Magnification of lens is 1. What does it mean?

The magnetic field in the region is into the paper and has a magnitude of 60 mT and the tension in either wire is 0.096 N.

To find the tension in either wire, we can apply the equation for the force experienced by a current-carrying wire in a magnetic field.

The force experienced by a current-carrying wire in a magnetic field is given by the equation F = B * I * L * sin(θ), where B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field.

In this case, the wire is suspended horizontally by two vertical wires, and the magnetic field is into the paper. Since the wire is horizontal, the angle between the wire and the magnetic field is 90 degrees, so sin(θ) = 1.

The force experienced by the wire due to the magnetic field is F = B * I * L.

Given:

Current (I) = 8.0 A

Magnetic field (B) = 60 mT = 60 * 10^(-3) T

Length of the wire (L) = 40 cm = 40 * 10^(-2) m

Substituting the given values into the equation, we get:

F = (60 * 10^(-3) T) * (8.0 A) * (40 * 10^(-2) m)

Simplifying the expression, we find:

F = 0.192 N

Since the wire is suspended by two vertical wires, the tension in each wire will be half of the total force. Therefore, the tension in either wire is 0.192 N / 2 = 0.096 N.

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The slope of a line perpendicular to y = 1/8x + 2 is -8.

The equation of a line in point-slope form is y - y1 = m (x - x1), where m is the slope and (x1, y1) is a point on the line.

The point-slope form of a line is given by y - y1 = m (x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

In this equation, y1 and x1 are the coordinates of a point on the line, and m is the slope of the line.

So, given a point on the line, and the slope, you can use this form to write the equation of the line.

So, the equation of the line through point (1, -5) and perpendicular to y = 1/8x + 2 is y + 5 = -8(x - 1) => y = -8x + 13.

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We're missing one essential piece of information that we need in order to answer this question.  You have not specified what planet the object is falling on.  The answer depends on the gravitational acceleration on that planet, and they're all different.

Without that information, we'll just go ahead and assume that the object is falling to the surface of the Earth.  Wherever on Earth this tense drama is unfolding, the acceleration of gravity is going to be around 9.8 m/s² everywhere.

So THAT's the object's acceleration if there is no air resistance.  The object's MASS makes no difference.  It doesn't matter whether the object is a sparrow feather or a school bus. Heavier objects DO NOT fall faster than light objects.

If there is no air resistance, then ALL objects fall with the same acceleration.    It's called the "acceleration of gravity" on that planet or moon, and you can easily look it up.  It's 9.8 m/s² on Earth, 1.62 m/s² on the Moon, 3.71 m/s² on Mars, 8.87 m/s² on Venus, and 24.8 m/s² on Jupiter.

Answer:

A) v = 1.47 10⁶ m / s, v = 0.5426 10⁴ m / s , B)  T = 4.7 10⁴ K, C) n₂ = 42

Explanation:

A)  For this part, let's calculate the speed of an electron that has an energy of 6.11 eV.

Let's reduce the units to the SI system

        E₀ = 6.11eV (1.6 10⁻¹⁹ J / 1eV) = 9.776 10⁻¹⁹ J

The kinetic energy of the electron is

        K = ½ m v²

         E₀ = K

         v = √ 2E₀ / m

         v = √ (2 9.776 10⁻¹⁹ / 9.1 10⁻³¹)

         v = √ (2.14857 10¹²)

         v = 1.47 10⁶ m / s

now the speed of a calcium ion is asked, let's find sum

        m = 40 1.66 10⁻²⁷ = 66.4 10⁻²⁷ kg

        v = √ (2E₀ / M)

         v = √ (2 9.776 10⁻¹⁹ / 66.4 10⁻²⁷)

        v = √ (0.2994457 10⁸)

        v = 0.5426 10⁴ m / s

B) the terminal energy of an ideal gas is

             E = 3/2 kT

              T = ⅔ E / k

              T = ⅔ (9,776 10-19 / 1,381 10-23)

