For which of these scenarios is total internal reflection possible? list all correct answers in alphabetical order. for example, if scenarios a and e are correct, enter ae.

Answers

Answer 1

The sequence is E,B,F,C. for the scenarios total internal reflection possible .

What is total internal reflection?

Total internal reflection is an optical phenomena when waves arriving at the interface between two media entirely reflect back into the first medium instead of being refracted into the second. total internal reflection, in physics, is defined as complete reflection of a ray of light within a medium like  as water or glass from the surrounding surface's back into the medium. The phenomenon occurs if the angle of incidence is higher than a certain limiting angle, known as  the critical angle

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For Which Of These Scenarios Is Total Internal Reflection Possible? List All Correct Answers In Alphabetical
For Which Of These Scenarios Is Total Internal Reflection Possible? List All Correct Answers In Alphabetical

Related Questions

Two balls of masses 4kg and 2kg move towards each other with a velocity of 4ms-1 and -2ms-1 respectively. if after collision they stick together and move with +2ms-1, what is

Answers

The change in the momentum of the balls is -8 kg.m/s.

Initial momentum of the balls

The initial momentum of the balls is calculated as follows;

Pi = 4 kg(4 m/s) + 2 kg(2 m/s)

Pi = 20 kg.m/s

Final momentum of the balls

Pf = 2 m/s (4 kg + 2 kg)

Pf = 2 m/s (6 kg)

Pf = 12 kg.m/s

Change in momentum of the balls

ΔP = Pf - Pi

ΔP = 12 kg.m/s - 20 kg.m/s

ΔP = -8 kg.m/s

Thus, the change in the momentum of the balls is -8 kg.m/s.

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The complete question is below:

What is is the change in momentum of the balls?

At a distance of 17 km, a 136 hz horn, assumed to be an isotropic point source, is barely audible. at what distance would it begin to cause pain?

Answers

At a distance of 1.7 cm, the horn will begin to cause pain.

The source is an isotropic point source.

Let the distance at which the horn is barely audible be

[tex]r _2.[/tex]

[tex]r _2= 17 km[/tex]

Let the distance at which the horn will cause pain to be

[tex]r _2.[/tex]

[tex]A _{phere} = 4\pi \times r ^{2} [/tex]

The intensity ratio between barely audible and painful threshold is,

[tex]I = \frac{P }{A}[/tex]

[tex] \frac{I _2}{I _1 } = \frac{\frac{P}{4\pi \times r ^{2} _2 } }{ \frac{ P}{4\pi \times r ^{2} _1 }} [/tex]

[tex] = ( \frac{r _1 }{r _2 } ) ^{2} [/tex]

[tex]10 ^{ - 12} \: is \: ratio \: of \: the \: intensity [/tex]

between barely audible and painful threshold.

So,

[tex] \frac{I_2 }{I _1 } =( \frac{r _1 }{r _2 } ) ^{2} [/tex]

[tex] \frac{I_2 }{I _1 } = 10 ^{ - 12} [/tex]

[tex]r _2 = 17000 \: m[/tex]

The distance at which the horn will begin to cause pain is,

[tex]r _1 = r _2 \sqrt{10 ^{ - 12} } [/tex]

[tex]r _1 = 17000 \sqrt{10 ^{ - 12} } [/tex]

[tex]r _1 = 0.017 \: m[/tex]

[tex]r _1 = 1.7 \: cm[/tex]

Therefore, at a distance of 1.7 cm horn will begin to cause pain.

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solve problem 2.5 if a 150 mm thick brick wall, which is 2.1 m high and 7.5 m long, bears directly on the top of beam cd.

Answers

The tributary region of the beam CD is indicated by the shaded area. The tributary area of the beam CD has a width of B=3.6m. The CD beam's tributary area is 7.5 meters long. The concrete slab has a thickness of H=100mm.

What is structural analysis?

The goal of structural analysis is to forecast how a structure will react to a set of arbitrary external loads.

The goal of the structural analysis is to determine how changes to the structure as a whole or in part will affect the ultimate limit states and service ability limit states as described in Section 8.

Establishing a sensible distribution of internal forces, moments, stresses, strains, and displacements over the entire or a portion of a structure is the goal of a structural study.

