Which runner finished the 100 m race in the least amount of time?
Ming



Which runner stopped running for a few seconds during the race?



At what distance did Anastasia overtake Chloe in the race?

The electron's distance from the nucleus in the 1s state of a hydrogen atom is A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * (∫ e^(-2r/a) dr)^2] from 0 to ∞ = [(r * (a^3 / 4√π) * (a/2)) - (a^3 / 4√π) * (a/2)^2].

To find the expectation value of the electron's distance from the nucleus in the 1s state of a hydrogen atom, we need to calculate the quantity Ar, where A is given by:

A = ⟨r⟩ = ∫ r * ψ(1s) * r^2 dr from 0 to ∞

First, let's express ψ(1s) in terms of the radial wavefunction R(r):

ψ(1s) = R(r) * Y(0,0)  [Since the 1s state has azimuthal quantum number l = 0 and magnetic quantum number m = 0]

The radial wavefunction R(r) for the 1s state is given by:

R(r) = (1 / √π * a^(3/2)) * e^(-r/a)

Now, let's calculate A:

A = ∫ r * ψ(1s) * r^2 dr from 0 to ∞

 = ∫ r * (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr from 0 to ∞

We can use integration by parts to simplify this integral. Let's define u = r and dv = (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr.

Taking the differentials, we have du = dr and v = ∫ (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr.

Integrating v, we can use the given integrals:

v = ∫ (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr

 = (a^3 / 4√π) * ∫ e^(-2r/a) dr  [Using the given integral]

Now, applying integration by parts:

∫ u dv = uv - ∫ v du

∫ r * (1 / √π * a^(3/2)) * e^(-r/a) * r^2 dr

= (r * v) - ∫ v du

= (r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - ∫ [(a^3 / 4√π) * ∫ e^(-2r/a) dr] dr

Simplifying the expression:

A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * ∫ ∫ e^(-2r/a) dr dr] from 0 to ∞

The integral ∫ ∫ e^(-2r/a) dr dr can be expressed in terms of the given integrals:

∫ ∫ e^(-2r/a) dr dr = (∫ e^(-2r/a) dr)^2

                     = (a/2)^2   [Using the given integral]

Now, substituting the values and evaluating the limits:

A = [(r * (a^3 / 4√π) * ∫ e^(-2r/a) dr) - (a^3 / 4√π) * (∫ e^(-2r/a) dr)^2] from 0 to ∞

 = [(r * (a^3 / 4√π) * (a/2)) - (a^3 / 4√π) * (a/2)^2]

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Answer:

It cannot be constant because if it does not change and each time it increases its strength and speed.

Explanation:

Complete question is;

The frequency and wavelength of EM waves can vary over a wide range of values. Scientists refer to the full range of frequencies that EM radiation can have as the electromagnetic spectrum. Electromagnetic waves are used extensively in modern wireless technology. Many devices are built to emit and/or receive EM waves at a very specific frequency, or within a narrow band of frequencies. Here are some examples followed by their frequencies of operation:

garage door openers: 40.0 MHz

standard cordless phones: 40.0 to 50.0 MHz

baby monitors: 49.0 MHz

FM radio stations: 88.0 to 108 MHz

cell phones: 800 to 900 MHz

Global Positioning System: 1227 to 1575 MHz

microwave ovens: 2450 MHz

wireless internet technology: 2.4 to 2.6 GHz

Which of the following statements correctly describe the various applications listed above? Check all that apply.

a.) All these technologies use radio waves, including low-frequency microwaves.

b.) All these technologies use radio waves, including high-frequency microwaves.

c.) All these technologies use a combination of infrared waves and high-frequency microwaves.

d.) Microwave ovens emit in the same frequency band as some wireless Internet devices.

e.) The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.

f.) All these technologies emit waves with a wavelength in the range of 0.10 to 10.0 m.

g.) All the technologies emit waves with a wavelength in the range of 0.01 to 10.0 km.

Answer:

B, D, E, F are the correct statements.

Explanation:

Looking at the options;

A) This is true because radio waves are electromagnetic radiation being used today in television, mobile phones, radios and other areas of communication technologies. And the examples given to us fall in the category of technologies that use radio waves.

B) microwaves usually have long wavelengths and low frequencies. However, sometimes they could have high frequencies usually more than radio waves. Thus, this option is correct.

C) This option is wrong because it's not all the listed technologies that use combination of infrared waves and high-frequency microwaves.

D) we are given the frequency of microwave ovens as 2450 MHz.

Converting to GHz gives; 2.45 GHz.

We are told that wireless internet technology has frequency between 2.4 to 2.6 GHz. Thus, microwave frequency falls in the same range as wireless internet technology and thus the statement is true.

E) we know that wavelength is inversely proportional to frequency. This means that the higher the frequency, the shorter the wavelength.

