The 88 sectors into which astronomers today divide the celestial sphere (the whole sky) are called:___.

A and B are orthogonal vectors, so projab=0 and projab = b

If the vectors a and b are present in, then b is projected onto an as

[tex]proj_{a} b[/tex] = [tex]\frac{a.b}{a^{2} }[/tex]a.

​Suppose a and b are orthogonal vectors. Then  and

[tex]proj_{a} b[/tex][tex]=\frac{a.b}{a^{2} }=0[/tex]

Suppose a and b are parallel vectors. Then a scaler c exists such that b=cx and

[tex]proj_{a} b=[/tex][tex]=\frac{a.b}{a^{2} }=c\frac{a.b}{a^{2} } a=ca=b[/tex]

[tex]proj_{a} b=0\\proj_{a} b=b[/tex]

The term "orthogonal unit vectors" refers to a collection of vectors that are mutually perpendicular to one another, that is, they intersect at an angle of 90° with a magnitude of one unit. Since Cos90 is zero, the dot product of an orthogonal vector is always zero.

Two orthogonal vectors have a zero dot product. The zero dot product of the two column matrices that represent them. It only matters in relation to orientation. In the case of orthogonal vectors, the dot product is zero.

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In the photoelectric effect, a beam of light impinges on metal, and it is observed that electrons are ejected from the metal in greater numbers as the intensity of light increases.

In physics, the photoelectric effect refers to a phenomenon in which the emission of charged particles takes place from a material or substance after absorbing electromagnetic radiation.

When light hits the surface of the material then electrons are released known as photoelectrons.

This phenomenon better explains the quantum nature of electrons and light.

Moreover, the study of the dual nature of wave particles has further expanded the scope, investigation, and understanding of the matter.

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There are 2501.3m³ in 88,263 ft³ the Olympic swimming pool.

Along with arithmetic, geometry is one of the oldest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions. Geometer is the term used to describe a mathematician who specializes in geometry.

The area of mathematics known as geometry is concerned with the characteristics of the surrounding environment as well as the shapes of particular objects and their spatial relationships.

swimming pool is approximately 88,263 ft³

assume there are 3.28 ft in 1 meter.

Now ,

Given that :

3.28ft = 1m

1 ft = 1/(3.28)m

So,

1 ft = (1/3.28)³m³

88,263 ft³ = 88263/(3.28)³

                = 2501.3m³

There are 2501.3m³ in the Olympic swimming pool.

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The reason why voltage across the inductor and capacitor can have higher magnitudes than that of input source voltage is because of electrical energy's oscillation between magnetic and electric field.

When current passes through an inductor a magnetic field is produced and the collapsing magnetic field produced by the inductor charges the capacitor. This process repeats itself causing the electrical energy to oscillate between magnetic and electric field. Because of this oscillation, at resonance, voltage across the inductor and capacitor can be greater than the input voltage.

For a RLC circuit,

[tex]V_{s}[/tex] = [tex]\sqrt[]{V_{R}^{2} + (V_{L} - V_{C})^{2} }[/tex]

where,

[tex]V_{R}[/tex] = Voltage across the Resistor

[tex]V_{L}[/tex] = Voltage across the inductor

[tex]V_{C}[/tex] = Voltage across the capacitor

At resonance,

[tex]V_{L}[/tex] = [tex]V_{C}[/tex]

Therefore, the reason why voltage across the inductor and capacitor can have higher magnitudes than that of input source voltage is because of electrical energy's oscillation between magnetic and electric field.

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Answer:

Fail-close

Explanation:

A failed open switch is a switching device (be it mechanical, relay, semiconductor) that has lost it's switching capabilities (it's defective) and the switched contacts are now constantly open (disconnected) regardless of the control signal to the switch.

Similarly a failed closed switch is the same just with the contacts connected through.

An inert atmosphere was obtained by adding nitrogen in a room that measures 11.0 ft x 11.0 ft and has a 8.00 ft ceiling. The number of liters of nitrogen that were used to fill the room is : (D) 2.74 x 104  Liters.

The number of liters of nitrogen that were used to fill the room

= Volume of room in cm3 x 1 Liters / 103 cm3

Volume of room in cm3 = 11.0 ft x  (30.48 cm / 1 ft) x  11.0 ft x  (30.48 cm / 1 ft) x 8.00 ft x (30.48 cm / 1 ft)

= 27410707.501 cm3  or 2.741 x 107 cm3

And since  1 Litres = 103 cm3

Volume of room in cm3  = 2.74 x 107 cm3

Now putting these values in the above equation we get

So, the number of liters of nitrogen that were used to fill the room

= Volume of room in cm3 x 1 Liters / 103 cm3

= 2.74 x 107 cm3  x 1 Liters / 103 cm3

= 2.741 x 104  Liters

Thus, an inert atmosphere was obtained by adding nitrogen in a room that measures 11.0 ft x 11.0 ft and has a 8.00 ft ceiling. The number of liters of nitrogen that were used to fill the room is 2.74 x 104  Liters.

