A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12 meters. If water is being pumped into the pyramid at a rate of 23m3sec, at what rate is the height of the water increasing when the water is 2 meters deep

Answer: 1.18

Explanation: The formula I used is:

f=1/(2pi) times the square root of k/m

F is the frequency, in this problem, 10 Hz.

K is the spring constant.

M is the mass.

So plugging everything in we would have:

10=1/(2pi)•sqrt x/0.00030

The answer I got was 1.18

The formula xy = k or y = kx can be used to represent an inverse variation. If a nonzero constant k exists such that xy = k or y = kx where x≠ 0, y ≠ 0, then y varies inversely as x.

A variable is inversely varying with respect to another variable when the term "inverse variation" is used. It symbolizes how two quantities are inversely related. This means that one variable is inversely proportional to another. Relationship in mathematics between two variables that can be described by an equation in which the sum of the two variables equals a constant.

As one quantity rises, the other falls for two quantities with inverse variation. For instance, as your speed increases while travelling to a specific location, it will take you less time to get there.

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When the package hits the ground, the plane will be 4,687.2 m away.

The time taken for the package to fall from the given height is known as the time of motion of the package and the magnitude is calculated by applying the following kinematic equation.

h = vt + ¹/₂gt²

where;

h = 0 +  ¹/₂gt²

t = √(2h/g)

t = √ [ (2 x 1390) / ( 9.8) ]

t = 16.8 seconds

The horizontal displacement of the plane at this time;

X = ut

where;

X = 279 x 16.8

X = 4,687.2 m

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Explanation:

K.E = 1/2mv²

K.E = 1/2 x 4 x 0.5²

K.E = 0.5J

Answer:

100 N left <--

Explanation:

Answer:

100 to the left

Explanation:

Answer:

297.38 meters

Explanation:

The height of the hill can be calculated using the principle of conservation of energy. This principle states that the total energy of a system is conserved, and that the change in potential energy of an object is equal to the work done on it.


The height of the hill can be calculated using the formula:

h = (1/2) m v^2 / g

where m is the mass of the child and sled, v is the final speed of the sled, and g is the acceleration due to gravity (9.8 m/s^2).

Plugging in the values, we get:

h = (1/2) * 50.0 kg * (9.0 m/s)^2 / 9.8 m/s^2

h = (1/2) * 50.0 kg * 81.0 m^2/s^2 / 9.8 m/s^2

h = 40.5 kg * 81.0 m^2/s^2 / 9.8 m/s^2

h = 2911.76 kg m^2/s^2 / 9.8 m/s^2

h = 297.38 m

So the height of the hill is 297.38 meters.

1. Connect the DC motor with a potentiometer to the Arduino board, along with a temperature sensor and an IR sensor with an LED.

2. Write the necessary code to integrate all the sensors and control the motor based on the inputs.

To connect a DC motor with a potentiometer to an Arduino board, you will need to use a motor driver module that can handle the power requirements of the motor. The motor driver module allows you to control the speed and direction of the motor using the Arduino. Connect the motor to the appropriate terminals on the motor driver module and the potentiometer to an analog input pin on the Arduino. The potentiometer will act as a voltage divider, allowing you to vary the input voltage to control the motor speed.

Next, connect a temperature sensor that can measure temperatures in the range of -10 to +45 degrees Celsius. Depending on the type of temperature sensor you are using, you may need to follow specific wiring instructions provided by the manufacturer. Connect the temperature sensor to the appropriate digital or analog input pin on the Arduino board.

Lastly, connect an IR sensor with an LED to detect motor overspeed. The IR sensor can be used to measure the rotational speed of the motor by detecting interruptions in the infrared beam caused by the rotating motor shaft. If the motor speed exceeds the threshold of 25,000 rpm, the IR sensor will trigger an output to activate the LED as a signal.

To make all the sensors work together, you will need to write code using the Arduino programming language. Use appropriate libraries and functions to read the sensor values and implement the desired logic for motor control and overspeed detection. You can define temperature thresholds and motor speed limits in the code and take appropriate actions based on the sensor readings.

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Answer:

2. Repulsion

Explanation:

number two is the answer

Answer:

Repulsion is the surest test which confirms that the given piece of the object is a magnet.

