018 10.0 points
A steam engine (assume a Carnot engine ) has
an efficiency of 73%.
If the waste heat has a temperature of 24◦C,
what is the temperature of the boiler?
Answer in units of ◦C.

As the ball is pulled inward, the radius of the circle decreases, which means that the tangential speed of the ball must increase in order to maintain uniform centripetal motion. Option (A)

This increase in tangential speed means that the angular velocity of the ball also increases, as angular velocity is directly proportional to tangential speed divided by the radius of the circle.

Since angular momentum is given by the product of rotational inertia and angular velocity, any change in angular velocity will result in a change in angular momentum.

As a result, the proper prediction for the angular momentum and rotational inertia of the ball about the axis of revolution as the ball is drawn inward is: A) The angular momentum of the ball rises. The rotational inertia of the ball about the axis of revolution remains constant.

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Yes, when a person is spinning in the x-y plane, they have a uniform circular motion.

Spinning is an exercise technique used to increase strength and endurance, as well as to burn fat. It involves using a stationary or spinning bike to simulate the experience of cycling outdoors. The intensity of the workout is determined by the instructor, usually by adjusting the resistance level of the bike. During a spinning session, the instructor will typically lead the class through a series of drills and exercises, while providing motivation and encouragement. Spinning is a great way to get a full body workout without having to go outdoors. It is also a low-impact activity that can be done by people of all fitness levels.

This is because the acceleration is constant and directed towards the centre of the circle, meaning that the speed and direction of the object remain the same throughout the motion. This is known as centripetal acceleration and it is what keeps the object moving in a uniform circle.

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The time taken for the car to reach the same final velocity with half the engine power will be twice as long as the time taken with the original engine power.

If a car accelerates from rest to a certain velocity in a certain time, and there is no friction and the engine power is constant, then we can use the following equation to relate the velocity of the car to its acceleration and the time taken:

v = at

where v is the final velocity of the car, a is the acceleration of the car, and t is the time taken for the car to reach the final velocity.If the engine power is halved, then the acceleration of the car will also be halved, assuming that the mass of the car remains constant. Therefore, we can use the same equation to calculate the time taken for the car to reach the same final velocity:

v = (1/2)a(2t)

where a is the halved acceleration, and 2t is the time taken for the car to reach the same final velocity with half the engine power.

Simplifying the equation, we get:

t = (1/2)(2t)

Therefore, the time taken for the car to reach the same final velocity with half the engine power will be twice as long as the time taken with the original engine power.

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The volume of the displaced water is 0.06 m^3. This is obtained by dividing the weight of the object in the air by the difference between the weight in the air and the weight in water, which gives the volume of water displaced.

To find the volume of the displaced water when an individual with a weight of 700 N in the air has an apparent weight of 40 N when submerged you need to follow these steps:

1. Calculate the loss of weight due to buoyancy. The loss of weight is the difference between the actual weight and the apparent weight:
Loss of weight = Actual weight - Apparent weight
Loss of weight = 700 N - 40 N = 660 N

2. Apply Archimedes' principle. The loss of weight is equal to the weight of the water displaced by the submerged individual:
Weight of displaced water = Loss of weight
Weight of displaced water = 660 N

3. Calculate the volume of the displaced water. To do this, you need to use the formula:
The volume of displaced water = Weight of displaced water / Density of water × Gravity
Since the density of water is approximately 1000 kg/m³, and the acceleration due to gravity is about 9.81 m/s²:
Volume of displaced water = 660 N / (1000 kg/m³ × 9.81 m/s²)
The volume of displaced water ≈ 0.0673 m³

So, the volume of the displaced water is approximately 0.0673 cubic meters.

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The amount of water that was displaced is 0.66 m3.

A weight in water is determined by subtracting the object's weight in air from the weight of the water it moves.

Given that the object's weight in air is 700 N, the weight of the water that was displaced must be 700 N – 40 = 660 N.

