define SI systems of units

The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.

Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.

Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:

∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du

The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.

Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.

Let us work through the steps:

Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x

Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du

Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.

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the average coefficient of friction while travelling on the incline is 59.24.

v0 = 11.0 m/sd = 15 mθ = 19°m = mass of the skier

The force acting on the skier are:

Gravity (mg), Normal force (N), Friction force (f)

The forces are related to the motion of the skier as:

ΣF = f - mgsinθ

Net work done = Change in Kinetic Energy

f = ma... equation 1

g = 9.8 m/s²

Step 1: Find the acceleration of the skier along the inclined plane.

Therefore, from equation 1;

a = g sinθ + f/m... equation 2

When the skier reaches the top of the hill, the velocity will be zero.

Using equation 2, we can calculate the acceleration of the skier along the incline:

a = g sinθ + f/m0 = 9.8 sin 19° - f/m15 = 11.2 - 1.96/f

Therefore,1.96/f = 11.2 - 15f = 1.96/3.8f = 0.52 N

Substitute the value of f in equation 2;

a = g sinθ + f/ma = 9.8 sin 19° + 0.52/ma = 3.36 m/s²

Step 2: Find the distance travelled by the skier.

Distance travelled (d) = 15 m

Step 3: Find the initial velocity of the skier using the work-energy principle.

ΣW = ΔKEf - ΔKEi + Wnc

Here, the final kinetic energy of the skier (KEf) is zero.

ΣW = -KEii = 1/2 mv0²

ΣW = ΔPE

ΔPE = mgh

v0 = √(2gh)

v0 = √(2 x 9.8 x 15)

v0 = 17.2 m/s

Step 4: Calculate the average coefficient of friction

The work done by the friction force f is

f d cos180° = -fdΣW = ΔKEf - ΔKEi + Wnc- fd = -1/2 mv0²f = mv0² / 2d cos180°f = (m/2d) v0²... equation 3

Substitute the given values in equation 3;

m = mass of the skier

v0 = 17.2 m/s

d = 15 m

f = 0.52 N

Numerator = 2mdf v0² = (2 x 72 x 0.52 x 17.2²)Denominator = 2d(15)(0.52)Denominator = 7.8

The average coefficient of friction = Numerator / Denominator= 462.14 / 7.8 = 59.24

Therefore, the average coefficient of friction is 59.24.

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The key observation enabled Edwin Hubble to prove this by observing individual Cepheid variable stars in Andromeda and applying the period-luminosity relation.

American astronomer Edwin Powell Hubble lived from November 20, 1889, through September 28, 1953. He was a significant contributor to the development of observational cosmology and extragalactic astronomy.

Hubble established that many objects formerly believed to be "nebulae" or clouds of gas and dust, were actually galaxies outside the Milky Way. He scaled galactic and extragalactic distances using the strong direct correlation between a classical Cepheid variable's luminosity and pulsation time, which was found in 1908 by Henrietta Swan Leavitt.

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Simple harmonic motion is a kind of periodic motion in which a physical system moves back and forth from its equilibrium position, oscillating with a certain frequency and amplitude.

Below are the correct statements about the motion of a simple harmonic oscillator: The frequency is inversely proportional to the square root of the oscillator mass: The frequency of a simple harmonic oscillator is determined by the mass of the object and the spring constant of the spring. It follows that the frequency is inversely proportional to the square root of the oscillator mass.

Doubling the spring constant and reducing the mass by one-half would make the period double: The period of a simple harmonic oscillator is determined by the mass of the object and the spring constant of the spring. Doubling the spring constant and reducing the mass by one-half would make the period half.

The period of the oscillator is proportional to the square root of the oscillator mass: As the frequency is inversely proportional to the square root of the oscillator mass, it follows that the period of the oscillator is proportional to the square root of the oscillator mass.

Simple Harmonic Oscillators must be subject to a linear restoring force as described by Hooke's Law: Hooke's Law states that the restoring force is proportional to the displacement from equilibrium and is in the opposite direction of the displacement.

Doubling the amplitude and cutting in half the mass of an oscillator would make the period increase by the square root of 2: The period of the oscillator would not increase by the square root of 2 if the amplitude is doubled and the mass is halved.

However, the frequency would double and the period would be halved.