The area of the walls is 2 ,160 ft ²

we know that,

The area of the walls is =  perimeter of the conference room *   the height of the ceiling

So,

A = 2 (40 + 50 ) (12)

A = 2 , 160ft²

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You could double the charge to 2Q in order to double the size of the field at P.

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This system's potential energy changed by 40 J.

Energy = charge * potential difference

=> Energy = (8v)*5

=> Energy = 40 J

Hence the answer is 40 J.

Potential difference, often known as voltage, is equal to the amount of current times the resistance. One Joule, or one Volt, of energy is required for one Coulomb of charge to flow from one place in a circuit to the another.

V=U q, The change in the potential energy of a charge q transported from point A to point B, divided by the charge, is what is used to determine the electric potential difference between points A and B, or VBVA. The joules per coulomb unit of the potential difference is called the volt (V).

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By uniform motion, the distance traveled is 11.24 meters.

We need to know about the uniform motion to solve this problem. The uniform motion is the motion of an object which has acceleration applied. It can be determined as

vt = vo + a . t

vt² = vo² + 2a . s

s = vo . t + 1/2 . a . t²

where vt is final velocity, vo is initial velocity, a is acceleration, t is time interval and s is displacement.

From the question above, we know that:

a = 1.25 m/s²

vo = 0 m/s

vt = 5.3 m/s

By using the second equation, we can calculate the distance

vt² = vo² + 2a . s

5.3² = 0² + 2 . 1.25 . s

2.5s = 28.09

s = 11.24 m

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An ethical dilemma​ describes a conflict between two morally correct courses of action.

Being able to reason effectively and logically about what to believe or do is known as critical thinking. It comprises the capacity for independent and thoughtful thought. These are some examples of what someone with critical thinking abilities can do:

The ability to think clearly and rationally is crucial whatever we choose to undertake. It should go without saying that critical thinking is crucial if you work in the fields of education, research, business, law, or management.

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Volume occupied by the drops is 0.46 cm^3

Given:

no. of drops of oil = 20 drops

mass of 20 drops = 407.7 mg

Density of 20 drops = 0.875g/cm3

To Find:

Volume occupied by the drops

Solution:

Density is define as mass per unit volume

by using the formula we can find volume

Density = mass/volume

0.875 = 0.4077 gram/ volume

Volume = 0.4077 gram/0.875 = 0.46 cm^3

Hence, volume occupied by 20 oil drops is

0.46 cm^3

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The apparent visual magnitude difference between the Star A is higher.

A star's apparent magnitude, or m, indicates how brilliant the star appears when it is far away from Earth. The scale is logarithmic and "backwards." Stars with larger magnitudes are also fainter stars. Be aware that brightness is another word for the flux of light that is coming at us and is measured in Watts per square meter.

The brightness of a star or other celestial object as seen from Earth is expressed in terms of apparent magnitude. The apparent magnitude of an object is determined by its inherent luminosity, its distance from Earth, and any light extinction brought on by interstellar dust in the path of the observer's line of sight.

The brightness of a star or other celestial object perceived from Earth is measured in apparent magnitude (m). The apparent magnitude of an object is determined by its inherent luminosity, its distance from Earth, and any light extinction brought on by interstellar dust in the path of the observer's line of sight.

The apparent visual magnitude difference between the Star A is higher.

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Using the Newton's second law the net force of the runner is 131.25 N

To solve this exercise the formula for net force and the formula for uniformly varied rectilinear motion (UVRM) to be applied are:

Where:

Information about the problem:

Applying the formula for UVRM we can calculate the acceleration of the runner:

a = (vf - vi) /t

a = (7 m/s - 0 m/s) / 4s

a = 7 m/s / 4s

a = 1.75 m/s²

With the acceleration we can apply the net force formula and get:

F = m * a

F = 75 kg * 1.75 m/s²

F = 131.25 N

It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.

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sine wave or sinusoidal wave -

sine wave can be described as a geometric waveform that oscillates periodically.

It retains its wave shape when added to the another sine wave of the same frequency.

It is a continuous wave.

the general form of sine wave is

y = asin(bx)

where

amplitude is the maximum displacement from its mean position to extreme position.

Periodicity is a repeating continuous pattern which determine its wavelength and frequency.

Frequency of sine wave.