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Describe the changes of energy in an electrical train as it approaches a station and breaks to halt

Answers

The changes of energy in an electrical train as it approaches a station and breaks to halt are potential energy friction heat and sound

- → friction on train wheels due to brakes reduces KE of train to zero

- → heat and sound to surroundings

What is energy?

Energy, according to scientists, is the capacity for work. The ability to transform energy from one form to another and use it to perform tasks is what makes modern civilization possible. People utilize energy to travel by foot and bicycle, drive vehicles on land and in water, prepare meals on stoves, create ice in freezers, illuminate our homes and workplaces, create goods, and launch people into space.

Energy comes in a wide variety of forms, including:

HeatLightMotionElectricalChemicalGravitational

These energies can be divided into two categories for working energy:

Potential or stored energyKinetic or working energy

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a rigid tank contains an ideal gas at 40°c that is being stirred by a paddle wheel. the paddle wheel does 200 kj of work on the ideal gas. it is observed that the temperature of the ideal gas remains constant during this process as a result of heat transfer between th

Answers

The total entropy generation is 0.67 kJ/K

Calculation

Since there is no increase in the temperature of the gas, so according to the 1st law of thermodynamics

δQ=dU+δW

⇒ δQ=δW=200KJ

Then here dU is zero because the temperature is constant.

Now, S2−S1=∫[tex]\frac{δQ}{T}[/tex]+ Sgen

Here as it can be seen, there is no increase in the temperature of the gas. So, here we apply the first law of thermodynamics.

∴ S2−S1=0

⇒ Sgen= [tex]-\frac{(-200)}{(27+273)}[/tex] = [tex]\frac{200}{300}[/tex] = 0.67kJ/K

What is the first law of thermodynamics?

The first law of thermodynamics expresses that the entire energy of the universe remains the same. Even though the energy can be exchanged between the system and its surroundings, it can never be created not destroyed.

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a pendulum clock runs fast, how should the length of the pendulum be adjusted to correct the problem?

Answers

If a pendulum clock is running fast, the length of the pendulum should be increased to correct the problem.

The time period of a simple pendulum clock is:

 T= 2π√(l/g)

Where,

l is the length of the simple pendulum and g is the gravity.

From the formula, we can see that the time period is directly proportional to the square root of the length. Decreasing the length will decrease the time period and the clock will move faster.

In order to slow the clock, increase the length of the pendulum to increase the time period.

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What phrase describes radioactivite decay

Answers

the splitting of a large nucleus into smaller nuclei is the phrase that describes radioactive decay

The process through which an unstable atomic nucleus loses energy through radiation is known as radioactive decay, also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration. A substance with unstable nuclei is regarded as radioactive decay

The complete question is

Which phrase describes radioactive decay? (1 point)

the triggering of one reaction by the products of another

the joining of small nuclei into a laroid nucleus

o the splitting of a large nucleus into smaller nuclei

o the spontaneous emission of radiation

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Were both sides of the single magnet attracted to the metal surface? use your results to support your answer.

Answers

YES both sides of the single magnet attracted to the metal surface because metals are not paramagnetic magnets, temporary magnetism can be induced in metal by bringing a magnet close to it . The pole of metal surface will be such that it is attracted by the magnet.

From result: A1 and A2 both side of magnet attract to metal surface.

when one magnet is removed from stack, magnetic poles of stack will not change because stack consist of many mgnet , after removing one magnet from stack pole strength of stack will reduce but pole of stack will remain same.

From result:

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#SPJ4interact with stack , they attract each other and after removal of one magnet from stack, stack repel with other side A2 of magnet. hence stack pole has not changed after removal of one magnet from it.

Initial most propble speed Vi= [tex]\sqrt 2RT/M[/tex]

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One of the pieces of evidence supporting energy quantization was the line spectra of elements. Why does this demonstrate energy quantization?.

Answers

There are distinct emission lines indicating discrete energy levels.

When a component transmits energy in the form of radiation, a spectrum of colors is produced on a photographic plate. This spectrum can be both continuous and discrete. The spectrum persists without distinction between two regions in a continuous spectrum. This represents the uninterrupted radiation emission and thus the uninterrupted emission of energy.

The line spectrum, on the other hand, is made up of discrete and sharp lines that show the emission of radiation in a specific amount over a specific time period, with a break between emission. As a result, the line spectra supports energy quantization.