              T = 4.7 10⁴ K

C) To calculate the energy of these lines we use the Planck expression

              E = h f

where wavelength and frequency are related

              c =λ f

              f = c /λ

let's substitute

              E = h c /λ

let's look for the energies

λ = 396.8 nm

  E₁ = 6.63 10⁻³⁴ 3 10⁸ / 396.8 10⁻⁹

           E₁ = 5.0126 10⁻¹⁹ J

λ = 393.3 nm

           E₂ = 6.63 10⁻³⁴ 3 10⁸ / 3.93.3 10⁻⁹

           E₂ = 5.0572 10⁻¹⁹ J

The difference in energy between these two states is

          ΔE = E₂ -E₁

          ΔE = (5.0572 - 5.0126) 10⁻¹⁹ J

          ΔE = 0.0446 10⁻¹⁹ J

let's reduce eV

         ΔE = 0.0446 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

         ΔE = 2.787 10⁻² eV

Now let's use Bohr's atomic model for atoms with one electron,

               E = -13.606 Z² / n²

where 13,606 eV is the energy of the base state of the Hydrogen atom, Z is the atomic number of Calcium

               n = √ (13.606 Z² / E)

λ = 396.8 nm

E₁ = 5.0126 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹J) = 3.132875 eV

               n₁ = √ (13.606 20² / 3.132875)

               n₁ = 41.7

since n must be an integer we take

               n₁ = 42

λ = 393.3 nm

E₂ = 5.0572 10⁻¹⁹ J (1eV / 1.6 10⁻¹⁹ J) = 3.16075 eV

              n₂ = √ (13.606 20² / 3.16075)

              n₂ = 41.5

Again we take n as an integer

               n₂ = 42

We can see that the two lines have the same principal quantum number, so for the difference of these energies there must be other quantum numbers, which are not in the Bohr model, because of the small difference they are possibly due to small numbers of the moment angular orbital or spin

Answer:

Explanation: y’all taking the same test as me hahahahah I got the answers but I can’t attach the picture here so hit me up on snap daniela_0789

The total energy at each point in the path of the skier is constant as the

skier travels down the slope.

Reasons:

1) Given that the total mechanical energy, M.E. is constant, we have;

M.E. = Kinetic Energy, K.E. + Potential Energy, P.E. = Constant

M.E. = K.E. + P.E.

At the start, we have;

P.E. = 25,000 J

K.E. = 0 J

Therefore;

M.E. = 25,000 J + 0 J = 25,000 J

At point 1A, we have, K.E = 10,000 J

P.E. = M.E. - K.E.

Therefore;

P.E. = 25,000 - 10,000 = 15,000

The potential energy at point 1A, P.E. = 15,000 J

At point 1B, we have; PE = 6000 J

K.E. = M.E. - P.E.

Therefore;

K.E. = 25,000 J - 6,000 J = 19,000 J

At 1B, K.E. = 19,000 J

At point 1C, we have; K.E. = 25,000 J

Therefore;

P.E. = 25,000 J - 25,000 J = 0 J

At 1C P.E. = 0 J

2) The Law of Conservation of Energy states that the energy in a closed

system is constant.

The energy transformation follows the Law of Conservation of energy

given that the total mechanical energy is constant at all points along the

path.

3) The energy of a system is not conserved when a external force is

applied.

If the skier experiences friction, the force of friction does work to reduce

the speed of the skier, thereby reducing the kinetic energy at a point

downslope, where the potential energy has already been reduced,

resulting in an reduction in the mechanical energy of the system.

Therefore, if the skier experiences friction, the total energy of the system is

not conserved, as energy will be consumed in the work done by friction

which is converted to heat and sound energies.

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Energy flows from the Sun to producers, then to primary consumers, secondary consumers, and potentially to tertiary consumers, forming a pyramid-shaped structure that represents the transfer of energy through different trophic levels in an ecosystem.

Energy flows in a specific order through various components of an ecosystem, starting with the Sun and progressing through producers and consumers. This flow of energy is known as the energy pyramid or trophic levels.

