Explain the forces acting on the skateboard and how the forces affect the motion of the skateboard.

The diameter of the sphere can be solved using the relationship between the tension in the string, the linear density of the string, and the frequency of the standing waves.

This relationship is given by the equation:
f = (n/2L) * sqrt(T/u)

where f is the frequency of the standing wave, n is the number of the harmonic, L is the length of the string, T is the tension in the string, and u is the linear density of the string.

Before the sphere was submerged, the tension in the string was equal to the weight of the sphere, or T = (2.1 kg) (9.8 m/s^{2}) = 20.58 N.

After the sphere was submerged, the tension in the string was reduced by the buoyant force of the water, which is equal to the weight of the water displaced by the sphere. The volume of the sphere is given by:

V = (4/3) * pi * (d/2)^{3}

where d is the diameter of the sphere. The weight of the water displaced is equal to the volume of the sphere times the density of water, or:

Fb = (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2})

The tension in the string after the sphere was submerged is equal to the weight of the sphere minus the buoyant force, or:

T' = 20.58 N - (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2})

Since the frequency of the fifth harmonic with the sphere submerged is equal to the frequency of the third harmonic before the sphere was submerged, we can set the two equations equal to each other and solve for d:

(5/2L) * sqrt(T'/u) = (3/2L) * sqrt(T/u)

Squaring both sides and rearranging terms gives:

(25/9) * (T'/T) = (u/u)

Substituting the expressions for T and T' and simplifying gives:

(25/9) * [(20.58 N - (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2}))/(20.58 N)] = 1

Solving for d gives:

d = 2 * [(9/25) * (20.58 N)/(4 * pi * (1000 kg/m^{3}) * (9.8 m/s^{2})) - (1/3)]^{(1/3)}

d = 0.117 m

Therefore, the diameter of the sphere is 0.117 m, or 11.7 cm.

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The volume of the gas balloon when the temperature becomes 20 degree Celsius and the pressure becomes 780 mmhg will be 58 L

There is a gas balloon that has a volume of 106 L when the temperature around it is 45 degree Celsius and the pressure is 740 mmhg.

Two conditions are changed to and the pressure is now 780 mmhg and the temperature is 20 degree Celcius.

In order to find the final volume of the gas balloon we are going to use the formula,

PV/T = constant

Initial condition = Final condition

P1V1/T1 = P2V2/T2

Now, getting all the values,

106x740/318 = V2(780)/293

V2 = 58 L.

The final volume of the gas balloon will be 58 L.

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The speed of the 20-kg ball after collision is 11.7 m/s, and it is traveling in the westward direction. We can also say that the direction of the velocity is opposite to the direction of the initial velocity of the first ball.

Mass of the first ball ([tex]m_{1}[/tex]) = 6 kg

Velocity of the first ball before collision ([tex]v_{1}[/tex]i) = 30 m/s, traveling westward

Mass of the second ball ([tex]m_{2}[/tex]) = 20 kg

Velocity of the second ball before collision ([tex]v_{2}[/tex]i) = 0 m/s, at rest

Velocity of the first ball after collision ([tex]v_{1}[/tex]f ) = 9.0 m/s, traveling eastward

Velocity of the second ball after collision ( [tex]v_{2}[/tex]f)

Equation:Conservation of momentum:

[tex]m_{1}[/tex][tex]v_{1}[/tex]i+ [tex]m_{2}[/tex][tex]v_{2}[/tex]i=[tex]m_{1}[/tex] [tex]v_{1}[/tex]f + [tex]m_{2}[/tex] [tex]v_{2}[/tex]f

We can use the conservation of momentum equation to solve for the final velocity of the second ball (v2f). First, we need to find the initial velocity of the first ball in the eastward direction, which can be found using the velocity formula:

[tex]v_{1}[/tex]i,east = -[tex]v_{1}[/tex]i,west = -30 m/s

Now, we can substitute the given values into the conservation of momentum equation and solve for [tex]v_{2}[/tex]f:

[tex]m_{1}[/tex][tex]v_{1}[/tex]i+ [tex]m_{2}[/tex][tex]v_{2}[/tex]i= [tex]m_{1}[/tex][tex]v_{1}[/tex]f + [tex]m_{2}[/tex] [tex]v_{2}[/tex]f

