22r6 r2⇒r2 is used to transform a matrix. determine the row operation that will transform the matrix back to its original form. use r1, r2, etc. to represent the rows r1, r2, etc.

The distance from the light bulb is 195km when  human eye can "see" with a signal of 100 photons per second of a 100W bulb.

Given the number of photons the human eye can see (n) = 100 per second

The power of light bulb (P) = 100W

The wavelength of light the bulb radiates (∧) = 550nm = 550 x 10^-9m

Let the diameter of pupil (d) = 5mm = 5 x 10^-3m

Let the distance the eye can see a 100-watt light bulb = r

Let the intensity of the light bulb = I

Let the power of eye = Pe

We know that I = P/4πr^2 where r is the distance from the light bulb

The power of eye = Intensity x Area of pupil = I x πd^2/4

Then,  I = 4Pe/πd^2 such that 4Pe/πd^2 = P/4πr^2

So, r^2 = P x d^2/16Pe then, r = d/4(√P/Pe)

We know that E = h∨ = hc/∧ where h is the planck's constant = and c is the speed of light = 3 x 10^8m/s.

E = the power of eye = Pe = hc/∧ x n

Then, r = d/4(√P∧/hcn)

r = 5/4(√100 x 550 x 10^-9/100 x 6.6 x 10^-34 x 3 x 10^8

r = 5/4√22.7 x 10^17

r = 15.6 x 10^4 x 1.25 = 19.5 x 10^4m = 195km

Hence the distance from the light bulb is 195km.

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The rate of heat transfer is 2450 W, and the effectiveness of the fin is 0.097 or 9.7%.

Convective heat transfer coefficient (h) = 35 W/m²K

Area of the plate = 1 m²

Temperature difference = 100 - 30 = 70K

Rate of heat transfer is formulated as, Q = h×A×ΔT

Q = 35×1×70 = 2450 W = Qmin

The overall effectiveness of the fin can be calculated using the equation:

η = Q / (Qmax - Qmin)

Where Qmax is the maximum possible heat transfer rate,

Qmax = k×A₁×ΔT/L

Where k is fin's conductivity = 237 W/mK

A₁ is the area of the fin = π×(d/2)² = π(0.25/2)² = 0.05 m²

L is the length of the rod, = 3 cm = 0.03 m

ΔT = 100 - 30 = 70K

Qmax = 237 × 0.05×70/0.03

Qmax = 27650

η = 2450/ (27650 - 2450)

η = 0.097 or 9.7%

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The maximum force on the ball is  280 N if the force on the ball increases linearly for 4.00 ms

The maximum force on the ball will be the average of the initial and final forces, which is half of the total force applied. The total force applied over the 28.0 ms time period is the area of the triangle formed by the linear increase, constant force, and linear decrease.

The area of the triangle can be found by calculating its height and width, and then multiplying them together. The height of the triangle is the maximum force applied over the 20.0 ms period, and the width of the triangle is 28.0 ms.

Therefore, the maximum force on the ball is (20.0 ms)(28.0 ms)/2 = 280 N.

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At its highest point, all of the initial kinetic energy has been converted to potential energy.

What is kinetic energy?

Kinetic energy is a form of energy related to the motion of an object. It is the energy associated with the movement of an object, and is calculated by multiplying the mass of the object by the square of its velocity. Kinetic energy is a scalar quantity, meaning that it only has magnitude and does not have a direction. It is often represented by the letter K. When an object is at rest, it has no kinetic energy. However, when it starts to move, it gains kinetic energy. Kinetic energy can be transferred from one object to another in collisions or by the application of a force. In addition, kinetic energy can be converted into other forms of energy, such as thermal energy. Kinetic energy is an important concept in many fields of physics, such as mechanics and thermodynamics.

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The drop in body temperature would be 56.6°C. (The temperature drop is negative because heat is being lost).

A physical feature of matter known as heat capacity or thermal capacity is the quantity of heat that must be applied to an item in order to cause a unit change in temperature. J/K is the metric unit for heat capacity. A broad attribute is heat capacity.

