Answers
Answer:
hope this helps and if you have any questions please feel free to ask me any time
Statement :- We assume the orthagonal sequence [tex]{{\{\phi\}}_{1}^{\infty}}[/tex] in Hilbert space, now [tex]{\forall \sf \:v\in \mathbb{V}}[/tex], the Fourier coefficients are given by:
[tex]{\quad \qquad \longrightarrow \sf a_{i}=(v,{\phi}_{i})}[/tex]
Then Bessel's inequality give us:
[tex]{\boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}[/tex]
Proof :- We assume the following equation is true
[tex]{\quad \qquad \longrightarrow \displaystyle \sf v_{n}=\sum_{i=1}^{n}a_{i}{\phi}_{i}}[/tex]
So that, [tex]{\bf v_n}[/tex] is projection of [tex]{\bf v}[/tex] onto the surface by the first [tex]{\bf n}[/tex] of the [tex]{\bf \phi_{i}}[/tex] . For any event, [tex]{\sf (v-v_{n})\perp v_{n}}[/tex]
Now, by Pythagoras theorem:
[tex]{:\implies \quad \sf \Vert v\Vert^{2}=\Vert v-v_{n}\Vert^{2}+\Vert v_{n}\Vert^{2}}[/tex]
[tex]{:\implies \quad \displaystyle \sf ||v||^{2}=\Vert v-v_{n}\Vert^{2}+\sum_{i=1}^{n}\vert a_{i}\vert^{2}}[/tex]
Now, we can deduce that from the above equation that;
[tex]{:\implies \quad \displaystyle \sf \sum_{i=1}^{n}\vert a_{i} \vert^{2}\leqslant \Vert v\Vert^{2}}[/tex]
For [tex]{\sf n\to \infty}[/tex], we have
[tex]{:\implies \quad \boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}[/tex]
Hence, Proved
Related Questions
Find the volume of the irregular object a marble
Answers
By using Displacement method we can find volume of irregular object like marble.
What is displacement method?In displacement method,
First , we measuring the volume of water displaced by an object which tell us the volume of the object.
Secondly We can use the physical balance to determine its mass.
Lastly , calculate the density by dividing the mass by the volume.
Procedure to find the Volume of irregular object i.e. marble
step 1 - Fill the graduated cylinder about half full and measure the initial volume of water.
step 2 - Drop the marble in the graduated cylinder.
step 3 -Now measure the final level of water.
Step 4 - Subtract both the values.
Here , comes the Volume of Irregular Object.
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1. Los Angeles lies on Pacific plate, San Francisco lies on North American plate. When will the two cities meet if the distance between them is 600 km and Pacific plate is moving (NW) at 5 cm/yr?
Answers
Los Angeles lies on the Pacific plate, San Francisco lies on the North American plate, and the meeting point of the two cities is mathematically given as
T = 120 x 105 years
What is the meeting point of the two plates?Generally, the equation for Distance is mathematically given as
D = Rate x Time
Therefore
T = D/R
T = (600 x 105) / 5
T = 120 x 105 years
In conclusion, the meeting point of the two plates will be
T = 120 x 105 years
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What is the average translational kinetic energy of nitrogen molecules at 1600 K? A. 1.31x10-20 J. B. 2.31x10-20 J. C. 3.31x10-20 J. D. 4.31x10-20 J.
Answers
KE
5/2KTFor nitrogen n=5
So
5/2(1.38×10^{-23})(1600)5500×10^{-23}5.5×10^{-20}J50 POINTS URGENT HELP NEEDED SPACE
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please answer all questions in complete sentences using your own words.
Using two to three sentences, summarize what you investigated and observed in this lab.
You completed three terra forming trials. Describe the how the sun's mass affects planets in a solar system. Use data you recorded to support your conclusions.
In this simulation, the masses of the planets were all the same. Do you think if the masses of the planets were different, it would affect the results? Why or why not?
How does this simulation demonstrate the law of universal gravitation?