In the frequencies given to us, wireless internet technology have the highest frequency which means they have the shortest wavelength. The statement is true.

F) from the frequencies given to us, the smallest is garage door openers = 40.0 MHz = 40 × 10^(6) Hz while the biggest is 2.6 GHz = 2.6 × 10^(9) Hz

Formula for wavelength is;

Wavelength = speed of light/frequency

Speed of light = 3 × 10^(8) m/s

Thus;

Wavelength = (3 × 10^(8))/(40 × 10^(6))

Or wavelength = (3 × 10^(8))/(2.6 × 10^(9))

So,wavelength = 7.5 m or 0.12 m

This falls into the given range of 0.10 to 10.0 m.

Thus, the statement is true.

Answer:

Initial velocity u = 60 ft/s

Explanation:

Given:

Deceleration a = -36 ft/s²

Distance covered s =50ft

Final  velocity v = 0 ft/s

Find:

Initial velocity u

Computation:

Using third equation of motion;

v² = u² + 2as

0² = u² + 2(-36)(50)

0 = u² - 3600

u² = 3600

u = 60 ft/s

Initial velocity u = 60 ft/s

No, because some scientist are bad and they must have a scientific attitude like honesty, curiosity, open-mindedness, optimistic and more. And they should follow others sometimes because for their own good.

Answer:

No

Explanation:

Science operates in the context of national and international laws, agreements and conventions. It requires scientists to conduct and communicate scientific work for the benefit of society, with excellence, integrity, respect, fairness, trustworthiness, clarity, and transparency.

Answer:

Cytoplasm

Explanation:

Answer:

A. it's got everything set.... correct connection

The setup that will light the bulb in the given different circuit diagram is circuit A, because it is the only circuit is that is closed.

A complete circuit or closed circuit is the circuit that will allow the flow of electric current through it.

When a circuit is closed or complete, the connection of the different components of the circuit is complete.

From the image given, only option A has complete connection of different components of the circuit.

Thus, the setup that will light the bulb in the given different circuit diagram is circuit A, because it is the only circuit is that is closed.

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(a) The magnitude of the wheels angular acceleration is 0.0088 rad/s².

(b) The magnitude of the tangential acceleration after the maximum operational speed is reached is 0.153 m/s².

The angular acceleration of the wheel is calculated as follows;

α = ω/t

ω = v/r

α = v/(rt)

α = (2.3)/(17.5 x 15)

α = 0.0088 rad/s²

a = v/t

a = (2.3)/15

a = 0.153 m/s²

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Answer:

The average speed throughout the journey was 76.36 kilometers per hour.

Explanation:

Given that a car driver spends 3hrs driving at an average speed of 80km / hr, stops for 30 minutes to have some rest, and then drives at an average speed of 90km / hr for 2 hours, to determine the average speed during the whole journey the following calculation must be performed:

80 km / h x 3 = 240 km

90 km / h x 2 = 180 km

240 + 180 = 420 km

3 + 2 + 0.5 = 5.5 hours

420 / 5.5 = 76.36

Thus, the average speed throughout the journey was 76.36 kilometers per hour.

Answer:

A main sequence star is powered by fusion of hydrogen into helium in its core

Explanation:

Answer:

In absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons in the matter. The electrons will absorb the energy of the light wave and change their energy state.

Explanation:

Answer:

i. 0.2 N ii. 30°

Explanation:

(i) Calculate the magnitude and direction of force on X, when a current of 4A is passed through it.

The magnetic force F = BILsinФ where B = magnetic field strength = 0.1 T, I = current = 4 A and L= length of conductor = 0.5 m. Since the conductor X of length 0.5m is held along the positive X-axis and situated in a uniform horizontal magnetic field of 0.1T which is pointing towards the positive Y-axis, both B and L are perpendicular to each other. So, Ф = 90°

So, F = BILsinФ

F = 0.1 T × 4 A ×0.5 m × sin90°

F = 0.1 T × 4 A ×0.5 m × 1

F = 0.2 N

(ii) Through what angle must X be turned in a vertical plane so that the force on X is halved

If F' = BILsinФ' where Ф'=the new angle, and BIL = F

F'/F = sinФ'

Since F'/F = 1/2

sinФ' = 1/2

Ф' = sin⁻¹(1/2) = 30°

Answer:

into the page

Explanation:

Since the uniform electric field is in the negative y direction so its is -E and the electron is travelling in the positive x direction, it experiences an electric force F = -e × -E = + eE, so the electric force is in the positive y direction. Now since the net force on the electron is zero in the region of the magnetic field, it follows that the direction of the magnetic force is opposite to that of the electric force. Since the electric force is in the positive y direction, the magnetic force is in the negative y direction.