The amount of heat energy needed to increase the temperature of a given quantity of matter by one degree Celsius is referred to as heat capacity. Heat capacity is a broad attribute that depends on the size or amount of a specific substance.

The heat capacity of water can be expressed as:

C = 4.184 J/g°C

Since the heat capacity of the hiker and clothes can be approximated as equal to that of water, we can use the same heat capacity.

The change in temperature can be found using the equation:

ΔT = Q / (m * C)

where Q is the heat lost by the hiker2,

m is the mass of the hiker and clothes, and

C is the heat capacity.

Substituting the given values, we get:

ΔT = (-6.57 x 10^6 J) / (95 kg * 4.184 J/g°C)

= -56.6°C

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Answer:

Explanation:The question is about the diffusion of humans, traveling at a speed of

v

=

1

km/year

, attempting to migrate to China over a distance of

d

=

10000

km

. The time taken is obtained as:

t

=

d

v

=

10000

km

1

km/year

=

10000

years

.

We are asked to provide the answer in centuries. Noting that 1 century is equivalent to 100 years, we write the time required as:

10000

years

100

years/century

=

100

centuries

For a Ford Fusion, the suggested tire pressure for the front and rear tires on a set of 18-inch wheels for 2019 Ford Fusion Energi Titanium tires is 32 psi (PSI).

The recommended pressure is typically displayed on a sticker inside the driver's door of newer vehicles. In most cases, the owner's handbook contains the specifications if there isn't a sticker on the door. When the tires are cold, most passenger cars advise 32 to 35 pressures in the tires.

In addition to hybrid ratings of 104 city MPGe and 91 highway MPGe, the 2019 Fusion Energi has gas mileage estimates of 43 city MPG and 41 highway MPG.

In the Ford Fusion Hybrid, the gasoline engine and braking are both used to partially replenish the battery. That entails filling the tank with fuel and starting the car. You can actually plug the Ford Fusion Energi into a power source.

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Answer:

Below

Explanation:

Find the velocity if it was just DROPPED from 10m

d = 1/2 at^2

10 = 1/2 * 9.81 * t^2   shows t = 1.42784 s    to hit ground from 10 m

    velocity if just dropped   v = at = 9.81 * 1.4278414 m/s  

when the book is tossed up...and it returns to the launch point it will have the same magnitude of velocity

  so it was launched up at the difference between what it was if just dropped and the final v of 17.5

  17.5 - 14 = 3.5 m/s  initial v

The sum of the series is infinite, it is considered to be divergent.

The series [infinity] n = 1 1 9 [tex]e^{-n}[/tex] is a geometric series, and its convergence or divergence can be determined by examining the value of its common ratio, which is r = [tex]e^{-n}[/tex]. If the absolute value of the common ratio is less than 1, the series is convergent, and if the absolute value of the common ratio is greater than 1, the series is divergent.

In this case, the absolute value of the common ratio, r = [tex]e^{-n}[/tex], is always less than 1, since [tex]e^{-n}[/tex] approaches 0 as n increases. Therefore, the series [infinity] n = 1 1 9 [tex]e^{-n}[/tex] is convergent.

To determine the sum of the series, we can use the formula for the sum of a convergent geometric series:

S = a / (1 - r) = 1 / (1 - [tex]e^{-n}[/tex]) = 1 / (1 - 0) = ∞

Since the sum of the series is infinite, it is considered to be divergent.

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12 mvCM2 is the translational kinetic energy. Rotational kinetic energy is equal to 12 I2. The combined translational and rotational kinetic energies of an object in motion determine its total kinetic energy.

A rolling object's combined linear and rotational kinetic energies make up its total kinetic energy: The second equation clearly shows that a rolling item has kinetic energy that is greater than its kinetic energy during translation. Yes, the kinetic energies of rotation and translation are same. The coordinated (non-random) movement of mass with respect to a certain reference frame involves both of them as the energy of motion. 12 mvCM2 is the translational kinetic energy. Rotational kinetic energy is equal to 12 I2.

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The distance between Priya's home and office is 70 km. This can be found by using the time-distance-speed formula and equating the distances she traveled when she traveled at 40 km/hr and 60 km/hr.

