A box is released from the top of a frictionless track. It starts from rest and has a speed of 14 m/s at the bottom. What is the height of the track

If three subintervals of equal length are used to do midpoint Riemann sum approximation of ∫f(x)dx from 3 to 6, then width of each subinterval is  1.

To find the midpoint Riemann sum, you first need to divide the interval of integration (from 3 to 6) into three subintervals of equal length. You can choose subintervals of equal length manually by dividing the interval of integration into smaller parts. If we let the width of each subinterval be x, then the length of the interval is 6-3 = 3 and the length of each subinterval, x is 3/3 = 1.

Then, you need to find the midpoint of each subinterval by adding the left and right endpoint of each subinterval and dividing by 2.

For example, the first subinterval is from 3 to 4, so the midpoint is (3+4)/2 = 3.5

the second subinterval is from 4 to 5, so the midpoint is (4+5)/2 = 4.5

and the third subinterval is from 5 to 6, so the midpoint is (5+6)/2 = 5.5

To approximate the area under the curve of f(x) for each subinterval, you can use the value of f(x) at the midpoint of each subinterval and multiply it by the width of the subinterval.

--The question is incomplete, answering to the question below--

"Let f be the function graphed below. If three subintervals of equal length are used, draw rectangles whose area represents a midpoint Riemann sum approximation of ∫f(x)dx from 3 to 6. Width of each subinterval is ____."

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Answer:

Approximately [tex](-61)\; {\rm m\cdot s^{-2}}[/tex], assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].

Explanation:

Under the assumptions, the vehicle would be in a free fall. Acceleration would be constant: [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex].

Let [tex]u[/tex] denote the initial velocity of the vehicle. Let [tex]v[/tex] denote the velocity of the vehicle at the bottom of the drop. Let [tex]x[/tex] denote the displacement of the vehicle during the drop.

It is given that the initial velocity is [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex]. During the drop, displacement would be [tex]x = (-190)\; {\rm m}[/tex] (negative since the vehicle is below where it started.) The value of final velocity [tex]v[/tex] needs to be found.

It is known that the vehicle is moving downwards at the end of the fall. Therefore, the value of [tex]v\![/tex] would be negative. Apply the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find [tex]v[/tex] from [tex]u[/tex], [tex]a[/tex], and [tex]x[/tex].

[tex]\begin{aligned}v^{2} &= u^{2} + 2\, a\, x\end{aligned}[/tex].

[tex]\begin{aligned}v &= -\sqrt{u^{2} + 2\, a\, x} \\ &= -\sqrt{(0\; {\rm m\cdot s^{-1}})^{2} + 2\, (-9.81\; {\rm m\cdot s^{-2}})\, (-190\; {\rm m})} \\ &\approx (-61)\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

(Note that [tex]v[/tex] is negative.)

In other words, the velocity of the vehicle would be approximately [tex](-61)\; {\rm m\cdot s^{-1}}[/tex] at the end of the drop.

A theory must meet certain requirements in order to be accepted as a physical law , 1. It must explain the available data 2. It need to offer hypotheses that can be verified by science.

A physical law outlines the broad relationships between and, when necessary, changes in the physical quantities that define the states of a physical system. Typically, this is described mathematically. These laws are also known as natural laws or are associated with them in the physical realm. A physical law applies with a very high probability when it falls within its scope of applicability. Physical experiments and observations that are specifically focused are used to test this validity range. The law is established if the outcomes match the predictions.

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A fish under water appears to be at a different depth than it actually is due to the refraction of light as it passes through the water.

When light travels through a medium with a different index of refraction, such as air to water, it bends, or refracts. This causes objects to appear displaced, or closer or farther away than they actually are. Because water has a higher refractive index than air, light bends more when it enters the water, causing objects, like fish, to appear closer to the surface than they actually are.

The result is that the fish will appear to be deeper in the water than it actually is.

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The angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰.