It is the year 2085, and the world population has grown at an alarming rate. As a space explorer, you have been sent on a terraforming mission into space. Your mission to search for a habitable planet for humans to colonize in addition to planet Earth. You found a planet you believe would be habitable, and now need to report back your findings. Describe the new planet, and why it would be perfect for maintaining human life.
DATA BELOW
sun's mass 1x—Trial One
1
5
2
3
1
1
sun's mass 1x—Trial Two
1
2
0
0
2
2
sun's mass 2x—Trial One
1
0
0
0
1
0
sun's mass 2x—Trial Two
1
3
2
0
4
0
sun's mass 3x—Trial One
1
2
0
0
2
0
sun's mass 3x—Trial Two
1
0
0
0
1
3
Answers
Answer:
Using two to three sentences, summarize what you investigated and observed in this lab. I investigated that Most of my planets and moons had the element carbon in them. I observed that Different elements absorb different wavelengths of light.
Astronomers use a wide variety of technology to explore space and the electromagnetic spectrum; why do you believe it is essential to use many types of equipment when studying space?
It is essential to use a number of telescopes sensitive to different parts of the electromagnetic spectrum to study objects in space. Even though all light is fundamentally the same thing, the way that astronomers observe light depends on the portion of the spectrum they wish to study. Tools are useful, such as detectors that help see the different wavelengths of light. Not all light can get through the Earth's atmosphere, so for some wavelengths we have to use telescopes aboard satellites.
If carbon was the most common element found in the moons and planets, what element is missing that would make them similar to Earth? Explain why. (Hint: Think about the carbon cycle.)
The missing element that would make moons and other planets similar to earth is oxygen. The two make carbon dioxide.
We know that the electromagnetic spectrum uses wavelengths and frequencies to determine a lot about outer space. How does it help us find out the make-up of stars?
electromagnetic radiation Explanation, astronomers observe the wavelengths by putting telescopes on mountain tops and take results of what they are seeing
Why might it be useful to determine the elements that a planet or moon is made up of?
It might be useful so we can make new discoveries of life or even plants on other planets and moons. And discover maybe even more moons one other planets.
Hope this helps!!!!
Explanation:
calculate the power output of a machine that lifts a 50kg crate through a height of 20.0m in one minute
Answers
Answer:
power= work done/ time
power=mgh/time
mass(m) =50kg
acelleration due to gravity (g)= 10g/m^2
height(h) =20.0m
time = 1min
Explanation:
power =50×10×20 /1
power = 10,000watts
power =10 ×10^3kw
p =10 Kilowatt's
Identrying the speed of the Cart
Complete the statements using data from Table A of your Student Guide.
cm/s.
The speed of the cart after 3 seconds of Low fan speed is
The speed of the cart after 5 seconds of Medium fan speed is
The speed of the cart after 2 seconds of High fan speed is
cm/s.
cm/s.
Answers
The speed of the cart after 3 seconds of Low fan speed is equal to 54 cm/s.
How to calculate the speed?Mathematically, speed can be calculated by using this formula;
Speed = distance/time
At Low fan speed after 3 seconds, the distance covered is 162 cm:
Speed = 162/3
Speed = 54 cm/s.
At Medium fan speed after 5 seconds, the distance covered is 600 cm:
Speed = 600/5
Speed = 120 cm/s.
At High fan speed after 2 seconds, the distance covered is 128 cm:
Speed = 128/2
Speed = 64 cm/s.
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The speed of the cart after 3 seconds of Low fan speed is 55 cm/s.
The speed of the cart after 5 seconds of Medium fan speed is 120 cm/s.
The speed of the cart after 2 seconds of High fan speed is 63 cm/s.
What is speed?
Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.
The graph in the attachment may be used to estimate the cart speed for various fan speeds.
Blue letters indicate the low fan speed. When the line drawn from x hits the blue line, the elapsed time is indicated on the x-axis cart speed after three seconds.
This is equivalent to 55 cm/s.Yellow markings indicate the medium fan speed. After 5 seconds, the line drawn from the point marked 5 on the x-axis crosses the yellow line, marking the time that has passed.
The intersection of the yellow line with the line drawn from the point marked 5 on the x-axis indicates the cart speed five seconds later. The y-axis measurement is roughly 120 cm/s.
