It takes 128 seconds for sorting an array using insertion sort having size 800000.
The straightforward sorting algorithm known as insertion sort produces the final sorted array one item at a time through comparisons. In comparison to more sophisticated algorithms like quicksort, heapsort, or merge sort, it performs significantly worse on huge lists.
The worst-case (and average-case) complexity of the insertion sort method is O ([tex]n^2[/tex]).
To put it another way, in the worst situation, the time needed to sort a list is inversely proportional to the square of the number of entries in the list.
The best-case time complexity of the insertion sort algorithm is O(n).
Therefore, we may argue that by considering the worst-case scenario for the problem.
We have, [tex]O(100000)^2[/tex] = 2 Sec
So for the array of size 800,000, it will take
[tex]= 8^2 \times O(100,000) = 8^2 \times 2[/tex]
=64*2 = 128 seconds
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during the game, the metabolism of basketball play- ers often increases by as much as 30.0 w. how much perspiration must a player evaporate per hour to dissipate this extra thermal energy?
Basketball players' metabolisms frequently accelerate by up to 30.0 w while they are playing. To release this extra thermal energy, a player must perspire 4.78x10-2kg.
Given that players release 30 J/s of heat (Q)
Heat is lost each hour given that
U=(30J/s)(3600s/h)=1.08x105J of thermal energy is lost per hour.
The amount of water that would be vaporized by this energy transmission is given by the formula:
m = U/Lwater
m=(1.08x105J)/(2.26X106J/kg)=4.78x10-2kg.
The temperature affects how hot water vaporizes. It is 2.257 x 106 J/kg at the boiling point (100C), but it is more like 2.40 x 106 J/kg at 37C.
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which of the following is fundamentally different from the others? a. sound waves b. x-rays c. gamma rays d. green light waves e. radio waves
Sound waves are fundamentally from the other waves.
A sound wave is a pattern of disruption brought on by the movement of energy moving through a medium as it propagates away from the source of the sound (such as air, water, or any other liquid or solid matter).
Sound waves are fundamentally from the other waves.A sound wave is a configuration of disruption brought on by an energy flow moving through a medium.Unlike electromagnetic waves, which do not require any medium for propagation, the medium can be air, water, liquid, or any other solid material.Electromagnetic waves include X-rays, radio waves, and light waves.Electric and magnetic waves combine to form electromagnetic waves.Know more about Sound waves at:
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a car increases its speed, changing its kinetic energy from 60,000 j to 80,000 j. assuming no friction, how much work is done by the car’s engine to cause this change?
The work required by the car's engine to raise its speed and change its kinetic energy from 60,000 J to 80,000 J is 2000 J.
Force multiplied by distance equals work done.
Joules are the unit used to measure work.
The difference between the car's starting and final kinetic energies is the result of the engine's work, which increased the vehicle's speed and increased its kinetic energy from 60,000 j to 80,000 j.
Final kinetic energy minus beginning kinetic energy is the formula for the work the car engine performs.
The car's engine produces work at a rate of 80000 J - 60000 J.
The car's engine generates 20,000 J worth of work.
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two objects attract each other with a gravitation force of magnitude 3.80 x 10-8 n when separated by a distance of 0.350 m. if the difference in mass of the objects is 7.50 kg, what is the mass for each of these objects?
The mass for each of these objects is 12.91kg and 5.41kg.
Gravitational Force:
The traditional hypothesis that explains gravity is Newton's law of gravitation. Only the masses of two objects and their distance from one another are taken into account by this law. According to Newton's law of gravitation, the following is how much gravitational force there is between two objects.
F = GMm/r²
Where,
r is the radius.
M and m are the masses of the objects.
G = Universal constant = 6.67 × 10⁻¹¹ [tex]\frac{m^{3} }{kgs^{2} }[/tex]
Given,
Gravitational Force = 3.8 × 10⁻⁸ N
Distance between two objects = 0.35 m
Let,
The mass of one object is x kg.
Then,
The mass of the second object = (x - 7.5) kg.
Now,
F = GMm/r²
3.8 × 10⁻⁸ = 6.67 × 10⁻¹¹ × x × (x - 7.5)/[tex](0.35)^{2}[/tex]
x² - 7.5x - 575.76 = 0
x = 12.91, 5.41
Hence,
The mass for each of these objects is 12.91kg and 5.41kg.