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7th GRADE SCIENCE QUESTION PLEASE ANSWER AS FAST AS YOU CAN I NEED IT (it can be 1 day late is fine... Ok I'll give you today like this minute and you can answer it when it is posted about 1-2 days but if you can answer it now that will be great)!!!

Question #1: State the role of a nucleus in a cell.

Answers

The primary functions of the nucleus are to store the cell's DNA, maintain its
integrity, and facilitate its transcription and replication.

Scientists are trying to create plasma in

Answers

An ionized plasma can be created in cyclotron with the help of superimposition of static magnetic field and electromagnetic field.

What is Plasma?

Plasma is superheated matter. It is so hot that the electrons are ripped away from the atoms forming an ionized gas. It comprises over 99% of the visible universe.

Given in the question is about Plasma, which is also fourth state of matter.

Scientists are trying to create Plasma in cyclotrons. Cyclotron is a device that propels a beam of charged particles in a circular path. It is also called particle accelerator. Electron cyclotron resonance (ECR) occurs when the natural frequency of the rotating electrons coincides with the frequency of incident radiation. One method to produce ionized plasma is to superimpose a static magnetic field with the high frequency Electromagnetic field at the electron cyclotron resonance frequency.

Therefore, an ionized plasma can be created in cyclotron with the help of superimposition of static magnetic field and electromagnetic field.

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If the maximum e-component of an electromagnetic wave is 600 v/m, what is the maximum b-component?

Answers

the maximum e-component of an electromagnetic wave is 600 v/m then the maximum b-component is B = 2.0 * 10^-6 T.

What is electromagnetic wave?

In terms of science, electromagnetic radiation is made up of electromagnetic field waves that are travelling through space while carrying radiant electromagnetic energy. It consists of X-rays, gamma rays, microwaves, infrared, light, and radio waves. These waves are all a component of the electromagnetic spectrum.

Em/Bm = c

Bm = c*Em

B = E/c

B = 600 V/m / 299,792,458 m/s

B = 2.0 * 10^-6 T

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Static charges are not dangerous

true
false

Answers

Answer:

false

Explanation:

You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. what is your average speed for the whole trip?

Answers

The average speed for the whole trip will be 40 miles per hour.

What is the average speed?

The average speed is the ratio of the total distance over the total time taken. Then the average speed is given as,

Average speed = (Total distance) / (Total time)

You drive for 30 minutes at 30 miles per hour. Then the distance covered will be

D₁ = 30 x 30 / 60

D₁ = 15 miles

And then for another 30 minutes at 50 miles per hour. Then the distance covered will be given as,

D₂ = 50 x 30 / 60

D₂ = 25 miles

Then the average speed for the whole trip will be

Average speed = (15 + 25) / (0.5 + 0.5)

Average speed = 40 / 1

Average speed = 40 miles per hour

Thus, 40 miles per hour will be the average speed for the whole trip.

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A 5kg object with a velocity of 6m/s strikes a motionless ball. the object stops moving as a result of the collision. what is the velocity of the ball after the collision?

Answers

mU1 + mU2 = mV1 + mV2

(5 × 6) + (3 × 4) = 5V + 3V

30 + 12 = 8V

42 = 8V

V = 5.25m/s

The velocity of the ball after the collision is 5.25m/s.

What is velocity ?

While velocity refers to the speed and direction of an object's motion, speed is the rate at which an object moves along a path over time.

The rate at which something moves in a certain direction is referred to as its velocity. as quickly as a car traveling north on a highway or a rocket taking flight. The magnitude of the velocity vector's absolute value will always be equal to the motion's speed because it is a scalar.

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High temperature and pressure tend to favor flow rather than breakage, so it is surprising that large, very deep earthquakes are sometimes observed, occurring in warm places where the pressure is high. What is accurate about these rare, deep earthquakes?.

Answers

They happen at subduction zones, where shifting mineral assemblages appear to "implode" as a result of increased pressure on the rock as it is subducted deeper.

The notion that is currently preferred is "Implosion." The building blocks often reorganize to take up less space as subduction zones move rocks deeper where pressure is stronger, moving from, say, a one-on-top-of-another pattern to a fit-in-the-gap-between-those-below pattern. This might sometimes seem to happen gradually before happening abruptly (I can't move till my neighbor does...), resulting in an implosion. Where temperatures and pressures are just so high that we don't imagine rocks can break, the largest, deepest earthquakes occur. Nowhere near as deep as the earthquakes, humans have never dug a hole. Atomic bomb testing has mostly ended. A large earthquake is also much larger than a large atomic weapon.)