At the base of the energy pyramid is the Sun, which is the ultimate source of energy for most ecosystems on Earth. Sunlight provides the energy needed for photosynthesis, a process carried out by plants, algae, and some bacteria, collectively known as producers. These organisms convert solar energy into chemical energy through photosynthesis, using carbon dioxide and water to produce glucose and oxygen. This process captures and stores energy in the form of organic compounds.

The next level in the energy pyramid consists of primary consumers, also known as herbivores. These are animals that feed directly on producers, such as grazing animals or insects that consume plants. Herbivores obtain energy by consuming plant material and breaking down the organic compounds present in the plants into simpler forms, such as sugars and amino acids, through digestion.

Above the primary consumers are the secondary consumers, which are carnivores or omnivores that feed on herbivores. They obtain energy by consuming primary consumers and breaking down the organic compounds in their prey through digestion. This energy transfer continues up the trophic levels, with each level consuming the one below it.

At the top of the energy pyramid are tertiary consumers, which are typically apex predators. They are carnivores that consume other carnivores. Tertiary consumers obtain energy by consuming secondary consumers and breaking down the organic compounds in their prey.

It's important to note that energy is not efficiently transferred between trophic levels. Only a fraction of the energy consumed at each level is converted into biomass and passed on to the next level. This inefficiency is due to processes such as respiration, heat loss, and incomplete digestion.

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To convert one system of unit to another  of derived quantities is not a use of dimensional analysis.

Checking for consistency in the dimensions on both sides of an equation entails looking at the dimensions of the physical quantities involved in a problem, such as length, mass, time, electric charge, and temperature.

The core tenet of dimensional analysis is that physical quantities, such as length, mass, and time, may be described in terms of their basic dimensions.

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All of the options listed are included in the uses of dimensional analysis.

Dimensional analysis is a powerful tool used in physics to:

The dimensional analysis involves analyzing the dimensions of physical quantities and using them to establish relationships between them.

By using the principles of dimensional analysis, we can simplify complex physical problems and gain insights into the behavior of physical systems.

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A car traveling 83.0 km/h on a straight road is 1900 m behind a truck traveling at 61.0 km/h. The required voltage is 10 Volts.

Electric current is defined as the rate at which charge passes a fixed unit cross sectional area.

Voltage is defined as the physical quantity required to move charge from one end to other.

Resistance is defined as the the factor which opposed the electric current.

It states that voltage is directly proportional to electric current

V=IR

Given:

current (I) = 0.1 A

resistance (R) = 100 Ω

Now from definition of voltage we have:

V = I × R

V = 100 × 0.1

V = 10 volts

Thus from the above conclusion we can say that therefore the required voltage is 10 volts.

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The Big Bang theory is the most widely accepted explanation for the origins of the universe, but it does not necessarily imply that the universe emerged from nothing.

It is possible that new discoveries or insights may shed light on this fundamental question in the future. The universe may have arisen from a pre-existing state or through some other natural process that we do not yet understand.

Instead, the theory describes how the universe underwent a rapid expansion from a very dense and hot state. The conditions and laws of physics that applied during the earliest moments of the universe may not necessarily be the same as those we observe today, and there are many unknowns and uncertainties in our understanding of these early stages.

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Air is a mixture

Water  and Saccharose are compounds.

Copper, Nitrogen,  and sulfur are elements.

A mixture is a combination of two or more substances, where each substance retains its chemical properties and can be separated from the mixture by physical means.

Mixtures can be either homogeneous, where the composition is uniform throughout, or heterogeneous, where the composition is non-uniform. Examples of mixtures include;

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The answers are 1) The value of R2 is not relevant as it implies a downward force on the plank, 2) The reactions at C and D are 66.3 N and 90 N, respectively, and 3) The vertical force at B to lift the plank clear of D is 686.4 N. The reaction at C is zero, and the reaction at D is 61.4 kg.

