f(n) is a member of omega(g(n)) can be defined as: question 1 options: f(n) is lower bounded by g(n). as n-> infinity f(n) will grow as fast or faster than g(n). f(n) is unbounded by g(n). as n-> infinity f(n) will approach infinity and g(n) will approach zero. f(n) is abelian bounded by g(n). as n-> infinity f(n) will approach zero as g(n) approaches infinity. f(n) is upper bounded by g(n). as n-> infinity f(n) will grow slower or as fast as g(n) but never faster.

Answer:

5.67 m/s

Explanation:

The speed of a wave can be calculated as the distance traveled by the wave divided by the time taken:

Speed = Distance/Time

In this case, the distance traveled by the wave is the length of the pool, which is 17 m. The time taken by the wave to travel this distance is 3 seconds.

So, the speed of the wave can be calculated as:

Speed = 17 m/3 s

Speed = 5.67 m/s

Therefore, the speed of the water wave in the 17 m long pool is 5.67 m/s.

If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The

wavelength of the wave is 1.69m.

The wavelength of a wave can be determined using the equation:

Wavelength = velocity / frequency

To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.

frequency = 1 / time

frequency = 1 / 0.230

frequency ≈ 4.35 Hz

Substitute the values into the wavelength equation:

wavelength = velocity / frequency

wavelength = 7.33 / 4.35

wavelength ≈ 1.69m

Therefore the wavelength of the wave is approximately 1.69 meters.

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Answer:

J = FΔt

J = mΔv

J = Δp

Explanation:

Answer:

Conduction: Touching a stove and being burned. Ice cooling down your hand. .

Explanation:

Answer:

Heat is flowing into the metal.

Explanation:

From the question given above, the following data were obtained:

Mass (M) of iron = 150 g

Initial temperature (T₁) = 25.0°C

Final temperature (T₂) = 73.3°C

Direction of heat flow =?

Next, we shall determine the change in the temperature of iron. This can be obtained as follow:

Initial temperature (T₁) = 25.0 °C

Final temperature (T₂) = 73.3 °C

Change in temperature (ΔT) =?

ΔT = T₂ – T₁

ΔT = 73.3 – 25

ΔT = 48.3 °C

Next, we shall determine the heat transfered. This can be obtained as follow:

Mass (M) of iron = 150 g

Change in temperature (ΔT) = 48.3 °C

Specific heat capacity (C) of iron = 0.450 J/gºC

Heat (Q) transfered =?

Q = MCΔT

Q = 150 × 0.450 × 48.3

Q = 3260.25 J

Since the heat transferred is positive, it means the iron metal is absorbing the heat. Thus, heat is flowing into the metal.

Answer:

The answer is (D): When the current flows up the wire, the magnetic field flows in on the left side of the wire and out on the right side of the wire.

Explanation:

Answer: mass is neither created nor destroyed

Explanation: For example, the carbon atom in coal becomes carbon dioxide when it is burned. The carbon atom changes from a solid structure to a gas but its mass does not change.

electricity

Explanation:

the position (2,o

Answer:

η = 0.84 = 84%

Explanation:

The efficiency of the man can be given by the following formula:

η = output/input

where,

η = efficiency of man = ?

output = potential energy gain of the block = mgh

input = work done by man = Fd

Therefore,

\(\eta = \frac{mgh}{Fd}\)

where,

m = mass of block = 225 kg

g = acceleration due to gravity = 9.81 m/s²

h = height gained by block = 1.2 m

F = force exerted by man = 315 N

d = distance covered by man = 10 m

Therefore,

\(\eta = \frac{(225\ kg)(9.81\ m/s^2)(1.2\ m)}{(315\ N)(10\ m)}\)

η = 0.84 = 84%

Answer:

100N.

Its 100n. :)

Answer:

strongest are at the points of the north pole and the south pole, specifically between the red box and the letter of each pole.

Explanation:

The lines of magnetic force are drawn so that the density of lines is proportional to the intensity of the magnetic field.

