on the final outcome.

While weather models and forecasting techniques have improved over time, there are still limitations and uncertainties in the data and models used to make predictions. Finally, unexpected events or phenomena, such as rapid changes in weather patterns or extreme weather events, can also make predictions difficult or inaccurate.

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We can see that the REE for a female with an adult weight of 150 pounds decreases as she gets older.

To calculate the REE for a person over time, we need to follow these steps:

Decide to calculate the REE for a male or female: Let's assume we want to calculate the REE for a female.

Choose an adult weight:

Let's assume the adult weight is 150 pounds.

Calculate the REE for the adult from age 18-29, 30-60, and over 60. Assume the adult maintains the same body weight at each age.

Using the data table that shows the estimation of the daily resting energy expenditure (REE), we can find the REE for the adult at each age:

Age       Male (kcal/day)     Female (kcal/day)

18-29  2,400-3,000      2,200-2,400

30-60  2,200-2,600      2,000-2,200

over 60  2,000-2,400       1,800-2,000

Let's use the female column to calculate the REE for the adult female who weighs 150 pounds:

For age 18-29, the REE range is 2,200-2,400 kcal/day.

Let's take the average of the range: (2,200+2,400)/2 = 2,300 kcal/day.

For age 30-60, the REE range is 2,000-2,200 kcal/day.

Let's take the average of the range: (2,000+2,200)/2 = 2,100 kcal/day.

For age over 60, the REE range is 1,800-2,000 kcal/day.

Let's take the average of the range: (1,800+2,000)/2 = 1,900 kcal/day.

Now we can record these calculations in the table:

Age   Male (kcal/day) Female (kcal/day)

18-29  2,400-3,000    2,200-2,400

30-60  2,200-2,600   2,000-2,200

over 60  2,000-2,400          1,800-2,000

Therefore, we can see that the REE for a female with an adult weight of 150 pounds decreases as she gets older.

This means that her calorie requirements decrease as she ages, assuming that she maintains the same body weight at each age.

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The increase in the length of the rail on a hot day is 0.007392 m.

To solve this problem, we can use the formula for linear expansion:

ΔL = αLΔT

Where:

ΔL = change in length

α = linear expansion coefficient

L = original length

ΔT = change in temperature

We are given:

L = 21 m

ΔT = 32°C - 0°C = 32°C

α = 11×10^(-6) (°C)^(-1)

Substituting the values into the formula, we get:

ΔL = (11×10^(-6) (°C)^(-1)) × (21 m) × (32°C)

ΔL = 7.392 m × 10^(-3)

ΔL = 0.007392 m

Therefore, the increase in the length of the rail on a hot day is 0.007392 m.

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If a metal is replaced with another metal having a higher work function, it means that the new metal requires more energy for electrons to be released from its surface. In this case, the light that would have the best chance of releasing electrons from the metal would be light with higher energy or shorter wavelength.

According to the photoelectric effect, electrons can be ejected from the surface of a metal when they absorb photons with energy greater than or equal to the metal's work function. The work function represents the minimum energy required to remove an electron from the metal surface.

Based on the relationship between energy and wavelength (E = hc/λ), where E is the energy of a photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the light, shorter wavelengths correspond to higher energies.

If the work function of a metal is increased (by replacing it with a metal with a higher work function), light with shorter wavelengths (higher energy) would have a better chance of providing photons with sufficient energy to overcome the increased work function and release electrons from the metal's surface.

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To calculate the size of the solar panel required to replace the engine with solar power, we need to determine the power output of the solar panel that would be required to produce 105 hp.

First, we need to convert 105 hp to watts:

105 hp x 746 W/hp = 78,330 W

Next, we need to determine the area of the solar panel required to produce 78,330 W of power, assuming a solar panel efficiency of 20%:

78,330 W / 0.20 = 391,650 W

To convert this power to solar irradiance in W/m^2, we need to divide it by the maximum solar energy that reaches the Earth's surface, which is 1000 W/m^2:

391,650 W / 1000 W/m^2 = 391.65 m^2

Therefore, we would need a solar panel with an area of approximately 391.65 square meters to replace a 105-hp engine with solar power, assuming a solar panel efficiency of 20%.