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a gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric pressure. when 254 kcal of heat is added to the gas, the volume is observed to increase slowly from 12.0 m3 to 16.2 m3 . Calculate the work done by the gas and the change in internal energy of the gas.
Upon absorbing 254 kcal of heat, a gas contained in a cylinder kept at atmospheric pressure sees a rise in volume from 12.0 m3 to 16.2 m3. The work performed by the gas is -1.01 × 10⁵ Kcal, and the internal energy has changed by -1.01 × 10⁵ Kcal
The volume of a gas contained in a cylinder at atmospheric pressure (P = 101325 Pa) increases from 12.0 m³ to 16.2 m³.
The following phrase can be used to determine the work (w) that the gas has performed.
w = -P × ΔV = -101,325 Pa × (16.2 m² - 12.0 m²) = -4.26 × 10⁵ J × 1kcal/4181J = -1.02 × 10⁵ Kcal
The gas receives 254 kcal of heat, making q equal to 254 kcal. The following phrase can be used to determine how the internal energy (E) has changed.
ΔE = q + w = 254 Kcal + (-1.02 × 10⁵ Kcal) = -1.01 × 10⁵ Kcal
When a gas is contained in a cylinder that is kept at atmospheric pressure, it absorbs 254 kcal of heat, increasing its volume from 12.0 m³ to 16.2 m³. The gas expends -1.02 × 10⁵ kcal of effort, and the internal energy changes by -1.01 × 10⁵ kcal.
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A grocery shopper tosses a(n) 8.5 kg bag of
rice into a stationary 17.4 kg grocery cart.
The bag hits the cart with a horizontal speed
of 5.5 m/s toward the front of the cart.
What is the final speed of the cart and bag?
Answer in units of m/s.
Answer:
3.1 m/sec
Explanation:
The contained in the flying bag of rice is applied to the stationary cart. Lets calculate the kinetic energy of the flying bag of rice. Kinetic energy (KE) is given by KE = (1/2)mv^2, where m is the mass and v is the velocity.
[Note: a kg*m^2/s^2 is 1 Joule]
KE(rice bag) = (1/2)(8.5kg)(5.5m/s)^2
KE(bag) = 129 Joules
When the bag hits the shopping cart, some of the energy tis transferred to the cart. We aill assume no energy in lost in the collision (conservation of energy). The kinetic energy is now contained in a body with a total mass of 25.9 kg (rice bag plus cart).
Use the kinetic energy expression again, using the same KE from the rice bag, but with a new mass.
KE = (1/2)mv^2
129 Joules = (1/2)(26.9 kg)v^2
129 kg*m^2/s^2 = (1/2)(26.9 kg)v^2
v^2 = (129 kg*m^2/s^2)/(12.95 kg)
v^2 = 9.96 m^2/s^2
v = 3.12 m/s (3.1 m/2 with 2 sig figs)
3.12 m/s will be the velocity of the grocery cart and rice bag. [That's 6.7 miles/hr, for the non-metric inclined]
If 2.5 minutes is the maximum access time for a magnetic tape, ____ is the average access time.
a. 0.5 minutes c. 1.25 minutes
b. 1 minute d. 2 minutes
The average access time of the magnetic tape is 1.25 minutes
What is access time of a magnetic disc?Disk access time is defined as the total time required by the computer to process a read/write request and then retrieve the required data from the disk storage.
The access time may be counted in nanoseconds for a semiconductor device, in milliseconds for a magnetic disk, or in minutes if the file containing the required data is on magnetic tape.
A magnetic field sensing read head and a magnetic field inducing write head are used for accessing data on each recording surface.
The average time of the magnetic tape is :
(0+2.5)/2
average access time = 2.5/2 = 1.25 minutes
Therefore the average access time of the magnetic tape is 1.25minutes.
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Please help me I have no idea
The fraction of kinetic energy which is transferred to the atomic nucleus is 30.3% and the final kinetic energy of the neutron is 2.93*10^-13.
What is kinetic energy?An object's kinetic energy refers to the energy it has as a result of motion. After the job is finished, the object will be traveling at a new, constant speed because energy has indeed been transferred to it.