Green markings indicate the high fan speed. On the x-axis is the elapsed time. Cart speed at the place where the green line and the line drawn from the x-point axis 2 connect. The y-axis reading is roughly 63 cm/s.
Hence, after the specified seconds, the cart's estimated speeds at low, medium, and high speeds are 55 cm/s, 120 cm/s, and 63 cm/s, respectively.
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what kind of soil is most likely found in the desert
Answers
Suppose an astronaut has landed on Planet * Fully equipped, the astronaut has a
mass of 120 kg and when the astronaut gets on a scale, the reading is 46 N. what is
the acceleration due to gravity on Planet X. (Answer to 2 decimal places) you
Answers
From the calculations, the value of the acceleration due to gravity is 0.38 m/s^2.
What is weight?The weight of an object is obtained as the product of the mass of the body and the acceleration due to gravity.
Thus;
When;
mass = 120 kg
weight = 46 N
acceleration due to gravity = 46 N/120 kg
=0.38 m/s^2
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PLS HELP A magnetic field is formed when
a. the spin of the electrons is
aligned.
b.protons in a material all spin in
the opposite direction.
c. the north and south poles align.
d. a permanent magnet is dropped.
Answers
Answer:
proton in a material all spin in the opposite direction
Kinetic energy is energy that is stored and not moving
O True
O False
Answers
If u add 1.362 and 25.2 what is the correct answer?
Answers
Answer:
26.562
Explanation:
1+25= 26
0.362+0.2= 0.562
26+0.562= 26.562
or just use a calculator
Write the laws of refraction.(It should be Snell's law)
Answers
Explanation:
Snell's Law of refraction:
Refraction of light obeys the following its two laws which's snell's law.
The incident ray, the normal at the point of incidence and the refracted ray, all lie in the same plane. For a given pair of media and given colour of light, the ratio of the sine of angle of incidence i to the sine of angle of refraction r is a constant i.e.[tex] \rm \cfrac{sin \: i}{sin \: r } = \mu[/tex]
This is known as the refractive index of the second medium with respect to the first medium. Mu is given as:
[tex] \rm\mu = \cfrac{Speed \; of \; light \; in\; the\; first \; medium}{Speed \; of \; light \; in\; the\; second \; medium}[/tex]
Let's take an example.
If a ray light travels from air to water,then mu = sin i/sin r is the refractive index of water with air.
[tex]\rm \cfrac{sin \: i}{sin \: r } = \mu[/tex]
Ex.1:Ray light from air to water
sin i = 3*10^6 m/s^1sin r = 2.25*10^8 m s^-1[tex] \rm \mu \: = \cfrac{3 \times {10}^{8} \: m \: s {}^{1} }{2.25 \times 10 {}^{8} \: m \: s {}^{ - 1} } = \cfrac{4}{3} = \boxed{ 1.33}[/tex]
Ex.2: Ray light from Air to glass:
sin i = 3*10^8 m s ^-1sin r = 2*10^8 m s^-1[tex] \rm \mu \: = \cfrac{3 \times {10}^{8} m \: s {}^{ - 1} }{2 \times {10}^{8 \: } m \: s {}^{ - 1} } = \cfrac{3}{2} = \boxed {1.5}[/tex]
[tex] \rule{225pt}{2pt}[/tex]
A bicycle moves from rest to 8.0 m/s in 4.3 seconds. What was the acceleration?
Can please show me how you got it, I am so confused.
Answers
Answer:
1,86
Explanation:
V=V0+a x t
8 m/s=0 m/s + a x 4,3 s
8m/s=a x 4,3 s
a= 8m/s / 4,3 s
a=1,86
V=Last speed
V0=Initial speed
a=acceleration
t=time
A lizard climbs up a building 15.5 m and then turns around and goes down the bulding 23.7 m. This takes the lizard 31.5s. what is the average velocity of the lizard?
1.24 m/s Down
0.26 m/s Down
258 m/s Down
3.8 m/s Down
Answers
The average velocity of the lizard for the whole journey is 0.26 m/s Down.