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Answer:

Therefore the answer is the precision in the speed DECREASES

Explanation:

In quantum mechanics, we have the uncertainty principle that establishes that when the accuracy of the position increases the accuracy  the speed decreases, being related by the expression

               Δx Δv ≥  h'/ 2

                h' = h/2π

Therefore the answer is the precision in the speed DECREASES

The term used to indicate different DNA nucleotide changes in humans exposed to radiation is called a mutation.

A mutation is any DNA nucleotide change or modification that occurs in the genome of a given organism.

Mutations may be caused by physical agents (e.g., UV radiation) or chemical agents.

In conclusion, the term used to indicate different DNA nucleotide changes in humans exposed to radiation is called a mutation.

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Answer: 2134

Explanation:

I just had this question on my exam

(a) The ball hits the wall 5.3 meters above the release point.

(b) The horizontal component of its velocity is 17.5 m/s. (c) The vertical component of its velocity is 17.1 m/s.

(d) Yes, it has passed the highest point on its trajectory.

(a) Using the equation for range, we can solve for time:

R = V*t*cosθ =>25*t*cos65 = 12 t = 0.75 s

We can then solve for the height using the equation for vertical displacement:

h = V*t*sinθ - 0.5*g*t^2

h = 25*0.75*sin65 - 0.5*9.8*0.75^2 h

= 5.3 m

(b) We can solve for the horizontal component of the velocity using the equation for range:

R = V*t*cosθ 17.5

    = 25*t*cos65 t

   = 0.7 s V = 17.5 m/s

(c) We can solve for the vertical component of the velocity using the equation for vertical displacement:

h = V*t*sinθ - 0.5*g*t^2 17.1

= 25*0.75*sin65 - 0.5*9.8*0.75^2 V = 17.1 m/s

(d) Yes, the ball has passed the highest point on its trajectory because the ball is traveling downwards when it hits the wall.

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Answer:

Photovoltaic detection is a technique that converts light into electrical energy. It is a process that involves the use of a photovoltaic cell, which is made up of semiconductor materials, to generate an electric current when exposed to light.

The photovoltaic cell absorbs the photons of light, which then knock electrons out of their orbits, creating a flow of electricity. The amount of electricity produced is proportional to the intensity of the light. The photovoltaic cell is commonly used in solar panels to generate electricity from sunlight. The efficiency of the photovoltaic cell is dependent on several factors, including the type of semiconductor material used, the purity of the material, and the thickness of the cell.

The photovoltaic cell has many applications, including in solar power generation, telecommunications, and remote sensing. The technique of photovoltaic detection is an important area of research, as it has the potential to provide a clean and renewable source of energy that can help mitigate climate change.

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Answer:

For example, a wave with a time period of 2 seconds has a frequency of

1 ÷ 2 = 0.5 Hz.

Explanation:

Answer:

Explanation:

(m1 + m2)*V1 = m2*V2 + m1*Vx

Vx = ((m1 + m2)*V1 -  m2*V2) / m1

Vx = ((82 + 48)*7.4 - 48*8.6) /82 = 6.7 m/s

The earth conducts seismic waves-- when an earthquake occurs, stations farther and farther away from the quake see the S and P waves propagated through deeper and deeper layers. By measuring the arrival time of the waves, the velocity of the waves can be found as a function of depth. There is clear evidence for several layers in the earth which both refract the waves and below which the velocities are different. This is a bit like holding a book under your desk while a friend (gently) taps the other end of the desk. If you listen closely to the sound (i.e. with your ear on the top of the desk) the sound changes noticeably if a large book is pressed up against the bottom of the desktop. You might also try to figure out how to tell if a golf ball is wound, liquid filled, or solid-- without looking at it. (You can tell if you hit one!)