Briefing:let the mass of neutron =m
Mass of neucleus= M
given: M=11.1m
by conservation of kinetic energy:
fraction of energy that will be transferred to the nucleus = [tex]\frac{4mM}{(M+m)^{2} }[/tex]
= 44.4/146.41
=0.303
let u be the initial velocities of neutron and nucleus
and v be the final velocities of neutron and nucleus
By conservation of linear momentum,
mu+Mu=mv+Mv
v(nucleus)=2*v(neutron)/12.1
the initial kinetic energy of neutron= 4.2*10^-13
so on solving the final kinetic energy of neucleus=1.27*10^-13
so,
final k.e.of neutron=4.2*10^-13 - 1.27*10^-13
= 2.93*10^-13
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in amps. a constant voltage of 77 volts is put across a resistance that is increasing at a rate of 0.20.2 ohms per second when the resistance is 55 ohms. at what rate is the current changing?
A constant voltage of 77 volts is put across a resistance that is increasing at a rate of 0.202 ohms per second when the resistance is 55 ohms. The current is changing at a rate of 0.0051amps per sec
Given voltage (V) = 77v
Resistance (R) = 55ohms
The relation among voltage (V), resistance (R) and current (I) is given as
I =V/R
The increasing rate of resistance is = dR/dt = 0.2ohms per second
By derivating the current to get rate of change in current
dI/dt = Vxd/dt(1/R) [ Because V is a constant ]
dI/dt = V x d/dt(R −1)
dI/dt = V(-1/R^2 x dR/dt) = 77x (-1/55x55) x 0.202 = -0.005amp per second
Hence the current is changing at a rate of 0.0051amps per sec
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when is the angle at which a ray of light strikes glass not the same as the angle it exits?
Answer:
Explanation:
Assuming the light travels through air, hits the glass and is then reflected back into air (in other words, the medium is the same), the only reason the angle of incidence would NOT equal the angle of reflection is if the surface of the glass is not smooth (is rough, scratched, etc.)
A football player pushes a training sled 20 meters while pushing with a constant force of 300 Newtons. If this is accomplished in 7.5 seconds, what power was exerted?
The Power exerted will be 800W
What is Power?Power is the quantity of energy that is transferred or transformed in a certain length of time. The watt, which is equal to one joule per second as in the International System of Units is the unit of power. A scalar concept is a power.
Using te formular;
Power = (Force x distance) / time
P = (F x d) / t
where F = 300N
d = 20m
t = 7.5s
P = (300 x 20) / 7.5
P = 800W
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(a) an electron has a kinetic energy of 3. 0 ev. Find its wavelength. (b) also find the wavelength of a photon having the same energy.
Its wavelength is 8.47 x 10-11 m and wavelength of a photon having the same energy is 1.01 x 10-7 m.
What is wavelentgh?Wavelength length is a distance between two consecutive peaks of a wave it is most commonly associated with light and sound wave but can also refer to electromagnetic radiation like gamma rays x-rays and radio wavelentgh is usually measured in meters or nanometers.
(a) The wavelength of an electron with a kinetic energy of 3.0 eV can be calculated using the formula λ= h/√(2mKE) , where h is Planck's constant (6.62607 x 10-34 Js), m is the electron's mass (9.10938 x 10-31 kg), and KE is the kinetic energy (3.0 eV). Plugging in the values gives us a wavelength of 8.47 x 10-11 m.
(b) The wavelength of a photon with the same energy as the electron can be calculated using the equation λ= hc/E, where h is Planck's constant (6.62607 x 10-34 Js), c is the speed of light (299792458 m/s), and E is the energy of the photon (3.0 eV). Plugging in the values gives us a wavelength of 1.01 x 10-7 m.
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the anti-lock brake system engages every time the driver applies the brakes. group of answer choices true false
Imagine aliens landed on earth. If the aliens learned English, from their perspective,
what would Earth be?
An interior planet
An exoplanet
An outsider planet
An irregular and planet
From aliens perspective, Earth would be an exoplanet in English language.
What is exoplanet?Any planet outside of our solar system is an exoplanet. The majority of exoplanets orbit other stars, while rogue planets—free-floating exoplanets that are unattached to any star—orbit the galactic centre.