........

The current that would pass through the 30 ohms resistor is 2 A.

Electric current is the rate of flow of electric charge round a conductor.

To calculate the electric current that would pass through the 30 ohms resistor, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The current that would pass through the 30 ohms resistor is 2 A.

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For the designing of differential amplifier following were found out :

the small-signal gain is zero.

the transconductance (gm) and output resistance (ro) of the NMOS transistors are  -640 * (W/L) μA/V and 1 / (8 * (W/L)) kΩ respectively.

the transconductance (gm) and output resistance (ro) of the PMOS transistors are -320 * (W/L) μA/V and  respectively.

NMOS transistor: Wn = 0.03 μm, L = 0.2 μm

PMOS transistor: Wp = 0.0075 μm, L = 0.2 μm

Bias current: Itail = 1 mA

Resistance: R = 0.3 kΩ

To design the differential amplifier according to the given specifications, we will follow these steps:

Step 1: Calculate the small-signal gain (Av)

Step 2: Determine the transconductance (gm) and output resistance (ro) of the NMOS transistors

Step 3: Determine the transconductance (gm) and output resistance (ro) of the PMOS transistors

Step 4: Calculate the tail current (Itail) based on the specified Iss

Step 5: Determine the resistance (R) value

Step 6: Calculate the width (Wp) of the PMOS transistor

Step 7: Calculate the width (Wn) of the NMOS transistors

Now let's go through each step in detail.

Step 1: Calculate the small-signal gain (Av)

Given: Av = 10, VOP = VON = 3.5V

Av = (vop - von) / (vip - vin)

10 = (3.5 - 3.5) / (0.1)

10 = 0 / 0.1

Since the numerator is zero, the small-signal gain is zero.

Step 2: Determine the transconductance (gm) and output resistance (ro) of the NMOS transistors

Given: unCox = 400 μA/V², Vtn = 0.8V, n = 0.02 V^(-1), L = 0.2 μm

gm = 2 * unCox * (W/L) * (Vgs - Vtn)

ro = 1 / (lambda * unCox * (W/L))

We need to design the amplifier for DC operation (Vin = Vbias), where the differential voltage (vgs = Vin - Vbias) should be zero to operate the transistors in the saturation region.

For the NMOS transistors:

Vgs = 0 (since Vin = Vbias)

gm = 2 * unCox * (W/L) * (Vgs - Vtn)

  = 2 * 400 μA/V² * (W/L) * (0 - 0.8)

  = -640 * (W/L) μA/V

ro = 1 / (lambda * unCox * (W/L))

  = 1 / (0.02 V^(-1) * 400 μA/V² * (W/L))

  = 1 / (8 * (W/L)) kΩ

Step 3: Determine the transconductance (gm) and output resistance (ro) of the PMOS transistors

Given: upCox = 200 μA/V², Vtp = -0.8V, p = 0.04 V^(-1), L = 0.2 μm

Similarly, for the PMOS transistors, we need to design the amplifier for DC operation (Vin = Vbias), where the differential voltage (vsg = Vbias - Vin) should be zero to operate the transistors in the saturation region.

For the PMOS transistors:

Vsg = 0 (since Vin = Vbias)

gm = 2 * upCox * (W/L) * (Vtp - Vsg)

  = 2 * 200 μA/V² * (W/L) * (-0.8 - 0)

  = -320 * (W/L) μA/V

ro = 1 / (lambda * upCox * (W/L))

  = 1 / (0.04 V^(-1) * 200 μA/V² *

  = 1 / (5 * (W/L)) kΩ

Step 4: Calculate the tail current (Itail) based on the specified Iss

Given: Iss = 2 mA

Itail = Iss / 2

= 2 mA / 2

= 1 mA

Step 5: Determine the resistance (R) value

Given: Vs = 0.3 V, VDD = 5 V

We can calculate the resistance (R) value using Ohm's Law:

Vs = Itail * R

0.3 V = 1 mA * R

R = 0.3 kΩ

Step 6: Calculate the width (Wp) of the PMOS transistor

To calculate Wp, we'll use the equation for the tail current:

Itail = 2 * upCox * (Wp/L) * (VDD - Vtp)^2

1 mA = 2 * 200 μA/V² * (Wp/0.2 μm) * (5 V + 0.8 V)^2

1 mA = 2 * 200 μA/V² * (Wp/0.2 μm) * (5.8 V)^2

Solving for Wp:

Wp = (1 mA * 0.2 μm) / (2 * 200 μA/V² * (5.8 V)^2)

Wp = 0.01 μm / (2 * 200 μA/V² * 33.64 V^2)

Wp ≈ 0.0075 μm

Step 7: Calculate the width (Wn) of the NMOS transistors

Given: Wn = 4 * Wp

Wn = 4 * 0.0075 μm

Wn = 0.03 μm

So, the design parameters for the differential amplifier are as follows:

the small-signal gain is zero.

the transconductance (gm) and output resistance (ro) of the NMOS transistors are  -640 * (W/L) μA/V and 1 / (8 * (W/L)) kΩ respectively.

the transconductance (gm) and output resistance (ro) of the PMOS transistors are -320 * (W/L) μA/V and  respectively.

NMOS transistor: Wn = 0.03 μm, L = 0.2 μm

PMOS transistor: Wp = 0.0075 μm, L = 0.2 μm

Bias current: Itail = 1 mA

Resistance: R = 0.3 kΩ

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The mass of water in the rectangular vessel can be calculated by multiplying the volume (400 cm³) by the density of water (1000 kg/m³), resulting in a mass of 0.4 kg.

To calculate the mass of the water in the rectangular vessel, we can use the formula:

Mass = Density × Volume

Given that the density of water is 1000 kg/m³ and the volume of the vessel is 400 cm³, we need to convert the volume to cubic meters before calculating the mass.

1 cm³ = 1 × 10^(-6) m³

Volume = 400 cm³ × (1 × 10^(-6) m³/cm³)

= 0.0004 m³

Now we can calculate the mass:

Mass = 1000 kg/m³ × 0.0004 m³

= 0.4 kg

Therefore, the mass of the water in the rectangular vessel is 0.4 kg.

It's important to note that the given information about the square cross-sectional area of length 10 cm is not directly used in this calculation since the volume is already provided. The square cross-sectional area is relevant to determine the volume if it was not given, but in this case, the volume is explicitly given as 400 cm³.

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To find the wavelength of the wave along the string, we first need to measure the distance between two consecutive points on the wave that are in the same phase.

We can look at the graph provided by the question, whose full cycle of the wave completes in 0.1sec, i.e. demonstrating that this is a complete up and down movement of the point.

As measured in the graph, we see that the distance between two consecutive points is 0.5 cm. Then we calculate the wavelength of the wave using the following formula:

Therefore, the wavelength of the wave corresponds to 0.005m.

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Answer:

1. The period is 1.74 s.

2. The frequency is 0.57 Hz

Explanation:

1. Determination of the the period.

Spring constant (K) = 30 N/m

Mass (m) = 2.3 Kg

Pi (π) = 3.14

Period (T) =?

The period of the vibration can be obtained as follow:

T = 2π√(m/K)

T = 2 × 3.14 × √(2.3 / 30)

T = 6.28 × √(2.3 / 30)

T = 1.74 s

Thus, the period of the vibration is 1.74 s.

2. Determination of the frequency.

Period (T) = 1.74 s

Frequency (f) =?

The frequency of the vibration can be obtained as follow:

f = 1/T

f = 1/1.74

f = 0.57 Hz

Thus, the frequency of the vibration is 0.57 Hz

The period of the vibration is  1.76 s and the frequency of the vibration is  0.57 s-1.

Using the formula;

T = 2π√(m/K)

Where;

T = period

m = mass

K = spring constant

Substituting values;

T = 2(3.142)√2.3/30

T = 6.284 × 0.28

T = 1.76 s

Recall that the period is the inverse of frequency;

f = 1/T

f = 1/1.76 s

f = 0.57 s-1

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The length of the nichrome wire that has the same resistance as the 12.0-meter copper wire is approximately \(\( 0.13 \, \text{m} \)\).

To find the length of the nichrome wire that has the same resistance as the 12.0-meter copper wire, we can use the formula for resistance:

\(\[ R = \frac{{\rho \cdot L}}{{A}} \]\)

where \(\( R \)\) is the resistance, \(\( \rho \)\) is the resistivity, \(\( L \)\) is the length of the wire, and \(\( A \)\) is the cross-sectional area.