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What is the potential difference between the plates of a 2.9-f capacitor that stores sufficient energy to operate a 75.0-w light bulb for one minute?

Answers

Answer:

Q = I t            charge * time where I = charge / time

Q = V * C     where Q is the charge stored on capacitor C

V C = I t

V = I t / C = 75 C/s * 60 sec / 2.9 farad = 1552 Volts

Note: farad = Coul / (J / Coul) = Coul^2 / J

A flat slab of styrofoam, with a density of 32 kg/m3, floats on a lake. what minimum volume must the slab have so that a 45 kg boy can sit on the slab without it sinking?

Answers

Minimum volume must the slab have so that a 45 kg boy can sit on the slab without it sinking is 0.465 m³.

What is buoyant force?

The buoyant force is the upward force exerted on an item that is fully or partially submerged in a fluid. This upward thrust is also known as an upthrust. Because of the buoyant force, a body submerged partially or entirely in a fluid appears to  be lighter or to lose weight.

Given:

Density of the styrofoam, ρ' = 32 kg/m³

Now, let the volume of the slab = V

the submerged volume be = V ;

now, the volume of water displaced will be V  

thus,

the buoyant force acting will be = ρVg

{where,

ρ is the density of water

g is the acceleration due to gravity}

now,

total downward force acting = weight of the boy + weight of the slab

total downward force acting =45 × g + ρ' × V × g

For the no sinking condition, buoyant force should be equal to the total downward force.

thus,

ρ × V × g = 45 × g + ρ' × V × g

or

ρ × V = 45 + ρ' × V

on substituting the values

V ( 1000 - 32 ) = 45 ;

or

V = 0.465 m³

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a torque of 12 n ∙ m is applied to a solid, uniform disk of radius 0.50 m. if the disk accelerates at 1.60 rad/s^2, what is the mass of the disk?

Answers

Mass of disc m =16.84 kg

Moment of inertia of disc about axis perpendicular to the plane of disc and passing through its centre = MR²/2

12 =  MR²/2 × 5.7

12 =  M(0.5)²/2 × 5.7

Mass = 12 × 2 /5.7 × 0.5² = 16.84 Kg

The atomic mass of an detail is described because the weighted common mass of that detail’s

The atomic mass of an detail is described because the weighted common mass of that detail’s is False

Atomic mass (Also referred to as Atomic Weight, even though this denomination is incorrect, for the reason that mass is belongings of the frame and the burden relies upon at the gravity) Mass of an atom similar to a positive chemical detail).  mean "unit of atomic mass". This unit is likewise typically referred to as Dalton (Da) in honor of the English chemist John Dalton.

It is equal to 1 12th of the mass of the nucleus of the maximum ample isotope of carbon, carbon-12. It corresponds more or less to the mass of a proton (or a hydrogen atom). It is abbreviated as "uma", even though it could additionally be located with the aid of using its English acronym "amu" (Atomic Mass Unit). However, the advocated image is simply "u".

The atomic masses of chemical factors are typically calculated using the weighted average of the masses of the exceptional isotopes of each detail while taking into account the relative abundance of each one. This is the cause of the discrepancy between an element's atomic mass in umas and the range of nucleons that contains the nucleus of its maximum uncommon place isotope.

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Electron affinity is the energy associated with the gain of an electron by an atom in the gaseous state. Which element will release the most energy when gaining an electron?.

Answers

The element which release most energy while gaining an electron is Chlorine.

Chlorine has a higher affinity for electrons than fluorine does, despite the fact that fluorine is intended to have halogens with higher electron affinity .Therefore, chlorine has the highest electron affinity among the all elements in the group.

When an electron is added to a neutral atom to create a negatively charged ion, how much energy is released. Only a few chemical elements, primarily the halogens, have values available since it is difficult to determine the affinities of atom’s electrons.

Low melting and boiling points characterize the halogens. They all react with hydrogen to create acids. Salts are easily formed when they react with metals. Their outer shell contains seven valence electrons.