What is average velocity?The term average velocity has to do with the velocity of the lizard for the whole journey. We can see that the downward displacement is greater than the upward displacement.
Thus;
Velocity = displacement / time = 23.7 m - 15.5 m/31.5s = 0.26 m/s Down.
Thus, the average velocity of the lizard for the whole journey is 0.26 m/s Down.
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A car starts from rest and coasts down a hill with a constant acceleration.If it goes 90m in 8s,find the acceleration and velocity after 8s.
Answers
According to the law of conservation of energy, which changes would INCREASE the total energy of a system?
A. An addition of 400 J of thermal energy and a loss of 550 J of kinetic energy
B. An addition of 200 J of thermal energy and a loss of 550 J of thermal energy
C. An addition of 300 J of GPE and a loss of 450 J of thermal energy
D. An addition of 500 J of kinetic energy and a loss of 450 J of thermal energy
Answers
The changes that would increase the total energy of a system is an addition of 500 J of kinetic energy and a loss of 450 J of thermal energy.
What is conservation of energy?The term conservation of energy means that energy can not be created nor destroyed.
In this case, the changes that would increase the total energy of a system is an addition of 500 J of kinetic energy and a loss of 450 J of thermal energy.
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Which words best describe the archer's results?
OA. High precision, low accuracy
B. Low precision, low accuracy
OC. Low precision, high accuracy
D. High precision, high accuracy
Answers
The words best describe the archer's results are The correct option is A.
What is accuracy?When in an experiment, a value is measured 5 times, then if the values measured are same for most of the time or like three times out of five, it said to be accurate. The phenomenon is accuracy.
Precision is about comparing the values to each other then find them near to each other.
Given is an archer's targets on the target board.
Accuracy compares the experimental value to the theoretical value (desired target)
So, when all the values are close to each other but not nearest to the theoretical value, then it is said to be precise but not accurate.
Thus, the correct option is A.
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What is the equivalent resistance of the
following two resistors in parallel?
R₁
www
200 Ωپیشهl
250 Ω
Req =
Answers
Answer:
Approximately [tex]111\; {\rm \Omega}[/tex].
Explanation:
It is given that [tex]R_{1} = 200\; {\Omega}[/tex] and [tex]R_{2} = 250\; {\Omega}[/tex] are connected in a circuit in parallel.
Assume that this circuit is powered with a direct current power supply of voltage [tex]V[/tex].
Since [tex]R_{1}[/tex] and [tex]R_{2}[/tex] are connected in parallel, the voltage across the two resistors would both be [tex]V[/tex]. Thus, the current going through the two resistors would be [tex](V / R_{1})[/tex] and [tex](V / R_{2})[/tex], respectively.
Also because the two resistors are connected in parallel, the total current in this circuit would be the sum of the current in each resistor: [tex]I = (V / R_{1}) + (V / R_{2})[/tex].
In other words, if the voltage across this circuit is [tex]V[/tex], the total current in this circuit would be [tex]I = (V / R_{1}) + (V / R_{2})[/tex]. The (equivalent) resistance [tex]R[/tex] of this circuit would be:
[tex]\begin{aligned} R &= \frac{V}{I} \\ &= \frac{V}{(V / R_{1}) + (V / R_{2})} \\ &= \frac{1}{(1/R_{1}) + (1 / R_{2})}\end{aligned}[/tex].
Given that [tex]R_{1} = 200\; {\Omega}[/tex] and [tex]R_{2} = 250\; {\Omega}[/tex]:
[tex]\begin{aligned} R &= \frac{1}{(1/R_{1}) + (1 / R_{2})} \\ &= \frac{1}{(1/(200\: {\rm \Omega})) + (1/(250\; {\rm \Omega}))} \\ &\approx 111\; {\rm \Omega}\end{aligned}[/tex].
when a metal sphere is dropped in to a tall cylinder containing liquid its acceleration is g÷2 (gravity over 2) show that : density of metal =2density of liquid
Answers
The density of the metal sphere is 2 times the density of the liquid as proved.
