The GAIA spacecraft is capable of measuring parallax angles as small as about 0.00002 arcsecond (20 microarcseconds). Based on this fact, GAIA should in principle be able to measure the distances of stars located __________. View Available Hint(s)for Part F throughout the observable universe only within about 1,000 light-years of Earth throughout the Local Group of galaxies (including the Andromeda galaxy), but not in more distant galaxies only within about 10,000 light-years of Earth throughout the Milky Way Galaxy, but not in the Andromeda galaxy or other more distant galaxies

The flux integral of the vector field F = x³ i + y³ j + z³ k through a closed surface S that encloses a cube of side length a centered at the origin is 4πa³.

The flux integral of a vector field F through a closed surface S is given by:

Φ = ∫∫_S F · dA

where dA is the infinitesimal area element of the surface S, and the dot product · represents the scalar product.

To compute the flux integral of the vector field F = x³ i + y³ j + z³ k through a closed surface S, we can use the Divergence Theorem, which states that the flux integral of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the enclosed volume:

Φ = ∫∫_S F · dA = ∫∫∫_V ∇ · F dV

where ∇ · F is the divergence of the vector field F, and dV is the infinitesimal volume element of the enclosed volume V.

The divergence of the vector field F can be computed as follows:

∇ · F = ∂(x³)/∂x + ∂(y³)/∂y + ∂(z³)/∂z

= 3x² + 3y² + 3z²

Substituting this into the Divergence Theorem, we get:

Φ = ∫∫_S F · dA = ∫∫∫_V (3x² + 3y² + 3z²) dV

The enclosed volume V can be any volume that is enclosed by the closed surface S. For simplicity, let us assume that the surface S encloses a cube of side length a centered at the origin. Then, we can express the volume integral as:

∫∫∫_V (3x² + 3y² + 3z²) dV = 3∫_0ᵃ ∫_0ᵃ ∫_0ᵃ (x² + y² + z²) dxdydz

Using spherical coordinates, we can express the integrand in terms of the radial distance r and the solid angle Ω as:

x²+ y² + z² = r² + r^2sin²θsin²φ + r²cos²θ

= r²(sin²θcos²φ + sin²θsin²φ + cos²θ)

= r²

where θ is the polar angle and φ is the azimuthal angle.

The volume integral then becomes:

∫_0ᵃ ∫_\(0^Pi\) ∫_0^{2π} r² sinθ dφ dθ dr

= 4π/3 a³

Substituting this back into the expression for Φ, we get:

Φ = 3∫_0ᵃ ∫_0ᵃ ∫_0ᵃ (x² + y² + z²) dxdydz

= 3(4π/3 a³)

= 4πa^3

Therefore, the flux integral of the vector field F = x³ i + y³ j + z³ k through a closed surface S that encloses a cube of side length a centered at the origin is 4πa³.

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Answer:

The measurement of an object's motion with respect to any other object that is moving or stationary is called Relative Motion.

The velocity of the horse is 20 meters/second.

To find the velocity of the horse, we can use the formula:

velocity = distance / time

In this case, the distance is 1900 meters and the time is 95 seconds. Plugging in these values into the formula, we get:

velocity = 1900 meters / 95 seconds

Simplifying, we find that the velocity of the horse is:

velocity = 20 meters/second

Speed is the speed and the bearing of movement of an item. Speed is a basic idea in kinematics, the part of traditional mechanics that depicts the movement of bodies. Velocity. As a shift in course happens while the dashing vehicles turn on the bended track, their speed isn't steady.

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Answer:

D - 3/5r

Explanation:

Khan Academy

Answer:

Hockey

Explanation:

plz mark on brainlist:)

Answer:

Reproduction

Explanation:

because reproduction produces variation within the species allowing the species to survive selection

Answer: D = reproduction

Explanation:

Answer: R = V / I

Explanation:

P = VI (power = voltage x current)

Ohm's Law tells us that V = IR.

Substitute IR for V in the first formula: P = (IR)I = I 2 R.

Rearrange to solve for resistance: R = P / I 2.

In a series circuit, the current across one component is the same as the total current. This is not true for a parallel circuit.

At the bottom of its swing, where its potential energy is minimum, a pendulum's KE reaches its maximum value. When a pendulum reaches the top of its swing and momentarily stops, its PE is at its maximum and its KE is zero.

At equilibrium, the velocity is at its highest point, and at the extreme, it is at its lowest. As a result, the mean position has the highest kinetic energy.

Position C has the highest kinetic energy; the lowest position has the highest kinetic energy. All of the potential energy from the beginning has been converted into kinetic energy by the time the bob reaches C.

The extreme position of a pendulum causes its velocity to become zero. The extreme position therefore has no kinetic energy.