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often a vector is specified by a magnitude and a direction; for example, a rope with tension t⃗ exerts a force of magnitude t

Answers

To study vectors it is best to select a coordinate system and manipulate it in that coordinate system and the component of A in x is 0.9396 while in y it is 0.342.

What is a vector?

An item with both magnitude and direction is referred to be a vector.

A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.

A vector has magnitude and direction so we can form a vector coordinate system and manipulate each vector in that such that it will be clear to study all vectors.

Given the vector A,

Magnitude |A| = 1 units

The angle of inclination from the x-axis is 20°.

Component of A in the x-axis

|A|cos20° = 1(0.9396) = 0.9396

Component of A in the y-axis

|A|sin20° =1(0.342) = 0.342

Hence "The component of A in x is 0.9396 while in y it is 0.342".

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Given question is incomplete with the missing image attached below;

What is the hybridization of the xe atom in the xecl4 molecule?
a. sp
b. sp2
c. sp3
d. sp3 d
e. sp3 d 2

Answers

Answer:

sp3 d 2

Explanation:

calculate the moment of inertia of a skater given the following information. the 58.0–kg skater is approximated as a cylinder that has a 0.102–m radius.

Answers

The Moment of Inertia of skater of mass 58 Kg with approximated radius of 0.102 m will be 0.301 kg m².will be 0.301 kg m².

We have a 58 kg skater who is approximated as a cylinder that has a radius of 0.102 m.

We have to determine the Moment of Inertia of the of the skater.

What is Moment of Inertia? What is its general formula?

Moment of inertia is the property of the body by which it resists angular acceleration. The general formula of Moment of Inertia is given by -

I = Σ m[i] r[i]².

According to the question -

Mass of skater = 58 Kg

Radius = 0.102 m

Now, the moment of inertia of the cylinder about the axis of cylinder is -

I = 1/2 MR²

I = 0.5 x 58 x 58 x 0.102 x 0.102

I = 1682 x 0.010404

I = 0.301 kg m²

Hence, the Moment of Inertia of skater of mass 58 Kg with  approximated radius of 0.102 m will be 0.301 kg m².

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a copper cube has a mass of 153.6g the density of copper is 8.96g/cm3 calculate both the volume of the cube in cm3 and also the edge length in cm

Answers

The Volume of Copper Cube with mass 153.6 g and density 8.96 g/cm³ is 17.14 cm³ and its Edge is 2.58 cm long.

We have a Copper Cube of mass 153.6 g and density 8.96 g/cm³.

We have to calculate the volume and length of the cube in cm³ and cm respectively.

How is density and mass of body related ?

The density and mass of body are related as follows -

M = ρV

Where -

M - mass of body

ρ - density of body

According to the question, we have →

Mass of copper cube = 153.6 g

Density of copper cube = 8.96 g/cm³

Using the formula discussed above -

M = ρV

V = M/ρ = 153.6/8.96 = 17.14 cm³

We know that the volume of cube is -

V = a x a x a

a³ = 17.14 cm³

a = 2.58 cm

Hence, the Volume of Cube is 17.14 cm³ and its Edge is 2.58 cm long.

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Question 6, “Some students observe drops of water falling from a tap that leaks, as shown in the diagram.
The students measure the time for 50 drops to fall from the tap. The time for 50 drops to fall is 20 seconds.

Calculate the average time between two drops falling.”

Answers

The average time between two drops falling t = 2/5 sec.

Equation :

To calculate average time use formula,

t + t / product

So,

given,

time = 20 s

drops = 50

average time = ?

From this,

measured time for 50 drops = 20sec

Time required for 1 drop = 20/ 50

Average time between two drops = (2/5 + 2/5) / 2

Hence,

The average time between two drops t = 2 / 5

What is average time?

Average Time on Page is a web analytics metric that gauges how long, on average, all website visitors stay on a single page. Only the average amount of time that users spend on non-exit pages is measured by this metric, which ignores exit pages and bounces.

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A car, travelling at 25 m/s, starts to accelerate uniformly at 3 m/s2 for 80 m.

Answers

A car, travelling at 25 m/s, starts to accelerate uniformly at [tex]3m/s^2[/tex]for 80 m.

The final velocity will be:

[tex]\sqrt{1105} m/s[/tex]

How to find the final velocity?