By using the parallelogram law of vector addition, it is possible to calculate the angle between the two wires.

a² + b² - 2abcosθ = R²

Where;

R = is the outcome vector = the frame's weight ⇒ W

Angle between the two wires equals 0.75W for the first wire's tension and 0.75W for the second wire's tension.

(0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ = W²

1.125W² - 1.125W² cosθ = W²

= 1.125W²(1 - cosθ)

W²/1.125W² = 1 - cosθ

0.8889 = 1 - cosθ

cosθ = 1 - 0.8889

cos θ = 0.1111

θ = arc cos(0.1111)

θ = 83.6⁰

So, the angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰

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Answer:

T (Period) = 2 π (L / g)^1/2         for a simple pendulum

L = g * T^2 / (4 π^2)

L = 9.98 m/s^2 * 9 s^2 / 39.5 = 2.27 m

The object accelerates at a constant rate as it moves down the slope because of the constant gravitational force acting on it in a major portion and the rolling tangential force on the object is acting in the smaller form.

Rolling motion of any object occurs when the object starts sliding in a different methods from the other objects such as when the objects starts to roll from the ramp or any other sloppy surface and it rolls down due to the gravitational force and with many other forces such as the rolling tangential force. many forces are acting on the object at the same moment and we are just seeing the gravitational force which is playing a major portion. Hence by this information we can consider that the ball accelerates at a constant rate as it moves down the slope because of the constant gravitational force acting on it in a major portion and the rolling tangential force on the object is acting in the smaller form.

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A very powerful vacuum cleaner has a hose 2.27 cm in diameter. The atmospheric pressure is 1.00 atm=101,300 Pa. then vacuume cleaner generate the force F = 65.1 N

A line that is straight and cuts through the middle of a body or figure. Particularly: the length of a diameter; a line segment passing through the center of a circle with its ends on the circumference.

Given,

diameter of the nose is d= 2.86 cm

radius of the nose r= 1.43 cm = 1.43× [tex]10^{-2}[/tex] m

We know F=P.A

where P is the atmospheric pressure and A is the surface area of the circulsr nose F is the force exerted by vacuume cleaner on the air

∴ F=P ( [tex]\pi r^{2}[/tex])

we know atmospheric pressure, p=1.013×[tex]10^{5}[/tex] pa

F = 1.013 × [tex]10^{5}[/tex] × 3.14 (1.43 × [tex]10^{-2}[/tex]) ^2

⇒ 65.1 N

⇒ F = 65.1 N

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Deviance has an effect on social power. Then, Powerful people in society keep their power by defining the laws of deviant .

Based on the nature is divided into two kinds, namely negative behavior and positive behavior.

a. Positive deviant behavior

Positive behavior is deviant behavior that gives or has a positive impact on social life, because it has innovative elements and ideas that emerge are also creative, so as to enrich people's insights.

Positive behavior is also directed primarily at the values to be achieved together as well as social interests and is often considered as something ideal in society. Positive behavior will usually be accepted by society, because it is a form of development and adjustment to the times.

b. Negative deviant behavior

Negative behavior is the opposite of positive behavior.

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Answer:

a

Explanation:

Put your finger over P to compute power; this leaves I and V; hence, P = I x V.

The quantity of current multiplied by the resistance equals the potential difference, which is the same as voltage. One Coulomb of charge uses one Joule of energy to move between two locations in a circuit, which is equal to a potential difference of one Volt.

Difference that might exist at all between the two points The amount of work required to move a unit positive charge along any path through one point to another without accelerating is referred to as the electric field.

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Solar energy is called renewable because it is abundant in nature and can be filled repeatedly.

Energy is power or strength that can be used for various activities. Energy cannot be created but can be changed from one form to another and can be transferred.

Solar energy is energy produced from the radiant heat of sunlight that can be utilized by all living things on earth, both humans, animals and plants. Solar energy can also be used as an alternative energy because it is environmentally friendly. This energy is included in renewable energy because the amount is abundant and endless even though it is used in large quantities.