Given:

Length of the copper wire, \(\( L_c = 12.0 \, \text{m} \)\)

Resistance of the copper wire, \(\( R_c = 1.50 \, \Omega \)\)

Resistivity of copper, \(\( \rho_c = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \)\)

Resistivity of nichrome, \(\( \rho_n = 1.5 \times 10^{-6} \, \Omega \cdot \text{m} \)\)

Let's calculate the cross-sectional area of the copper wire using the resistance formula:

\(\[ A_c = \frac{{\rho_c \cdot L_c}}{{R_c}} \]\\\\\ A_c = \frac{{1.7 \times 10^{-8} \cdot 12.0}}{{1.50}} \\\\= 1.36 \times 10^{-7} \, \text{m}^2 \]\)

Next, we can use the resistance formula to find the length of the nichrome wire:

\(\[ R_n = \frac{{\rho_n \cdot L_n}}{{A_c}} \]\)

We need to solve for \(\( L_n \)\):

\(\[ L_n = \frac{{R_n \cdot A_c}}{{\rho_n}} \]\)

Substituting the given values:

\(\[ L_n = \frac{{1.50 \cdot 1.36 \times 10^{-7}}}{{1.5 \times 10^{-6}}} \\\\= 0.13 \, \text{m} \]\)

Therefore, the length of the nichrome wire that has the same resistance as the 12.0-meter copper wire is approximately \(\( 0.13 \, \text{m} \)\).

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The person's final displacement is approximately 227 meters at an angle of 17.9 degrees North of West.

The first displacement of 20 m [N 20° E] can be broken down as follows,

The x-component is 20 cos(20°) = 18.8 m to the East

The y-component is 20 sin(20°) = 6.8 m to the North

The second displacement of 120 m [N 50° W],

The x-component is 120 cos(50°) = -91.9 m to the West

The y-component is 120 sin(50°) = 92.2 m to the North

The third displacement of 150 m [W] has no y-component, and the x-component is simply -150 m to the West.

The fourth displacement of 30 m [S 75° E],

The x-component is 30 cos(75°) = 7.4 m to the East

The y-component is 30 sin(75°) = -28.6 m to the South

The total x-component is 18.8 m - 91.9 m - 150 m + 7.4 m = -215.7 m to the West. The total y-component is 6.8 m + 92.2 m + 0 m - 28.6 m = 70.4 m to the North

To find the magnitude of the resultant vector,

|d| = sqrt((-215.7 m)^2 + (70.4 m)^2) ≈ 227 m

To find the direction of the resultant vector,

θ = tan^-1(70.4 m / 215.7 m) ≈ 17.9° N of W

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The commonality between an engine using gasoline to power a car and boiling an egg is that they both involve a transformation of energy from one form to another.

Gasoline is a liquid fuel that is primarily used to power internal combustion engines, such as those found in cars, trucks, and motorcycles. It is a mixture of various hydrocarbons, typically derived from crude oil through the refining process. The composition of gasoline can vary depending on the source and refining process, but it typically contains hydrocarbons with between 4 and 12 carbon atoms per molecule. The most common hydrocarbons found in gasoline are isooctane and heptane, which are used to determine the octane rating of gasoline.

Gasoline is a highly flammable substance that must be handled and transported with care. It is typically stored in underground tanks at gas stations and delivered to vehicles through pumps. In addition to its use as a fuel, gasoline is also used as a solvent and a raw material to produce other chemicals.

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It is to be noted that Cynthia with her device, is most likely trying to demonstrate "Newton's second law of motion" (Option D).

Note that Cyntia is carrying out a sort of experiment that involves various items with different masses while comparing them to how fast they can travel.

Recall that Newton's Second Law of Motion (Force) indicates that the acceleration of an entity depends on the mass of the object and the amount of force applied.

Given that Cyntia's experiment is in this line, it is therefore correct to state that Cynthia, using her device, is most likely trying to demonstrate "Newton's second law of motion"

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Full Question:

Cynthia constructed a small device called a catapult shown below.

