The rate constant of a reaction is affected by the nature of the reactants, temperature, and the presence of catalysts.

Dividing the equation by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.

The roots can be found using the factorization method: (x - 2)(x - 3) = 0, hence the roots are 2 and 3.

Enthalpy refers to the heat content of a system at constant pressure, defined as internal energy plus pressure times volume.

According to the second law of thermodynamics, the entropy of an isolated system always increases over time.

When the current in a solenoid is reversed, the direction of the magnetic field also reverses.

The magnetic field around a long straight conductor decreases with distance. Specifically, it is inversely proportional to the distance from the conductor.

According to Boyle's Law, if the volume decreases and temperature is constant, the pressure increases.

During an isothermal expansion, the temperature of the gas remains constant as the system absorbs heat to do work.

According to Charles's Law, the volume of a gas increases with an increase in temperature at constant pressure.

The 3rd term is C(5,2) * (3)^2 * (x)^3 = 10 * 9 * x^3 = 90.

The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.

The 3rd term is C(6,2) * (4)^2 * (x)^4 = 15 * 16 * x^4 = 240x^4.

The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.

The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.

Radius = diameter/2 = 16/2 = 8 cm. Area = πr² = π(8)² = 64π cm².

Radius = diameter/2 = 16 cm / 2 = 8 cm. Area = πr² = 3.14 * 8² = 201.06 cm².

Area = πr² = π * 10² = 314 m².

Area = πr² = π * 3² = 28.26 cm².

Area = πr²; = π * 3² = 28.26 m².

Area = πr^2 = π(7^2) = 49π ≈ 154.

Area of sector = (θ/360) * πr²; = (90/360) * π * 4² = 12.56 cm².

Area of sector = (θ/360) * πr² = (90/360) * π * 7² = 38.5 cm².

Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².

Area of base = πr² = π(3²) = 9π square units.

Area of base = πr² = π(4)² = 16π square units.

The argument of -1 + 0i is π (180 degrees) since it lies on the negative x-axis.

The atomic mass of Oxygen is approximately 16 u.

The atomic mass of Sodium (Na) is approximately 22.99 u.

The atomic number of Carbon is 6, which is the number of protons in its nucleus.