The majority of the exoplanets found so far are in the Milky Way, which is a rather tiny area of our galaxy. The Kepler Space Telescope of NASA has revealed that the galaxy has more planets than stars.
We can determine the sizes (diameters) and weights (weights) of exoplanets and determine their compositions, which range from extremely stony (like Venus and Earth) to extremely gas-rich (like Jupiter and Saturn). Exoplanets contain elements that are comparable to those found in our solar system, but their compositions of those elements may vary.
If aliens arrived on earth. Earth would be considered an exoplanet in the language of them.
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cumulus clouds often indicate a. a dry adiabatic lapse rate. b. a temperature inversion. c. possible turbulence.
Cumulus clouds often indicate Optiion C. possible turbulence.
Turbulence, associated with thunderstorms, may be extremely risky, having the ability to motivate overstressing of the aircraft or lack of manipulation. Thunderstorm vertical currents can be sturdy sufficient to displace a plane up or down vertically as plenty as 2000 to 6000 ft.
Turbulence is only one type of alternate in the air around your aircraft. Air is not nothingness; it's a fluid, like water. Currents of airflow up and down, ripple out, trade direction, and change speed. some of the things that reason turbulence are simpler to expect.
Turbulence is an unexpected and every-so-often violent shift in airflow. the ones irregular motions within the atmosphere create air currents that may purpose passengers on an aircraft to enjoy stressful bumps throughout a flight, or it is able to be extremely sufficient to throw an airplane out of manage.
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arrange the colors of the visible spectrum in order from highest to lowest energy.- Violet - Indigo - Blue- Green- Yellow- Orange- Red
From lowest energy to highest energy, the hues of the spectrum are violet, indigo, blue, green, yellow, orange, and red. Can the visible spectrum be divided up into the several hues that make up visible light?
590–620 nm for orange Red: 620-750 nm (400–484 THz frequency) The violet spectrum of light has the maximum frequency and energy because it has the shortest wavelength. Red has the highest energy, the longest wavelength, and the lowest frequency. the hues that make up the visible light spectrum, including blue, green, red, yellow, orange, violet, and indigo. Actually, these are the hues of the rainbow. How many colours are there in the visible spectrum of light? They are all. A visible light spectrum is the name given to a rainbow of colours. What's the name of the
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imagine that you are an olympic sprinter, running at a speed of 11 m/s around the curve of a circular track with a radius of 36.5 m. what is your centripetal acceleration?
When an Olympic sprinter runs around the curve of a circular track with a radius of 36.5 m, they experience centripetal acceleration of 3.31m/s2.
Given that the runner's speed(v) = 11 m/s
Circular track radius (r) equals 36.5 meters
Centripetal acceleration (ac) is calculated as follows:
(11x11)/36.5 = 3.31 m/s2.
Centripetal acceleration is a characteristic of an object's motion along a circular path. Centripetal acceleration applies to any item travelling in a circle with an acceleration vector pointing in the direction of the circle's center. The centripetal acceleration, denoted by the symbol AC, has a magnitude equal to the square of the velocity of the body along the curve divided by the radius of the circle, denoted by the symbol r. This is also known as the formula ac = v2/r.
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Approximately how much work do you do when you lift your 10.0 kg sister to a height of 1.5 m?
The amount of work done in lifting the sister to a height of 1.5m is approximately 147 J.
The height to which the sister of mass 10.0 Kg is lifted is 1.5m.
The work done to lift sister is given by,
W = MgH
Where,
M is the mass of the sister,
g is the acceleration due to gravity,
H is the height to which the sister as lifted,
The value of acceleration due to gravity of earth is 9.8m/s².
Now, putting all the values accordingly,
W = 10.0 x 9.8 x 1.5
W = 147 Joules.
So, the amount of work done in lifting the sister is 147 J.