We will use Newton's third law.

[tex]v^2-u^2=2as[/tex]

where,

v = final velocity

u = initial velocity

a = acceleration

s = distance

Substituting the values, we get:

[tex]v^2=480+625=1105\\v=\sqrt{1105}[/tex]

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At what distance from the wire is the magnitude of the electric field equal to 2.41 n/cn/c ?

Answers

The correct answer is 1.07m.

The area surrounding an electric charge where its impact may be felt is known as the electric field. When another charge enters the field, the presence of an electric field may be felt. The electric field will either attract or repel the charge depending on its makeup. Any electric charge has a property known as the electric field. The charge and electrical force working in the field determine the strength or intensity of the electric field.

Here, is the charge per unit length, r is the distance from the wire, and

is the free space permittivity  ε_0. Electric field due to the long straight wire is,

E= λ/2πε_0r

Rearrange the equation for r.

r=λ/2πε_0E

Substitute 2.41 N/C for E,

E=1.44×10^-10C/m

λ=8.85×10^-12C^2/Nm^2

r=(1.44×10^-10C/m)/(2(3.14)(8.85×10^-12C^2/Nm^2)(2.41N/C))

r=1.07m

At a distance of 1.07 m the magnitude of electric field is 2.41 N/C.

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You push on a block on frictionless ice with a force of 8 n, causing it to accelerate at 2 m/s 2. the mass of the block is:________

Answers

The mass of the block is:_force

Given, force f=8N.

acceleration (a) = 2 m/s 2. Now, a cording to

Newtons Law of force where, me mass

or,

m-Ea

= 8 = 4kg

What is force ?

In physics, a force is a power that could exchange the motion of an item. A force can reason an item with mass to alternate its velocity (e.g. moving from a kingdom of relaxation), i.e., to accelerate. force also can be described intuitively as a push or a pull. A pressure has each significance and course, making it a vector amount. it's far measured within the SI unit of newton (N). force is represented by the symbol F (formerly P).

The original form of Newton's second regulation states that the net pressure acting upon an object is same to the price at which its momentum adjustments with time. If the mass of the item is consistent, this regulation means that the acceleration of an item is without delay proportional to the internet pressure performing on the item, is in the route of the net force, and is inversely proportional to the mass of the item.

principles associated with pressure include: thrust, which will increase the velocity of an item; drag, which decreases the velocity of an item; and torque, which produces changes in rotational velocity of an item.

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A transverse wave travels along a string. where are the points of maximum kinetic energy? at the points of zero displacement at the points of extreme displacement

Answers

A transverse wave travels along a string. where are the points of maximum kinetic energy.

At instantaneous t=T/4 and t=3T/4, the incident wave travels a distance threeλ/4 to the right and the pondered wave travels the equal distance at the string to the left. transverse The equal path difference some of the waves is lambda/2 or threeλ/2. therefore, crest of 1 wave falls on trough of the opposite and vice-versa. the resultant displacement at all factors is 0 and is represented via thick horizontal line in determine. transverse, all of the particles are passing simultaneously via their suggest position, however in a route opposite to the path at t=T/four.what's the temperature you want in Kelvin to start fusing hydrogen to heliumas the protostar profits mass, its middle receives hotter and extra dense. in some unspecified time in the future, transverse it's miles going to be hot sufficient and dense enough for hydrogen to begin fusing into helium. It needs to be 15 million Kelvin within the middle for fusion to start.

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Write the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) 7x (x 6)(3x 2)

Answers

We have the given equation as [tex]\frac{7x}{(x+6)(3x+2)}[/tex] that we have to convert through partial fraction decomposition.

What is Partial Fraction?

The partial fraction decomposition or partial fraction expansion of a rational fraction in algebra is the process of expressing the fraction as the product of a polynomial (possibly zero) and one or more fractions with a simpler denominator.

A rational fraction is defined as one that has a polynomial as both the numerator and the denominator.

Theory and solution

We have to find the form of the partial fraction decomposition of the function.

The given rational function has two factors in multiplication form in the denominator.

Also, the degree of the numerator is less than the denominator. Hence, the form of partial fraction decomposition of the function is:

[tex]\frac{7x}{(x+6)(3x+2)}[/tex] = [tex]\frac{A}{x+6} + \frac{B}{3x+2}[/tex]

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