The solutions are x = 2π/3 and 4π/3.

The solutions are x = 2π/3 and x = 4π/3.

The solutions are x = π/4, 3π/4, 5π/4, and 7π/4.

The solutions are x = 0, π, and 2π.

sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.

The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.

Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.

A large negative value of ΔG indicates that the reaction is highly spontaneous and favors the formation of products.

A negative ΔG indicates that the reaction is spontaneous under the given conditions.

A positive ΔG indicates that the reaction is non-spontaneous.

A positive ΔG indicates that the reaction is non-spontaneous.

A positive ΔS indicates an increase in disorder or randomness in the system.

A ΔG value of zero indicates that the reaction is at equilibrium, meaning the forward and reverse reactions occur at the same rate.

Ampere's Law states that the magnetic field around a closed loop is proportional to the electric current passing through the loop.

Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface.

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, which can be expressed as V = IR.

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent.

The Biot-Savart Law describes the magnetic field generated by a steady current flowing through a conductor.

The first law of thermodynamics states that the total energy of an isolated system is constant, meaning energy can neither be created nor destroyed.

The Gibbs free energy change indicates the spontaneity of a reaction; a negative value suggests spontaneity.

The enthalpy of reaction refers to the heat absorbed or released at constant pressure.

Entropy is a measure of the disorder or randomness in a system.

Gibbs free energy indicates the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure.

Surface tension is the energy required to increase the surface area of a liquid due to intermolecular forces.

Adding salt to water generally increases its viscosity.

For an endothermic reaction, increasing temperature generally decreases ΔG, making the reaction more favorable.

Increasing the concentration of a reactant in a first-order reaction increases the rate of the reaction.

According to F = ma, if the force is doubled, the acceleration also doubles.

The average kinetic energy of gas molecules is directly proportional to the absolute temperature. Therefore, increasing the temperature increases the average kinetic energy.

As the temperature of a gas increases, the average speed of gas molecules also increases due to the increase in kinetic energy.