(6 kg)(-30 m/s) + (20 kg)(0 m/s) = (6 kg)(9.0 m/s) + (20 kg)( [tex]v_{2}[/tex]f )

-180 kgm/s = 54 kgm/s + 20 kg [tex]v_{2}[/tex]f

-234 kgm/s = 20 kg [tex]v_{2}[/tex]f

[tex]v_{2}[/tex]f = (-234 kgm/s) / (20 kg)

[tex]v_{2}[/tex]f = -11.7 m/s

Therefore, the speed of the 20-kg ball after collision is 11.7 m/s, and it is traveling in the westward direction. We can also say that the direction of the velocity is opposite to the direction of the initial velocity of the first ball.

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We can see here that the galaxy classes illustrated by the shapes are:

A1:  Irregular (Irr)

A2: Lenticular (SO)

A3: Spiral (SA)

A4: Intermediate spiral (SAB)

B1:  Lenticular (SO)

B2: Irregular (Irr)

B3:  Intermediate spiral (SAB)

B4: Elliptical (E)

A galaxy is a vast system of stars, gas, dust, and other matter that is held together by gravity. It is one of the fundamental building blocks of the universe.

Galaxies come in a variety of shapes and sizes, ranging from small dwarf galaxies to massive elliptical galaxies. Our own Milky Way galaxy contains billions of stars and is just one of countless galaxies in the observable universe.

Galaxies play an important role in the evolution of the universe, as they are the sites of star formation, supernovae explosions, and the merging of smaller galaxies into larger ones.

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Projectile motion is the motion of an object that is projected into the air and then follows a path determined by the forces acting on it.

Velocity, displacement, angle, and time are all related in projectile motion. The velocity of a projectile determines its speed and direction. The initial velocity of the projectile is composed of two components, the horizontal velocity and the vertical velocity. The horizontal velocity remains constant throughout the projectile motion, while the vertical velocity changes due to the force of gravity. The displacement of the projectile is its change in position during the motion. The displacement is dependent on both the initial velocity and the time elapsed. The horizontal displacement is determined by the horizontal velocity and time, while the vertical displacement is determined by the vertical velocity and time. The angle of projection is the angle at which the projectile is launched into the air. The angle affects the initial velocity components and determines the shape of the projectile path. The time of flight is the total time that the projectile is in the air. The time of flight is dependent on the vertical velocity component, the angle of projection, and the height of the launch point. In summary, the velocity, displacement, angle, and time are all related in projectile motion, and changes in any one of these factors will affect the trajectory of the projectile.

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Answer:

2,500,000,000,000 = 2,5 x 10^12

0.00023 = 2.3 x 10^-4

101 = 1.01 x 10^2

0.0000000032 = 3.2 x 10^9

Explanation:

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"The required kelvin temperature when celsius temperature is given is calculated to be 305.65 K."

There are three main scales to measure temperature. They are Celsius, Fahrenheit and Kelvin scales of measurement. Kelvin is said to be the official metric unit of temperature.

The temperature of water is given as 32.5 °C.

The same temperature in kelvins should be found out.

Converting celsius scale temperature to kelvin scale, we should add up 273.15 to the temperature in celsius scale.
Kelvin temperature = 273.15 + Celsius temperature

Kelvin temperature = 273.15 + 32.5 °C = 305.65 K

Thus, the kelvin temperature is calculated to be 305.65 K.

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Answer:

When a car brakes, it experiences a forward deceleration force, which is generated by the braking system. This force acts in the opposite direction to the car's motion and causes the car to slow down. As a result of this force, the horizontal forces acting on the car change.

When the brake is applied, the friction between the brake pads and the rotors generates a braking force that acts on the wheels. This force causes the wheels to slow down and, as a result, the car's forward motion is slowed down as well.

At the same time, the car's weight shifts forward, causing a decrease in the vertical force acting on the rear wheels and an increase in the vertical force acting on the front wheels. This increase in the front wheel's vertical force creates more friction between the tires and the road, which in turn generates a larger horizontal force that acts to slow down the car.

Additionally, as the car slows down, the aerodynamic drag acting on the car decreases, resulting in a smaller horizontal force acting on the car. However, the net effect of all these changes is a decrease in the car's forward motion and a corresponding decrease in the horizontal forces acting on the car.