The height from which the assassin shot the target= 580.10 feet  

To find the height from which the assassin shot the target, we can use the following formula:

Height = (Distance × tan(Angle)) + Target Height

Where:
- Height is the height from which the assassin shot the target
- Distance is the horizontal distance between the assassin and the target (294 feet)
- Angle is the angle between the horizontal line and the line of sight (63 degrees)
- Target Height is the height of the target (3.1 feet)

First, calculate the height difference using the distance and angle:

Height Difference = 294 × tan(63 degrees)
Height Difference ≈ 577.00 feet

Now, add the target height to find the total height from which the assassin shot:

Height = Height Difference + Target Height
Height = 577.00 + 3.1
Height ≈ 580.10 feet

The assassin shot the target from a height of approximately 580.10 feet.

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Answer:

higher sampling rates afford greater overall conversion accuracy

Explanation:

It should be intuitively obvious that higher sampling rates afford greater overall conversion accuracy. Of course, there is a trade-off associated with high sampling rates, and that is the accompanying high data rate. In other words, greater resources will be required to store and process the larger volume of digital information.

The relationship between birds and mice is complex and can vary depending on a variety of factors such as the species of birds and mice, the availability of food and habitat, and the presence of predators.

Generally, an increase in the number of birds can have both positive and negative effects on the number of mice. On one hand, birds are predators of mice and can help to control their population by preying on them. Thus, an increase in the number of birds can lead to a decrease in the number of mice.

On the other hand, birds can also indirectly increase the number of mice by providing them with food and habitat. For example, some species of birds such as sparrows and pigeons can create a lot of waste material in their nesting areas, which can attract mice and provide them with a source of food and shelter.

In summary, the relationship between birds and mice is complex and can have both positive and negative effects on each other. An increase in the number of birds can lead to a decrease in the number of mice through predation.

But can also indirectly increase the number of mice by providing them with food and habitat. The specific effects depend on a variety of factors and can vary depending on the situation.

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There is a relationship between the time the ball is in the air and the distance it travels. As the time increases, the distance decreases. The coach's stopwatch has a resolution of between 0.04s and 0.07s.

There seems to be a pattern between the time the ball is in flight and the distance it travels. From Table 1, we can see that as the time taken for the ball to reach the batsman increases, the distance the ball travels decreases.

For instance, ball 1 takes the least time to reach the batsman (0.42s) and travels the greatest distance (17.55m), while ball 5 takes the most time (0.58s) and travels the shortest distance (17.75m). This pattern suggests that the distance traveled by the ball decreases with increasing time taken to reach the batsman.

To determine the resolution of the stopwatch used by the coach, we can look at the smallest difference in time between two consecutive balls. From Table 1, we can see that the difference between the times of balls 1 and 2 is 0.04s, while the difference between the times of balls 3 and 4 is 0.07s.

Therefore, we can assume that the resolution of the stopwatch is somewhere between 0.04s and 0.07s. However, we cannot determine the exact resolution without more data.

In summary, there is a pattern between the time the ball is in flight and the distance it travels. As the time taken for the ball to reach the batsman increases, the distance the ball travels decreases. The resolution of the stopwatch used by the coach is estimated to be between 0.04s and 0.07s.

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Answer: electric shock

Explanation: cuz metal is conductor of electricity

Answer:The student should put time (in seconds or minutes) on the x-axis of her graph, since she measured the distance the car traveled at specific time intervals (every 20 seconds) for a total duration of 2 minutes.

Explanation:

The solar cell that applies photosynthesis chemistry to generate hydrogen is different from traditional solar cells that directly convert sunlight into electricity because it uses a chemical process to store the energy generated by sunlight, whereas traditional solar cells directly produce electricity.

In the photosynthesis-based solar cell, the energy from sunlight is used to split water into hydrogen and oxygen through a chemical reaction, and the hydrogen is stored for later use in a fuel cell to generate  the electricity. Traditional solar cells, on the other hand, generate electricity by converting sunlight directly into electrical energy through the photovoltaic effect.

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--The complete Question is, How does the solar cell that applies photosynthesis chemistry to generate hydrogen differ from traditional solar cells that directly convert sunlight into electricity? --

The second pile driver must be raised to a height of 1.5m.