The amplitude of a simple harmonic oscillator is proportional to the period: The amplitude of a simple harmonic oscillator is determined by the energy of the system. It follows that the amplitude is not proportional to the period.

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Answer:

5 m/s²

Explanation:

Acceleration = change in speed/time taken

20-5=15

15/3= 5 m/s²

An oscillating LC circuit consists of a 60.0 mH inductor and a 4.00 uF capacitor, the maximum current in the circuit is approximately 3.06 A.

We may use the following calculations to calculate the total energy and maximum current in the oscillating LC circuit:

(a) The total energy in the circuit:

E = 0.5 * C * \(V^2\)

Qmax = C * V

V = Qmax / C

V = (3.00 * \(10^{(-6)\) C) / (4.00 * \(10^{(-6)\) F)

V = 0.75 V

The total energy:

E = 0.5 * C * \(V^2\)

E = 0.5 * (4.00 * \(10^{(-6)\) F) * \((0.75 V)^2\)

E = 0.5 * 4.00 * \(10^{(-6)\) * 0.5625

E = 1.125 * \(10^{(-6)\) J

The total energy in the circuit is 1.125 * 10^(-6) J.

(b) The maximum current:

Imax = Qmax / √(L * C)

Imax = (3.00 * \(10^{(-6)\) C) / √((60.0 * \(10^{(-3)\) H) * (4.00 * \(10^{(-6)\)F))

Imax = (3.00 *  \(10^{(-6)\) C) / √(240.0 * \(10^{(-9)\) H * 4.00 * \(10^{(-6)\)F)

Imax = (3.00 *  \(10^{(-6)\) C) / √(0.960 * \(10^{(-14)\) H * F)

Imax = (3.00 *  \(10^{(-6)\) C) / (0.980 * \(10^{(-7)\) A)

Imax ≈ 3.06 A

Thus, the maximum current in the circuit is approximately 3.06 A.

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The speed of the  Toyota Corolla would have  been 143.9 mph.

The acceleration of the F-15 can be calculated as follows:

Acceleration = Velocity Change / Time = (Take-off Speed) / Time

where;

Take-off Speed = √(2dg /t²)

Take-off Speed = √(2 x  (270 ft)  x 32.2 ft/s² / (2 s)²)

T  = √(17496) = 131.6 ft/s

Acceleration = Velocity Change / Time

= (131.6 ft/s) / (2 s) = 65.8 ft/s²

We can use the same acceleration to launch the Toyota Corolla, and calculate its final velocity:

Final Velocity = Initial Velocity + Acceleration x Time

where;

Final Velocity = 0 + (65.8 ft/s²) * (2 s) = 131.6 ft/s

Finally, we can convert the velocity from feet per second to miles per hour:

Velocity (mph) = Velocity (ft/s) x (1 hour/3600 s) x (5280 ft/mile)

= 131.6 ft/s x  (1 hour/3600 s)  x (5280 ft/mile)

= 143.9 mph

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Answer:

chemical change

Explanation:

Answer:

d) 5.88

Explanation:

.2 * .3 * 9.8

Gas particles can change to solid particles if the temperature decreases.

The state of matter of a substance is determined by its temperature and pressure. When the temperature of a gas decreases, its particles lose kinetic energy and slow down. This decrease in kinetic energy leads to a decrease in the average speed of gas particles.

As the temperature continues to decrease, the particles lose energy and move closer together. At a certain temperature known as the condensation point or the freezing point, the gas particles no longer have enough energy to overcome the intermolecular forces holding them together.

At this point, the gas undergoes a phase transition and changes into a solid. The process of gas turning into a solid is called condensation or freezing, depending on the specific substance.

During condensation, the gas particles arrange themselves in a more orderly and structured manner, forming a solid. The transition from gas to solid involves the release of energy, known as heat of fusion.

In summary, when the temperature of a gas decreases below its condensation or freezing point, the gas particles lose energy, slow down, and eventually come together to form a solid.

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The kinetic energy of the car is 300,000J

Kinetic energy is the energy of motion.

The formula for kinetic energy is given as \(K.E = \frac{1}{2} mv^{2}\)

where m = mass of object , v = speed of object.

An object having some speed and mass will have kinetic energy while an object at rest will not have any kinetic energy since the speed of object at rest is zero.

Since at rest speed is zero, an object has kinetic energy only when it is in motion.

