5. in each case, find the inverse of the element under the given operation. a. 13 in z20 b. 13 in u(14) c. n21 in u(n) (n . 2) d. 322i in c*, the group of nonzero complex numbers under multiplication

Answer:

By increasing the perpendicular distance between the force and the pivot point

Explanation:

Due to the formula \(force * distance\),

An increase in distance would cause the turning force to increase

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Answer:

Anything that has motion cannot be stopped

Explanation:

Answer:

equal and opposite reaction

Explanation:

Answer:

1

Explanation:

because every number has coffitiant of 1

Answer:

defined as the mean volume of all the parts of an object which can be seen unobscured in all directions from a particular point inside the object.

for a neutron star : a6 = 3/5(Gm^2 / Ro)

= 5.8 × 10^-37MeV

Me - Mass of electron = 9.11 × 10^-31 kg

V - Volume of a neutron star

a6 - constant

V = a6 / 5.8 × 10^-37Me

Answer:

Explanation:

Given :

We need to find the frequency of the wave

Using formula:

Where,

On substituting the required values, we get:

\( \dashrightarrow \sf \: F = \dfrac{80}{0.3} \\ \\ \dashrightarrow \sf \: F = 266.6 \: Hz\)

Therefore,

Answer:

B. Large mountain ranges

The velocity of the cart is 19.8 m/s.

The velocity of the cart is calculated by applying the principle of conservation of energy as shown below;

P.E ( at the top) = K.E (at the bottom)

mgh = ¹/₂mv²

v = √ (2gh)

where;

The velocity of the cart is calculated as follows;

v = √ (2gh)

v = √ (2 x 9.8 x 20 )

v = 19.8 m/s

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GPE = mgh

3.36 x 10⁹ J = m x 9.8 m/s² x 1.45 x 10³ m

m = 2.36 x 10⁵ kg

The initial vertical velocity of the object is 2.5 m/s .

Initial Velocity, denoted as u, is the velocity at time period t = 0. It is the speed at which motion first occurs. There are four equations for starting velocity: (1) The starting velocity is expressed as u = v - at if time, acceleration, and final velocity are given.

Keep in mind that the INITIAL VERTICAL VELOCITY of the projectile is equal to ZERO because it is launched horizontally.

Given,

base  =1m

height = 2.5

vertical velocity =2.5/1

The initial vertical velocity of the object is 2.5 m/s .

A projectile's initial velocity has both a horizontal component and a vertical component if it is thrown at an angle to the horizontal. The projectile's displacement horizontally as a result of velocity is shown by the horizontal velocity component (vx).

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Answer:

C.

Explanation:

Swapping electrical charges will always have to do with electrons, so A & B can be eliminated easily.

Electrons will be the ones transferring over to the new object. Electrons are naturally negatively charged, so anything that gains electrons will become negatively charged themselves. Whereas if they lose electrons, they will become positively charged.

It's worth noting that protons and electrons have the same exact numerical charge, but they are both opposites. Electrons are negative, and protons are positive. Neutrons on the other hand have no charge (hence the "neutral" root in its name).

Answer:

1.26 m/s²

Explanation:

Given:

Δx = 172 m

v₀ = 17.3 m/s

v = 27.1 m/s

Find: a

v² = v₀² + 2aΔx

(27.1 m/s)² = (17.3 m/s)² + 2a (172 m)

a = 1.26 m/s²

1. The Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of particles. The general solution represents the wave function of a particle and provides information about its position and momentum.

3.Tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even though it does not have enough energy to overcome the barrier classically.

1. The Schrödinger equation is a partial differential equation that was developed by Erwin Schrödinger in 1925 as a mathematical formulation of quantum mechanics. It describes how the wave function of a particle evolves over time. The equation takes the form:

Ĥψ = Eψ

Where Ĥ is the Hamiltonian operator, ψ is the wave function, E is the energy of the particle, and Ĥψ represents the operation of the Hamiltonian on the wave function.