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The initial velocity of a ball kicked off the ground at an angle of 37° to the horizontal is 25 m/s.

Thus, the vertical displacement of the ball can be calculated using the following formula:

Δy = vi(t) + (1/2)at²

Δy = 25(2.2) + (1/2)(-9.81)(2.2)²

Δy = 55 - 23.081Δy = 31.919 m

After 2.2 s, the vertical distance that the ball has traveled is 31.919 meters.

Now we can calculate the vertical component of the velocity of the ball using the following formula:

vf = vi + at

Here, vi = 25 m/s is the initial velocity, t = 2.2 s is the time interval and a = -9.81 m/s² is the acceleration of the ball due to gravity.

vf = 25 + (-9.81)(2.2)

vf = 2.558 m/s

Finally, we can use the Pythagorean theorem to find the magnitude of the ball's velocity after 2.2 seconds. This is given by:

V = sqrt[(25 m/s)² + (2.558 m/s)²]

V = 25.424 m/s

Thus, the ball's speed 2.2 seconds after being kicked is 25.424 m/s.

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Explanation:

A position versus time graph gives the position of an object at a certain point in time. The slope, also known as the derivative, will give the change in the position with respect to time. The slope will give you the instantaneous velocity of the object due to velocity being defined as the change in position over time

Answer:

see below

Explanation:

This graph shows an object initially travels at a constant velocity for 4 seconds.....the velocity is the slope of the graph for these 4 seconds.  

   then it remains stationary from t = 4 to t =6  ...see the graph is flat (slope = 0   means no velocity) ...at position 3  

  at t = 6 it reverses course ....a negative velocity (steeper slope ...higher velocity)  until it reaches position 0 at t = 9  

These times are what I think I can see...the graph is kind of fuzzy.

A boy blows softly across the top of a soda bottle. the sound waves vibrate with a frequency of 1580 hz at the second lowest harmonic. The depth of the bottle is approximately 0.109 meters.

Sound waves can be described as longitudinal waves because the particles in the medium vibrate parallel to the direction of wave propagation. As the sound wave travels, it creates areas of compression and rarefaction, where the air particles are closer together or farther apart, respectively.

Humans perceive sound waves through their ears, where the vibrations of the sound waves are detected by the eardrums and converted into electrical signals that the brain interprets as sound. Sound waves are not only important for communication and music but also have various applications in fields such as acoustics, medicine, and engineering.

To determine the depth of the bottle, we need to use the formula:

L = (n/2) x (v/f)

Where L is the length of the air column in the bottle, n is the harmonic number (in this case, it is the second lowest harmonic, which means n=2), v is the speed of sound in air (which is approximately 343 m/s at room temperature), and f is the frequency of the sound wave (which is 1580 Hz).

Plugging in these values, we get:

L = (2/2) x (343/1580)

L = 0.109 m

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Answer:

The first one is 9 times the original

The second one is 1/2 times

The third one is 1/3 times

Answer:

31.86m

Explanation:

recall that one of the equations of motion can be written

v² = u² + 2as

where

u = initial velocity = 25m/s

v = final velocity = 0m/s because at maximum height, the ball will momentary stop moving (i.e have zero velocity)

a = acceleration = -9.81m/s²  (i.e a deceleration as it moves upwards equal to the magnitude of the gravitational acceleration)

s = distance (we are asked to find this)

substituting these into the equation:

v² = u² + 2as

0² = 25² + 2(-9.81)s

0 = 625 - 19.62s

19.62s = 625

s = 625 / 19.62

s = 31.86m

Answer:

Area of the circle = 49*pi square m

Explanation:

Answer:

35%

Explanation:

Given data

Amount of energy transferred (Input) = 270J

Amount of energy converted to sound (Output)=  94.5J

Efficiency = output/input*100

Efficiency= 94.5/270*100

Efficiency=0.35*100

Efficiency=35%

Hence the efficiency is 35%

Answer:

C

Explanation:

The composition of a comet compared with that of the Sun is C "Comets are made of ice and dust, while the Sun is made of gas".

Comets are small, icy bodies that originate from the outer solar system and are composed mainly of frozen water, carbon dioxide, methane, and ammonia, along with dust and small rocky particles. When a comet approaches the Sun, its icy material vaporizes, creating a glowing coma (a hazy atmosphere around the nucleus) and a tail that points away from the Sun due to the solar wind.

On the other hand, the Sun is a giant ball of hot, glowing gas, composed mainly of hydrogen (about 73% of its mass) and helium (about 25% of its mass), with trace amounts of other elements like oxygen, carbon, and iron. The Sun generates energy through nuclear fusion reactions in its core, which convert hydrogen into helium and release a tremendous amount of energy in the process.

