Perhaps the greatest of the Greek astronomers, Hipparchus compiled the first catalog of stars, 49) accurately measured their positions, and defined the basic system of stellar brightnesses which we now call the magnitude system. A particular star in his catalogue has an apparent magnitude of 4 and an absolute -12. Determine the distance to the star.

Answer:

A. Increases

Explanation:

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Answer:

f = 4.67 cm

Explanation:

Here, we can use the thin lens formula, as follows:

[tex]\frac{1}{f}= \frac{1}{p}+ \frac{1}{q}\\\\[/tex]

where,

f = focal length of lens = ?

p = distance of object from lens = 12.4 cm

q = distance of image from lens = 7.5 cm

Therefore,

[tex]\frac{1}{f} =\frac{1}{12.4\ cm} +\frac{1}{7.5\ cm}\\\\\frac{1}{f} = \frac{1}{4.67\ cm}[/tex]

f = 4.67 cm

Answer:

Gy = 3.14x10⁻⁴ Gy

Explanation:

To get the dose in Gy we need to use the following expression:

Gy = E / m  (1)

Where:

Gy: dose

E: energy absorbed per atom

m: mass of the human body.

We don't have the energy per atom, but we can calculate that by following the next procedure.

First, let's determine the number of atoms of potassium in our body. For that we need to determine the moles in the 140 g of potassium, with the molecular mass and then, use the avogadro's number:

moles = m/MM

moles = 140 / 39.1 = 3.58 moles

N° atoms = 3.58 * 6.02x10²³ atoms = 2.16x10²⁴ atoms of K.

The abundance of the ⁴⁰K is 0.012% so the atoms of this isotope would be:

N = 2.16x10²⁴ * (0.012/100) = 2.59x10²⁰ atoms of ⁴⁰K.

With this number, and the half life rate, we can determine the number of decay atoms in a year (λ) using the following expression:

λ = ln2 / t(1/2)

λ = ln2 / 1.3x10⁹ = 5.33x10⁻¹⁰ year⁻¹

This number, multiplied by the number of atoms:

R = 5.33x10⁻¹⁰ * 2.59x10²⁰ = 1.38x10¹¹ atoms/year

Now, each atom of K gives an average energy of 1 MeV, so with the atoms we have:

E = 1.38x10¹¹ * 1x10⁶ eV = 1.38x10¹⁷ eV

This value can be expressed in Joules so:

E = 1.38x10¹⁷ eV * (1 J / 6.24x10¹⁸ eV) = 0.022 J

Finally, we can use (1) to get the dose in Gy:

Gy = 0.022 / 70

Hope this helps

Answer:

5.0-5.5 is the answer to your question

Answer:

D

Explanation:

Answer:

upward

Explanation:

In the electromagnetic system of force if the direction of motion of proton does not changes it means that the electric and magnetic forces are such a ways that they are cancelling each other's effect.

Since, electric field lines will exert a force on the proton to the west, hence, the magnetic force must force it to the east. It is well known that magnetic force acts perpendicular to the direction of magnetic field.  magnetic field should point upward direction.

Answer:

Solution given:

Radius of small sphere[r]=5cm=0.05m

Radius of large sphere[R]=10cm=0.1m

capacitance of small sphere[c]=4πε0r

=[tex]4π*8.85×10^{-12}×0.05=5.56*10^{-12}F[/tex]

Charge for small sphere[Q1]=100C

Charge for small sphere[Q2]=50C

Potential difference [V1]=[tex] \frac{charge}{capacitance}=\frac{100}{5.56*10^{-12}}=1.8×10^{13}[/tex]V

.

again

capacitance of small sphere[C]=4πε0R

=[tex]4π*8.85×10^{-12}×0.1=1.11*10^{-11}F[/tex]

Potential difference [V2]=[tex] \frac{charge}{capacitance}=\frac{50}{1.11*10^{-11}}=4.5×10^{12}[/tex]V

Now

Loss of energy:

[tex] \frac{cC(V1-V2)^{2}}{2(c+C)}[/tex]

=[tex] \frac{5.56*10^{-12}*1.11*10^{-11}(1.8*10^{13}-4.5*10^{12})^{2}}{2(5.56*10^{-12}+1.11*10^{-11})}[/tex]

=25Joule

B. The energy transformation that is correct is From C to D, kinetic energy is transformed into gravitational potential energy.

The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another.

Energy transformation in the pendulum;

Thus, the energy transformation that is correct is From C to D, kinetic energy is transformed into gravitational potential energy.

option B is the correct answer.