The general solution to the Schrödinger equation represents the wave function of a particle. The wave function provides information about the probability distribution of the particle's position and momentum. It contains both real and imaginary components and is typically represented as a complex-valued function.

The wave function, ψ, can be written as a product of a spatial part and a temporal part:

ψ(x, t) = Ψ(x) * Φ(t)

The spatial part, Ψ(x), represents the probability amplitude of finding the particle at position x, while the temporal part, Φ(t), describes how the wave function evolves over time.

The Schrödinger equation and its general solution are essential tools in quantum mechanics, as they allow us to predict the behavior of particles on a microscopic scale. By solving the equation, we can determine the wave function of a particle and calculate probabilities associated with its position and momentum.

2.Case 1: Particle in a Box

In the case of a particle confined to a one-dimensional box, the potential energy is zero within the box and infinite outside of it. This situation can be represented by the following potential function:

V(x) = 0,  0 < x < L

V(x) = ∞,  x ≤ 0 or x ≥ L

To solve the Schrödinger equation for this case, we need to find the wave function (Ψ) and the corresponding energy levels (E). The general form of the wave function inside the box is given by:

Ψ(x) = A * sin(kx)

Where A is a normalization constant, and k = (2π/L).

Applying the boundary conditions, we find that the wave function must go to zero at both ends of the box (x = 0 and x = L). This leads to the quantization of the wave vector k:

k = nπ/L,  where n = 1, 2, 3, ...

The corresponding energy levels are given by:

E = (ħ²π²/2mL²) * n²

Where ħ is the reduced Planck's constant and m is the mass of the particle.

Case 2: Harmonic Oscillator

In the case of a particle in a harmonic oscillator potential, the potential energy can be described by:

V(x) = (1/2)kx²

Where k is the spring constant. To solve the Schrödinger equation for this potential, we use the harmonic oscillator equation:

- (ħ²/2m) * (d²Ψ/dx²) + (1/2)kx²Ψ = EΨ

The solutions to this equation are given by Hermite polynomials, and the corresponding energy levels are quantized. The wave function for the harmonic oscillator potential can be expressed as a product of a Gaussian function and a Hermite polynomial:

Ψ(x) = (A/π)\(^{(1/4)\) * exp(-αx²/2) * Hₙ(√αx)

Where A is a normalization constant, α = (√(mk/ħ)), and Hₙ is the Hermite polynomial of degree n.

The energy levels in the harmonic oscillator potential are given by:

E = (n + 1/2)ħω

Where n = 0, 1, 2, ... and ω = (√(k/m)) is the angular frequency of the oscillator.

These solutions provide insights into the behavior of electrons traveling in these potential systems, including the quantization of energy levels and the spatial distribution of the wave functions.

3. Tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even though it does not have enough energy to overcome the barrier classically. This effect arises from the wave nature of particles, as described by the Schrödinger equation.

Tunneling has important implications in various areas of physics, such as nuclear fusion, quantum computing, and scanning tunneling microscopy. It allows for phenomena such as alpha decay, where alpha particles escape from atomic nuclei, and the operation of tunneling diodes in electronic devices.

Overall, tunneling is a fascinating quantum mechanical phenomenon that challenges our classical intuition and plays a crucial role in understanding the behavior of particles in the presence of potential barriers.

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Answer:

The mass has gained a height of 5 meters.

Explanation:

To calculate the height gained by a 2kg mass when 100J of gravitational energy is transferred to it, we can use the equation:Height (h) = Gravitational Potential Energy (GPE) / Weight (w)where GPE = mgh (mass x acceleration due to gravity x height)Therefore,h = (100 J) / (2 kg x 10 N/kg)h = 5 metersThe mass has gained a height of 5 meters.

Answer:

a. I =  -3mv₀/2 b. F = -3mv₀/2t

Explanation:

a. Use the impulse-momentum to write an equation for the  system which is the cart only.

We know Impulse , I = Δp where Δp = change in momentum.

