Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.

Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.

The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.

The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.

The equation of a line through the origin with slope m is y = mx. Thus, y = -5x.

The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.

Equation of the plane: 1(x-1) - 1(y-2) + 1(z-3) = 0 => x - y + z = 1.

The points are collinear, hence the equation of the plane is 0 = 0.

The dissociation constant (K) for acetic acid is approximately 1.8 x 10^-5, indicating it is a weak acid.

The equilibrium constant Kc is defined as the concentration of the products raised to the power of their coefficients divided by the concentration of the reactants raised to the power of their coefficients. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).

The equilibrium constant Kc is defined as the ratio of the concentrations of the products to the reactants, each raised to the power of their coefficients in the balanced equation.

The equilibrium constant Kc for the formation of ammonia from nitrogen and hydrogen is typically around 1.0 × 10^5 at standard conditions.

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/4 + 1/4 = 1/2, thus R_eq = 2Ω.

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/4 + 1/12 = 1/3, so R_eq = 3Ω.

Escape velocity v = √(2gR) = √(2 * 9.8 * 6.4 × 10^6) ≈ 11.2 km/s.

The major product of the elimination reaction of 2-bromobutane is But-2-ene due to the formation of the more stable alkene.

The reaction of 1-chlorobutane with zinc in dry ether leads to the formation of Butane via Wurtz reaction.

The expected product is Butanol due to nucleophilic substitution with hydroxide ion.

Faraday's constant is approximately 96485 C/mol.

Faraday's constant is approximately 96485 C/mol.

Using M1V1 = M2V2, (1 M)(0.1 L) = M2(0.5 L). M2 = 0.2 M.

Using heat balance: m_ice * L_f + m_water * c * (T_final - 80) = 0. Solving gives T_final = 20°C.

Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. Solving gives a final temperature of 20°C.

Using the dilution formula C1V1 = C2V2, we have 3 M * 100 mL = 1 M * V2. Thus, V2 = 300 mL.

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (9 × 10^9) * |2 × 10^-6 * -3 × 10^-6| / (0.5)^2 = -24 N.

The formula for gravitational force is F = G(m1m2)/r², where G is the gravitational constant.

The number of moles is calculated using the formula: Moles = Mass / Molar Mass.

The average power P in an AC circuit is given by P = VI cos(φ), where φ is the phase angle.

The complex formed is [Fe(SCN)3] as iron(III) can bond with three thiocyanate ions.

The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).