The catapult is able to accelerate objects in order to propel them in a certain direction. After placing a small toy in the end of the spoon, she pulls back with her finger on the tip of the spoon to a point and releases.

She uses toys of the same shape and size, but different masses and compares how much each travels when released. Which of the following is Cynthia most likely trying to demonstrate with her device?

A. Newton's universal law of gravitation

B. Newton's third law of motion

C. Newton's first law of motion

D. Newton's second law of motion

Answer:

mass= 20kg

g=10m/s2

weight is F=mg

F=20×10

F=200N

\(\Large \boxed{\displaystyle density \ (kgm^{-3})=\frac{mass\ (kg)}{volume \ (m^3)} }\)

A change in temperature frequently causes substances to change phases. Most substances are solid at low temperatures; as the temperature rises, they become liquid; and at still greater temperatures, they become gaseous.

Melting is the conversion of a solid into a liquid (an older term that you may see sometimes is fusion). Solidification is the process where a liquid turns into a solid. The melting point, or the temperature at which a pure substance begins to melt, is a property of that substance. A solid must expend energy to become a liquid. A specific quantity of energy is required by every pure substance in order to transform from a solid to a liquid. This amount is known as the substance's enthalpy of fusion (or heat of fusion).

The complete question is- The diagram shows how states of matter can change when energy is either added or removed.

System before change

System after change

00000

00000

00000

00000

00000

00000

00000

All of these statements below are true EXCEPT

Energy was added to the matter causing the particle movement to increase.

The matter changed states which is a physical change.

The particles in the matter before the change had more energy than after the change.

The particles in the matter before the change had less energy than after the change.

the diagram is attached below.

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The iron core of an evolved massive star collapses due to a process known as gravitational collapse.

This occurs when the fusion reactions that were occurring in the core of the star cease, leading to the lack of outward pressure that was balancing the force of gravity. The collapse is triggered by the core reaching a critical density.

During the evolution of massive stars, nuclear fusion reactions in their cores create progressively heavier elements through a process called nucleosynthesis. This fusion process releases energy and produces elements up to iron.

Iron, however, has the highest binding energy per nucleon (the energy required to separate its nucleus into individual nucleons) among all elements. Beyond iron, fusion reactions can no longer release energy, and instead, they require an input of energy. As a result, the core of the massive star becomes dominated by iron.

Since the iron core cannot support the star against its own gravitational pull, gravity takes over, causing the core to collapse rapidly. The collapse generates enormous temperatures and pressures, leading to a supernova explosion, known as a Type II supernova, in which the outer layers of the star are expelled into space, while the core collapses further.

The extreme conditions during core collapse are thought to compress atomic nuclei and electrons together, resulting in the formation of an extremely dense object called a neutron star. In some cases, if the core is massive enough, the collapse may continue until it forms a black hole, a region of space with gravity so intense that nothing, not even light, can escape from it.

In summary, the collapse of the iron core in an evolved massive star occurs because iron fusion cannot sustain the necessary pressure to counteract the force of gravity, leading to a gravitational collapse and subsequent supernova explosion.

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Answer:

1/2 m v^2 = m g h       speed of pendulum related to change in potential energy

v^2 = 2 g h

v^2 = 2 * 9.8 m/s^2 * .65 m = 12.7 m^2 / s^2

v = 3.57        max speed attainable by pendulum

v^2 = 2 g * .25       speed attainable when falling thru .25 m

v^2 = 4.9 m^2/s^2

v = 2.21 m/s speed of pendulum after falling thru .25 m

The initial acceleration of proton and electron is 3.45 x 10¹⁸ m/s² and 6.33 x 10²¹ respectively.

The electrostatic force F between two charged objects placed distance apart is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.