The force exerted to push the 25 Kg wooden box across the wooden floor at a constant speed of 1.0 m/s is 49 N (2nd option)

Frictional force is given by the following formula

Frictional force = coefficient of friction (μ) × normal reaction (N)

Since the speed is constant,

Frictional force = Force exerted

Thus,

Force exerted = coefficient of friction (μ) × normal reaction (N)

F = μN

Now, we shall determine the force exerted to push the box. Details below:

F = μN

F = 0.2× 245

F = 49 N

Thus, the force exerted to push the box is 49 N (2nd option)

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To ensure accurate and reliable melting point determinations, it is important to avoid reusing a sample that has been melted and solidified.

It is important to avoid reusing a sample that has been melted and solidified when determining its melting point because the process of melting and cooling can cause changes in the sample's structure and purity, which can affect the accuracy of subsequent melting point determinations.

When a solid sample is melted, its molecules or ions are rearranged, and the sample's crystal lattice structure is disrupted. Upon solidification, the sample's structure may not fully reform, resulting in impurities or defects in the crystal lattice. These impurities or defects can cause the sample to have a lower melting point than it would have had if it had not been melted.

Reusing a sample that has been melted and solidified can introduce additional impurities and defects into the sample, which can further lower its melting point. As a result, using the same sample for subsequent melting point determinations can lead to inconsistent and inaccurate results.

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The drawbacks of burning fossil fuels to generate power include their role in climate change and air pollution, their limited supply, and the environmental harm that their extraction and transportation create.

Our infrastructure is essentially based on the usage of fossil fuels, which are relatively cheap, and abundant, and on which we rely extensively to produce electricity. Furthermore, many individuals might not be aware of the harmful effects that using fossil fuels has on the environment or might not have access to alternate energy sources.

Because they emit few to no greenhouse gas emissions or other pollutants, renewable energy sources like solar, wind, and hydropower are typically regarded as the least damaging to the environment. Furthermore, they do not generate toxic waste or need to mine or dig for fuel. Yet, depending on elements like the location of the power generation facilities and the materials employed in the manufacture of renewable energy technology, the environmental impact of renewable energy sources might change.

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The distance between the two stars is approximately 35.65 light-years.

To determine the distance between the two stars in light-years, we need to use the parallax formula:

distance = 1 / (parallax angle in arcseconds)

For the first star, the distance is:

distance = 1 / 0.11 = 9.09 parsecs

For the second star, the distance is:

distance = 1 / 0.13 = 7.69 parsecs

To determine the distance between the two stars, we can use the law of cosines:

c² = a² + b² - 2abcos(C)

where;

We know that the angle between the two stars is 5 degrees, or 300 arcminutes, or 18,000 arcseconds.

Converting the distances to light-years:

a = 9.09 x 3.26 = 29.59 light-years

b = 7.69 x 3.26 = 25.06 light-years

Substituting into the law of cosines:

c² = (29.59)² + (25.06)² - 2 x 29.59 x 25.06 * cos(18,000 arcseconds)

c² = 1,271.57

c = 35.65 light-years

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Here are three ideas for a biodiversity project that are affordable and budget-friendly: Create a pollinator garden, Conduct a citizen science project, and Host a wildlife-friendly event.

Biodiversity refers to the variety of living organisms that exist in a particular ecosystem, region, or entire planet. It includes all species of plants, animals, fungi, and microorganisms, as well as the genetic diversity within these species and the ecological diversity of the ecosystems they inhabit.

Biodiversity plays a crucial role in maintaining the balance and stability of ecosystems and the natural processes that support life on Earth. It provides us with a range of essential services, such as pollination, soil formation, water purification, and climate regulation, that are vital for human well-being. It is, therefore, essential to protect and conserve biodiversity by promoting sustainable use and management of natural resources, restoring degraded habitats, and implementing effective conservation measures.

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Complete Question:

Top 3 ideas based upon affordability biodiversity project that is affordable and budget-friendly?

Answer:

Explanation:

Distinguish between physical and chemical changes. Include examples in your explanations.

Physical changes are changes in the physical properties of a substance that do not alter its chemical composition. For example, changes in state such as melting, boiling, freezing, and condensation are all physical changes. Other examples of physical changes include changes in shape, size, and color.