Given that water has a density of 1000 kg/m3, its mass is 660/9.81, or 67.25 kg, and that its weight is equal to its mass times the acceleration caused by gravity.

67.25/1000 = 0.06625 m3 or roughly 0.66 m3 is the volume of the displaced water, which is equal to the mass of the displaced water divided by its density.

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The current in the circuit is 0.698 A.

We can start by finding the reactance of the inductor using the formula:

XL = 2πfL

where XL is the inductive reactance, f is the frequency, and L is the inductance.

XL = 2π(59.9 Hz)(0.639 H) = 240.3 Ω

Since the lamp is a pure resistive load, its resistance is equal to the voltage across it divided by the current flowing through it:

R = V/I

where R is the resistance, V is the voltage, and I is the current.

R = 24.7 V / I

The total impedance of the circuit is given by:

Z = √([tex]R^2[/tex]+ X[tex]L^2)[/tex]

Since the inductor and lamp are connected in series, the current flowing through both is the same, and we can use Ohm's Law to find the current:

I = V/Z

Substituting in the values we have:

Z = √(R^2 + X[tex]L^2[/tex]) = √[(24.7 Ω/I[tex])^2[/tex] + (240.3 Ω[tex])^2[/tex]] = 242.2 Ω

I = V/Z = (169 V)/(242.2 Ω) = 0.698 A

Therefore, the current in the circuit is 0.698 A.

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To make bulb H dimmer than it was in Circuit 9 (when 1 glow flowed through it), you will need to decrease the flow through H. To achieve this, you can:

1. Increase the resistance in the circuit, specifically in the path that includes bulb H. This can be done by adding more resistors or increasing the resistance of the existing components.
2. Decrease the voltage across the circuit. This will result in a reduced current flow, making bulb H dimmer.

By decreasing the flow through H, you will effectively make the bulb dimmer than it was in Circuit 9.

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The acceleration of the plane is: -55,090 km/(hour)²

What is an acceleration?

The initial velocity of the plane (758 km/sec) is much greater than the maximum possible speed of an airplane. It is possible that the initial velocity was meant to be 758 km/hour instead.

Assuming that the initial velocity was meant to be 758 km/hour and final velocity is 30 km/hour, the acceleration of the plane can be calculated using the formula:

acceleration = (final velocity - initial velocity) / time

Here, final velocity = 30 km/hour, initial velocity = 758 km/hour, and time = 48 seconds converted to hours is 48/3600 = 0.01333 hours.

Therefore, the acceleration of the plane is:

acceleration = (30 - 758) / 0.01333

acceleration = -55,090 km/(hour)²

The negative sign indicates that the plane is decelerating or slowing down. However, this answer seems unlikely as the acceleration is very high and may not be possible for an airplane to achieve. It is possible that the initial velocity was meant to be a lower value.

What is velocity?

Velocity is a physical quantity that describes the rate of change of an object's position with respect to time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

In other words, velocity is the speed of an object in a particular direction. For example, a car moving at 60 km/hour to the east has a velocity of 60 km/hour to the east.

Velocity can be calculated as the change in position divided by the change in time:

velocity = change in position / change in time

The standard unit of velocity is meters per second (m/s) in the SI system, but it can also be expressed in other units such as kilometers per hour (km/hour) or miles per hour (mph).

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Complete question is: A plane lands on the runway and slows from 758 km/sec to 30 km/sec in 48 seconds, The acceleration of the plane is: -55,090 km/(hour)².

If Canada were to build its own rockets and launch them into space, it would need to adhere to international standards and regulations set by the Fédération Aéronautique Internationale or FAI.

The FAI is a governing body that oversees international aviation and spaceflight activities, and its mission is to promote safe and responsible practices in air and space travel. The FAI maintains records of achievements in air and space activities and coordinates with national and international organizations to ensure compliance with regulations and guidelines.

In order for a mission to qualify as an official spaceflight, the FAI would need to be petitioned and the mission would need to adhere to its standards and regulations. These regulations include safety measures, technical specifications, and environmental impact assessments, among others.