Now, Δp = m(v - u) where m = mass of cart, u = initial velocity of cart = v₀ and v = rebound velocity of cart = -v₀/2 (negative since it moves in the opposite direction to u)

So, I =  Δp = m(v - u)

Substituting the values of the variables into the equation, we have

I = m(-v₀/2 - v₀) = -3mv₀/2

So, I =  -3mv₀/2

b. If the time during which the bumper exerts a force on the cart is t, write an expression for the force F exerted on the cart in terms of the given variables.

We know impulse I = Ft where F = force exerted on the cart and t = time force acts

Also, I = -3mv₀/2

So, Ft = -3mv₀/2

F = -3mv₀/2t

Answer:

Gravitational potential energy is energy an object possesses because of its position in a gravitational field.

It is given by P.E = mgh

where m = mass

Explanation:

g= acceleration due to gravity

h = height of the object

Here,

h = 1.45km = 1450 m

P.E = 3.36 x J

g = 9.8m/

therefore, m = P.E/ gh = (3.36 x s J)/ 9.8 x 1450

m = 2.36 x

Hence mass of the airplane is 2.36 x

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The differential of the process X(t)Y(t) is:  d(X(t)Y(t)) = tY(t)dW(t) + 2tW(t)dY(t).

To find the differential of the process X(t)Y(t), we can use Itô's Lemma. Let's start by applying Itô's Lemma to the product X(t)Y(t).

Let Z(t) = X(t)Y(t).

By Ito's Lemma, we have:

dZ(t) = (∂Z/∂t)dt + (∂Z/∂X)dX(t) + (∂Z/∂Y)dY(t) + (1/2)(∂²Z/∂X²)d[X(t)]² + (∂²Z/∂X∂Y)dX(t)dY(t) + (1/2)(∂²Z/∂Y²)d[Y(t)]².

Now let's calculate each partial derivative term by term:

(∂Z/∂t) = 0

(∂Z/∂X) = Y(t)

(∂Z/∂Y) = X(t)

(∂²Z/∂X²) = 0

(∂²Z/∂X∂Y) = (∂Z/∂Y) = X(t)

(∂²Z/∂Y²) = 0

Now we substitute these derivatives back into the expression for dZ(t):

dZ(t) = (∂Z/∂t)dt + (∂Z/∂X)dX(t) + (∂Z/∂Y)dY(t) + (1/2)(∂²Z/∂X²)d[X(t)]² + (∂²Z/∂X∂Y)dX(t)dY(t) + (1/2)(∂²Z/∂Y²)d[Y(t)]²

= 0 + Y(t)dX(t) + X(t)dY(t) + 0 + X(t)dY(t) + 0

= Y(t)dX(t) + 2X(t)dY(t).

Now let's substitute the expressions for X(t) and dX(t):

dX(t) = tdW(t),

X(t) = tW(t).

Substituting these back into dZ(t):

= Y(t)(tdW(t)) + 2(tW(t))dY(t)

= tY(t)dW(t) + 2tW(t)dY(t).

Therefore, we have:

d(X(t)Y(t)) = tY(t)dW(t) + 2tW(t)dY(t).

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Answer:

d. wavelength/2.

Explanation:

The circular motion of water molecules extends from regions of shallow water to deep water. It ranges from a depth, H < L/20 for shallow water to a depth of H > L/2 for deep water where L is the wavelength of the wave.

For depths greater than L/2,the circular motion is not affected by the wave energy. So, the maximum depth for the circular motion is L/2 = wavelength/2.

Explanation:

The weight is 40 * 6.2 = 248N.

Answer:

248 N

Explanation:

Weight= Gravity*mass

W= 6.2*40

W= 248N

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Answer:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Answer:

It’s actually A) Inversely

Explanation:

The final speed of the piece of clay after it is stuck to the rod is 0.7792 m/s.

What is speed?

Speed is a scalar quantity that measures the rate at which an object covers a certain distance in a given amount of time.

Given:

Mass of the clay (m_clay) = 40 g = 0.04 kg

Initial speed of the clay (v_initial) = 30 m/s

Mass of the rod (m_rod) = 1.5 kg

Length of the rod (L) = 2 m

Let's assume the final speed of the clay-rod system after sticking is v_final.

