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The velocity of the fluid at point B is 4V. This can be explained by the principle of continuity, which states that the mass flow rate of an incompressible fluid remains constant along a flow path. Since the fluid is incompressible, the mass flow rate at point A is equal to the mass flow rate at point B. The mass flow rate is given by the product of the cross-sectional area and velocity of the fluid. As the radius at point B is half of the radius at point A, the cross-sectional area at point B is one-fourth of the cross-sectional area at point A. Therefore, to maintain a constant mass flow rate, the velocity at point B must be four times the velocity at point A, which is 4V.

The set of natural numbers is closed with respect to addition because when you add two natural numbers, the result is always a natural number. Similarly, the set of natural numbers is closed with respect to multiplication because when you multiply two natural numbers, the result is always a natural number. However, the set of natural numbers is not closed with respect to subtraction because when you subtract two natural numbers, the result may not always be a natural number.

The maximum pressure that the smaller piston would have to bear can be calculated using the formula P = F/A, where P is the pressure, F is the force, and A is the area. In this case, the force is equal to the weight of the car, which can be calculated as mass multiplied by acceleration due to gravity (F = mg). The area is given as 425 cm2, which needs to be converted to m2 by dividing by 10000. Plugging in the values, we get P = (3000 kg)(9.8 m/s2) / (425 cm2 / 10000) = 69.2 N/m2.

The molality of a solution is calculated by dividing the moles of solute by the mass of the solvent in kilograms. In this case, we need to find the moles of sugar (sucrose) and the mass of water. The molar mass of sucrose (C12H22O11) is 342.3 g/mol. The moles of sugar can be calculated by dividing the mass of the sugar cube (4 g) by the molar mass of sucrose. The mass of water is given as 0.5 kg. Dividing the moles of sugar by the mass of water gives us the molality of the sugar solution, which is 0.023 mol/kg.

Concentration in terms of percentage weight/weight is given by the weight of the solute dissolved per 100 parts by weight of the solution. This means that the concentration is expressed as a percentage of the weight of the solute relative to the weight of the entire solution. It is a common method to express concentration in chemistry and is useful for comparing the relative amounts of solute in different solutions.

The vapour pressure of a dilute solution is determined by the concentration of the solute in the solution, temperature, and the nature of the solvent. The melting point of the solute does not affect the vapour pressure of the solution because the vapour pressure is related to the concentration of the solute particles in the solution, not their physical state. The melting point only indicates the temperature at which the solute transitions from a solid to a liquid state, but it does not directly influence the vapour pressure.

A solution is a homogeneous mixture, meaning that it is uniform throughout and has the same composition in all its parts. It is made up of two or more kinds of different substances that are evenly distributed at a molecular level. This means that the particles of the substances are mixed together on a microscopic level and cannot be easily separated.

The expression X + 2 is a factor of X4 + 2X3 – X – 2 because when X + 2 is divided into X4 + 2X3 – X – 2, the remainder is zero. This means that X + 2 evenly divides into X4 + 2X3 – X – 2 without leaving any remainder.

Rault's law states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution. This means that as the mole fraction of the solvent increases, the vapor pressure of the solution also increases.

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