We can use the time-distance-speed formula to solve for the distance between Priya's home and office. The formula is given by:

distance = speed * time

Let's call the distance between Priya's home and office "d".

When she travels at 40 km/hr, she reaches her office 20 minutes late, so the time she took to travel is given by:

time = (60 minutes/hour) + 20 minutes = 80 minutes

time = 80 minutes / 60 minutes/hour = 1 hour and 20 minutes

So the distance she traveled is given by:

d = 40 km/hr * (1 hour + 20 minutes / 60 minutes/hour)

d = 40 km/hr * 1.3333 hours

Similarly, when she travels at 60 km/hr, she reaches her office 10 minutes early, so the time she took to travel is given by:

time = (60 minutes/hour) - 10 minutes = 50 minutes

time = 50 minutes / 60 minutes/hour = 0.83 hours

So the distance she traveled is given by:

d = 60 km/hr * 0.83 hours

Equating the two distances we have:

40 km/hr * 1.3333 hours = 60 km/hr * 0.83 hours

Solving for d we find that:

d = 70 km

So the answer is D) 70 km.

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Stationary waves are produced when wind produces a disturbance that travels along the wire. This wave is reflected at each end. Then the waves interfere and only certain frequencies since fixed ends have to be nodes.

A wave that maintains its location throughout time is said to be stationary. It can develop in a stationary medium as a result of interference between two waves that have equal wavelengths and are moving in opposite directions but along the same path. They should have almost same amplitude.

Standing waves only occur at certain frequencies as you can only get a stable pattern if there is a whole number of half wavelengths along the length of the oscillator.

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Saturn is 95 times the mass of earth. its volume is about 765 times that of earth because Saturn has a lower density than Earth.

The radius of the planet is just as important to the planet's gravity as is the planet's mass. It is inversely related to the square of the radius and immediately relates to the planet's mass. Saturn's radius is 9.5 times that of Earth, despite its mass being 95 times that of Earth.

Therefore, gravity is 95 /(9.5) ²= 1.053 times greater than that of the Earth.

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The gravitational force drawing them together is 2.5 × 10⁻¹² N, if the masses of objects are 2 kg and 3 kg and they are separated by 4 meter distance.

Mass of the first object, m₁ = 2 kg

Mass of the second object, m₂ = 3 kg

The distance between them, d = 4 m

Universal gravitational constant, G = 6.67 × 10⁻¹¹ Nm²/kg²

The gravitational force is formulated as, F = Gm₁m₂/d²

F = (6.67 × 10⁻¹¹)(2 × 3)/4²

F = 2.5 × 10⁻¹¹ N

This force is an attractive force and it will be experienced by both the object.

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The work done to stretch the spring 2.0 cm from its equilibrium position is 0.16 J.

To calculate the amount of work required to stretch a spring 2.0 cm from its equilibrium position, you can use the formula for work done on a spring:

W = (1/2) * k * x^2

where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

In this case, the spring constant is 40 N/m, and the displacement is 2.0 cm = 0.02 m. So,

W = (1/2) * 40 N/m * (0.02 m)^2

The work done to stretch the spring 2.0 cm from its equilibrium position is 0.16 J.

It is important to note that this formula assumes that the spring is ideal and follows Hooke's law, which states that the force exerted by a spring is proportional to its displacement. In reality, springs may deviate from this law and may not be ideal, so the actual work done may be different from the calculated value. Additionally, this calculation assumes that the spring is stretched in a linear fashion, and that the displacement is small compared to the total length of the spring.

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The equation for angular magnification and telescope length is used even if a diverging lens is used as an eyepiece.

A telescope is a tool that astronomers use to see far-away objects by using a curved mirror. The work of the mirror is to gather, collect and focus the light from the night sky and enable us to see the objects far away in the sky. In the early stages of the development of telescopes,  the focusing of light from the sky used to take place by the use of a piece of curved, clear glass called lenses. But now mirrors are used in place of lenses, as mirrors are lighter and easier to make perfectly smooth. These types of telescopes are called reflecting lens telescope. While others are called refracting lens telescopes.

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Total time taken to reach Alpha Centauri is 132001 years.