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what is b(r) , the magnitude of the magnetic field inside the toroid and at a distance r from the axis of the toroid?
the strength of the magnetic field within the toroid and at a distance of r from the toroid's axis
the magnitude of the magnetic field inside the toroid be
B(r)=[tex]\frac{\mu IN}{2\pi r}[/tex]
when only in [tex]r^{\cap}[/tex] any [tex]k^{\cap}[/tex] direction
B=[tex]\frac{\mu_{0} I }{2R}[/tex]
A magnetic field is a vector field that explains the magnetic influence on moving electric charges, electric currents, and magnetic materials. A force perpendicular to the charge's own motion and the magnetic field acts on it while the charge is traveling through a magnetic field. The magnetic field of a permanent magnet pulls on ferromagnetic elements like iron and attracts or repels other magnets. The three other magnetic effects of paramagnetism, diamagnetism, and antiferromagnetism also exert minute forces on "nonmagnetic" materials in a nonuniform magnetic field, albeit these forces are often so minute that they can only be measured by laboratory equipment. Electric currents, like those utilized in electromagnets, and electric fields that change over time produce magnetic fields that surround magnetized things.
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Howard i moving a 90 kg wooden crate from one ide of hi office to the other. To accomplih thi, he tie a rope around hi wait and begin to walk, o that the crate i dragged horizontally acro the floor. If the coefficient of friction between the crate and the floor i 0. 159, what force mut Howard apply to to the rope to move at a contant peed?
The force exerted by Howard on the rope to make it move at a constant speed is 140.24 N.
The force that Howard must exert on the rope to move at a constant speed is calculated by applying Newton's second law of motion as follows:
F - Ff = ma
F: the applied force
Ff: the frictional force
m: the mass of the crate's mass
a: the acceleration of the crate (at a constant speed, acceleration: a = 0)
F = Ff
F = μmg
Given in question
Friction coefficient: μ = 0.159Gravity speed: g = 9.8 m/sCrate mass : m = 90 kgF = μmg
F = 0.159 x 90 x 9.8
F = 140.24 N
Then the force Howard exerts on the rope to move at a constant speed is 140.24 N
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light travels at about 300 million meters per second, and the sun is about 150 million kilometers from the earth. how long does it take light from the sun to reach earth?
The sun is 150 million kilometres away from the earth, and light travels at a speed of 300,000 km/sec. As a result, it takes over 8 minutes for sunlight to reach earth.
What is Light Year?
The light-year is a unit of distance, not of time (as the name might imply). A light-year is the distance a light beam travels in one year on Earth, which is around 6 trillion miles (9.7 trillion kilometers).
Given the extremely enormous numbers being discussed, it is difficult to measure lengths in miles or kilometres on the size of the universe. Astronomers can measure the distances of stars from Earth in a much less time than it takes for light to cross that vast distance. For instance, Proxima Centauri, the star closest to our sun, is 4.2 light-years distant from us, which means it takes little over four years for the star's light to reach us.
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A mass of sunken lead is resting against the bottom in a glass of water. You take this lead, put it in a small boat of negligible mass, and float the boat in the water.
1.) Which of the following statements are true? (There may be more than one correct choice.)
A. The sunken lead displaces a volume of water equal to the lead's own volume.
B. The floating lead displaces a volume of water equal to the lead's own volume.
C. The sunken lead displaces a volume of water whose weight equals the lead's weight.
D. The floating lead displaces a volume of water whose weight equals the lead's weight.
The sunken lead displaces a volume of water equal to the lead's own volume. The floating lead displaces a volume of water whose weight equals the lead's weight.
What is Mass?
It is the most fundamental characteristic of matter and one of the fundamental quantities in physics. Mass is a term used to describe how much matter is there in a body. The kilograms is the SI unit of mass (kg).
A body's mass does not alter at any point in time. only in rare instances where a significant quantity of energy is supplied to or taken away from a body. A nuclear reaction, for instance, results in the mass of the substance being reduced as a very little amount of matter is transformed into a very large amount of energy.
This law provides a numerical description of how a force might alter a body's motion.
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which of the following materials can be used to estimate the age of the earth and our solar system?
The materials used to determine the age of earth and the age of our solar system is the fragments from the Canyon Diablo iron meteorite.
The age of earth can be determined by the radio uranium dating. In 1920's, Earth's age crept up toward 4.5 billion years, making it for a time even older than the universe, which was then estimated to be about 13.7 billion years old.
All the rocks and minerals contain long-lived radio active elements that were incorporated into earth when the solar system formed.
According to research on meteorites, the age of the solar system is close to 5 billion years old, whereas the age of the Earth is assumed to be 4.6 billion years. The Earth's oldest rocks are estimated to be 3.8 billion years old.