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Important Formulas:
[tex]KE=.5mv^2[/tex]

Kinetic energy(measured in joules) = .5 * mass(measured in kg) * velocity(measured in m/s)^2

__________________________________________________________

Given:

[tex]m=0.5kg[/tex]

[tex]v=22m/s[/tex]

[tex]KE=?[/tex]

__________________________________________________________

Finding kinetic energy:

[tex]KE=.5mv^2[/tex]

[tex]KE=.5(0.5)(22)^2[/tex]

__________________________________________________________

[tex]\fbox{KE = 121 Joules}[/tex]

The kinetic energy of Flying pluff is 121 KJ.

The energy that an object has as a result of motion is known as kinetic energy.  It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

The body holds onto the kinetic energy it acquired during its acceleration until its speed changes. The body exerts the same amount of effort when slowing down from its current pace to a condition of rest.

Formally, a kinetic energy is any term that includes a derivative with respect to time in the Lagrangian of a system. According to classical physics, an object with mass m moving at a speed of v has kinetic energy equal to mv2.

Therefore, The kinetic energy of Flying pluff is 121 KJ.

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An object that falls twice as far will be moving twice as fast when it hits the ground is true.

Whath is object?
Objects are entities that have properties and state. They are the fundamental building blocks of a programming language. They are physical or abstract items that have a set of characteristics, such as a name, a type, and a value.Objects are items that can be seen and touched, such as a toy, a computer, a chair or a book. They are physical items that can be owned or interacted with. Objects can also exist in a virtual or abstract form, such as a software program or a mathematical concept. They can also be a combination of both, such as a website or a mobile app. Objects are made up of properties and behavior, which can be seen in the way they interact with other objects in the environment.

Objects can also contain other objects, known as properties. Objects can also have methods which are functions that can be performed on the object. Examples of objects in programming include variables, classes, functions, and arrays.

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The independent variable in this investigation is the type of surface which is changing whereas, the dependent variable is the mobility of earth worm.

In a experiment or investigation, there are two types of variables which are dependent and independent variable. Dependent variable are those which are dependent on other variables and are changing with respect to other variables.

Independent variables are those not dependent on any other variables and  we can change the independent variable to study the change in dependent variable.

Here, the one we studying is the mobility of earth worm which is the dependent variable and the type of surface rough or smooth is the independent variable.

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The correct answer to the given question is -6.944 * 10^-28 Joules

a. To find the electron's initial speed, we can use the conservation of energy. The initial kinetic energy of the electron must equal the final potential energy of the electron at its closest approach to the sphere.

Ki = 1/2 * me * v^2

v = sqrt(2Ki/me)

Ki = qe * V = (1.6 x 10^-19 C) * (-4.4 x 10^-9 C) = -6.944 x 10^-28 J

b. At the point where the speed of the electron is half of its initial value, the kinetic energy of the electron is half of its initial value. Therefore,

Ki/2 = 1/2 * me * (v/2)^2

we can solve for the distance from the surface of the sphere using the same equation as in part a, and substituting Ki/2 and v/2 for Ki and v respectively

c. The acceleration of the electron at its turning point can be found using the equation for centripetal acceleration:

a = v^2/r

where a is the acceleration, v is the speed of the electron, and r is the distance of the electron from the center of the sphere at its closest approach. We can use the value of v from part a and the distance from part b to find the acceleration.

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Part A: The angular momentum of each particle about the origin

Part B: The total angular momentum of the four-particle system is 0.95 kg.m²/s.

The expression used to calculate angular momentum L is:

                             L = r x mv

Here, r is the position vector of the object m is the mass and v is the velocity vector.

According to the superposition principle, the resultant angular momentum due to many particles is the vector sum of the individual angular momentum.

L = L₁ + L₂ + L₃ + ...

Here, L₁ is the angular momentum of a particle, L₂ is the angular momentum of the particle, and so on.

In the question

Mass of a particle = 5.0 kg

vector r = (2.0i - 3.0j) m

vector v = (3.0i) m/s

Part A (seen in the picture for instruction)

For particle 1

The position vector is 2.0j m

Substitute 0.10 kg from m₁, 2.0j from r, and 2.0i m/s for v₁ in the expression of angular momentum

L = r x mv

L₁ = (2.0jm) x [(0.10 kg)( 2.0i m/s)]

L₁ = -4.0 kg.m²/s

The angular momentum for the first particle is -4.0 kg.m²/s.