Scientists can tell by observing the seismic waves that are recorded all over the surface of the earth from distant earthquakes. The seismic waves are reflected (bounced off) layers of different densities, and they are refracted (bent) when they enter layers of different densities. Some of them don't go through liquid at all (the S waves). Scientists have been monitoring earthquakes and studying the phases of seismic waves that arrive at different stations for - hmm, well I don't exactly know - but certainly at least the last 75 years, with more and more sophisticated equipment. Seismologists look at the little wiggles that are made by pens on paper, connected to seismometers, every time a wave from an earthquake anywhere in the world passes under their station. It is by studying many of these seismic records, for many years, and pooling all our knowledge, that we have been able to come up with a working model of what the inside of the earth is made of, where the boundaries between layers of different density and composition lie, and why we have earthquakes where we do.

to Something you can do to model how seismologists "listen" to earthquakes is densitieshave a friend tap on a big table while you put your ear on the table at the other end. We put sensitive instruments in the ground that act like ears so we can detect seismic waves from distant earthquakes.

Answer:

This is true Hope it helped brainiest plz

Explanation:

Clinical psychologists are concerned with everyday problems of adjustment true.

Answer:

The answer to your problem is, C. \(1.0 * 10^{3}\)

Explanation:

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The length of a wave is measured in its propagation direction. The wavelength is measured in meters, centimeters, nanometres, and other units since it is a distance measurement.

The relationship between the wave's wavelength, frequency, and speed is given as

Formula ( That I use and you should use ) !

wavelength = speed of light / frequency

\(y = \frac{c}{v}\)

\(y = \frac{3*10^{3} }{3.0*10^{21} }\)

\(y = 1 * 10^{-13}\)

Thus the answer to your problem is, C. \(1.0 * 10^{3}\)

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Answer: geothermal

Explanation:

The geothermal energy source has no greenhouse gas emissions or health impacts on humans.

Geothermal energy can be described as the thermal energy in the Earth's crust which arises from the formation of the planet and from the radioactive decay of materials.

The high temperature in Earth's interior cause rock to melt and solid mantle to behave plastically. The mantle convects upward since it is lighter than the surrounding rock. Temperatures at the core-mantle boundary reach over 4000 °C.

Geothermal heating can use water from hot springs and geothermal power means the generation of electricity from geothermal energy, which has gained importance.

Earth's geothermal resources are more than adequate to supply humanity's energy needs, although a small fraction is currently being profitably exploited, commonly in areas near tectonic plate boundaries.

The greenhouse gas emissions of geothermal stations are on average 45 g of CO₂ per kWh of electricity or less than 5% of that of conventional coal-fired plants.

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Answer:

The bat and the ball were in contact for 1.8 x 10⁻³ s

Explanation:

Given;

mass of baseball, m = 0.14 kg

initial velocity of the baseball, u = 27.1 m/s

applied force in opposite direction, F = -5000 N

final velocity in opposite direction, v = -37 m/s

Note: The applied force and final velocity are negative because they act in opposite direction to the initial velocity.

impulse received by the body = change in momentum of the  body

Ft = Δmv

Ft = mv - mu

Ft = m(v-u)

t = m(v-u) / F

\(t = \frac{0.14(-37-27.1)}{-5000} \\\\t = \frac{0.14(-64.1)}{-5000} \\\\t = \frac{-8.974}{-5000} \\\\t = 0.0018 \ s\\\\t = 1.8*10^{-3} \ s\)

Therefore, the bat and the ball were in contact for 1.8 x 10⁻³ s

Answer:

it will be base on the climate change.

Explanation: so let just say tomorrow it will be cold so the atmosphere will circle on the coolest atmosphere away from the sun.

An object's position in the solar system affects both its motion and temperature. Objects closer to the Sun experience a stronger gravitational force, causing faster or slower orbits. Other planets and moons also influence an object's orbit and speed. Objects closer to the Sun receive more solar radiation and are hotter, while those farther away receive less radiation and are colder. Additionally, the composition of an object's surface can affect its temperature.

The solar system refers to the group of celestial bodies that orbit around the Sun, including planets, dwarf planets, moons, asteroids, comets, and other small bodies. It is located in the Milky Way galaxy and spans a distance of about 4.6 billion years in age. The eight planets in the solar system, in order from the Sun, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. The solar system is held together by the gravitational force of the Sun and is a subject of scientific study to understand the formation and evolution of our own planet and the other bodies in the solar system.