The initial linear momentum (p_initial) of the clay is given by:

p_initial = m_clay * v_initial

The final linear momentum (p_final) of the clay-rod system is given by:

p_final = (m_clay + m_rod) * v_final

According to the conservation of linear momentum:

p_initial = p_final

m_clay * v_initial = (m_clay + m_rod) * v_final

Simplifying the equation:

(0.04 kg) * (30 m/s) = (0.04 kg + 1.5 kg) * v_final

1.2 kg·m/s = (1.54 kg) * v_final

v_final = 1.2 kg·m/s / 1.54 kg

v_final ≈ 0.7792 m/s

Therefore, the final speed of the piece of clay after it is stuck to the rod is  0.7792 m/s.

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Answer:

A Benjamin Franklin

B George Washington

C Abraham Lincoln

D John Adams

Answer:

Force Increases and Mass remains the same.

Explanation:

Answer:

D.

Explanation:

Frequency is what measures in hertz.

Correct Answer:

D. frequency

Answer:

A parliamentary republic with a 3 tier system

Explanation:

The judiciary is independent, with everything operating in a parliementary republic. Legislative authority is held by the Parliament of South Africa.

Answer:

Igneous

Explanation:

The vectors point along the axis of rotation with a direction determined by an arrow.

There are two types of physical quantity one is a scaler and another one is a vector.

The quantity that requires only megnitude to define is known as the scalar quantity. While the vector quantities need both megnitude and the direction to define.

The vector quantity is represented by an arrow. The vectors point along the axis of rotation with a direction determined by an arrow.

The angular quantities L, omega, and alpha are vector quantities.

Hence arrow is the correct answer for the blank.

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The direction of the vectors of angular momentum and L, angular velocity omega and the mass alpha is determined using the right hand rule.

Righthand rule in physics states that, when we curl our right hand fingers, the direction of the angular momentum and velocity will be in the direction of thumb and curl of fingers determine the axis of rotation.

Angular momentum is a vector quantity defined as the product of moment of inertia and angular velocity where, the angular velocity ω is the rotational analogue of linear velocity i.e.. product of the linear velocity and radius of rotational path.

Therefore, the angular quantities L, angular velocity ω along the axis of rotation can be determined using the right hand rule. Where direction of thump represents the direction of vector components.

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flat disk like shape

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The big, soft clouds darkening as a storm approaches in the visual scene represent low spatial frequencies.

Spatial frequency refers to the rate of change of intensity or color in an image across space. It is commonly associated with the level of detail or fine-grained texture in a visual scene. In this case, the description of big, soft clouds darkening as a storm approaches suggests a decrease in fine details and a more uniform appearance, indicating a dominance of low spatial frequencies.

Low spatial frequencies correspond to large-scale variations in an image. They represent smooth and slowly changing features such as broad contours, large objects, and overall patterns. In the context of clouds, low spatial frequencies would capture the overall shape, size, and general structure of the cloud masses as they darken before a storm.

The darkening of the clouds may result from increased cloud thickness or the presence of rain or other atmospheric conditions associated with a storm. These factors can reduce the amount of light scattering through the cloud, resulting in decreased brightness and contrast, which further emphasizes the low-frequency content in the visual scene.

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Matter from space can condense to form a nebula or matter from a star can explode to form a nebula.

The nebula is made up of dust and gas, most of which are Helium and Hydrogen gases. Dust and gas in the Nebula spread easily, but due to the gravitational pull, these clumps of dust and gas slowly coalesce. The bigger the lump that is produced, the stronger the gravitational pull.

Finally, the resulting lump of dust and gas becomes very large and explodes under its gravity. The collapse of this gas column causes the substance at the center of the cloud to heat up. Later this hot nebula core will become a new star.

Complete questions:

Matter from space can ____ to form a nebula or matter from a star can____ to form a nebula.

The correct choice is B and C

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Answer:

F = G M m / R^2

F1 = G M m / R1^2

F2 = 4 G M m / R2^2

F2 = 16 F1