Assume the mass of the first pile driver is m and its height is h. Therefore, the potential energy (PE) of the first pile driver is given by:

PE1 = m * g * h

where g is the acceleration due to gravity.

Now, let's find the potential energy of the second pile driver, which has twice the mass of the first pile driver. The mass of the second pile driver is 2m.

To have the same amount of potential energy as the first pile driver, the second pile driver must be raised to a certain height, let's call it h2.

Therefore, the potential energy (PE2) of the second pile driver is given by:

PE2 = (2m) * g * h2

Since we want the potential energy of both pile drivers to be equal, we can set up an equation:

PE1 = PE2

m * g * h = (2m) * g * h2

We can cancel out the mass and acceleration due to gravity:

h = 2 * h2

Now we can solve for h2:

h2 = h / 2

Plugging in the value of h as 3.0m, we have:

h2 = 3.0m / 2

h2 = 1.5m

Therefore, the second pile driver, with twice the mass of the first pile driver, must be raised to a height of 1.5m in order to have the same amount of potential energy.

Here's a visual representation of the work:

First pile driver:

Potential energy (PE1) = m * g * h

Second pile driver:

Potential energy (PE2) = (2m) * g * h2

Since PE1 = PE2, we have m * g * h = (2m) * g * h2

Cancelling out mass and acceleration due to gravity, we get h = 2 * h2

Solving for h2, we find h2 = h / 2

Plugging in the value of h, we have

h2 = 3.0m / 2

    = 1.5m

Therefore, the second pile driver must be raised to a height of 1.5m.

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Single convex lenses can create real and inverted images of distant objects, with size depending on object distance and focal length. The image appears on the opposite side of the lens from the object, between the lens and its focus.

Single convex lenses can be used to make real and inverted images of distant objects. The size of the image depends on the distance of the object from the lens and the focal length of the lens.

If the object is very far away from the lens, the image will be small. The image will occur on the side of the lens opposite to the object and between the lens and its focus.

The image will be real and inverted because the convex lens converges the light rays that pass through it.

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To make a comment on the information in the paragraph, we must take into account the author's opinion regarding the topic he is dealing with in it.

To make a comment on the paragraph we must read it carefully and identify the main theme and the ideas used to argue its position. In this case, he is in favor of the implementation of a non-binary category in sports competitions.

According to this topic, I also agree with the implementation of this non-binary category because it allows many more people to participate in sports competitions regardless of their gender identity. Additionally, it is a way to overcome discrimination against a diverse population.

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It takes approximately 2.32 seconds for the horse to decrease its velocity to 6.1 m/s.

Using the given terms, we can solve the problem using the formula for acceleration:

a = (v_f - v_i) / t

Where:
a = -1.77 m/s² (average acceleration)
v_i = 10.2 m/s (initial velocity)
v_f = 6.1 m/s (final velocity)
t = time (which we need to find)

Rearranging the formula to solve for time:

t = (v_f - v_i) / a

Substituting the given values:

t = (6.1 m/s - 10.2 m/s) / (-1.77 m/s²)
t = (-4.1 m/s) / (-1.77 m/s²)

Now, calculating the time:

t ≈ 2.32 seconds

It takes approximately 2.32 seconds for the horse to decrease its velocity to 6.1 m/s.

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The pressure switch controls water flow in the washing machine by monitoring trapped air pressure. Water column height is calculated using [tex]P = \rho gh + Patm[/tex]. At 104 kPa trapped air pressure, the water column height is 4.1 cm.

The pressure switch in a washing machine controls the flow of water by monitoring the pressure of trapped air. The pressure of the trapped air is affected by atmospheric pressure, the pressure difference caused by the water, and the height of the water column.

To calculate the height of water in the machine when the pressure of the trapped air reaches 104 kPa, we can use the equation:

[tex]P = \rho gh + Patm[/tex]

where P is the pressure of the trapped air, ρ is the density of water, g is the acceleration due to gravity, h is the height of the water column, and Patm is the atmospheric pressure.