Here in the Question,

An object's position in the solar system can affect both its motion and temperature. Here's how:

Motion: The motion of an object in the solar system is affected by its distance from the Sun and the gravitational forces of other celestial bodies. An object closer to the Sun will experience a stronger gravitational force than an object farther away. This can cause the object's orbit to be faster or slower depending on its position. Additionally, the gravitational pull of other planets and moons can affect the object's orbit and speed.

Temperature: An object's temperature in the solar system is affected by its distance from the Sun and the composition of its surface. Objects closer to the Sun receive more solar radiation and thus have a higher temperature. Objects farther away receive less radiation and are colder. Additionally, the composition of the object's surface can affect its temperature. For example, objects with high albedo (reflectivity) will reflect more solar radiation and have a lower temperature than objects with low albedo.

Therefore, an object's position in the solar system has a significant impact on its motion and temperature. By studying the positions of celestial bodies and their effects on each other, scientists can gain a better understanding of the dynamics of the solar system and the properties of objects within it.

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Answer:

A. Negative values

Explanation:

Answer:

A-negative values

Explanation:

As per the new modified method of classifying the magnitude of stars, what kind of values were the brightest stars assigned?

A.

negative values

B.

positive values

C.

fractional values

D.

letters

In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.

Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct

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Due to light refraction, any fish in the water can see a fisherman on the bank a little more clearly than one might anticipate. When the light hits the water's surface, it “bends” down by around 13 degrees, leaving the image. Thus option A is correct.

When it reaches the surface, light emanating from the fish refracts (changes direction). When viewed from above the water, a fish appears to be closer to the surface than it actually is.

Therefore, Fred the fisherman has been told that, because of refraction, a fish in water will appear.

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Answer: A (\(\sqrt{61}\),309.8°)

              B (2\(\sqrt{2}\), 315°)

             C (\(3\sqrt{5}\), 26.56°)

Explanation: To transform rectangular coordinates into polar coordinates use:

\(r=\sqrt{x^{2}+y^{2}}\) and \(\theta=tan^{-1}(\frac{y}{x})\)

For point A:

\(r=\sqrt{(-5)^{2}+6^{2}}\)

\(r=\sqrt{61}\)

\(\theta=tan^{-1}(\frac{6}{-5})\)

\(\theta=tan^{-1}(-1.2)\)

\(\theta=-50.2\)°

Point A is in the II quadrant, so we substract the angle for 360° since it is in degrees:

\(\theta=360-50.2\)

\(\theta=\) 309.8°

Polar coordinates for point A is (\(\sqrt{61}\), 309.8°)

For point B:

\(r=\sqrt{2^{2}+(-2)^{2}}\)

\(r=\sqrt{8}\)

\(r=2\sqrt{2}\)

\(\theta=tan^{-1}(\frac{-2}{2} )\)

\(\theta=tan^{-1}(1)\)

\(\theta=-45\)°

Point B is in IV quadrant, so:

\(\theta=360-45\)

\(\theta=\) 315°

Polar coordinates for point B is (\(2\sqrt{2}\), 315°)

For point C:

\(r=\sqrt{(-6)^{2}+(-3)^{2}}\)

\(r=\sqrt{45}\)

\(r=3\sqrt{5}\)

\(\theta=tan^{-1}(\frac{-3}{-6} )\)

\(\theta=tan^{-1}(0.5)\)

\(\theta=\) 26.56°

Polar coordinates for point C is (\(3\sqrt{5}\), 26.56°)

Answer:

This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.

The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.

The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).

The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:

R(n) = √(X² + Y²)

Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.

However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:

<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2

<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2

Because <X²> = <Y²>, we can write:

<R²> = <X²> + <Y²> = n A²

So, the root mean square distance (the square root of the mean square displacement) after n steps is:

R(n) = √(<R²>) = √(n) * A

Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.