Therefore, the composition of a comet is quite different from that of the Sun. While both objects contain some water (in the form of ice for comets and vapor for the Sun), comets are predominantly made of ice and dust, while the Sun is predominantly made of gas, with only a small amount of solid material in its core.

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Answer:

because of tungsten's high melting point

Explanation:

Answer:

Velocity = Distance

Time

Circumference is otherwise known as distance, thus V = C/T

Substitute the values and you get the answer.

T = C/V

T = 44460000

7800

T = 5700 seconds

Based on the position vs. time plot, we can see that at point P, the mass is at the equilibrium position of the spring, meaning that it is not displaced from its resting position. Therefore, we can conclude that the mass has zero velocity at point P. Therefore, the correct answer is option 3: zero velocity and zero acceleration.

We know that the acceleration of the mass is directly proportional to the displacement from equilibrium and is always directed toward the equilibrium position. Therefore, if the mass is moving towards the equilibrium position at point P, it will have a negative acceleration. Conversely, if the mass is moving away from the equilibrium position at point P, it will have a positive acceleration.

Therefore, the correct answer is option 3: zero velocity and zero acceleration. The mass is neither moving away from nor toward the equilibrium position, so it has zero acceleration. Additionally, since it is at the equilibrium position, it has zero velocity.

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Answer:

Earth rotates on its axis

Explanation:

A star is a giant astronomical or celestial object that is comprised of a luminous sphere of plasma, binded together by its own gravitational force.

It is typically made up of two (2) main hot gas, Hydrogen (H) and Helium (He).

Some of the examples of stars are; Canopus, Sun (closest to the Earth), Betelgeus, Antares, Vega etc.

Earth rotation can be defined as the amount of time taken by planet earth to complete its spinning movement on its axis.

This ultimately implies that, the rotation of earth refers to the time taken by earth to rotate once on its axis. One spinning movement of the earth on its axis takes approximately 24 hours to complete with respect to the sun.

As a result of the Earth's rotation on it's axis, stars generally appear to move in circular paths through the sky.

Answer:

Humans can have major impacts on all the spheres.

Piling up our waste in landfills affects the geosphere. Pumping waste into the oceans harms the hydrosphere. And overfishing and habitat destruction can reduce the diversity of living things in the biosphere. However, people everywhere are working to change things.

Explanation:

(a) The power required for the car to climb the hill at a steady speed is 15.56 kW.

(b) The power required for the car to climb the hill at a changing speed is  19.44 kW.

The power required for the car the move the incline is calculated as follows;

When the speed is steady, the average speed is calculated as;

v = ( 80km/h + 80 km/h) / 2 = 80 km/h = 22.22 m/s

P = Fv

where;

P = ( 700 N x 22.22 m/s )

P = 15,555.56 W = 15.56 kW

When the speed changes from 90 km/h to 110 km/h, the average speed is calculated as;

v = ( 90 km/h + 110 km/h ) / 2 = 100 km/h = 27.78 m/s

P = ( 700 N x 27,78 m/s )

P = 19,444.44 W = 19.44 kW

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Answer:

The flat Earth model is an archaic conception of Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat Earth and due to this people still belive earth is flat but scientist proven earth is round .

Explanation:

The volume of the freon-12 at STP is 75.3 L if a sample of freon-12 (cf2cl2) occupies 30.0 l at 25.0°c and 150.0 kpa.

To solve this problem, we need to use the Ideal Gas Law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

First, we need to find the number of moles of freon-12 in the sample. We can use the formula n = PV/RT, where P = 150.0 kPa, V = 30.0 L, R = 8.31 J/mol-K, and T = 25.0 + 273 = 298 K. Plugging in these values, we get:

n = (150.0 kPa)(30.0 L)/(8.31 J/mol-K)(298 K) = 3.55 moles

Next, we need to find the volume of the freon-12 at STP (standard temperature and pressure). STP is defined as 0°C (273 K) and 1 atm (101.3 kPa). To find the volume at STP, we can use the formula V = nRT/P, where R and n are the same as before, but P = 101.3 kPa and T = 273 K. Plugging in these values, we get:

V = (3.55 moles)(8.31 J/mol-K)(273 K)/(101.3 kPa) = 75.3 L

Therefore, the volume of the freon-12 at STP is 75.3 L.

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Answer:

477.75cm^2

Explanation:

Area formula is L x W

27.3cm x 17.5cm = 477.75cm^2

Answer:

477.75

Explanation:

multiply one side by the other

Answer:

Electric current is electric charge in motion. It can take the form of a sudden discharge of static electricity, such as a lightning bolt or a spark between your finger and a ground light switch plate. ... Most electric charge is carried by the electrons and protons within an atom.

Explanation:

because it is