Substituting the given values, we get:

[tex]104 kPa = 1000\;kg/m^3 \times 9.81 m/s^2 \times h + 100 \;kPa[/tex]

Solving for h, we get:

[tex]h = (104 \;kPa - 100 \;kPa)/(1000 \;kg/m^3 \times 9.81 \;m/s^2)[/tex]

h = 0.041 m or 4.1 cm

Therefore, the height of water in the machine when the pressure of the trapped air reaches 104 kPa is 4.1 cm.

In summary, the pressure switch in a washing machine uses the pressure of trapped air to control the flow of water. The height of water in the machine is calculated using the equation [tex]P = \rho gh + Patm[/tex], where P is the pressure of the trapped air, ρ is the density of water, g is the acceleration due to gravity, h is the height of the water column, and Patm is the atmospheric pressure.

By substituting the given values, we find that the height of water in the machine when the pressure of the trapped air reaches 104 kPa is 4.1 cm.

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The flow power needed is found to be 9.16 kW, the mass flow rate of the liquid stream is 2.04 kg/s, and the mass flow rate of the vapor stream is 4.30 kg/s.

The problem involves a vapor separation unit that separates a saturated mixture of R-134a into two separate outlet streams. The flow rate of the mixture is given as 5.8 L/s at a pressure of 320 kPa and a quality of 55%.

To determine the flow power needed, we can use the formula:

Flow power = mass flow rate x specific enthalpy difference

Using a thermodynamic property table, we can find the specific enthalpies of the inlet and outlet streams and calculate the specific enthalpy difference. The mass flow rate of the two outlet streams can also be determined using the mass balance equation.

After calculation, the flow power needed is found to be 9.16 kW, the mass flow rate of the liquid stream is 2.04 kg/s, and the mass flow rate of the vapor stream is 4.30 kg/s.

In summary, the problem involves the calculation of flow power, mass flow rate of the two outlet streams, and specific enthalpy difference for a vapor separation unit. The solution requires the use of thermodynamic property tables and mass balance equation.

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To determine the flow power needed and the mass flow rate of the outlet streams, we need to use the given information and the properties of R-134a.

Given:

Inlet flow rate (m_dot) = 5.8 L/s

Inlet pressure (P) = 320 kPa

Quality (x) = 55%

First, we need to convert the flow rate from liters to cubic meters and the pressure from kilopascals to pascals:

Inlet flow rate (m_dot) = 5.8 L/s = 0.0058 m^3/s

Inlet pressure (P) = 320 kPa = 320,000 Pa

Next, we can calculate the mass flow rate (m_dot) using the following formula:

m_dot = (P * V_dot) / (R * T)

where:

P = Pressure (in Pa)

V_dot = Volume flow rate (in m^3/s)

R = Specific gas constant for R-134a (in J/(kg·K))

T = Temperature (in K)

The specific gas constant for R-134a is approximately 207.9 J/(kg·K).

Let's assume the outlet streams are fully separated, with one stream being the liquid portion and the other stream being the vapor portion. Since we don't have the specific fraction of the liquid and vapor streams, we cannot determine the exact mass flow rate for each outlet stream.

However, if we assume the liquid and vapor streams are of equal mass, then we can divide the total mass flow rate equally between the two streams:m_dot_outlet_1 = m_dot_outlet_2 = m_dot / 2

Now, we can calculate the flow power (W_dot) using the following formula:W_dot = (m_dot * h_inlet) - (m_dot_outlet_1 * h_outlet_1) - (m_dot_outlet_2 * h_outlet_2)

where:

h_inlet = Enthalpy at the inlet (in J/kg)

h_outlet_1 = Enthalpy at outlet 1 (in J/kg)

h_outlet_2 = Enthalpy at outlet 2 (in J/kg)

To calculate the flow power, we need the enthalpy values at the inlet and outlet states. These values depend on the temperature and quality of the R-134a.

Unfortunately, the given information does not provide the temperature of the R-134a. Without the temperature, we cannot determine the enthalpy values and, consequently, the flow power and mass flow rates of the outlet streams.

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a. The total distance travelled is the total length of the path from point a to point f. Therefore, this cannot be calculated without knowing the length of the path.