From the question,

m = 1,500kg

v = 20m/s

K.E = (1/2) x 1,500 x 20 x 20

K. E = 300,000J

The car now possess a kinetic energy of 300,000J

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To determine the resultant force produced by two concurrent forces, we can use vector addition. The resultant force is the vector sum of the individual forces.Based on the calculations, none of the given options (2), (3), or (4) can be the resultant force produced by the combination of the forces.

Given that a force of 30 newtons and a force of 20 newtons act concurrently, we need to add these two forces together to find the resultant force.

Option (1) 0 N: This cannot be the resultant force because adding two non-zero forces will never result in a zero force.

Option (2) 25 N: To calculate the resultant force, we add the magnitudes of the forces together: 30 N + 20 N = 50 N. Therefore, a resultant force of 25 N is not possible.

Option (3) 5 N: Similarly, adding the magnitudes of the forces together: 30 N + 20 N = 50 N. Therefore, a resultant force of 5 N is not possible.

Option (4) 60 N: Adding the magnitudes of the forces together: 30 N + 20 N = 50 N. Therefore, a resultant force of 60 N is not possible.

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A tree is placed cm from the converging mirror, and the radius of curvature is 20 cm. The distance of the image is 30 cm.

A converging mirror is also known as a concave mirror, whose inner side has a reflecting surface. They are called converging mirror because it converges all parallel beam of light incident on them.

u = -15cm, object distance

R = -20cm (Converging mirror)

f = R/2 = -10 cm focal length

1/v + 1/u = 1/f

1/v + 1/-15 = 1/-10

1/v – 1/15 = -(1/10)

1/v = 1/15 – 1/10 = (2 -3)/30 = - (1/30)

v = - 30 cm

Therefore, the image is formed 30 cm in front of the mirror.

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Answer:

mass = GPE divided by gxh

Explanation:

Answer:

69.9 kg

Explanation:

w = mg

m = w/g

m = 685/9.8

m = 69.9 kg

2 equal-mass entities are positioned at heights of h/2 and h, respectively. Their gravitational potential energy ratio is 1:4.

potential energy= mgh (h= H/2) potential energy for an item at H

Potential energy of the item is given by 2H= mg₂H (h=2H) mg(H/2)/ mg₂H = 1/4, resulting in a ratio of 1:4.

The energy that an item has as a result of being in a gravitational field is known as gravitational potential energy. It is a type of potential energy as it is the energy that an item would release if it moved in response to gravity.

For example, when an object is lifted to a certain height above the ground, it gains gravitational potential energy because it is now further away from the center of the Earth and has the potential to fall back down and release that energy. The amount of gravitational potential energy gained by the object is proportional to its mass, the acceleration due to gravity, and the height above the ground.

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The projectiles launch allows to find the answer for the initial velocity of the stone is:

            v = 17.71 m / s

Projectile launching is an application of kinematics for motion in two dimensions, where there is no acceleration on the x axis and the acceleration on the y axis is the gravity acceleration.

In the attached diagram we can see a corner of the movement. Where the x axis is horizontal and the y axis is vertical, where the zero of the system is at the base of the cliff

In this case the stone is thrown horizontally, therefore its initial vertical speed is zero, let's find the time it takes to reach the base of the cliff

           y = y₀ + \(v_{oy}\) t - ½ g t²

where y and y₀ are the current and initial position, \(v_{oy}\) is the initial vertical velocity, g the acceleration of gravity and t the time

When reaching the bottom its height is zero (y = 0) and the highest part its initial height is y₀ = 25.00 m

           0 =y₀ + 0 - ½ g t²

          t = \(\sqrt{\frac{2y_o}{g} }\)

Let'se calculate

           \(t = \sqrt{ \frac{2 \ 2.25 }{9.8 } }\)

           t = 2,259 s

They indicate that the stone fell at a horizontal distance of 40 m,

           x = \(v_{ox}\) t

            v_{ox} = \(\frac{x}{t}\)

           v_{ox}  = \(\frac{40}{2.259}\)

           v_{ox} = 17.71 m / s

In conclusion, using theprojectiles launch we can find the answer for the initial velocity of the stone is:

            v = 17.71 m / s

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Answer:

i = 5.28 A

Explanation:

The magnetic force is given by the expression

          F = i l x B

the bold letters indicate vectors, let's write the modulus of that expression, where the direction between the conductor and the magnetic field is 90º, therefore the sine 90 = 1

           F = i l B

           i = F / l B

let's reduce the length to the SI system

           l = 10 cm (1m / 100 cm) = 0.10 m

let's calculate

           i = 12.9 / 0.1 3.6

           i = 5.28 A

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Answer:

Lightning is an electrical discharge caused by imbalances between storm clouds and the ground, or within the clouds themselves. Most lightning occurs within the clouds. ... This heat causes surrounding air to rapidly expand and vibrate, which creates the pealing thunder we hear a short time after seeing a lightning flash.