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All of are following are same process. EXCEPT
A.Condensation
B.Freezing
C.Crystallization
D.Solidification
Condensation, freezing, solidification are same process while crystallization is different from condensation, freezing and solidification.
A. Condensation - It is the process of conversion of water vapours or gas to liquid. For example conversion of steam into water. Condensation occurs at 100 degree celcius.
B. Freezing - It is the phase when liquid gets converted into solid. For example conversion of water into ice. It starts at 0 degree celcius for water.
C. Crystallization - It is the process of forming Crystals. For example evaporation of salt water.
D. Solidification - The process of conversion of liquid into solid. For example formation of snow and solidification of melted candle wax.
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Condensation, freezing and solidification are same process of phase transformation whereas Crystallization is different from others.
What is phase transformation?The physical process of changing a medium's state from one to another is known as a phase transition (or phase change) in the domains of chemistry, thermodynamics, and other related sciences. The phrase is frequently used to describe transitions between the three fundamental states of matter—solid, liquid, and gas—and, in rare instances, plasma.
The physical characteristics of a phase of a thermodynamic system and the states of matter are constant. Certain properties of a given medium change during a phase transition as a result of a change in the environment, such as temperature or pressure. This change can be discontinuous. The phase transition point is identified by the external circumstances in which a change takes place.
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B) Calculate the maximum force of static friction that could exist in this system.
Give any Two Proops Proops to show that the Earth rotates from West to East
The earth rotates from west to east that why sun rises at east and sets in the west. Similarly we see that the moon also visible from the east then at west.
What is prograde rotation?The earth rotates counterclockwise, from west to east, as seen from above the north Pole. This is also referred to as a Prograde rotation.We know that the earth rotates once every 24 hours.
As the earth rotates from west to east, the moon, sun, and all other celestial bodies appear to move from east to west in the opposite direction of the earth's rotation. This is the primary reason for the sun rising in the east and setting in the west.
Therefore, it is proven that the earth is rotating from west to east.
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what change in entropy occurs when a 27.9 g ice cube at -12°c is transformed into steam at 115°c?
Upon calculation the change in entropy is found to be 244 J/K.
Entropy is a generic phrase that describes the trend toward disorder as well as the spontaneous changes that take place in everyday situations. Entropy is not only a term used in academia; it is also frequently characterized as a physical feature connected to uncertainty.
For a reversible process the change in entropy is given by:
S= [tex]\frac{dQ}{T}[/tex]
dQ= heat
T= temperature
The change in entropy when the temperature of ice comes to 273 K is:
S= [tex]\int\limits^{273}_ {261} \, \frac{dQ}{T}[/tex]
dQ= mcdT
m= mass of ice= 27.9 gm= 0.0279 kg
c= specific heat capacity= 2090 J/kg C
T= temperature
S=[tex]mc\int\limits^{273}_{261} \, \frac{dT}{T}[/tex]
S= 0.0279× 2090×㏑[tex]\frac{273}{261}[/tex]
S= 2.62 J/K
For conversion of ice into water dQ= mL
m= mass of ice
L= latent heat of fusion= 3.33 ×10⁵
S= [tex]\frac{mL}{T} =\frac{3.33* 100000*0.0279}{273}[/tex]
S= 34 J/K
Change in entropy when the water turns into steam is given by
S= [tex]\int\limits^{373}_{273} \, \frac{mcdT}{T} =mc ln\frac{373}{273}[/tex]
c= heat capacity of water= 4186
S= 0.0279× 4186×㏑[tex]\frac{373}{273}[/tex]
S= 36.5 J/K
Change in entropy at 373 K for steam is given by
S= [tex]\frac{dQ}{T} = \frac{mL}{T}= \frac{2.26*1000000*0.0279}{373} -=169 J/K[/tex]
Here L= 2.26×10⁶
Change in entropy for steam when it rises to a temperature 115 degree Celsius= 388K
S= [tex]\int\limits^{388}_{373} \, \frac{dQ}{T} =\int\limits^{388}_{373} \, \frac{mcdT}{T} =mc\int\limits^{388}_{373} \, \frac{dT}{T} = 0.0279*2010*ln\frac{388}{373} =2.21 J/K[/tex]
Adding all the entropies obtained in the cases we get
Total entropy= 2.62+34+36.5+169+2.21
S= 244J/K
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The temperature at a point in a ball with conductivity K is inversely proportional to the distance from the center of the ball. Find the rate of heat flow across a sphere S of radius a with center at the center of the ball.