Chemical changes, on the other hand, result in a new substance with different properties than the original substance. This is due to a change in the chemical composition of the substance. Examples of chemical changes include burning, rusting, fermentation, and decomposition.

What are the differences among elements, compounds, and mixtures?

An element is a substance that cannot be broken down into simpler substances by chemical means. It is made up of only one type of atom. Examples of elements include gold, carbon, and oxygen.

A compound is a substance that is made up of two or more different elements chemically combined in a fixed ratio. The properties of a compound are different from the properties of the elements that make it up. Examples of compounds include water (H2O), carbon dioxide (CO2), and table salt (NaCl).

A mixture is a combination of two or more substances that are not chemically combined. Mixtures can be homogeneous (uniform in composition) or heterogeneous (non-uniform in composition). Examples of mixtures include air (a mixture of gases), saltwater (a mixture of salt and water), and soil (a mixture of minerals, organic matter, and water).

Fill in the chart below to identify the properties of shape and volume for each type of matter.

Shape Volume

Solid Definite Definite

Liquid Indefinite Definite

Gas Indefinite Indefinite

Explain how atomic mass and molecular mass are determined.

Atomic mass is determined by adding the number of protons and neutrons in the nucleus of an atom. Since protons and neutrons have almost the same mass, the atomic mass of an element is approximately equal to the number of protons and neutrons.

Molecular mass is determined by adding the atomic masses of the atoms that make up a molecule. For example, the molecular mass of water (H2O) is determined by adding the atomic masses of two hydrogen atoms and one oxygen atom.

Fill in the chart below to identify and describe the parts of an atom.

Location Charge

Proton Nucleus Positive

Neutron Nucleus Neutral

Electron Outside the nucleus Negative

Identify the assumptions made as part of Dalton’s atomic theory.

Dalton's atomic theory, which was proposed in the early 19th century, made the following assumptions:

All matter is made up of tiny particles called atoms.

Atoms are indivisible and cannot be created or destroyed.

Atoms of the same element are identical in mass and properties.

Chemical reactions occur when atoms are rearranged, separated, or combined.

Compounds are formed when atoms of different elements combine in fixed ratios.

1.) Physical changes involve a change in the physical properties of a substance, but the substance itself remains the same. Examples include changes in state, such as melting or boiling, and changes in shape or size, such as cutting or crushing. Chemical changes involve a change in the chemical composition of a substance, resulting in the formation of a new substance with different properties. Examples include combustion, rusting, and digestion.

2.) Elements are substances made up of only one type of atom, such as oxygen or carbon. Compounds are substances made up of two or more different elements chemically combined, such as water (made up of hydrogen and oxygen). Mixtures are combinations of two or more substances that are not chemically combined, such as saltwater.

Shape Volume

Solid Definite

Liquid Indefinite

Gas Indefinite

3.) Atomic mass is determined by adding up the number of protons and neutrons in an atom's nucleus. Molecular mass is determined by adding up the atomic masses of the atoms in a molecule.

4.)

Location Charge

Proton Nucleus Positive

Neutron Nucleus Neutral

Electron Electron cloud Negative

5.) The assumptions made as part of Dalton's atomic theory include:

All matter is made up of atoms.

Atoms of the same element are identical in mass and properties.

Compounds are formed by the combination of atoms of different elements in specific ratios.

Chemical reactions involve the rearrangement of atoms, but the atoms themselves are not created or destroyed.

The two stones will meet at a height of approximately 83.1 meters above the ground.

y1 = 0.5 * g * t^2

At the same time, another stone is projected vertically upwards from the ground with a velocity of 20 m/s.

y2 = v0 * t + 0.5 * g * t^2

0.5 * g * t^2 = 100 - v0 * t - 0.5 * g * t^2

Simplifying and rearranging, we get:

t = (2 * v0) / g

Substituting the values of v0 and g, we get:

t = (2 * 20) / 9.81 ≈ 4.08 s

So the two stones will meet after 4.08 seconds.

To find the height at which they meet, we can substitute this value of t into either of the equations for y1 or y2. Let's use the equation for y1:

y1 = 0.5 * g * t^2 = 0.5 * 9.81 * (4.08)^2 ≈ 83.1 m

Velocity is a fundamental concept in physics that describes the rate at which an object's position changes with respect to time. It is a vector quantity that specifies both the magnitude and direction of motion.