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Answer:

Lightning can be explained in terms of charges produced due to rubbing. During a thunderstorm, the air currents move upwards and the water droplets move downwards. And this caused due to the separation of charge due to this vigorous motion.

Explanation:

The statement that is true about the time constant is that the product of the resistance R and the capacitance C is equal to the time constant τ of the charging capacitor.

A time constant describes the rate of change of current or voltage in a circuit. When an RC (resistance-capacitance) circuit is charged, the time constant represents the duration required for the capacitor to charge to 63.2% of its maximum charge potential. It also represents the time required for the capacitor to discharge to 36.8 percent of its maximum potential.

The formula for calculating the time constant of an RC circuit is:τ = RC.

Where R is resistance, and C is capacitance.

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The swimmer will land a distance of 180 * (v_r / 1.4) meters downstream from the starting point, where v_r represents the velocity of the river.

To determine how far downstream the swimmer will land, we can use the concept of relative velocity. Let's consider the swimmer's velocity relative to the river, which is the vector sum of the swimmer's velocity in still water and the velocity of the river.

Given that the swimmer's velocity in still water is 1.4 m/s, we need to determine the velocity of the river. To do this, we'll use the fact that the swimmer swims directly across the river, perpendicular to the current. This means that the swimmer's velocity relative to the river is equal to the velocity of the river itself.

Let's assume the velocity of the river is v_r. Since the swimmer is swimming directly across a 180 m wide river, the time taken to cross can be calculated as t = 180 m / (1.4 m/s). During this time, the river current will push the swimmer downstream by a distance equal to the velocity of the river multiplied by the time taken, i.e., d = v_r * t.

Substituting the known values, we get d = v_r * (180 m / 1.4 m/s). Since the units cancel out, the answer will be in meters.

Therefore, the swimmer will land a distance of 180 * (v_r / 1.4) meters downstream from the starting point, where v_r represents the velocity of the river.

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a)

i. The force exerted on the piston by the air in the freezer is 240 N.

ii. The work done on the piston by the air as it pushes the piston 0.021 m into the cylinder is 5.04 J.

b) The change in the internal energy of the cylinder is 3486 J.

a)  

i. To calculate the force exerted on the piston by the air in the freezer, we can use the formula:

Force = Pressure * Area

Given:

Pressure (P) = 1.0 × \(10^5\) Pa

Area (A) = 2.4 ×\(10^(^-^3^) m^2\)

Substituting these values into the formula, we have:

Force = (1.0 × 10^5 Pa) * (2.4 ×\(10^(^-^3^) m^2)\)

      = 240 N

ii. To calculate the work done on the piston by the air in the freezer as the air pushes the piston, we can use the formula:

Work = Force * Distance

Given:

Force = 240 N

Distance (d) = 0.021 m

Substituting these values into the formula, we have:

Work = (240 N) * (0.021 m)

     = 5.04 J

b) To calculate the change in the internal energy of the cylinder, we can use the formula:

ΔU = mcΔT

Given:

Initial temperature (T1) = 21°C = 21 + 273 = 294 K

Final temperature (T2) = -18°C = -18 + 273 = 255 K

Thermal capacity (c) = 89 J/°C

Substituting these values into the formula, we have:

ΔU = (89 J/°C) * (294 K - 255 K)

   = 3486 J

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Answer:

Answer:

See Explanation

Explanation:

The principle of conservation of energy states that; energy can neither be created nor destroyed but is converted from one form to another.

In view of this principle, Ella can not be correct when she says that a lot of energy has disappeared. The use of the term "disappeared" connotes the idea that the energy no longer exists which does not happen.

Hence, energy can not "disappear" from hot water rather the energy in the water may be transferred to the surroundings.