By adhering to these regulations, Canada could ensure safe and responsible spaceflight activities and contribute to the development of the international space community and NASA.

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To find the acceleration of the 1-kg wrench after it leaves the 100-kg astronaut's hand when thrown with a force of 1 N, you can use Newton's second law of motion:

Newton's second law of motion, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. Mathematically, the second law can be expressed as:

Force = mass x acceleration.

Step 1: Identify the known values.
Force (F) = 1 N
Mass (m) = 1 kg

Step 2: Use Newton's second law of motion to calculate acceleration (a).
F = m * a
1 N = 1 kg * a

Step 3: Solve for acceleration (a).
a = F / m
a = 1 N / 1 kg
a = 1 m/s²

The acceleration of the wrench after it leaves the astronaut's hand is 1 m/s².

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Newton's second law of motion can be used to determine the acceleration of the 1-kg wrench after it leaves the 100-kg astronaut's hand when thrown with a force of 1 N:

The acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass, according to Newton's second rule of motion, commonly referred to as the law of acceleration. The second law can be defined mathematically as:

Mass times acceleration equals force.

Determine the values that are already known.

Mass (m) = 1 kg and Force (F) = 1 N

Step 2: Determine the acceleration (a) using Newton's second rule of motion.

F = m * a

1 N = 1 kg * a

Calculate acceleration (a) in step three.

a = F/m, a = 1 N/kg, a = 1 m/s2, etc.

After leaving the astronaut's hand, the wrench accelerates at a rate of 1 m/s2.

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This statement is incorrect. The correct form of solid waste recycling in which the energy value of combustible waste materials is recovered is called "waste-to-energy" or "energy recovery."

Composting is a different form of solid waste recycling that involves the biological decomposition of organic materials to create a nutrient-rich soil amendment.

Here is a step-by-step explanation of the correct process:

Waste-to-energy (WTE) facilities receive solid waste, typically municipal solid waste, which is then sorted to remove recyclable materials such as plastics, metals, and paper.

The remaining waste is then burned in a specially designed furnace, called an incinerator, at high temperatures to create steam.

The steam drives turbines, which generate electricity that can be sold to the grid.

In addition to electricity generation, WTE facilities also recover the heat generated by the incineration process to provide heat to nearby buildings or industries.

The remaining ash from the incineration process can be used as a construction material, such as for roadbeds or building foundations.

WTE facilities are highly regulated and must meet strict emissions standards to ensure that the air and water quality in surrounding communities is not negatively impacted.

Overall, WTE is a form of solid waste recycling that can provide both energy generation and waste reduction benefits, while also reducing the need for landfill space.

Composting, on the other hand, is a separate process that involves the natural decomposition of organic waste materials to create a valuable soil amendment for use in agriculture and landscaping.

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The velocity at which the peak voltage of the generator is 475 V is 95.0 revolutions per minute.

The peak voltage (V) of a generator is given by the equation V = NBAω, where N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, and ω is the angular velocity of the coil.

We are given that the coil has 475 turns, a diameter of 8.00 cm, and rotates in a 0.250 T field. We can use these values to find the area of the coil:

radius = diameter/2 = 4.00 cm

[tex]area = π(radius)^2 = 50.27 cm^2[/tex]

Now we can solve for ω:

V = NBAω

[tex]ω = V/(NBA) = (475 V)/(475 turns)(0.250 T)(50.27 cm^2)(1 m^2/10,000 cm^2)(1 rev/2π radians)[/tex]

ω = 95.0 rev/min

Therefore, the velocity at which the peak voltage of the generator is 475 V is 95.0 revolutions per minute.

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1260 RPM. RPM = (Peak Voltage / (2 * pi * coil diameter * magnetic field strength)) * 60 can be used to compute this.