1kHz that is sine wave goes through thousand complete cycle in one second.

Speed of sine wave.

Speed = frequency x wavelength

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The correct answer is 369.2765m

Speed of tortoise = v_t= 16.3cm/s=0.163m/s

Speed of hare= v_h=220.2cm/s=2.202m/s

Rest time of hare is t_r=1.6min

Tortoise wins by distance of x = 108cm=1.08m

Consider that S is the length of a racetrack.

At the conclusion of the race, calculate the tortoise's distance travelled.

S=v_t×t

S=0.163m/s×t ______(1)

Here, t is the race's actual time.

Find out how long the hare spent racing.

t_h=t-t_r

t_h=t-1.6min×(60s/1min)

t_h=(t-2160)s

At the conclusion of the race, determine the hare's distance travelled.

S-x=v_h×t_h

S-1.08m=2.2×(t-2160)s

S=2.2×(t-2160)s+1.08m_____(2)

To determine the race time, substitute equation (1) for equation (2).

0.163m/s×t=S=2.2×(t-2160)s+1.08m

0.163t=2.26t-4752+1.08

4752-1.08=2.26t-0.163t

4750.92=2.097t

4750.92/2.097=t

2265.5=t

To determine the length of the race or the track, substitute the amount of time in equation (1).

S=0.163m/s×t

S=0.163×2265.5

S=369.2765m

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A high-mass star has layers that are arranged in order of b. Temperature for fusion.

The temperature at which a substance transforms from a solid to a liquid is known as its melting point. The solid and liquid phases are in equilibrium at the melting point. Pressure affects a substance's melting point, which is typically reported at a standard pressure such 1 atmosphere or 100 kPa. There are two main categories of fusion reactions: those that maintain the ratio of protons to neutrons and those that convert protons to neutrons. The solid-liquid and liquid-to-gas transitions are connected with the typical heats of fusion and vaporization, respectively, for each substance.

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The electric potential at point p is 86.53 KV

We know that,

Electric potential V = kQ / r

where,

k = Coulomb's constant

Q = Point charge

r = Distance

Given that,

r = 24 cm = 0.24m

Q = 2.31 mC = 2.31 * [tex]10^{6}[/tex] C

k = 8.99 * [tex]10^{9}[/tex] N [tex]m^{2}[/tex] / [tex]C^{2}[/tex]

V = ( 8.99 * [tex]10^{9}[/tex] * 2.31 * [tex]10^{6}[/tex] ) / 0.24

V = 86.53 KV

Electric potential is the amount of work energy required to move a unit charge from a reference point to a specific point inside an electric field. It is a scalar quantity.

Therefore, the electric potential at point p is 86.53 KV

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The strength of this electric field is 10.64×10⁸ N/C.

Electric field strength is a quantitative expression of the intensity at a particular location of a electric field.

It is a vector quantity.

Electrostatic force on the  charge :

[tex]F_{e} = mg[/tex]          (equation1).

m = mass

g = gravity

electrostatic force of a charge on an electric field :

[tex]F_{e} = Eq[/tex]           (equation2).

E = magnitude of electric field

q = charge

using equation 1 and 2 we get

Eq = mg

m = 1.67×10⁻²⁷ kg

g = 10.2 m/s²

q = 1.6 ×10⁻¹⁹

E = mg/q

     =  1.67×10⁻²⁷ kg ×10.2 m/s² /  1.6 ×10⁻¹⁹ C

     E= 10.64×10⁸ N/C

The strength of this electric field is 10.64×10⁸ N/C.

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The work done in the isothermal process is 10 joule.

We need to know about the isotherm process to solve this problem. The isotherm process can be described as a process where the initial temperature system will be the same as the final temperature. Hence, the internal energy change will be zero.

ΔU = 0

Hence,

ΔU = Q - W

0 = Q - W

Q = W

It means that the heat transferred is the same as the work done.

From the question above, we know that the heat transferred is 10 joule. Thus, the work done in the isothermal process is 10 joule.

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The compound f is increasing at the rate of 0.46 mol per second.

The number of moles of a compound is defined as the mass of the compound divided by its molecular mass. The SI unit of the number of moles is mol. The number of moles is represented by the symbol 'n'.

[tex]Number \: of \: moles = \frac{ Mass}{ Molecular \: mass}[/tex]

[tex]n = \frac{m}{M} [/tex]

The balanced equation for the reaction is,

2 d (g) + 3 e (g) + f (g) => 2 g (g) + h (g)

In the reaction, 3 moles of compound e are consumed to give 2 moles of compound g.