Net upward force acting on the metal sphereThe net upward force acting on the sphere as it is dropped into the liquid is calculated as follows;
F = σVg - ρVg
ma = σVg - ρVg
where;
ρ is density of the liquidσ is the density of the metala is acceleration of the metalσV(a) = σVg - ρVg
σ(a) = σg - ρg
σ(g/2) = σg - ρg
g(σ/2) = g(σ - ρ)
σ/2 = σ - ρ
σ/2 - σ = - ρ
-σ/2 = - ρ
σ = 2ρ
Thus, the density of the metal sphere is 2 times the density of the liquid as proved.
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A train travels a distance of 20miles for 50min. Calculate the speed of the train.
Answers
Answer:
24 mph
Explanation:
Speed = Distance / Time
Speed = 20 ÷ 5/6
Speed = 24 mph
NOTE: 5/6 is a fraction in this case and is equivalent to 50/60 and 60 minutes = 1 hour of course.
Hope this helped!
Answer:
[tex]\textsf {speed = 24 mph}[/tex]
Explanation:
[tex]\textsf {Formula used :}\\\implies \textsf {speed = distance/time}[/tex]
[tex]\mathsf {Given :}[/tex]
[tex]\implies \textsf {distance = 20 miles}[/tex]
[tex]\implies \textsf {time = 50 minutes = 5/6 hour}[/tex]
[tex]\textsf {Solving :}[/tex]
[tex]\implies \mathsf {speed = 20 \div 5/6 }[/tex]
[tex]\implies \mathsf {speed = 20 \times 6/5}[/tex]
[tex]\implies \mathsf {speed = 4 \times 6}[/tex]
[tex]\implies \textsf {speed = 24 mph}[/tex]
Calculate the density of the baseball. Use the formula
D = m/V
where D is the density, m is the mass, and V is the volume.
Determine whether the density of baseball is within the legitimate range for an official baseball.
Record your answers in Table C of your Student Guide.
What is the density of the baseball?
1.38
g/cm3
The acceptable density range of official baseballs is between 0.70 g/cm3 and 0.80 g/cm3. Is the questionable ball in this range of acceptable density?
Answers
If the density of the baseball is within the acceptable density range of 0.70 g/cm³ and 0.80 g/cm³, then your response would be Yes and vice-versa.
What is density?Density can be defined as a ratio of mass to the volume of an object such as a baseball. Mathematically, the density of a baseball can be calculated by using this formula:
Density = Mass/Volume
Since the necessary parameters weren't provided in the question, I would give an insight on how to answer the question. You should substitute the mass and volume of the given baseball into the above formula and then solve.
Furthermore, if the density of the baseball is within the acceptable density range of 0.70 g/cm³ and 0.80 g/cm³, then your response would be Yes. However, if the density of the baseball is above or below the acceptable density range, then your response would be No.
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The area under a force-time graph represents
Answers
Answer:
Area under force time graph gives ‘impulse ‘
two forces x and y are acting at 120 degrees to each other, if the magnitude are 8N and 10N respectively determine their resultant
Answers
The resultant force of both forces is 15.62 N.
What is resultant?The Resultant of forces is a single force obtained when two or more forces are combined.
To calculate the resultant of the force, we use the formula below.
Formula:
R = √[a²+b²-2abcos∅]..................... Equation 1Where:
R = Resultant of the forces.∅ = Angle between both forcesFrom the question,
Given:
a = 8 Nb = 10 NSubstitute these values into equation 1
R = √[8²+10²-2×8×10cos120°]R = √[64+100-160cos120°]R =√ [164-160(-0.5)]R = √[164+80]R = √(244)R = 15.62 NHence, the resultant force of both forces is 15.62 N.
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Using the parallelogram law of vectors to obtain the resultant, we have the value 16 N.
What is the resultant force?The resultant force is that force that has the same effect in magnitude and direction as two forces acting together. In this case, we have two forces , 8 N and 10 N inclined at an angle of 120 degrees
Using the parallelogram law of vectors to obtain the resultant;
R = √([8²+10²)-2×8×10cos120°]
R = √164 +80
R = 16 N
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a car travels at 50 m/s for first 20 seconds , 30 m/s for next 30 seconds and finally 20 m/s for next 10 seconds . find its average speed
Answers
The average speed traveled by car is [tex]35m/s[/tex].