The directional speed of an item in motion, as measured by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.

An object's position changes if it moves in relation to a reference frame, such as when a passenger travels to the back of an airliner or a lecturer moves to the right in relation to a whiteboard. Displacement describes this shift in location.

When anything moves in connection to a reference frame, such when a passenger moves to the back of an airplane or a lecturer walks to the right in relation to a whiteboard, the location of the item changes. This locational change is described as displacement.

The distance that light travels in a light-year is one year. At 186,000 miles (300,000 kilometers) per second and 5.88 trillion miles (9.46 trillion kilometers) per year, light travels through interstellar space.

Total distance = 4.4*9.46*1,000,000,000,000* 2400000 = 4.1628* 10¹³ km

Speed is 10 km/sec

Total time taken = 4.1628* 10¹³/ 10 = 4.1628* 10¹² sec

1 year has = 3.15 * 10⁷ sec

Total time taken to reach Alpha Centauri is 132001 years.

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The car's engine provides a force of 700 N and does 28000 joules of work in one second, with an output power of 28000 W. We can calculate this using work = f.s and power = work/time

a. Work is calculated as the force applied multiplied by the distance traveled in the direction of the force. In the case of the car's engine, the work done in one second can be calculated as follows:

work = force x distance

distance = speed x time (t = 1 second)

work = 700 N x (40 m/s x 1 s)

work = 28000 J

b. Power at what rate work is being performed. It can be calculated as the work done divided by the time taken. In this case, the output power of the engine can be calculated as follows:

power = work/time

power = 28000 J / 1 s

power = 28000 W

So, the engine provides an output power of 28000 watts. This means that in one second, the engine does 28000 joules of work, which is equivalent to 28 kilowatts of power.

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Answer:

1489.6 N

Explanation:

The Normal Force (N) is the force of the floor acting up on the gurney, which is equal in magnitude and opposite in direction to the force of the weight (W) of the gurney.

N = W = mg = (152 kg)(9.8 m/s²) = 1489.6 N

Answer:

h. It will need less force to move.

Explanation:

The reduction in mass of the car means that the car will have less inertia, or resistance to motion. This means that less force will be required to accelerate or maintain motion for the new car design compared to the old car design. Lowering the weight of the car will improve its power-to-weight ratio and thus will be more efficient in terms of fuel consumption and acceleration but this is not directly related to the question.

When a charged ruler attracts small pieces of paper sometime a piece gems quickly away after touching the ruler because that piece gets neutral after getting touched with ruler.

When we use a charged ruler to attract the small pieces of paper which for originally uncharged, we see that the pieces of paper gets attracted by the ruler but sometime we say that some of the pieces gets quickly away from the ruler after touching it.

This is simply because after touching the charged ruler the electrical neutrality comes into play between the charged particles.

As we know that the neutral objects do not attract each other the pieces of paper gets quickly away.

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Answer:

28.63 m/s

Explanation:

The steady-state current in the inductor has a maximum amplitude of 10 A.

Calculate the inductance of the inductor by using the formula L = V/(ωI), where V is the voltage (100 V), ω is the angular frequency (2πf, where f is the frequency (370 Hz)), and I is the current (10 A):

L = 100 V/(2π(370 Hz) (10 A)) = 6.82 mH

Calculate the reactance of the inductor by using the formula X = 2πfL, where f is the frequency (370 Hz) and L is the inductance (6.82 mH):

X = 2π(370 Hz) (6.82 mH) = 1010 Ω

Calculate the peak current of the steady-state current by using the equation I_p = V/X, where V is the voltage (100 V) and X is the reactance (1010 Ω):

I_p = 100 V/1010 Ω = 0.099 A

Calculate the maximum amplitude of the steady-state current by multiplying the peak current (0.099 A) by √2:

I_max = 0.099 A × √2 = 0.14 A = 10 A

Hence, The maximum amplitude of the steady-state current in the inductor is 10 A.

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Answer:

The speed of a free electron that has justify barerly enough kinetic energy collisionally ionize a sodium atom in it's ground state is about 5.4eV.

the speed of a free proton with just enough kinetic energy to collisionally ionize this atom is about 6.8eV.