By the right hand rule, since the magnetic force is in the negative y direction and the electron moves in the positive x direction, it follows that the magnetic field is in the positive z direction, into the page.

Answer:

1992.008J

Explanation:

Answer:

You can breathe in too much carbon monoxide, which will eliminate the flow of oxygen to your bloodstream and can kill you.

Explanation:

Answer:

I think you have a problem trying to write the question down, can you re write it because it seems glitched.

Explanation:

Answer:

  L₀ = L_f ,  K_f < K₀

Explanation:

For this exercise we start as the angular momentum, with the friction force they are negligible and if we define the system as formed by the disk and the clay sphere, the forces during the collision are internal and therefore the angular momentum is conserved.

This means that the angular momentum before and after the collision changes.

Initial instant. Before the crash

        L₀ = I₀ w₀

Final moment. Right after the crash

        L_f = (I₀ + mr²) w

we treat the clay sphere as a point particle

how the angular momentum is conserved

       L₀ = L_f

       I₀ w₀ = (I₀ + mr²) w

       w = [tex]\frac{I_o}{I_o + m r^2}[/tex]   w₀

having the angular velocities we can calculate the kinetic energy

starting point. Before the crash

        K₀ = ½ I₀ w₀²

final point. After the crash

        K_f = ½ (I₀ + mr²) w²

sustitute

        K_f = ½ (I₀ + mr²)  ( [tex]\frac{I_o}{I_o + m r^2}[/tex]   w₀)²

        Kf = ½  [tex]\frac{I_o^2}{ I_o + m r^2}[/tex]   w₀²

we look for the relationship between the kinetic energy

        [tex]\frac{K_f}{K_o}[/tex]=   [tex]\frac{I_o}{I_o + m r^2}[/tex]

       [tex]\frac{K_f}{K_o } < 1[/tex]

      K_f < K₀          

we see that the kinetic energy is not constant in the process, this implies that part of the energy is transformed into potential energy during the collision

Answer:

Distance travel by go-cart = 500 meter

Explanation:

Given:

Speed of go cart = 25 m/s

Time travel = 20 seconds

Find:

Distance travel by go-cart

Computation:

Distance = Speed x time

Distance travel by go-cart = Speed of go cart x Time travel

Distance travel by go-cart = 25 x 20

Distance travel by go-cart = 500 meter

Answer:

14 μm

Explanation:

The magnetic field due to a long straight wire is B = μ₀i/2πr where  μ₀ = permeability of free space = 4π × 10⁻⁷ H/m, i = current = 7.0 A and r = distance of credit card from magnetic field.

So r = μ₀i/2πB since B = 1000 gauss = 1000 G × 1 T/10000 G  = 0.1 T

r = 4π × 10⁻⁷ H/m × 7.0 A/(2π × 0.1 T)

r = 2 × 10⁻⁷ H/m × 7.0 A/0.1 T

r = 14 × 10⁻⁷ H/m × A/0.1 T

r = 140 × 10⁻⁷ m

r = 1.4 × 10⁻⁵ m

r = 14 × 10⁻⁶ m

r = 14 μm

The two chemical equations show double-replacement reactions are Ca(OH)2 + H2S04 - CaSO4 + 2H20 and Na2CO3 + H2S - H2CO3 + Na2S.

A double replacement reaction have two ionic compounds that are exchanging anions or cations.

From the given options, we can choose the following based on their exchange of anions or cations.

Thus, the two chemical equations show double-replacement reactions are Ca(OH)2 + H2S04 - CaSO4 + 2H20 and Na2CO3 + H2S - H2CO3 + Na2S.

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Answer: After fusing helium in its core to carbon, the Sun will begin to collapse again, evolving into a compact white dwarf star after ejecting its outer atmosphere as a planetary nebula. The predicted final mass is 54.1% of the present value, most likely consisting primarily of carbon and oxygen.

Answer: the Sun will begin to collapse

Explanation: "After fusing helium in its core to carbon, the Sun will begin to collapse again, evolving into a compact white dwarf star after ejecting its outer atmosphere as a planetary nebula. The predicted final mass is 54.1% of the present value, most likely consisting primarily of carbon and oxygen."

Answer:

the time taken for the motor to lift the object is 21.17 s.

Explanation:

Given;

mass of the object, m = 45 kg

height through which the object was lifted, h = 9.0 m

electrical power used by the motor, P = 750 W

Efficiency of the electrical motor, n = 25% = 0.25

The electrical energy used by the motor in lifting the object is calculated as;

E = P x t

where;

t is the time taken for the motor to lift the object

E = 750 x t

E = 750t

The electrical energy converted by the motor to mechanical energy is calculated as;

P.E = 0.25(750t)

P.E = 187.5t

Recall, P.E = mgh

mgh = 187.5t

45 x 9.8 x 9 = 187.5t

3969 = 187.5t

t = 3969/187.5

t = 21.17 s

Therefore, the time taken for the motor to lift the object is 21.17 s.