Learn more about energy transformation here: https://brainly.com/question/2667612

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Answer:

B is Correct

Explanation:

From C to D, kinetic energy is transformed into gravitational potential energy.

Answer:

C

Explanation:

edge 2020... Using elimination it's the only one that makes sense.

The statement third "an increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass" is correct.

The gravitational force is a force that attracts all mass-bearing objects. The gravitational force is referred to as attractive because it always strives to pull masses together rather than pushing them apart.

As we know, the gravitational force is given by:

[tex]\rm F = \dfrac{Gm_1m_2}{r^2}[/tex]

Where, G is the gravitational constant.

m1 and m2 are masses.

r is the distance between the masses.

From the data given in the table, shows that:

The gravitational force is indirectly proportional to the square of the distance.

Thus, the statement third "an increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass" is correct.

Learn more about the gravitational force here:

https://brainly.com/question/12528243

#SPJ2

Answer:

ω = 0.05 rad/s

Explanation:

In order to produce the acceleration equal to the acceleration due to gravity at the surface of Earth, the centripetal acceleration must be equal to the value  of g:

[tex]a_c = g\\g = \frac{v^2}{r}\\\\but,\ v=r\omega\\therefore,\\\\g = \omega^2r\\\\\omega = \sqrt{\frac{g}{r}}[/tex]

where,

ω = angular speed = ?

g = acceleration due to gravity on the surface of the Earth = 9.81 m/s²

r = radius of cylinder = 8 km/2 = 4 km = 4000 m

Therefore,

[tex]\omega = \sqrt{\frac{9.81\ m/s^2}{4000\ m}}[/tex]

ω = 0.05 rad/s

Answer

the wavelength is 90

Explanation:

Answer:

Alternating voltage leads to electromagnetic induction which is necessary for the transformer to work.

Explanation:

According to Oxford dictionary; an alternating current is "an electric current that reverses its direction many times a second at regular intervals".

A transformer works on the principle of electromagnetic induction. A transformer requires an alternating current which can create a changing magnetic field leading to induced voltage in the coil.

Hence, a transformer requires alternating voltage because alternating voltage leads to electromagnetic induction which is necessary for the transformer to work.

Answer:

i have no idea i came here to find out too :(

Explanation:

Answer:

Explanation:

Density = Mass / Volume = 850 / 40*10*5 = 0.425 g /cm^3

Answer and Explanation:

The answer is the second answer choice. This is because we humans can rebuild or build memories during the day, it doesn't have to happen via sleep.

The first answer choice IS a reason because you aren't working your brain as hard, so your brain has time to heal. A mouse study suggests that sleep helps restore the brain by flushing out toxins that build up during waking hours.

The third answer choice IS a reason because of the idea of Wish Fulfillment: Sigmund Freud suggested that dreams provide a psychic safety valve to discharge unacceptable feelings. The dream's manifest (apparent) content may also have symbolic meanings (latent content) that signify our unacceptable feelings.

The forth answer choice IS a reason because of the idea of Cognitive Development: Some researchers argue that we dream as a part of brain maturation and cognitive development.

#teamtrees #PAW (Plant And Water)

Answer:

The correct answer is -

B. The velocity would double (v = 2v).

C. The wavelength would be half (λ = λ/2).

Explanation:

A wave has a speed or velocity that is related to the wavelength of the wave and the frequency of the wave and this relationship can be represented by the following equation-

Wave velocity V = Wavelength (λ) * Frequency (f)

Frequency (f) = Velocity (V) / Wavelength(λ).

The frequency and wavelength are inversely proportional and frequency and velocity are directly proportional to each other.

So, if f = 2f then,

putting value in the formula,

2f = 2v/λ, which means, f = 2v and f = λ/2

when the frequency is doubled, the wavelength will be halved and velocity will be doubled.

Answer: 0.390625 grams

Explanation:

A half-life of an element is the amount of time that it takes for half the mass of the element to decay.

Gold-198 having a half-life of 2.5 days therefore means that every 2.5 days, the mass is cut in half.

If there are 20 days, find out how many half-life periods there are:

= 20 / 2.5

= 8 periods

The half life is:

= Original mass * 0.5^number of half-life periods

= 100 * 0.5⁸

= 0.390625 grams

Answer:

a. True

Explanation:

The law of conservation of Energy states that energy cannot be destroyed but can only be converted or transformed from one form to another. Therefore, the sum of the initial kinetic energy and potential energy is equal to the sum of the final kinetic energy and potential energy.

