6. A force of F = (6x²i+4j) N acts on a particle that moves from point A with coordinates (2,2) m to point B with coordinates (3,4) m. How much work is done on the particle as it moves from point A to point B?​

Since he runs a company in the US He exchanges goods and services with parties, Jack is engaged in international trade.

International trade is the exchange of goods and services between countries. It is a major driver of economic growth and prosperity. Jack's company can benefit from international trade in a number of ways. First, it can access new markets and customers. Second, it can source lower-cost inputs from other countries. Third, it can diversify its risk by selling to customers in multiple countries.

However, Jack's company also faces some challenges when engaging in international trade. First, it must deal with different languages, cultures, and legal systems. Second, it must comply with import and export regulations. Third, it must manage the risk of currency fluctuations.

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The examples of light behaving like an electromagnetic wave are Compton scattering, interference through two slits, diffraction through one slit, and refraction.

Light is a type of electromagnetic radiation that is composed of electromagnetic waves. Light behaves like an electromagnetic wave in several ways. Electromagnetic waves are transverse waves that travel through a vacuum. They don't need a medium to propagate. Light can behave like an electromagnetic wave in several ways. Let's discuss each option in the question.
Compton scattering: Compton scattering is a phenomenon in which an incident X-ray or gamma-ray photon collides with an electron resulting in a scattered photon and a recoiling electron. It can only be explained by assuming that light behaves as both waves and particles. Therefore, Compton scattering is an example of light behaving like an electromagnetic wave.
Interference through two slits: When light passes through two narrow slits separated by a distance that is small compared to the wavelength of the light, it will diffract and interfere. The interference pattern will be characterized by bright and dark fringes. This phenomenon is an example of light behaving like an electromagnetic wave.
Diffraction through one slit: When light passes through a single narrow slit, it diffracts and creates an interference pattern similar to that produced by two slits. This phenomenon is an example of light behaving like an electromagnetic wave.
Photoelectric effect: The photoelectric effect is a phenomenon in which electrons are ejected from a metal surface when light shines on it. The photoelectric effect can be explained by assuming that light behaves as a stream of particles or photons. Therefore, the photoelectric effect is not an example of light behaving like an electromagnetic wave.
Refraction: Refraction is the bending of light as it passes from one medium to another, such as from air to water. It can be explained by assuming that light behaves like an electromagnetic wave. Therefore, refraction is an example of light behaving like an electromagnetic wave.

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Fan made of plastic bottle is an innovative way to reuse plastic bottles and can be easily made at home. This can be done by following simple steps, and a few materials are required to make it. The fan can be created by using a plastic bottle, scissors, string, a ruler, and a marker.

First, the bottle needs to be cut into half, and the upper part needs to be cut into three equal sections, then fold each section to make a blade. With the help of a ruler and marker, make a mark on each section, then make a hole in the center of each blade. Insert a string through the holes and tie the ends of the strings. The fan is ready to use by holding the string and swinging it back and forth.

The use of plastic bottle fans can significantly reduce the number of plastic waste and provide a practical solution to avoid environmental pollution. Besides, it is easy to make, and the materials are readily available, which can be used for various occasions, such as picnics, camping, or any outdoor activities.

In conclusion, the creation of a fan made of plastic bottle with string is an excellent way to reuse plastic bottles and can be made with simple steps. This project encourages everyone to contribute to environmental protection by utilizing what is available at home and reducing the number of plastic wastes.

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The given statement, "A precondition for perfect competition is that the product should be homogeneous" is true.

Perfect competition is a market structure in which numerous small firms compete against each other with identical or homogeneous products, and no one firm can influence the market price independently.

In a perfectly competitive market, there is free entry and exit of firms, perfect knowledge of the market, and no barriers to entry.What does homogeneous mean?Homogeneous products refer to goods or services that are identical or very similar in nature and have the same level of quality and features. Examples of homogeneous products include agricultural goods, basic raw materials, commodities, and so on.

In perfect competition, all firms offer identical products to customers. Homogeneous products are essential to ensure that no single firm has an advantage over others in terms of quality or price. If there were differences in quality or price, customers would prefer to buy from the firm with the lowest price or highest quality. This would give that firm a competitive advantage over others in the market.

As a result, it would no longer be a perfectly competitive market, since one firm could influence the market price independently. Therefore, the precondition for perfect competition is that the product should be homogeneous, which means that all firms should offer identical or very similar products to their customers.