The formula Vp = NABw/2, where N is the number of turns in the coil, A is the coil's area, B is the strength of the magnetic field, and w is the coil's angular velocity, determines the peak voltage produced by a revolving coil. We arrive at w = 2Vp/(NAB) after solving for w. Since the coil diameter rather than the area is provided, we can apply the calculation A = pi*d2/4 to determine the area. After simplifying and substituting the given variables, we get at w = 2 * 475 / (475 * pi * 0.082 * 0.25) = 420 rad/s. Finally, we increase this by 60 / (2 * pi), which gives us 1260 RPM.

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Option (a).

A converging lens is used to make a magnifying glass, which works by bending light to create a magnified image.

The curved surface of the lens helps to focus and magnify the object being viewed.

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the acceleration of the mass is 0.7212 m/s^2.

To find the acceleration of the mass, we need to first determine the net force acting on it. We can do this by using vector addition to add the two forces together.

Using the Pythagorean theorem, we can find the magnitude of the diagonal force:

sqrt[[tex](15N)^{2}[/tex] + [tex](10N)^{2}[/tex]] = sqrt[225 + 100] = sqrt(325) = 18.03 N

The direction of this force can be found using the inverse tangent function:

theta =[tex]tan^{-1}(10.0N/15.0N)[/tex] = 33.69 degrees north of east

We can now use vector addition to find the net force on the mass:

F_net = sqrt[[tex](15N)^{2}[/tex] + [tex](10N)^{2}[/tex]] = 18.03 N, at an angle of 33.69 degrees north of east

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

F_net = ma

Solving for the acceleration, we get:

a = F_net / m = 18.03 N / 25.0 kg = 0.7212 m/s^2

Therefore, the acceleration of the mass is 0.7212 m/s^2.

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According to Heisenberg's uncertainty principle, the product of the uncertainties in position and momentum of a particle along a given axis must be greater than or equal to Planck's constant divided by 4π.

Therefore, the minimum uncertainty in the momentum component px of the electron can be calculated by dividing Planck's constant by twice the uncertainty in position along the x axis. This gives a minimum uncertainty in momentum of approximately 1.05 × 10^-24 kg·m/s. The uncertainty in position of the electron is relatively large, which results in a correspondingly large minimum uncertainty in momentum. This uncertainty in momentum implies that the electron's motion cannot be precisely predicted or determined, which is a fundamental characteristic of quantum mechanics.

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Protons have a positive charge, neutrons have no charge, and electrons have a negative charge.

The three fundamental particles in an atom are protons, neutrons, and electrons. Protons have a positive charge and are located in the nucleus of the atom, along with neutrons, which have no charge. Electrons have a negative charge and orbit the nucleus. The number of protons in an atom determines its atomic number, which in turn determines the element to which it belongs.

The number of electrons in an atom determines its chemical properties, as they are involved in chemical bonding with other atoms. The charges of the particles are important in determining the behavior of atoms in chemical reactions and in the formation of molecules and compounds.

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--The complete question is, Which fundamental particles have positive charges, and which have negative charges?--

The amplitude of the magnetic field of the electromagnetic wave is 6.53 x 10^-7 T.

To find the amplitude of the magnetic field of an electromagnetic wave, we need to use the relationship between the electric and magnetic fields in an electromagnetic wave.

According to this relationship, the amplitude of the magnetic field is equal to the amplitude of the electric field divided by the speed of light (c). Therefore, if the amplitude of the electric field of an electromagnetic wave is 196 V/m, the amplitude of the magnetic field can be calculated as follows:

Amplitude of magnetic field = Amplitude of electric field / Speed of light
Amplitude of magnetic field = 196 V/m / 3 x 10^8 m/s
Amplitude of magnetic field = 6.53 x 10^-7 T

It is important to note that the amplitude of the magnetic field and the electric field of an electromagnetic wave are perpendicular to each other and are responsible for the wave's propagation through space.

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The best comment Francesca could make to Leonardo about his music is A. "I get why you like it, but you know it's not real life, right?"