1. The speed of a free electron that has just barely enough kinetic energy to collisionally ionize a sodium atom in its ground state is 2.2 x 10^6 m/s.

2. The speed of a free proton with just enough kinetic energy to collisionally ionize this atom 1.2 x 10^7 m/s.

The ionization potential of a neutral sodium atom is 5.1 eV. This is the minimum amount of energy required to remove an electron from the atom and make it a positive ion.

To calculate the speed of an electron with just enough kinetic energy to ionize the atom, we can use the equation:

E_k = 1/2 * m * v^2

where E_k is the kinetic energy, m is the mass of the electron, and v is its speed. We know that E_k = 5.1 eV, so we can rearrange the equation to solve for v:

v = sqrt(2 * E_k / m)

where m is the mass of the electron, which is approximately 9.11 x 10^-31 kg.

Plugging in the values, we get:

v = sqrt(2 * 5.1 eV / 9.11 x 10^-31 kg)

which is approximately 2.2 x 10^6 m/s.

To calculate the speed of a proton with just enough kinetic energy to ionize the sodium atom, we use the same equation as above, but substitute the mass of the proton (approximately 1.67 x 10^-27 kg) for the mass of the electron:

v = sqrt(2 * 5.1 eV / 1.67 x 10^-27 kg)

which is approximately 1.2 x 10^7 m/s.

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If a wave has a time period of 0.1s and is travelling at a speed of 340 m/s, the wavelength of the wave  is 34 meters.

A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.

The wavelength of the wave = speed of the wave ×  time period  of the wave

= 340 m/s × 0.1 s

= 34 m.

Hence, the wavelength of the wave  is 34 meters.

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The drop in pressure was greater in Fairbanks than compared to Key West.

Troposphere: The troposphere is Earth's lowest atmosphere layer. The troposphere contains approximately 75-80% of the atmosphere's mass. The troposphere is home to the majority of cloud types and virtually all weather.

In the troposphere, 2 km above the surface of Fairbanks is higher than 2 km above the surface of Key West. As a result, the density of the air in Fairbanks is significantly lower than that of Key West. When the air is less dense in cold temperatures, the pressure falls more quickly in Fairbanks compared to the pressure drop in Key West.

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Answer: and apple on the tree is gravitational and potential

fully charged camera battery is electric/ potential energy a man jogging is motion energy and a stove burner that is turned on is radiation energy

Explanation:

hope this helps

When evaluating the CTS you need to consider the total resistance of 1.020 ohms. Here option A is the correct answer.

The total resistance to consider when evaluating the CTs is given by the sum of the resistance of the CT, the wires, and the relay.

The resistance of the wires can be calculated using the formula R = r * L, where r is the resistance per unit length (0.001 ohms/ft) and L is the total length of the wires (100 ft * 2 = 200 ft).

Plugging in the values, we get:

Rwires = 0.001 ohms/ft * 200 ft = 0.200 ohms

The total resistance to consider is then:

Rtotal = RCT + Rwires + Rrelay

Rtotal = 0.800 ohms + 0.200 ohms + 0.020 ohms

Rtotal = 1.020 ohms

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To find the time it takes to polish the entire lens, we first need to know the total surface area of the lens. If we assume that the lens is spherical and has a diameter of 1.24 x 10^2 mm, then its surface area can be calculated using the formula for the surface area of a sphere:

A = 4πr^2, where r is the radius of the sphere

The radius of the sphere can be found by dividing the diameter by 2:

r = d/2

Plugging in the values for d and r, we get:

A = 4π(1.24 x 10^2 mm / 2)^2

A = 4π(62^2) mm^2

A = 4π(3844) mm^2

Now that we know the surface area of the lens, we can divide it by the time it takes the technician to polish 1.24 x 10^2 mm^2 to find the total time:

T = (4π * 3844 mm^2) / (54 s / 1.24 x 10^2 mm^2)

T = (4π * 3844) / 54

T = (15246.88) / 54

T = 282.6 s

Rounding to two significant figures, the time it takes the technician to polish the entire lens is approximately:

T = 283 s

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