Therefore, the sections where the magnetic field is strongest are at the points of the north pole and the south pole, specifically between the red box and the letter of each pole.

The normal force on the car when it is at the bottom of the track is 8.84 N.

At the top of the track (point B), the normal force (N) acting on the car is equal to the weight of the car (mg) plus the centrifugal force (mv²/r) acting outwards:

N = mg + mv²/r

where m is the mass of the car, g is the acceleration due to gravity, v is the speed of the car, and r is the radius of the track.

Since the car is traveling at constant speed, its acceleration is zero, so the centrifugal force is balanced by the force of gravity, and we have:

N = mg

Substituting the given values, we get:

6.00 N = (0.610 kg)(9.81 m/s²)

Solving for g, we get:

g = 9.68 m/s²

At the bottom of the track (point A), the normal force acting on the car is equal to the weight of the car minus the centrifugal force acting downwards:

N = mg - mv²/r

Substituting the known values, we get:

N = (0.610 kg)(9.81 m/s²) - (0.610 kg)(v²/5.00 m)

Since the car is traveling at constant speed, we can use the fact that its kinetic energy is equal to its gravitational potential energy to solve for v:

mg(2r) = (1/2)mv²

where 2r is the total distance traveled by the car (i.e., the circumference of the circle), so 2r = 2πr = 31.4 m. Solving for v, we get:

v = sqrt(2gr)

Substituting the known values, we get:

v = sqrt(2(9.68 m/s²)(5.00 m)) = 6.19 m/s

Substituting this value of v into the equation for N, we get:

N = (0.610 kg)(9.81 m/s²) - (0.610 kg)((6.19 m/s)²/5.00 m) = 8.84 N

Therefore, the normal force on the car when it is at the bottom of the track is 8.84 N.

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Answer:

Asch's experiment showed that about 75% of people were "yielders" who conformed and 25% were "independent" who didn't conform. Asch concludes that people ignored reality and gave an incorrect answer in order to follow the rest of the group.

Answer:

Iron wheels of roller skates rusting when it rains outside

Explanation:

A chemical change happens when one chemical substance is transformed into one or more different substances, such as when iron becomes rust.

Answer:

a)  v = 3.116 m / s,  b)  μ = 1.65 10⁻²

Explanation:

a) to find the velocity of the set, let's define a system formed by the person and the sled, so that the forces during the collision are internal and the moment is conserved

initial instant. Before the crash

        p₀ = M v₀

final instant. After the crash

        p_f = (M + m) v

the moment is preserved

       M v₀ = (M + m) v

       v = \(\frac{M}{M+m} \ v_o\)

let's calculate

      v = \(\frac{41.6}{41.6 + 14.6} \ 4.21\)

      v = 3.116 m / s

b) for this part let's use the relationship between work and kinetic energy

        W = ΔK

as the body has its final kinetic energy is zero

the work of the friction forces is

          W = - fr x

the negative sign is because the friction forces always oppose the movement

let's write Newton's second law

Y axis  

        N - W_sled -W_person = 0

        N = mg + M g

        N = (m + M) g

X axis

        fr = ma

the friction force has the expression

        fr = μ N

        fr = μ g (m + M)

we substitute

        - μg (m + M) x = 0- ½ (m + M) v²

          μ = \(\frac{1}{2} \ \frac{v^2 }{g \ x }\)

let's calculate

        μ = \(\frac{1}{2} \ \frac{3.116^2}{9.8 \ 30.0}\)

        μ = 0.0165

        μ = 1.65 10⁻²

1 mole of nitrogen atoms moving at 35.0 m/s possesses approximately 27.8 joules of energy.

To calculate the energy possessed by 1 mole of nitrogen atoms moving at 35.0 m/s, we need to consider both the kinetic energy and the molecular mass of nitrogen.

The kinetic energy (KE) of an object is given by the equation KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

The molar mass of nitrogen (N₂) is approximately 28.0134 g/mol, which can be converted to kilograms by dividing by Avogadro's number (6.022 × 10^23). This gives us a mass of approximately 4.65 × 10^(-26) kg for one nitrogen atom.