[tex]1^{st}[/tex] case
Speed[tex]=50m/s\\[/tex]Time [tex]=20s[/tex]Distance [tex]=[/tex] [tex]speed*time= 50*20=1000m[/tex]
[tex]2^{nd}[/tex] case
Speed[tex]=30m/s[/tex]Time[tex]=30s[/tex]Distance[tex]=30*30=900m[/tex]
[tex]3^{rd}[/tex] case
Speed[tex]=20m/s[/tex]Time[tex]=10s[/tex]Distance[tex]=20*10=200m[/tex]
Now, The total distance[tex]=(1000+900+200)m=2100m[/tex]
Total time[tex]=(20+30+10)s=60s[/tex]
Average distance [tex]=\frac{total distance}{total time} = \frac{2100}{60}=35m/s[/tex]
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The height of the cylinder is manipulated. This is the
variable.
The temperature of the water changes as the height of the cylinder changes. The temperature of the water is therefore the
variable.
A “constant” is a parameter that stays the same regardless of the variables. One parameter of the system that is held constant is the
.
Answers
One parameter of the system that is held constant that can be considered is the mass of the water.
What is a constant?In science, the constant is a type of unmodified variable that remains equal along with the experimental procedure.
The constants of a particular system must be considered and they cannot change in experiments or observations.
In conclusion, one parameter of the system that is held constant that can be considered is the mass of the water.
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Andrea is investigating how increasing the concentration of sugar affects the boiling point of the solution. What would be the best way to present the results to help Andrea see if there is a pattern?
Answers
An increase in the concentration of sugar in a solution leads to the increase in boiling point of the solution.
What is boiling point?Boiling point of a solution is that pressure exerted on a liquid by its surrounding is equal to the vapour pressure of the liquid.
When there is an increase in concentration of solute, more space will be occupied in the fluid leading to an increase in the boiling point of the fluid.
Therefore, An increase in the concentration of sugar in a solution leads to the increase in boiling point of the solution.
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Why is friction useful between your feet and the ground?
Answers
Answer:
It allows you to walk faster.
Explanation:
It is the same force that allows you to accelerate forward when you run. Your planted foot can grip the ground and push backward, which causes the ground to push forward on your foot. We call this grip type of friction, where the surfaces are prevented from slipping across each other, a static frictional force.
Calculate how many half-lives are required for a number of radio-active nuclei to decrease to one-millionth of
the initial number.
Answers
Answer:
it would depend on which element u would be considering
Explanation:
as helium , oxygen , carbon ,sodium and other would be easier while plutonium , americium and other very radioactive elements would be harder
Answer:
~ 20 half lives
Explanation:
(1/2) ^n = 1/1,000,000 n = number of half-lives
LOG both sides to get
n LOG 1/2 = -6
n = -6/(LOG (1/2)) = 19.931 or approx 20 half lives
the resistivity of
Copper is 1.7x10^-8ohm-m
What is the Current
density, J in the Copper
When placed inside a
Souce supply of 12v?
Answers
The current density of the copper wire is determined as (7.059 x 10⁸ A/m²)/L
Current density of the copper wire
The current density of the copper wire is calculated as follows;
J =1/ρ(E) = 1/ρ(V/L)
where;
E is electric fieldV is voltageL is length of the wireCurrent density the wireJ =1/ρ(E) = 1/ρ(V/L)
J = (1/1.7 x 10⁻⁸) x (12)/L
J = (7.059 x 10⁸ A/m²)/L
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Electron grops could be considered which of the following
Answers
Answer:
Electron groups could be considered as Lone pair electrons and bonded pairs of electrons.
Answer: Option D & B
Explanation:
The two or more electrons can be bonded by single bond, double bond, covalent bond of electrons can simply be lone pair of electrons. Unshared pair of electrons are generally termed as lone pair of electrons in an atom which are generally present in the outermost shell of atoms. Hence electron groups can be determined by bonded pairs and lone pairs of electrons.
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