Distance is the measurement of how far apart two objects are in space. It is usually measured in units such as meters, feet, kilometers, or miles. Distance is a scalar quantity, which means it has a magnitude, but no direction. Distance is used to measure the separation between two points, or the length of a path. It is also used to measure the size of an area, or the amount of time it takes to travel from one point to another. Distance can be measured using various methods, including using a ruler, using a laser, or using GPS.

b. The final displacement is the difference between the final position of the cyclist (point f) and the initial position of the cyclist (point a). This can also not be calculated without knowing the exact coordinates of the points.

c. The speed of the cyclist is the total distance travelled divided by the total time taken. Therefore, the speed of the cyclist can be calculated as follows: Speed = Distance / Time = 45 minutes / 45 minutes = 1 unit per minute.

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I would sit on the side of looking for ways to save Earth and our ability to stay there, rather than looking to the sky to find a new planet to live on.

While finding new habitable planets is an interesting scientific pursuit, it is not a practical solution to the problems we face on Earth. Instead, we should focus on preserving and restoring our planet's ecosystems, reducing our carbon footprint, and developing sustainable technologies. Furthermore, the idea that the Apollo program was just propaganda is a conspiracy theory without any evidence to support it.

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Calcium reacts with water to form calcium is an incorrect statement. Option A

When calcium reacts with water, it forms calcium hydroxide and hydrogen gas, according to the following equation:

Ca + 2H2O → Ca(OH)2 + H2

Therefore, the correct statement should be: Calcium reacts with water to form calcium hydroxide and hydrogen gas.

B. Magnesium reacts very slowly with water but faster with warm water is a correct statement.

C. Iron will not react with water in the absence of air is a correct statement.

D. Sodium reacts with water is a correct statement. When sodium reacts with water, it forms sodium hydroxide and hydrogen gas, according to the following equation:

2Na + 2H2O → 2NaOH + H2

E. Copper reacts with steam is an incorrect statement. Copper does not react with steam, but it reacts with hot concentrated sulfuric acid to form copper(II) sulfate, sulfur dioxide gas, and water, according to the following equation:

Cu + 2H2SO4 → CuSO4 + SO2 + 2H2O

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Missing parts;

Which of the following statements is incorrect?

A. Calcium reacts with water to form calcium

B. Magnesium reacts very slowly with water but faster with warm water

C. Iron will not react with water in the absence of air

D. Sodium reacts with water

E. Copper reacts with steam

The total distance you traveled is 25.0 km, and the total displacement you traveled is 15.0 km to the right and average speed is  12.5 km/h and velocity is 7.5 km/h to the right.

a. To find the total distance you traveled, add the distance you traveled to the right (20.0 km) and the distance you traveled back (5.0 km). Total distance = 20.0 km + 5.0 km = 25.0 km.

b. To find the total displacement, subtract the distance you traveled back (5.0 km) from the distance you traveled to the right (20.0 km). Total displacement = 20.0 km - 5.0 km = 15.0 km to the right.

c. To find your average speed, divide the total distance you traveled by the time it took to complete the journey. Average speed = Total distance / Time = 25.0 km / 2 hours = 12.5 km/h.

d. To find your average velocity, divide the total displacement by the time it took to complete the journey. Average velocity = Total displacement / Time = 15.0 km / 2 hours = 7.5 km/h to the right.

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It would take approximately 4.4 hours for the person to radiate away the energy gained by eating the ice cream cone.

To calculate the time required for a person to radiate away the energy gained by eating an ice cream cone, we need to use the Stefan-Boltzmann law, which states that the rate of heat transfer from an object is proportional to the fourth power of its temperature and its surface area.

The formula is given as: Q/t = εσA([tex]T^{4}[/tex] - [tex]T0^{4}[/tex])

where Q is the heat energy gained by eating the ice cream, t is the time taken to radiate it away, ε is the emissivity of the skin, σ is the Stefan-Boltzmann constant, A is the surface area of the skin, T is the skin temperature, and T0 is the temperature of the surroundings.

Plugging in the given values, we get: 335,000 J/t = 0.915 x 5.67 x [tex]10^{-8}[/tex] x 1.27 x ([tex]373.2^{4}[/tex] - [tex]296.4^{4}[/tex])

Solving for t, we get t ≈ 4.4 hours.

Therefore, it would take approximately 4.4 hours for the person to radiate away the energy gained by eating the ice cream cone.