Mathematically, velocity can be defined as the change in an object's position over a given time interval. The formula for velocity is v = Δx/Δt, where v is the velocity, Δx is the change in position, and Δt is the change in time. Velocity is different from speed, which only describes the magnitude of motion and not its direction. In other words, velocity takes into account the direction of motion while speed does not.

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Complete Question:

A stone is allowed to fall from the top of a tower 100m high and at the same time, another stone is projected vertically upwards from the ground with a velocity of 20m/s. Calculate when and where the two stones will meet.

The potential energy of an object at a height h above the earth’s surface is given by the formula U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the earth’s surface.

Given that the object has a potential energy of 1200 J and a mass of 20 kg, we can rearrange the formula to find the height h:

h = U / (mg)

Substituting the given values, we get:

h = 1200 J / (20 kg x 9.81 m/s^2) = 6.12 m

Therefore, the object is at a height of 6.12 meters above the earth’s surface.

Given that mass is independent of everything, the first part of the question's response is straightforward: As mass does not change as you move from one location in the universe to another, the boy on the moon will still have the same mass as the boy on Earth.

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Answer:

(a) The research method that would be used to test this theory is an experimental method.

(b) The independent variable would be the amount of time participants spend watching cooking shows on television, and the dependent variable would be their cooking ability. Cooking ability can be measured by objective measures such as speed and accuracy in preparing dishes, as well as subjective measures such as taste and presentation.

(c) One potential confounding variable could be prior cooking experience. Participants with prior cooking experience may have a higher cooking ability regardless of the amount of time they spend watching cooking shows, whereas those without prior cooking experience may have a lower cooking ability regardless of the amount of time they spend watching cooking shows. To control for this variable, participants could be randomly assigned to groups based on their prior cooking experience, or prior cooking experience could be measured and included as a covariate in the analysis.

Explanation:

The distance covered by the truck would be 188.4 meters.

Initial velocity, u = 63 km/h = (63 x 1000 m) / (3600 s) = 17.5 m/s

Final velocity, v = 84 km/h = (84 x 1000 m) / (3600 s) = 23.3 m/s

We can use the equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, s is the distance traveled.

Substituting the values we get:

(23.3)^2 = (17.5)^2 + 2(1.25)s

Simplifying and solving for s, we get:

s = [(23.3)^2 - (17.5)^2] / (2 x 1.25) = 188.4 meters (rounded to one decimal place)

Therefore, the truck travels a distance of 188.4 meters as it accelerates uniformly from 63 km/h to 84 km/h with an acceleration of 1.25 m/s^2.

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Series field windings are a type of electric motor winding that is connected in series with the armature.

They are designed to provide a strong magnetic field that interacts with the current flowing through the armature to produce torque and rotational motion. The series field windings are typically wound with a large number of turns of fairly thin wire. The number of turns is chosen to provide the required magnetic field strength for the motor's operation. The wire used for the winding is usually made of copper or aluminum, and it is coated with an insulating material to prevent short-circuits between the turns. Because the field windings are connected in series with the armature, the current flowing through them is the same as the current flowing through the armature. This means that the strength of the magnetic field produced by the field windings varies with the armature current. As a result, the torque produced by the motor increases with the load, making series-wound motors well-suited for applications that require high starting torque, such as in electric locomotives and cranes.

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The work done by the three forces can be determined by the equation W=Fd, where W is the work done, F is the force, and d is the displacement.

For this problem, the force of gravity is 6.8N, the force of friction is 4.5N, and the force of tension is 2.3N.

The displacement is 2.5m. Using the equation, the work done by gravity is 17 kilojoules (KJ),

work done by friction is 11.25KJ, and work done by tension is 5.75KJ.

Thus, the work done by the three forces is 17KJ, 11.25KJ, and 5.75KJ, respectively.

The work done by the three forces can be compared to the total work done by a single force. In this case, the total work done is 34KJ, which is the sum of the work done by each force.

Since the work done by each force is less than the total work done, we can conclude that the forces are working together, rather than in opposition. This is a common occurrence in physics, where multiple forces can combine to produce a greater result than a single force.

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Answer:

a.  3.37 m/s²

Explanation:

F = ma

a = F/m = 172N / 51kg = 3.37 m/s²

A type of eye surgery called a vitrectomy is performed to repair issues with the retina and vitreous of the eye.