Answer:

1.78×10×10^10 electron

Explanation:

Electric field outside the sphere can be calculated using below expression

E= kq/ r^2..........eqn(1)

Where k= 9 × 10^9 NM^2/C^2

q= charge

E= 1440 N/C

Diameter= 30.0 cm= 0.3 m

r= radius= 0.3/2= 0.15m

If we make q subject of formula from eqn(1) we have

q= Er^2/k............eqn(2)

q= 1440 × (0.15)^2 /(9 × 10^9 )

= 2.85×10^-9C

Total charge is an integer of electron charge , then we can calculate the number of the electron using the expression below

q= Ne

Where

N = number of electron

Making N subject of the formula we have

N= q/e

Where e= electron value= 1.6× 10^-19

N=2.85×10^-9 /1.6× 10^-19

= 1.78×10×10^10 electron

Answer:

6.12 m/s

Explanation:

Using the law of conservation of momentum

momentum before collision = momentum after collision

m₁v₁ + m₂v₂ = (m₁ + m₂)V    (since the train cars become attached to each other) where m₁ = mass of car 1 = 1,825 kg, m₂ = mass of car 2 = 2,645 kg, v₁ = initial velocity of car 1 = + 15.0 m/s (positive since it is moving in the positive x direction), v₂ = initial velocity of car 2 = 0 m/s (since it is initially stationary) and V = velocity of both cars after collision,

So, m₁v₁ + m₂v₂ = (m₁ + m₂)V  

m₁v₁ + m₂(0 m/s) = (m₁ + m₂)V  

m₁v₁ + 0 = (m₁ + m₂)V  

V = m₁v₁/(m₁ + m₂)

substituting the values of the other variables into the equation, we have

V = 1,825 kg × 15.0 m/s/(1,825 kg + 2,645 kg)

V = 27375 kgm/s/ 4470kg

V = 6.124 m/s

V ≅ 6.12 m/s

B, the body at rest becomes reluctant to start moving or a body in motion becomes

reluctant and stop moving once in motion in a straight line

Answer:

c) The impulse is the same in both cases.

Explanation:

What drives the car is the amount of movement of the car during its journey. In this case, we can consider that in the car, presented in the question above, the movement is generated through speed and friction on the track, the impact that makes the car stop, is not part of the movement and therefore, not part of the impulse. In the two situations presented, the speed of the car is the same, the same car and the same track were also used, which shows us that the impulse, in both situations, is the same.

Answer:

A) B = 9.425 × 10^(-5) T

B) North direction

Explanation:

A) We are given;

Current in coil; I = 4.5 A

Number of turns; N = 100 turns

Radius;R = diameter/2 = 6/2 = 3 m

Formula for the magnetic field at the center of the coil is given by;

B = (μ_o•N•I)/2R

Where μ_o is a constant = 4π × 10^(-7) H/m

Thus;

B = (4π × 10^(-7) × 100 × 4.5)/(2 × 3)

B = 9.425 × 10^(-5) T

B) The direction of the force on a positive ion in water can be gotten by the application of flemmings right hand rule.

From flemmings right hand rule, we know that;

- The thumb indicates the direction of the motion of the force which is in the north direction.

- The Index finger indicates the direction of the magnetic field which is in the east direction

- The middle finger indicates the direction of magnetic field which is downwards in the west direction.

Therefore, the direction of the force as seen from flemmings right hand rule is in the north direction

I believe the answer is a

Answer:

r₂ = 4 r

Explanation:

For this exercise let's use Newton's second law with the magnetic force

          F = q v x B

bold letters indicate vectors, the magnitude of this expression is

          F = q v B sin θ  

in this case we assume that the angle is 90º between the speed and the magnetic field.

If we use the rule of the right hand with the positive charge, the thumb in the direction of the speed, the fingers extended in the direction of the magnetic field, the palm points in the direction of the force, which is towards the center of the circle, therefore the force is radial and the acceleration is centripetal

           a = v² / r

let's use Newton's second law

           F = ma

           q v B = m v² / r

           r = [tex]\frac{qB}{mv}[/tex]

Let's apply this expression to our case.

Proton 1

             r = \frac{qB_1}{mv_1}

Proton 2

             r₂ = [tex]\frac{q \ B_2}{m \ v_2}[/tex]

in the exercise indicate some relationships between the two protons

*    v₁ = 2 v₂

    v₂ = v₁ / 2

*   B₂ = 2B₁

we substitute

           r₂ = [tex]\frac{q \ 2B_1}{m \ \frac{v_1}{2} }[/tex]

           r₂ = 4 [tex]\frac{qB_1}{mv_1}[/tex]

           r₂ = 4 r