Plugging in the values, we have KE = 1/2 * (4.65 × 10^(-26) kg) * (35.0 m/s)^2.

Evaluating the equation, we find that the kinetic energy possessed by one nitrogen atom is approximately 4.62 × 10^(-23) joules.

Since we are considering 1 mole of nitrogen atoms, we need to multiply this value by Avogadro's number to get the energy possessed by 1 mole. Avogadro's number is 6.022 × 10^23, so the total energy is approximately 2.78 × 10^1 joules, or 27.8 J.

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the ball will strike the opposite wall 6.22 m below its original level.

To solve this problem, we need to use the equations of motion for a projectile. The horizontal and vertical components of the initial velocity are:

V₀x = V₀ cosθ = 6.1 cos(40°) = 4.65 m/s

V₀y = V₀ sinθ = 6.1 sin(40°) = 3.91 m/s

The time it takes for the ball to reach the opposite wall can be found using the horizontal distance and the horizontal component of velocity:

d = V₀x t

t = d / V₀x = 15.24 m / 4.65 m/s = 3.28 s

The vertical distance traveled by the ball can be found using the equation:

y = V₀y t - 1/2 g t²

where g is the acceleration due to gravity, which is -9.81 m/s² (negative because it acts downward). Substituting the known values, we get:

y = 3.91 m/s × 3.28 s - 1/2 × 9.81 m/s² × (3.28 s)² = 6.22 m

Therefore, the ball will strike the opposite wall 6.22 m below its original level.

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Since the car masses are unknown, we are unable to calculate the numerical value of the x-component of Car A's tangential acceleration.

The energy that is held in any object or system as a function of its position or component arrangement is known as potential energy. The object or system is unaffected by external factors like air pressure or altitude. Kinetic energy, on the other hand, describes the power of moving particles within a system or an object.

They are being affected by the kinetic frictional force, which is caused by:

f = μk * N

Therefore,

fB = μk * N = μk * mB * g

Car C is at its highest point at the top of the hill, where the normal force acting on it is equal to the force of gravity. Therefore,

fC = μk * N = μk * mC * g

where mC is the mass of Car C.

For Car A, the x-component of the tangential acceleration is given by:

aA = (fB - fC) / mA

where mA is the mass of Car A.

We can substitute the following values and simplify by assuming that the mass of each of the three automobiles is the same:

aA = (μk * mB * g - μk * mC * g) / mA

aA = μk * g * (mB - mC) / mA

Since μk = 1.00 and g = 9.81 m/s², we can plug in the values and get:

aA = (mB - mC) * 9.81 / mA

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We are asked to determine the momentum of a particle that is moving at a velocity of 1.75 m/s and has a mass of 325 kg.

To do that we will use the following formula:

Where:

Now, we substitute the values:

Now, we solve the operations:

Therefore, the momentum is 568.75 kg m/s.

528.65 kgm/s

Since mass of body=325 kg

(we will not change kilograms into grams as kilograms is the standard international unit .)

velocity of the ball rolling down the hill=1.75meter/second

since we know momentum=mass x velocity

and standard international unit of momentum is kgm/s that is kilogram meter per second

hence substituting the values of mass and velocity in the above expression  we get :-

momentum=(325 x 1.75) kgm/s

momentum =568.75 kgm/s

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Answer:

Explanation:

The acceleration of an object given it's mass and the force acting on it can be found by using the formula

\(a = \frac{f}{m} \\ \)

m is the mass

f is the force

From the question we have

\(a = \frac{126}{56.2} \\ = 2.241992...\)

We have the final answer as

Hope this helps you

Given :

Magnitude of vector, v = 15.3 m

Angle of vector from horizon, \(\theta = 65^o\) .

To Find :

The x - component of the given vector.

Solution :

We know, a vector is given by :

\(\vec{v} = vsin\ \theta \hat{i} + v cos \ \theta \hat{j}\\\)

Now, the x - component is :

\(\vec{v_x} = vcos\ \theta \hat{j}\\\\\vec{v_x} = 15.3 \times cos\ 65^o \hat{j}\\\\\vec{v_x} = 15.3 \times 0.42\ \hat{j}\\\\\vec{v_x} = 6.426\ \hat{j}\)

Hence, this is the required solution.