This comment acknowledges Leonardo's interest in the music and doesn't come across as an attack on his taste or his friends. At the same time, it gently challenges the idea that the lyrics represent a desirable or realistic lifestyle.

It's important for Leonardo and his friends to understand that the behavior celebrated in the songs is often illegal or harmful and doesn't lead to long-term success or happiness.

Option B comes across as insulting and judgmental, which may cause Leonardo to become defensive or dismiss Francesca's concerns. Option C is not a helpful comment because it reinforces the idea that criminal behavior is a viable path to success. Option D is not necessarily true, and even if it were, it doesn't address the larger issue of the negative influence the music may have on Leonardo and his friends.

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Battery-powered devices require the correct orientation of the battery to function properly.

The difference between being able to reverse the orientation of a plug in a wall outlet versus a battery has to do with the type of electrical current being used.

Wall outlets provide AC (alternating current) power, which means that the direction of the electrical flow switches back and forth rapidly. This means that the orientation of the plug doesn't matter, since the current will flow in either direction.

In contrast, batteries provide DC (direct current) power, which means that the electrical flow only goes in one direction. If a battery is inserted backwards, the current will flow in the wrong direction and the device won't work properly or may even be damaged. Therefore, battery-powered devices require the correct orientation of the battery to function properly.

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For battery-powered gadgets to operate properly, the battery must be positioned correctly.

The type of electrical current being utilised determines whether a plug in a wall outlet can be turned around vs whether a battery can.

The electricity that comes out of wall plugs is AC (alternating current), which means that the flow of electricity rapidly changes direction. Because the current can flow in either direction, the plug's orientation is irrelevant.

Batteries, on the other hand, deliver DC (direct current) power, which refers to electrical flow that only occurs in one direction. The device won't function properly or might even be harmed if a battery is inserted backwards since the current will flow in the wrong direction. As a result, batteries must be oriented appropriately for battery-powered gadgets to work properly.

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The angular velocity of the track star is approximately 0.105 radians/second.

The time taken to run the race is 60 seconds, and the distance covered by the track star is one lap, which is the circumference of the circle. Therefore, the average speed of the track star is:

Average speed = distance / time

Average speed = 2πr / 60 seconds

Average speed = (2π x 63.66 meters) / 60 seconds

Average speed = 6.67 meters/second (rounded to two decimal places)

The angular velocity (ω) of the track star can be calculated using the formula: ω = v / r

where v is the linear velocity of the track star, and r is the radius of the circular track. Since the track star is running at a constant speed, the linear velocity is equal to the average speed calculated above. Therefore, the angular velocity of the track star is:

ω = v / r

ω = 6.67 meters/second / 63.66 meters

ω = 0.105 radians/second (rounded to three decimal places)

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Escape velocity is the minimum speed required for an object to escape the gravitational pull of a celestial body. It depends on the mass and radius of the celestial body, as well as the temperature and mass of the gas molecules in the atmosphere.

Based on a plot of escape velocity versus atmospheric temperature, we can see that lighter gases such as hydrogen and helium require lower escape velocities, while heavier gases such as nitrogen and oxygen require higher escape velocities. The plot also shows that the escape velocity decreases as the temperature of the gas increases.

Mars has a relatively low escape velocity compared to Earth, which means that lighter gases such as hydrogen and helium are more likely to escape into space. This suggests that Mars' atmosphere should retain heavier gases such as nitrogen and oxygen, which have higher escape velocities and are less likely to escape into space due to their mass. Therefore, it is likely that Mars' atmosphere is rich in heavier gases, which is consistent with current observations.

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The forces at the left support are 1.61 x 105 N upward and the forces at the right support are 8.88 × 105 N downward by taking into account the forces acting on the bridge and the vehicle.

Finding the forces on a bridge with a truck positioned 15.0 metres from one end and piers supporting it at each end is the task at hand in this challenge. The truck weighs 2.50 x 104 kg, whereas the bridge is 50.0 metres long and 8.20 x 104 kg in weight.