For particle 2

Position vector is (2.0i - 2.0j) m

Substitute 0.20 kg from m₂, (2.0i - 2.0j) m from r, and (3.0i - 3.0j)m/s for v₂ in the expression of angular momentum

L₂ = (2.0i - 2.0j) m x [ (0.20 kg) (3.0i - 3.0j) m/s]

L₂ = 0

The angular momentum for the second particle is 0

For particle 3

The position vector is (-3.0i + 1.0j) m.

Substitute 0.30 kg from m₃,  (-3.0i + 1.0j) m from r, and  -5.0j m/s for v₃ in the expression of angular momentum

L₃ = (-3.0i + 1.0j) m x [((-3.0i + 1.0j) m) ( -5.0j m/s)]

L₃ = 1.35 kg.m²/s

The angular momentum for three particles is 1.35 kg.m²/s.

For particle 4

The position vector is 4.01i m.

Substitute 0.40 kg from m₄, 4.0i m from r, and -4.0i m/s for v₄ in the expression of angular momentum

L₄ = (4.0i m) x [(0.40 kg) (-4.0i m/s)

L₄ = 0

The angular momentum for four particles is 0.

Part B

Formula used: L = L₁ + L₂ + L₃ + L₄

The total angular momentum of the four-particle system is calculated as follows:

By superposition principle

L = L₁ + L₂ + L₃ + L₄

L = -4.0 kg.m²/s + 0 + 1.35 kg.m²/s + 0

L = 0.95 kg.m²/s

Hence, the total angular momentum of the four-particle system is 0.95 kg.m²/s.

Your question is incomplete but most probably your full question was:

Suppose the particles in the preceding problem have masses m₁ =0.10 kg, m₂=0.20 kg, m₃ = 0.30 kg, m₄ = 0.40 kg. The velocities of the particel are  v₁= 2.0i m/s,v₂= (3.0i - 3.0j) m/s,  v₃= - 1.5j m/s,  v₄= -4i m/s.

(a) Calculate the angular momentum of each particle about the origin.

(b) What is the total angular momentum of the four-particle system about the origin?

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molecule possesses neutrons and a total electric charge of one Coulomb. e is the electronic value, 1.60 x 10-19 Coulombs, and the proton has a cost of +e while the electron has a fee of -e.

The quantity of charge carried by a present of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a quality of a substance that causes magnetic and electric effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.

A coulomb is an unit of power charge that represents the charge that is transmitted over one ampere of current in one second. Colomb's rule. depending on the charged items, electric force.

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The distance between Platform 9 and 3/4 and Hogwarts at a speed of 100miles/hour is 400miles.

Distance is defined as an object's total movement with or without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point. Distance can be measured as Speed multiplied by Time.

If it takes 4 hours from Hogwarts express, at a speed of 100mi/hr to Platform 9 and 3/4 to Hogwarts, using the formula;

Distance = Speed x Time

Distance = 100 miles/hour x 4 hours

Distance = 400 miles

Therefore, the distance to platform 9 and 3/4 from Hogwarts express is 400 miles.

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The girl should sit 2.14 m from the center to keep the board in equilibrium.

What is equilibrium?

Equilibrium is a state in which the net force and net torque acting on an object are both equal to zero. This means that the object is either at rest or moving at a constant velocity. In other words, the object is not accelerating or rotating.

In order for the board to be in equilibrium, the sum of the forces acting on it must be equal to zero. Since the board is uniform and supported at the center, the only forces acting on it are the weights of the person and the girl.

To find the distance from the center that the girl should sit, we can set up the following equation:

F_net = 0 = (500 N)(1.5 m) - (350 N)(x)

where F_net is the net force acting on the board, x is the distance from the center where the girl is sitting, and the 1.5 m is the distance from the center where the person is sitting.