C.S. Lewis calls the rule of Right and Wrong or the "Law of Human Nature" the Moral Law which states that, this law is universal and applies to all people, regardless of their faith or lack thereof.

In Mere Christianity, Lewis argues that the Moral Law is not something that can be created or invented by humans, but is instead something that is discovered. He explains that the Moral Law is like a set of rules that can be found in nature, just as one can discover the laws of mathematics or physics. The Moral Law is a set of moral principles that underlie all our ethical decisions, such as the notion of “do unto others as you would have them do unto you.” C.S. Lewis claims that this Law is universal and unchanging, and is the basis of all moral decisions and argues that it is not something that can be altered or changed by humans.

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complete question: C.S. Lewis says (1) the "Law of Human Nature" (ie. the "Moral Law") and (2) the other "laws of nature," such as the law of gravitation and the biological laws, are _______________. (Bk I, Mere Christianity)

Answer:

a.

gravity decreases by distance

thickness doesn't change

Less heat.

Answer:

3

5

4

Explanation:

x = (8=(9+9)

(9+9) = 4, 5, 3

Answer:

D

Explanation:

because of the the side of the bottom

With 20 windings, the generator will produce a higher EMF and, consequently, a larger current. This increased current will provide more power to the light bulb, resulting in a brighter illumination compared to the dim illumination observed with only 5 windings.

When you increase the number of wire windings in the generator from 5 to 20, the effect on the light bulb will be a brighter illumination. The brightness of the light bulb is directly proportional to the number of windings in the generator.

By increasing the number of windings, you are increasing the amount of wire wrapped around the magnet. This results in a higher number of turns per unit length, leading to an increased magnetic flux passing through the wire coils.

According to Faraday's law of electromagnetic induction, a change in magnetic flux induces an electromotive force (EMF) in a conductor, which in this case is the copper wire. The induced EMF causes electric current to flow through the wire, creating a flow of electrons.

The 30-W light bulb requires a certain amount of electrical power to produce its specified brightness. With 20 windings, the generator will produce a higher EMF and, consequently, a larger current. This increased current will provide more power to the light bulb, resulting in a brighter illumination compared to the dim illumination observed with only 5 windings.

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The heating time constant is 13 seconds and the steady state temperature is 38°C.

To find the heating time constant and steady state temperature, use the formula:

ΔT = P × R × (1 - e^(-t/τ))

where ΔT = temperature rise, P = power, R = thermal resistance, t = time, τ = heating time constant, and e = natural logarithmic constant.

Let's use the given information to solve for τ:

ΔT1 = 25°C (for the first 25 minutes)

ΔT2 = 40°C (for the second 25 minutes)

t = 25 + 25 = 50 minutes

The temperature rise over the entire 50 minutes is:

ΔT = ΔT1 + ΔT2 = 25°C + 40°C = 65°C

The average power can be calculated as:

P = ΔT / (t × R)

Assume that the power output is the rated power of the motor. Let's assume that the rated power is 100 W.

Then, solve for R:

R = ΔT / (t × P) = 65°C / (50 min × 100 W) = 0.13 °C/W

Now, solve for the heating time constant:

τ = R × C

where C = thermal capacitance. Value of C is unknown, but make an assumption that the thermal time constant is on the order of minutes to hours. Let's assume that C = 100 J/°C.

Then, τ = 0.13 °C/W × 100 J/°C = 13 seconds

Finally, solve for the steady state temperature:

ΔT = P × R

T_ss = T_amb + ΔT = 25°C + 100 W × 0.13°C/W = 38°C

Therefore, the heating time constant is 13 seconds and the steady state temperature is 38°C.

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Answer:

4. pressure is defined as force per unit area

Pressure is defined by force per unit area.

Therefore, according to this question, it can be said that pressure is defined by force per unit area

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