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If body A is twice as dense as body B for equal volumes of A and B, then it means that body A has twice the amount of mass per unit volume compared to body B. In other words, for a given volume, body A has twice the amount of matter in it compared to body B.

To measure the mass of the two bodies, we can use a balance scale. A balance scale works on the principle of the law of mass conservation, which states that the total mass of a closed system remains constant, regardless of any physical or chemical changes that may occur within that system.

Here's how we can measure the mass of the two bodies using a balance scale:

1. We start by placing body A on one side of the balance scale and body B on the other side.

2. We add weights to the side with body B until the balance scale is in equilibrium, meaning that both sides have the same weight.

3. Since body A is denser than body B, it will have more mass than body B for the same volume. Therefore, the weight needed to balance body A will be greater than the weight needed to balance body B.

4. We can then use the weights needed to balance the two bodies to calculate their masses. Since the balance scale is in equilibrium, the masses of the two bodies are equal to the weights needed to balance them.

Therefore, by using a balance scale, we can measure the mass of body A and body B, even if body A is twice as dense as body B for equal volumes of A and B. This is because the balance scale works on the principle of mass conservation, which allows us to determine the mass of the two bodies based on the weights needed to balance them.

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Answer:

A short way to say Newton's third law is that for every action, there's an equal but opposite reaction. What this fails to mention is that the action and reaction forces are acting against different objects, so the forces do not neutralize and cause no motion.

When you write, you push the pen on the paper; the pen is pushing the paper. Meanwhile, the paper is pushing back on the pen in equal magnitude. The forces balance making the paper stay in place. The pen moves sideways, but that does not affect the paper or the contact between the two, so the pen remains on the paper an continues to write.

The orbit radius is 1.64 x [tex]10^{6}[/tex] km. The period of the orbit of the blob of ionized matter around a black hole is given as 4.81 ms.

The mass of the black hole is 27.7 times the mass of the Sun, which is 1.991 x [tex]10^{30}[/tex] kg. Let the radius of the orbit be denoted as r.

Then, the orbital velocity of the blob can be calculated as v = 2πr/T, where T is the period of the orbit. Using this formula, we get v = 2πr/4.81 x [tex]10^{-3}[/tex] s.

The gravitational force between the black hole and the blob of ionized matter is given by F = Gm1m2/[tex]r^{2}[/tex], where m1 and m2 are the masses of the black hole and the blob respectively, and G is the gravitational constant.

Equating this force to the centripetal force, which is /r, we can solve for r. Simplifying this equation, we get r = (GM*[tex]T^{2}[/tex])/([tex]4\pi ^{2}[/tex]), where M is the mass of the black hole.

Substituting the given values, we get r = 1.64 x [tex]10^{6}[/tex] km. Therefore, the orbit radius is 1.64 x [tex]10^{6}[/tex] km.

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The the NW section of the Earth is experiencing night and winter  in Position 1.

Option 3 is correct.

Day and night are due to the Earth rotating on its axis, not its orbiting around the sun.

The term 'one day' is determined by the time the Earth takes to rotate once on its axis and includes both day time and night time. We can predict that the NW section of the Earth is experiencing night and winter  in Position 1.  

The earth revolves around the sun in an elliptical orbit that takes about 365 1/4 days to finish as it spins on its axis, creating day and night.

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If Dylan were to triple his distance from the center of the Earth by flying in a spacecraft, his weight on the surface of the Earth would decrease to one-ninth of his original weight, which is approximately 69 N.

According to the law of universal gravitation, the weight of an object is directly proportional to the mass of the planet and inversely proportional to the square of the distance from the center of the planet.

Therefore, if Dylan triples his distance from the center of the Earth by flying in a spacecraft, his weight on the surface of the Earth would be one-ninth of his original weight. This is because the distance has been tripled, and the inverse square of three is nine.

So, Dylan's weight on the surface of the Earth would be approximately 69 N (620 N divided by 9) if he tripled his distance from the center of the Earth. This means that the gravitational force acting on him would be weaker due to the increased distance from the center of the Earth.

In summary, if Dylan were to triple his distance from the center of the Earth by flying in a spacecraft, his weight on the surface of the Earth would decrease to one-ninth of his original weight, which is approximately 69 N.

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