A sphere S with a radius of a and a centre in the centre of the ball will conduct heat flow at a rate of 4πcK
Given In a ball with conductivity K, the temperature at a given place is inversely proportional to the distance from the ball's centre. If the scalar field u(x, y, z) exists and the divergence of u is ∇u = ∂u/∂xi+∂u/∂yj+∂u/∂zk
The surface integral is used to calculate the rate of heat flow over the body's surface S. ∬F⋅dS = F⋅n∬dS
Equation for the radius of a sphere is x^2+y^2+z^2 = a^2
And if the temperature of a ball is u(x, y, z), then u(x, y, z) ∝ 1/√x^2+y^2+z^2
The proportionality constant is denoted by c. So, u(x, y, z) = c/√x^2+y^2+z^2
Then ∇u = ∂(c/√x^2+y^2+z^2)/∂xi+∂(c/√x^2+y^2+z^2)/∂yj+∂(c√x^2+y^2+z^2)/∂zk
∇u = -(cx/√x^2+y^2+z^2)i-(cy/√x^2+y^2+z^2)j-(cz/√x^2+y^2+z^2)k
Hence F = -K.∇u
F = cK(xi+yj+zk)/(x^2+y^2+z^2)^3/2
And the outward unit normal is, n = 1/a(xi+yj+zk)
Thus F.n = cK(xi+yj+zk)/(x^2+y^2+z^2)^3/2 x 1/a(xi+yj+zk)
F.n = cK/a*(x^2+y^2+z^2)^1/2 but x^2+y^2+z^2 = a^2
F.n = cK/a^2
The rate of heat flow = F⋅n∬dS = cK/a^2∬dS
cK/a^2(4πa^2) = 4πcK
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How do we learn about what is going on in the center of our own galaxy (the Milky Way)?
A) We have learned it only recently, thanks to the great photographs obtained by the Hubble Space Telescope.
B) We cannot see the galactic center with visible or ultraviolet light, but radio and X rays from the center can be detected.
C) The gas and dust in the Milky Way prevent any type of direct observation of the galactic center, but theoretical models allow us to predict what is happening there.
D) We must look at the centers of other galaxies and hope that ours is just like others.
The things which are going on in the centre of our own galaxy (the Milky Way), We cannot see the galactic centre with visible or ultraviolet light, but radio and X-rays from the centre can be detected.
Milky Way GalaxyThe galaxy that contains our Solar System is known as the Milky Way, and its name refers to how it appears to us on Earth: a hazy strip of light in the night sky made up of stars that are too close together to be seen individually. The phrase Milky Way is a translation from Greek (galaktikos kklos), which means "milky circle," into Latin via lactea. The Milky Way is a disk-shaped structure, yet when viewed from Earth, it seems like a band. In 1610, Galileo Galilei used his telescope for the first time to separate the band of light into individual stars. Most astronomers believed that the Milky Way held all of the universe's stars until the early 1920s.
Observations by Edwin Hubble proved that the Milky Way is only one of many galaxies after the 1920 Great Debate between the astronomers Harlow Shapley and Heber Curtis.
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a lateral chest technique calls for 110 kvp, 10 mas and result in an x-ray intensity of 0.32 mgy. what will be the intensity if the kvp is increased to 125 kvp and the mas remains fixed.
If the kvp is increased to 125 kvp then the intensity becomes 41.32 mR.
We know the relation between kvp and intensity as,
I₁ / I₂ = kvp₁²/ kvp₂²
where, I is intensity in mR
kvp is kilovoltage peak
Given that, kvp₁ = 110 kvp
kvp₂ = 125 kvp
I₁ = 0.32 mgy
To convert mgy to mR, we know 1 mgy = 100 mR
I₁ = 0.32 mgy = 0.32* 100 = 32 mR
Substituting the values in the above equation, we have
32 / x = 110²/ 125²
32 * 125² = x * 110²
x = (32 * 125²) / 110² = 41.32 mR
Thus, the new intensity becomes 41.32 mR.
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