Solving this equation for x:

x = (500 N)(1.5 m) / 350 N = 2.14 m

Hence, the girl should sit 2.14 m from the center to keep the board in equilibrium.

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With the Sun and Moon in this position, the side of the earth facing the moon experiences a spring high tide. Thus Option C is the answer.

A spring tide is a tide that occurs when the gravitational pull of the Moon and the Sun are in alignment. During a new moon or full moon phase, the gravitational pull of the Moon and the Sun combine to produce stronger than normal high tides and stronger than normal low tides. The term "spring tide" does not refer to the season of spring, but rather the tide's "springing forth" of water.

During a spring tide, the difference between high tide and low tide is at its greatest, and the water level rises higher and falls lower than during a neap tide. This is because the gravitational pull of the Moon and Sun are working together to produce the tide, rather than against each other. This results in a high tide that is higher than a normal high tide, referred to as a spring high tide.

It is important to note that spring tides occur twice a month, around the time of the new and full moon, when the Moon and Sun are in alignment.

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32. 6 kg m/s will be the total momentum of the system before the collision.

In physics, a collision is any circumstance in which two or more bodies rapidly apply forces to one another.

Despite the fact that the most common usage of the word "collision" relates to instances in which two or more objects smash violently, the scientific usage of the word makes no such assumptions.

If most or all of the total kinetic energy from the collision is lost (dissipated as heat, sound, etc., or absorbed by the objects themselves), the collision is said to be inelastic; such collisions result in the objects coming to a complete stop. A collision involving a car serves as an example of this type of collision since cars fold inward rather than colliding with one another.

pf = Final momentum of the system = 32.6 kg m/s

According to the principle of conservation of angular momentum we have

pi = pf => pi = 32.6 kg m/s

The wall is not moving so the initial and final momentum of the system are equal.

Therefore, the total momentum of the system before the collision is 32.6 kg m/s

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According to the given statement The pressure exerted by the tooth is 506,315.78 Pa.

Pressure is a measure of the force exerted on a surface per unit area. It is a scalar quantity and is measured in units of force per unit area, such as pascals (Pa), pounds per square inch (psi), or atmospheres (atm).

It can be calculated using the formula:

Pressure (Pa) = Force (N) / Area (m²)

Given that the force exerted is 480 N and the area of contact with the tooth is 0.95 mm^2, we can use the formula to find the pressure exerted:

Pressure (Pa) = 480 N / (0.95 x 10⁻³ m²)

To convert mm² to m², we divide by 10⁶

Pressure (Pa) = 480 N / (0.95 x 10⁻³ m²) = 506,315.78 Pa

Hence, the pressure exerted by the tooth is approximately 506,315.78 Pa.

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Answer:

increase the length of the handle from the bolt, the torque will increase even if you have the same force

Explanation:

It allows them to apply more torque to the bolt. Torque is the turning or twisting force that causes rotation, in this case, it's applied to the bolt in an effort to loosen it. By lengthening the handle of the wrench, the mechanic is able to leverage more of their body weight and strength behind the wrench, increasing the torque they are able to apply to the bolt.

When a bolt is very tight, it can be difficult to turn it with a standard wrench. The increased torque provided by the longer handle allows the mechanic to apply more force to the bolt, which can help to loosen it. This can be particularly useful in situations where the bolt is corroded, rusted, or otherwise stuck due to a buildup of debris or other factors.

Correct option is C)  the acceleration of gravity at that altitude is 9.75m/s².

The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.

The following formula is used to determine the acceleration of gravity:

g= GM/r2

What G The general gravitational constant is what it is.

G is equal to 6.674x10⁻¹¹ Nm2/kg2, and M is the earth's mass:

M = 5.972x10²⁴kg

The radius of the earth plus the airplane's altitude, or r, is the distance from the earth's center in this case:

r = 6.37x10⁶ m + 20000 m equals 6.39x10⁶ m

Consequently, the acceleration in g is equal to:

(6.674x10⁻¹¹ Nm²/kg²)(5.972x10²⁴ kg) / (6.39x100m)₂

g = 9.75m/s²

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Complete Question -

You are on an airplane traveling with a constant velocity at an altitude of 20,000m. What is the acceleration of gravity at that altitude? The earth's radius is 6.37 x 10^6m.. . A) 9.81 m/s^2. B) 9.78 m/s^2. C) 9.75 m/s^2. D) 9.72 m/s^2. E) 9.69 m/s^2.