For 1 mole of compound e consumed to form =

[tex] \frac{2}{3} \: moles \: of \: g \: formed.[/tex]

The compound e is decreasing at the of = 0.69 mol/s

So, the rate at which g is increasing is,

[tex] = \frac{2}{3} \times 0.69[/tex]

[tex]= 0.46 \: mol/ s[/tex]

Therefore, compound f is increasing at the rate of 0.46 mol per second.

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The true airspeed will increase and true altitude will increase.

True airspeed is the airspeed of an aircraft relative to undisturbed air.

It's the aircraft speed relative to the airmass in which it's flying.

If the outside air temperature increases during a flight at constant power and at a constant indicated altitude, the true airspeed will increase and true altitude will increase.

Thus, the true airspeed will increase and true altitude will increase.

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3000 N of friction exists between the bear and the tree.

How does friction force work?

Between solid surfaces, there are three basic types of friction:

Explanation:

The bear goes down at a constant speed, thus there is no acceleration. The forces add up to zero. As a result, upward friction and downward weight result in zero  

i.e.,

F-mg=0

F = mg

F = (300 kg)/10 [tex]m/s^{2}[/tex] (gravitational acceleration)

3000 N frictional force equals F.

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The acceleration of this item will remain constant if I double the force and double the mass.

The rate at which a moving object's speed and direction change over time. When something moves faster or slower, it is considered to be accelerating. Motion on a circle accelerates even while the speed is constant because the direction is always changing.

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The density of galena is 7.56 g/cm³.

We need to know about the density to solve this problem. Density can be described as how much the mass is in a volume unit. It can be written

ρ = m / V

where ρ is density, m is mass and V volume

From the question above, we know that

m = 12.4 g

V = 1.64 cm³

By substituting the given parameter, we can calculate the density

ρ = m / V

ρ = 12.4 / 1.64

ρ = 7.56 g/cm³

Hence, the density of galena is 7.56 g/cm³.

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The answer is 4.96 * 10⁻¹⁹ kg m / s

Proton is an elementary particle that is identical to the nucleus of the hydrogen atom, along with the neutron is a constituent of all other atomic nuclei, that carries a positive charge numerically equal to the charge of an electron, and has a mass of 1.673 × 10−27 kilogram

nonrelativistic equation for the magnitude of the momentum of the proton is p = m * v

Then: p = m * v

Then Let's calculate its value

            After that p = 1.67 * 10⁻²⁷ * 0.99 * 3 * 10⁸

            Now, p = 4.96 * 10⁻¹⁹ kg m / s

hence the answer is 4.96 * 10⁻¹⁹ kg m / s

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Left of z = 0.49 and right of z = 2.05, the area underneath the standard normal curve is equal to 0.7081.

The horizontal axis is approached by the standard normal bend as it extends indefinitely both in directions without ever being touched by it. The center of the bell-shaped, z=0 standard normal curve. Between z=3 and z=3, almost the entire area underneath the standard normal curve is located.

Use the normal distribution's standard form to calculate probability. Since the standard normal distribution is indeed a probability distribution, the probability that a variable will take on a range of values is indicated by area of the curve between two points. 100% or 1 is the total area beneath the curve.

the region to the left of the standard normal curve,

z=0.49

To the right of,

z = 2.05

So,

The area will be:

= P[z < 0.49] + P[ z >2.05]

= P[z < 0.49] + 1 -  P[ z < 2.05]

= .6879 + 1 - .9798

= 0.7081

Left of z = 0.49 and right of z = 2.05, the area underneath the standard normal curve is equal to 0.7081.

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I understand that the question you are looking for is:

Find the area under the standard normal curve to the left of z = 0.49 and to the right of z = 2.05. Round your answer to four decimal places, if necessary.

A short to voltage failure would occur if the copper conductors of two insulated wires came into contact and melted together.

The difference in electric potential between two points, also known as voltage, electric potential difference, electric pressure, or electric tension, is measured as the amount of work required to move a test charge per unit of energy between the two sites.

The formula reads voltage = current x resistance, or V = A x, or volts = amps x ohms.

Electrical services are categorized:

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The race car that is moving at 40.0 m/s around a circular racetrack of radius 265 m has a period of motion of 41.63 s

To solve this tangential velocity problem the formula and the procedure we will use is:

v = (2 * π * r) / T

Where:

Information about the problem:

Applying the tangential velocity formula and isolating the period, we get:

v = (2 * π * r)/ T

T = (2 * π * r)/ v

T = (2 * 3.1416* 265 m) / 40.0 m/s

T = (1665.04 m) / 40.0 m/s

T = 41.63 s

In physics is the length of arc traveled in each unit of time in uniform circular motion. It is expressed in units of distance per time (m/s), (km/h).

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