F = kq₁q₂/r²

where k = 9 x 10⁹ N.m²/C²

Given is the charge on proton and electron  is q =1.6 x 10⁻¹⁹ C, distance r =2 x 10⁻¹⁰m , then the force will be

F = k q²/r²                          

Substituting the above values in the formula, we get the electrostatic force,

F = (9 x 10⁹) (1.6 x 10⁻¹⁹)²/(2 x 10⁻¹⁰)²    

F = 5.76 x 10⁻⁹ N

The acceleration of electron when both proton and electron released is

acceleration =  electrostatic force / mass of electron

Putting the values, we have initial acceleration of electron

a = (5.76 x 10⁻⁹)/(9.1 x 10⁻³¹)

a = 6.33 x 10²¹ m/s²

The acceleration of proton is due to the electrostatic force of attraction between proton and electron is given by

acceleration =  electrostatic force / mass of proton

inserting the values, we get the initial acceleration

a '= (5.76 x 10⁻⁹)/( 1.67 x 10⁻²⁷)

a'= 3.45 x 10¹⁸ m/s²

Thus, initial acceleration of proton and electron is 3.45 x 10¹⁸ m/s² and 6.33 x 10²¹ respectively.

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Answer:

Option C. Rate of change of velocity

Explanation:

To know the correct answer to the question, it is important we know the definition of power.

Power can be defined as the rate at which work is done. Mathematically, it is expressed as:

Power = work / time

Work and energy has the same unit of measurement i.e joule. Thus, power can also be defined as the rate at which energy is transferred i.e

Power = enery / time

Energy is measured in Joules and time in second. Thus, power can also be defined as amount of joules transfered per second.

Power = Joule / sec

The rate of change of velocity on the other hand is termed acceleration.

Thus, the answer to the question is option C.

You can improve how you handle stress and difficulties (adversity) in your life by using a variety of stress management techniques. You may lead a more well-balanced existence by controlling your stress.

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The average speed of the sea floor expansion during this time has been approximately 8.03 x \(10^{-7\) meters per second.

The sea floor expansion can be calculated using the age of the oldest rocks and the width of the strip. In this case, the oldest rocks are 750,000 years old, and the strip is 19 km wide. To find the average speed of expansion, we need to divide the width of the strip by the age of the rocks.

Average speed of sea floor expansion = (Width of the strip) / (Age of the oldest rocks)

Average speed = (19 km) / (750,000 years)

To convert years to seconds, multiply by the number of seconds in a year (365.25 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute):

750,000 years * 365.25 * 24 * 60 * 60 = 23,652,060,000 seconds

Now, divide the width of the strip by the age of the rocks in seconds:

Average speed = (19,000 meters) / (23,652,060,000 seconds)

Average speed ≈ 8.03 x \(10^{-7\) meters/second

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Answer:

3x10^8=3f f=1x10^8 It think it is hopeful

The required frequency of light with a wavelength of 3 meters is \(1 * 10^{8}\).

Given that,
The frequency of light with a wavelength of 3 meters is to be determined.

Frequency is defined as the amount to waves passes through per unit course of time.

A wave is defined as a disruption in a system that bears energy without the action of particles. It may take the form of adaptable deformation, a divergence of stress, electric or magnetic intensity, electric potential, or temperature.

Here,
The formula for the frequency of light is
F = c / λ
Where C = speed of light = \(3 * 10^8\) and,
λ = wavelength = 3

F =  \(3 * 10^8\) * / 3
F =    \(1 * 10^{8}\)

Thus, the required frequency of light with a wavelength of 3 meters is \(1 * 10^{8}\).

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The correct answer is

B. corona.

The corona is the outermost layer of a star's atmosphere and extends millions of kilometers into space.

It is composed of extremely hot plasma and is most easily observed during a total solar eclipse when it appears as a faint, pearly-white glow surrounding the darkened disk of the Moon. The other options mentioned are also parts of a star, but they do not extend to the same distances as the corona.

Hot plasma is a state of matter in which particles, such as electrons and ions, are so energized that they become completely or partially ionized. Plasma is often referred to as the fourth state of matter, in addition to solid, liquid, and gas. It is characterized by its ability to conduct electricity and respond to magnetic fields.

When a substance is heated to high temperatures, the thermal energy causes the atoms or molecules to move rapidly, eventually leading to the breaking of chemical bonds. In the case of plasma, the extreme heat causes the atoms to lose electrons, resulting in a mixture of positively charged ions and negatively charged electrons. This ionization process gives rise to a highly conductive medium with unique properties.

Plasmas can be found naturally occurring in phenomena such as lightning, the Sun's corona, and certain types of flames. They can also be created in laboratory settings using various methods, including heating a gas to high temperatures, subjecting it to strong electromagnetic fields.

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