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Answer:

Measurement is the comparison of any physical quantity of an object to a standard unit which is pre-determined. The standard units such as length, time, mass etc are known as the Fundamental units of Measurement.

Explanation:

Any object that can be measured is known as a physical quantity. So, to measure the physical quantity, we require some standard units. A measurement consists of two parts - the numerical measurement and the standard unit which is pre-determined. For example, the length of a given table is 10cm, which implies that 10 is the numerical value and the standard unit of measurement is centimeter (cm).

Measurements can be both Fundamental and Derived. Examples of Fundamental quantities are Length, Time etc, while example of Derived quantity is speed which is derived from Length and Time.

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To see what is happening outside the car using the available materials, you can design a periscope using mirrors, cardboard, masking tape, and scissors.

To design an instrument to see what is happening outside the car, we can make a periscope using the materials available. A periscope uses mirrors to reflect the light and images, allowing us to see around corners or over obstacles. Using the mirrors, cardboard, masking tape, and scissors, we can create a periscope by positioning one mirror at a 45-degree angle, reflecting the image towards the second mirror which is positioned horizontally to observe the outside environment. By adjusting the angles and positions of the mirrors, we can see what is happening outside the car without directly looking out.

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A car is moving north at 5.2 m/s². SI unit in this value is m/s² (meter per second square), expressing Acceleration. Thus, Option D is the correct answer.

Here Acceleration of any object is given by the Rate of change in velocity in relation to time.

[tex]Acceleration = \frac{velocity}{time}[/tex] ............(i)

The standard Indian (SI) unit of Acceleration is meter per second square(m/s²).

The velocity of any object is displacement per unit time.

[tex]velocity = \frac{Displacement}{Time}[/tex]............(ii)

The standard Indian (SI) unit of Velocity is meter per second(m/s)

The Displacement of any object is the shortest distance covered by any object considering the direction of motion also.

The standard Indian (SI) unit of displacement is meter(m).

The standard Indian (SI) unit of Time is Second(s).

We can find standard Indian (SI) unit of Acceleration using formula as follows:

[tex]Acceleration= \frac{Velocity}{time*time}[/tex]  (we got this formula from (i), (ii) )

The standard Indian (SI)  units of acceleration are [tex]=\frac{m}{s*s}[/tex]

[tex]=m/s^{2}[/tex]

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The marble will take approximately 12 seconds to hit the ground, ignoring air resistance.

To solve this problem we can use the equations of motion that are given as below:

Vf = Vi + atX =[tex]Vi*t + 1/2*a*t^2Vf^2 = Vi^2 + 2*a*X[/tex]

Where:Vf = final velocity, Vi = initial velocity, a = acceleration, X = distance traveled, and t = time taken.For a freely falling object near the surface of the earth, we can assume that the acceleration due to gravity is constant at 9.8 [tex]m/s^2[/tex] (downward direction).

At the top of the building, the initial velocity is zero. Hence, using the equation, [tex]Vf^2 = Vi^2 + 2*a*X[/tex], we can find the final velocity, Vf, just before the marble hits the ground.

So, we have:[tex]Vf^2 = 2*a*X[/tex]

where, X = 890 m (height of the building) and

a = 9.8[tex]m/s^2Vf[/tex]

  = sqrt(2*9.8*890) ≈ 118 m/s

Now, using the equation, Vf = Vi + at, we can find the time, t, taken by the marble to reach the ground. So, we have:118 = 0 + 9.8*t.

Therefore, t = 118/9.8 ≈ 12 seconds.

Therefore, the marble will take approximately 12 seconds to hit the ground, ignoring air resistance.

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To calculate the torque required to create an angular acceleration, we can use the formula:

Torque = Moment of Inertia × Angular Acceleration

The moment of inertia of a disk can be calculated using the formula:

Moment of Inertia = (1/2) × Mass × Radius^2

Given:

Mass = 15,000 kg

Radius = 6.14 m

Angular Acceleration = 0.0500 rad/s^2

First, calculate the moment of inertia:

Moment of Inertia = (1/2) × Mass × Radius^2

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Next, calculate the torque:

Torque = Moment of Inertia × Angular Acceleration

Torque = Moment of Inertia × 0.0500 rad/s^2

Now, let's plug in the values and calculate:

Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2

Moment of Inertia ≈ 283,594.13 kg·m^2

Torque = 283,594.13 kg·m^2 × 0.0500 rad/s^2

Torque ≈ 14,179.71 N·m

Rounding to three significant figures, the torque required to create an angular acceleration of 0.0500 rad/s^2 is approximately 14,180 N·m.

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