Answer:

The adapted expression for average acceleration is \(a = \frac{v}{t'}\).

Explanation:

Let be \(v = v_{o} + a\cdot t\), which can be adapted by using the following substitution:

\(t = t'-t_{o}\)

Where:

\(t'\) - Final instant, measured in seconds.

\(t_{o}\) - Initial instant, measured in seconds.

\(v = v_{o}+a\cdot (t-t_{o})\)

Where:

\(v\) - Final velocity, measured in meters per second.

\(v_{o}\) - Initial velocity, measured in meters per second.

\(a\) - Average acceleration, measured in meters per square second.

Now, average acceleration is cleared:

\(a = \frac{v-v_{o}}{t'-t_{o}}\)

Given that \(t_{o} = 0\,s\) and \(v_{o} = 0\,\frac{m}{s}\), then:

\(a = \frac{v}{t'}\)

Answer:

a = (v-v0)      

     ____      where v = final velocity, v0

         t

Explanation:

Using algebra, , where v = final velocity, v0 = initial velocity, and t = time. So,

= -9.3 m/s2.

Answer:

-1.46 m/s^2

Explanation:

Write down what is given first:

v0 = 12 m/s

vf = 0 m/s

d = 45 m

We are trying to find acceleration, so we will use the equation vf^2 = v0^2 + 2ad

Plug in the values we have:

0^2 = 12^2 + (2 x 45 x a)

a = - 1.46 m/s^2

Note that this acceleration is negative because the body is slowing down, so the acceleration with be negative, because the change in velocity is negative.

According to the given statement - 1.46 m/s²  is the acceleration of the body.

Acceleration is the rate of change in a moving asteroid's speed and direction over time. When something moves faster or slower, it is considered to be accelerating.

Use the formula a = v / t to determine acceleration, where v stands for the change in velocity and t for the time it took for the change to take place. Use the formula v = vf - vi to determine v, where vf stands for final velocity and vi for starting velocity.

Write down what is given first:

v0 = 12 m/s

vf = 0 m/s

d = 45 m

We are trying to find acceleration, so we will use the equation

vf² = v0² + 2ad

Plug in the values we have:

0² = 12² + (2 x 45 x a)

a = - 1.46 m/s²

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The shear deformation of the disk under the given conditions is approximately 0.00589 meters. To find the shear deformation of the disk, we can use the formula Shear Deformation = (Shear Force * Disk Height) / (Shear Modulus * Disk Area)

Shear Force = 540 N

Shear Modulus = 1.00×10^9 N/m^2

Disk Height = 0.700 cm = 0.007 m

Disk Diameter = 4.20 cm = 0.042 m

First, we need to calculate the area of the disk. Since the disk is equivalent to a solid cylinder, its area can be calculated using the formula:

Disk Area = π * (Disk Diameter/2)^2

Disk Area = π * (0.042 m/2)^2

Next, we can substitute the values into the shear deformation formula:

Shear Deformation = (540 N * 0.007 m) / (1.00×10^9 N/m^2 * π * (0.042 m/2)^2)

Shear Deformation ≈ 0.00589 m

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The electric potential energy increases when a positive charge is moved from position i to position f in case (a).

Electric potential energy is the energy that a charged object possesses due to its position in an electric field. In case (a), the point charges are arranged in a straight line, with two positive charges and two negative charges. If a positive charge is moved from position i to position f, it would be moving closer to the two negative charges and further away from the positive charges. This means that the potential energy of the system would increase since the positive charge would experience a greater force of attraction from the negative charges. Therefore, the correct answer is A. Electric potential energy increases.

In order to understand why the electric potential energy increases when a positive charge is moved from position i to position f in case (a), we need to consider the interactions between the charges. When a positive charge is at position i, it is closer to the two positive charges and farther away from the negative charges. This means that the electric potential energy of the system is at a certain level. When the positive charge is moved to position f, it is closer to the two negative charges and farther away from the positive charges. This means that the electric potential energy of the system increases.
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Answer:

Having begun as a "science of mental life", psychology evolved in the 1920's into the "scientific study of observable behavior". ... Today's science emphasizes the interaction of genes and experiences in specific environment

Answer:

Psychology continues to develop over the years all the way up to today by new and better scientific like science emphasizes. Also new experiences in specifics enviroment.

Explanation:

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