It is clear the retina of any blood or other substances preventing correct light focus. Scar tissue that is causing the retina to wrinkle or tear and impairing vision should be removed. It assist in repairing a detached (ripped away) retina from the eye wall.

It was from a wound, remove a foreign object that is lodged inside the eye. The ophthalmologist removes some or all of the vitreous from the centre of your eye during a vitrectomy. A gas or oil bubble, or a salt water (saline) solution, is used to replace the vitreous.

It is eye refills the saline fluid or the bubble throughout the healing process following surgery.

Thus, A type of eye surgery called a vitrectomy is performed to repair issues with the retina and vitreous of the eye.

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Answer:

Generally. the index of refraction of the solid is greater than 1

V(air) / V(solid) = N   (index of refraction)

Since V (solid) = V (air) / N     and   V(soiid) = λ(solid) * f

V(solid) / V(air) = [V (air) / N] / (V air) = 1 / N

The velocity is less in the solid and the wavelength is also less

The electromagnetic waves with an energy of [tex]1.5 \times 10^{-24} J[/tex] are likely X-rays.

The energy of an electromagnetic wave is related to its frequency and wavelength by the equation:

E = hf = hc/λ

where:

E = energy of the electromagnetic wave

h = Planck's constant ([tex]6.626 \times 10^{-34} J s[/tex])

f = frequency of the electromagnetic wave

c = speed of light ([tex]3.00 \times 10^8 m/s[/tex])

λ = wavelength of the electromagnetic wave

Solving for λ:

λ = hc/E = [tex](6.626 \times 10^{-34} J s)(3.00 \times 10^8 m/s)/(1.5 \times 10^{-24} J)[/tex]

λ ≈ [tex]4.40 \times 10^-8 m[/tex]

This corresponds to a wavelength of about 44 nanometers, which falls in the range of X-rays. Therefore, the electromagnetic waves with an energy of [tex]1.5 \times 10^{-24} J[/tex] are likely X-rays.

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The plastic affects how light hits the screen due to the different index of refraction that plastic has.

Any material that light passes through can affect how the light hits the screen. The way that a material affects light depends on its optical properties, such as its index of refraction, absorption, and scattering.

For example, if the clear plastic has a different index of refraction than the air or glass, it can cause the light to bend or refract as it passes through, which can affect the direction of the light as it hits the screen. Additionally, if the plastic absorbs or scatters certain wavelengths of light, it can affect the color or intensity of the light that hits the screen.

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Two resistors have resistances r(smaller) and r(larger), where r(smaller) When the resistors are connected in series to a 12.0-V battery, the current from the battery is 1.13 A. When the resistors are connected in parallel to the battery, the total current from the battery is 10.6 A.the two resistances are 2.40 Ω and 8.30 Ω.

The current through both resistors is the same, and can be found using Ohm's law:

I_series = [tex]\frac{V}{R}[/tex]_series

where V is the voltage of the battery. We are given that I_series = 1.13 A and V = 12.0 V, so we can solve for R_series:

R_series = [tex]\frac{V}{I}[/tex]_series = 12.0  [tex]\frac{V}{I}[/tex] 1.13 A = 10.62 ΩWhen the resistors are connected in parallel, the total resistance is:

[tex]\frac{1}{R}[/tex]_parallel = 1/r(smaller) + 1/r(larger)

The total current from the battery is the sum of the currents through each resistor:

I_parallel = [tex]\frac{V}{R}[/tex]_parallel

where V is the voltage of the battery. We are given that I_parallel = 10.6 A and V = 12.0 V, so we can solve for R_parallel:

R_parallel =  [tex]\frac{V}{I}[/tex]_parallel = 12.0 V / 10.6 A = 1.13 Ω

Now we have two equations with two unknowns (r(smaller) and r(larger)):

R_series = r(smaller) + r(larger)

1/R_parallel = 1/r(smaller) + 1/r(larger)

We can solve for r(smaller) and r(larger) using algebra. Rearranging the first equation, we get:

r(larger) = R_series - r(smaller)

Substituting this expression into the second equation and simplifying, we get:

1/R_parallel = 1/r(smaller) + 1/(R_series - r(smaller))