The forces acting on the bridge at its places of support must be determined using Newton's laws of motion. We may determine that the forces at the left support are 1.61 x 105 N upward and the forces at the right support are 8.88 × 105 N downward by taking into account the forces acting on the bridge and the vehicle.

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The complete question:

A bridge of length 50.0 m and mass 8.20×10^4 kg is supported on a smooth pillar at each end as shown. A truck of mass 2.50×10^4 kg is located 15.0 m from one end. What are the forces of the bridge at the points of support?

To find the focal length of a convex lens, we can use the formula:
1/f = 1/di + 1/do

Where f is the focal length, di is the distance of the image from the lens, and do is the distance of the object from the lens.

We are given that the student is 2.50m away from the lens, so do = 2.50m. We are also given that the image is 1.80m from the lens, so di = 1.80m.

Plugging these values into the formula, we get:
1/f = 1/1.80 + 1/2.50

Simplifying this equation, we get:
1/f = 0.5556

Multiplying both sides by f, we get:
f = 1.80 / 0.5556

Solving for f, we get:
f ≈ 3.24 meters

Therefore, the focal length of the convex lens is approximately 3.24 meters.

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A convex lens is 1.80 meters from a student who is 2.50 meters distant, and its focal length is 1.04 meters.

To solve this problem, we can use the lens equation:

1/f = 1/do + 1/di

where f is the focal length of the lens, do is the object distance (distance of the object from the lens), and di is the image distance (distance of the image from the lens).

In this problem, the object distance is do = 2.50 m and the image distance is di = 1.80 m. We can plug these values into the lens equation and solve for the focal length:

1/f = 1/do + 1/di

1/f = 1/2.50 + 1/1.80

1/f = 0.4 + 0.56

1/f = 0.96

f = 1/0.96

f ≈ 1.04 meters

Therefore, the focal length of the convex lens is approximately 1.04 meters.

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The velocity of the astronaut as he moves backward is -0.33 m/s.

Velocity is the rate of change of dispalcement.

To calculate the velocity the astronaut moves backward, we use the formula below

Formula:

Where:

From  the question,

Given:

Substitute these values into equation 1 and solve for v

Hence, the velocity is -0.33 m/s.

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In the heat transfer relation for a heat exchanger, the quantity f is called the "effectiveness." It represents the ratio of the actual heat transfer rate in the heat exchanger to the maximum possible heat transfer rate under the given conditions.

The quantity f in the heat transfer relation for a heat exchanger is called the heat transfer coefficient correction factor. It represents the ratio of the actual heat transfer coefficient to the theoretical heat transfer coefficient. It takes into account the effects of fluid properties, flow conditions, and heat exchanger geometry on the heat transfer process.

Yes, f can be greater than 1. This occurs when the actual heat transfer coefficient is higher than the theoretical heat transfer coefficient, which can happen when there are enhancements to the heat transfer surface or when the fluid flow is optimized.

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Please note that without the specific energy value of the photons in question, it is not possible to give a definitive answer to the number of photons needed.

To determine how many photons need to be absorbed simultaneously by a molecule with a binding energy of 10.0 electron volts (eV) to break it apart, you must first know the energy of each individual photon.

The energy of a photon can be calculated using the formula E = hf, where E is the energy, h is Planck's constant (6.63 x 10^-34 Js), and f is the frequency of the photon.

Once you have calculated the energy of a single photon, you can determine how many photons are required to reach the 10.0 eV binding energy by dividing the binding energy by the energy of one photon.

For example, if the energy of a single photon is 2.0 eV, then you would need 5 photons (10.0 eV / 2.0 eV) to be absorbed simultaneously to break the molecule apart.

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James' gun emits the most energetic light as ultraviolet light has a higher frequency and shorter wavelength than infrared, red, and blue light.

The energy of light is determined by its frequency and wavelength. James' gun produces the most energetic light because ultraviolet light has a higher frequency and shorter wavelength than infrared, red, and blue light. This means that each photon of ultraviolet light carries more energy than a photon of blue, red, or infrared light.