A camera that draws certain current with specified resistance needs a voltage supply which is calculated to be 18 V.

Given that,

Current i = 0.25 A

Resistance r = 72 ohms

Voltage supply v = ?

From Ohm's law, it is defined that, voltage across the conductor is directly proportional to the current flowing through it. Mathematically, it is represented as v = i r

where,

v is the voltage

i is the current

r is the resistance

Putting in the values, we have,

v = i r

v = 0.25 × 72 = 18 V

Thus, the required voltage supply by the camera is calculated to be 18 V.

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Answer:

1.04 x 10-3 J.

Explanation:

The total rotational kinetic energy of the two hands about the axis of rotation is calculated using the formula:

Kinetic Energy = 1/2 I ω2,

where I is the moment of inertia and ω is the angular velocity.

For this scenario, the moment of inertia is calculated by

I = 1/3 ML2,

where M is the total mass and L is the length of the arm.

Since the total mass of the two hands is 169.5 kg, and the length of the arms is 2.71 m and 4.4 m, the moment of inertia is calculated to be I = 5.35 x 10-5 kg m2. Substituting this value of I into the equation, the total rotational kinetic energy of the two hands about the axis of rotation is calculated to be 1.04 x 10-3 J.

A baseball player throws a ball which has a certain change in momentum. The magnitude of the net force on the ball is 72.22 N.

Given that,

Change in momentum Δp = 6.5 kg m/s

Time t = 90 ms = 90 × 10⁻³ s

Change in momentum can be written as,

Δp = m Δv = F×t

As we need net force on the ball,

Δp = F×t

Making F as subject and putting the values we have,

F = Δp/t = 6.5/(90 × 10⁻³) = 72.22 N

Thus, the required net force on the ball is calculated to be 72.22 N.

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This is an exothermic reaction because it releases energy in the form of heat (181kJ). When an exothermic reaction occurs, energy is released into the environment.

What is exothermic reaction?

An exothermic reaction is a chemical reaction that releases energy in the form of heat. This heat is released into the environment, making the surrounding area warmer.

Exothermic reactions can occur naturally and can also be artificially induced. Examples of exothermic reactions include burning fuels, neutralization reactions, and even certain biological processes.

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The electric field in the region r ≤a is E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]

The total charge is enclosed within the Gaussian surface.

Q[tex]_{enc}[/tex] = 2Q - Q = Q

Therefore, applying Gauss's law over the Gaussian surface

∫[tex]_{s}[/tex]E.dS = Q[tex]_{enc}[/tex]/ε₀ ⇒ E.4πr² = Q/ε₀ ⇒ E = Q/4πε₀r²(r)

In question solution:

A[tex]_{sphere}[/tex] = 4πr²

ΦE = ∫E⋅dA

ΦE = q/ε₀

  E = q/(A⋅ε₀)

  E = q/(4πr²ε₀)

for r≤a, qin = -Q

               E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]

So, the electric field in the region is   E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]

Your question is incomplete but most probably your full question was:

A uniformly charged ball of radius a and charge −Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a net charge of +2Q.

Part A: Determine the electric field strength in the region r ≤a. Give your answer as a multiple of Q/E0. Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.

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Platform moves towards to west with a speed of v0/2 when the dog moves towards to east at a speed of v0, in accordance with the rule of conservation of momentum.

The speed at which an object's location changes in any direction. The distance travelled to the time needed to travel that distance is known as speed. Since speed only has a magnitude and no direction, it is a scalar quantity.

Acceleration is the method of changing a speed with which an object moves. If a substance's velocity does not change, it is not accelerating. Acceleration is a vector quantity.

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