Multiplying both sides by r(smaller)(R_series - r(smaller)), we get:

r(smaller)(R_series - r(smaller))/R_parallel = R_series - r(smaller) + r(smaller)

Simplifying, we get:

[tex]r(smaller)^{2}[/tex] - R_series r(smaller) + R_series/R_parallel = 0

Using the quadratic formula, we get:

r(smaller) = [R_series ± [tex]\sqrt{(R_series^2 - 4R_series/R_parallel)}[/tex]] / 2

Plugging in the values for R_series and R_parallel, we get:

r(smaller) = [10.62 Ω ± [tex]\sqrt{(10.62^2 - 4(10.62/1.13))}[/tex]] / 2 = 2.40 Ω or 8.30 Ω

Since r(smaller) is the smaller resistor, it must be 2.40 Ω and r(larger) must be 8.30 Ω.

Therefore, the two resistances are approximately 2.40 Ω and 8.30 Ω.

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The speed of the star is approximately 29979.2458 m/s.

The speed of star can be solved using the Doppler shift formula:

Δλ/λ = v/c

where Δλ is the shift in wavelength,

λ is the rest wavelength,

v is the velocity of the object (in this case, the star), and

c is the speed of light.

Substituting the given values, we get:

(1000.1 nm - 1000.0 nm) / 1000.0 nm = v/c

Simplifying, we get:

0.1 nm / 1000.0 nm = v/c

v = (0.1 nm / 1000.0 nm) * c

v = 299792458 m/s * (0.1 nm / 1000.0 nm)

v = 29979.2458 m/s

Therefore, the speed of the star is approximately 29979.2458 m/s.

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The volume of water needed to fill the outdoor decorative pond in the shape of a hemispherical tank with a radius

r is (2/3)πr³.

The volume of the hemispherical tank can be found by using the formula for the volume of a sphere and dividing it by 2, since a hemisphere is half of a sphere. The formula for the volume of a sphere is

V = (4/3)πr³,

where r is the radius of the sphere.

So, the volume of the hemispherical tank would be

V = (1/2)(4/3)πr³

V = (2/3)πr³.
To fill the tank with water, the volume of water pumped into the tank through the inlet must equal the volume of the tank. So, the volume of water needed to fill the tank is (2/3)πr³.

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To read text at a near-point distance of 22 cm, a person who has had cataract surgery would need a corrective lens with a refractive power of +4.5 diopters.

If a person has had the surgical removal of the variable lens of the eye, they would have lost the ability to accommodate (change the shape of the lens to focus on objects at different distances). Therefore, they would require corrective lenses to see clearly at different distances.

To determine the power of the corrective lenses required to read text at a near-point distance of 22 cm, we can use the following formula:

[tex]1/f = 1/d_o + 1/d_i[/tex]

where:

f = focal length of the corrective lens

[tex]d_o[/tex] = object distance (distance from the eye to the object)

[tex]d_i[/tex]= image distance (distance from the eye to the image formed by the corrective lens)

We want to find the power of the corrective lens, which is given by:

[tex]P=1/f[/tex]

The near-point distance [tex](d_o)[/tex]  is 22 cm = 0.22 m. Since the cornea's refractive power focuses objects at infinite distances onto the retina, we can assume that the object distance is effectively at infinity, i.e., [tex]d_o = \infty[/tex]

Therefore, the formula becomes:

[tex]1/f = 1/\infty + 1/d_i[/tex]

[tex]1/f = 0 + 1/d_i[/tex]

[tex]f = d_i[/tex]

We want to find the focal length [tex](d_i)[/tex]  of the corrective lens required to form an image of the text at a distance of 22 cm from the eye.

Using the formula, we get:

[tex]f = d_i = \frac{1}{(1/d_o + 1/d_i)}[/tex]

[tex]d_i = \frac{1}{(1/d_o + 1/f)}[/tex]

[tex]d_i = \frac{1}{(1/0.22 + 1/\infty)}[/tex]

[tex]d_i = 0.22 m[/tex]

Now, we can calculate the power of the corrective lens required as follows:

[tex]P = 1/f[/tex]

[tex]P = 1/0.22[/tex]

[tex]P = +4.5[/tex]  diopters (to the nearest tenth of a diopter)

Therefore, the power of the corrective lenses required to read text at a near-point distance of 22 cm is +4.5 diopters (convex lenses).

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