The half-life of a first-order reaction is independent of the initial concentration and is directly proportional to the rate constant.

For a first-order reaction, the half-life is constant and is given by the formula t1/2 = 0.693/k.

The half-life of a first-order reaction is given by the formula t1/2 = 0.693/k, where k is the rate constant.

The Langmuir isotherm assumes that adsorption occurs at specific sites, leading to a monolayer coverage of the adsorbate.

In the Langmuir isotherm, the maximum coverage of adsorbate on the adsorbent is referred to as a monolayer.

The maximum displacement from the rest position is defined as the amplitude of the wave.

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.

100 ÷ 4 = 25, then 25 + 25 = 50.

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.