Therefore, James' gun emits light with the highest energy. It is important to note that high-energy light, such as ultraviolet light, can be harmful to live organisms and precautions should be taken to limit exposure.

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The new velocity of the less massive train car has a velocity of 10 m/s after the collision.

Velocity is a measure of the rate and direction of an object's motion. It is a vector quantity, meaning it has both magnitude and direction. Velocity is typically represented by the equation v = s/t, where v is the velocity, s is the displacement (or distance travelled), and t is the time taken. Velocity is often confused with speed, which is the measure of the magnitude of an object's motion. Speed is a scalar quantity and is represented by the equation s = t/v.

The total momentum of the two train cars before the collision is calculated by multiplying the mass of each car by its velocity.

The total momentum of the system before the collision is 2000 kg x 10 m/s + 1000 kg x 3 m/s = 23000 kg m/s.

The total momentum of the system after the collision is 2000 kg x 6 m/s + 1000 kg x v, where v is the velocity of the less massive train car after the collision.

Therefore, we can set up the equation 23000 = 12000 + 1000v and solve for v.

v = 10 m/s.

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The reason we do not see the lines of hydrogen in the spectra of the hottest stars is due to the ionization of hydrogen atoms at high temperatures.

In these stars, the temperatures are so high that the electrons in the hydrogen atoms are stripped away, leaving behind only the protons. This ionized hydrogen does not produce the same spectral lines as neutral hydrogen, which is what we typically observe in cooler stars. Instead, the spectra of hot stars are dominated by lines from ionized metals, such as helium, carbon, and oxygen. So while hydrogen is indeed the most common element in the universe, its presence in the spectra of hot stars is not as prominent due to ionization.

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The order of increasing energy per photon is radar signals (lowest), radiation in a microwave oven, and gamma rays from nuclear radiation (highest).

To rank the following types of radiation in order of increasing energy per photon, we have: a. radar signals, b. radiation in a microwave oven, c. gamma rays from nuclear radiation.

1. Radar signals: These have the lowest energy per photon among the three mentioned types of radiation. Radar signals are a type of radio wave, which are on the lower end of the electromagnetic spectrum.

2. Radiation in a microwave oven: Microwaves have higher energy per photon compared to radar signals but lower than gamma rays. They are located between radio waves and infrared waves on the electromagnetic spectrum.

3. Gamma rays from nuclear radiation: These have the highest energy per photon among the three types of radiation. Gamma rays are on the higher end of the electromagnetic spectrum and are produced by nuclear reactions, cosmic rays, and other high-energy processes.

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The rate of change of the distance between the two airliners at 3:00 pm is 720 mph.

We can use the Pythagorean theorem to determine the distance between the two airliners at any time t, and then differentiate the equation with respect to time to find how fast the distance is changing.

Let d be the distance between the two airliners, and let x and y be the distances traveled by the first and second airliners respectively, from their respective starting points. Then, we have:

d² = x² + y²

Differentiating both sides with respect to time, we get:

2d(dd/dt) = 2x(dx/dt) + 2y(dy/dt)

At 3:00 pm, the first airliner has traveled for 3 hours, covering a distance of 1590 miles (530 miles/hr * 3 hours) due east from the airport. Similarly, the second airliner has traveled for 2 hours, covering a distance of 1160 miles (580 miles/hr * 2 hours) due south from the airport.

Substituting these values, we get:

d² = (1590)² + (1160)²

d = √[(1590)² + (1160)²] = 1934 miles (approx.)

Differentiating with respect to time, we have:

2d(dd/dt) = 2(1590)(530) + 2(1160)(-580)

Simplifying, we get:

dd/dt = [-1590(530) + 1160(580)] / 1934

dd/dt = -48.5 mph (approx.)

Therefore, the distance between the two airliners is decreasing at a rate of approximately 48.5 mph at 3:00 pm.

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