Mathematically, it is given by the formula;

Ki + Ui = Kf + Uf .......equation 1

Where;

Ki and Kf are the initial and final kinetic energy respectively.

Ui and Uf are the initial and final potential energy respectively.

The First Law of Thermodynamics is another way to describe the Law of Conservation of Energy. Typically, the First Law of Thermodynamics states that the change of internal energy of a system is equal to the sum of external work and heat spent on the system.

Mathematically, the First Law of Thermodynamics is given by the formula;

ΔU = Q − W

Where;

ΔU represents the change in internal energy of a system.

Q represents the net heat transfer in and out of the system.

W represents the sum of work (net work) done on or by the system.

Hence, the direction in which any thermodynamic process in nature can spontaneously occur isn't stated by the First Law of Thermodynamics.

Answer:

a. ε = 21,014sin(120πt) V

b. 0.476cosec(120πt)  

Explanation:

a. Induced emf

We know the induced emf, ε = -dΦ/dt where Φ = magnetic flux through coil = NABcosθ where N = number of turns of coil =, 100, A = area of coil = 10 ft × 6 ft = 60 ft² = 60 × 1 ft² = 60 × (0.3048)² m² = 5.574 m², B = magnetic field strength = 0.1 T and θ = angle between B and normal to A = ωt.

So, Φ = NABcosθ = 100 × 5.574 m² × 0.1 T cosθ  = 55.74cosθ Tm²

So, ε = -dΦ/dt = ε = -d(55.74cosθ Tm²)/dt = -d(55.74cosθ Tm²)/dθ × dθ/dt = -55.74 ×(-sinθ) Tm²)/dθ × ω (ω = dθ/dt = angular frequency of shaft = 2πf where f = frequency of rotor = 60 Hz )

ε = 55.74sinθ Tm²) × 2πf

ε = 55.74sinθ Tm²) × 2π(60 Hz)

ε = 6689πsinθ V

ε = 21,014sinθ V

ε = 21,014sinωt V

ε = 21,014sin(2πft) V

ε = 21,014sin(2π(60 Hz)t) V

ε = 21,014sin(120πt) V

b. Current in coil

Since power P = Iε where I = current and ε = induced emf = 21,014sinθ V.

Since power, P = 10 kW = 10000 W

I = P/ε

= 10000 W/21,014sinθ V

= 0.476/sinθ

= 0.476cosecθ

= 0.476cosecωt

= 0.476cosec(120πt)  

The maximum current is obtained when θ = 90°

I =  10000 W/21,014sin90 V

I = 10000 W/21,014 V

I = 0.476 A

I = 476 mA

Answer:

A)    q₂ = 75.98 cm, B)     q₂' = 115.38 cm, C)

Explanation:

A) This is an exercise in geometric optics, as the two lenses are separated by a greater distance than their focal lengths from each lens, they must be worked as independent lenses.

Lens 1. More to the left

let's use the constructor equation

         [tex]\frac{1}{f} = \frac{1}{p} + \frac{1}{q}[/tex]

where f is the focal length, p and q are the distance to the object and the image, respectively,

We must assume a distance to the object to perform the calculation, suppose that the object is 50 cm from lens 1 that is further to the left of the system.

          [tex]\frac{1}{q_1} = \frac{1}{f} - \frac{1}{p}[/tex]

         [tex]\frac{1}{q_1} = \frac{1}{14.8} - \frac{1}{50}[/tex]  

          1 / q₁ = 0.04756

           q₁ = 21.0227 cm

this image is the object for the second lens that has f₂ = 14.8 cm

the distance must be measured from the second lens

          p₂ = 39.4 -q₁

          p₂ = 39.4 -21.0227

          p₂ = 18.38 cm

let's use the constructor equation

            1 / q₂ = 1 / f - 1 / p2

             [tex]\frac{1}{q_2} = \frac{1}{14.8} - \frac{1}{18.38}[/tex]

            [tex]\frac{1}{q_2}[/tex] = 0.01316

            q₂ = 75.98 cm

measured from the second lens

B) the position of the final image with respect to the first lens is

            q₂’= q₂ + 39.4

             q₂'= 75.98 +39.4

              q₂' = 115.38 cm

C) the magnification of a lens is

              m = - q / p

in this case the image measured from lens 2 is q2 = 75.98 cm

the distance to the object from the first lens is p1 = 50cm

          m = - 75.98 / 50

          m = -1.5 X

the negative sign indicates that the image is inverted

Answer:

E = 1.45 x 10⁹ J = 1.45 GJ

Explanation:

According to the law of conservation of energy:

Potential Energy Lost by Satellite = Kinetic Energy + Internal Energy

[tex]mgh = \frac{1}{2} mv^2 + E\\\\E = mgh - \frac{1}{2} mv^2[/tex]

where,

E = Internal Energy = ?

m = mass = 400 kg

g = acceleration due to gravity = 9.81 m/s²

h = height = 500 km = 500000 m

v = speed on ground = 1.6 km/s = 1600 m/s

Therefore,

[tex]E = (400\ kg)(9.81\ m/s^2)(500000\ m)-\frac{1}{2} (400\ kg)(1600\ m/s)^2\\E = 1.962\ x\ 10^9\ J - 0.512\ x\ 10^9\ J[/tex]

E = 1.45 x 10⁹ J = 1.45 GJ

Answer:

 y_lower = 0.915 m,   y_superior = 1,905 m

Explanation:

In this exercise we use the law of reflection for a flat mirror.

         θ’= θ

To see the feet of the person a ray of light that part of them must reach the bottom of the mirror and its reflection has to reach the eyes.

As the law of reflection the incident and reflected angles are equal, the distance from the floor to the point where the two rays (incident and reflected) touch the mirror must be symmetrical, oses from the floor

           y = 1.83 / 2

           y = 0.915 m

To see the head, a ray of light that comes from the tip of the head and is reflected in the mirror must reach the eyes. As the head is 0.15 m above the eyes and the incident and reflected rays have the same angle, the mirror must be at half the height, that is, the mirror is 0.075 m below the tip of the head.

In summary

* the bottom of the mirror is 0.915 m from the ground

* the top of the mirror is at 1.83 + 0.075

                 y_superior = 1,905 m

ground

Answer:

P = 756.84 Watts

Explanation:

As the tension is stationary or innitial, T₀ = 31 N, the mean would be:

T₁ + T₂ / 2 = T₀    (1)

T₁ + T₂ = 2 * 31 = 62 N

Now, with the following expression we can determine the linear speed:

V = πWD  (2)

W: angular speed of the wheel  (rev/s)

D: diameter of the wheel (in meters)

W = 1547 rev/min * (1 min/60 s) = 25.78 rev/s

V = π * 25.78 * 0.379 = 30.695 m/s

We also know that:

T₁ / T₂ = exp (μθ)

T₁ = T₂ exp(μθ)   (3)

We already have those values so replacing:

T₁ = T₂ exp(0.3 * 161 * π/180)

T₁ = 2.32T₂   (4)

We can now replace (4) in (1) like this:

T₁ + T₂ = 62 N

2.32T₂ + T₂ = 62

3.32T₂ = 62

T₂ = 18.67 N

Which means that T₁:

T₁ = 2.32(18.67)

T₁ = 43.33 N

Finally, the power can be determined using the following expression:

P = (T₁ - T₂)V  (5)       Replacing we have:

P = (43.33 - 18.67)*30.695

Hope this helps

Answer:

convex       f = 33 cm

concave     f = -33 cm

Explanation:

In geometric optics the focal length of a lens is given by

         [tex]\frac{1}{f} = ( n-1) \ (\frac{1}{R_2} - \frac{1}{R_1} )[/tex]

where n is the refractive index of the medium, R₁ and R₂   are the focal lengths on each side of the lens.

In this case one of the sides is flat so its focal length is infinite, if the lens is convex the focal length is positive, convergent lens and if it is concave the focal length is negative, divergent lens.

         [tex]\frac{1}{f} = (n-1) \ \frac{1}{R}[/tex]

the refractive index of the glass is n = 1.5

let's calculate

         1 / f = (1.5 -1) 1 / 16.5

         1 / f = 0.03030

          f = 33 cm

convex       f = 33 cm

concave     f = -33 cm

Answer:

DragonFly or a dog

Explanation:

Answer:

The total resistance is 106 Ω and the current in the circuit is 0.11 A.

Explanation:

Given that,

Voltage of the battery, V = 12 V

Resistors 34 Ω, 42Ω, and 30Ω are connected in series.

The total resistance is given by :}

R = 34 + 42 +30

= 106Ω

Let I is the total current in the circuit. Using ohm's law to find it such that,

[tex]I=\dfrac{V}{R}\\\\I=\dfrac{12}{106}\\\\I=0.11\ A[/tex]

Hence, the total resistance is 106 Ω and the current in the circuit is 0.11 A.