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

Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.

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 = -3x.

Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.

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

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

Using point-slope form: y - y1 = m(x - x1) => y - 2 = 3(x - 1).

Using point-slope form: y - 2 = 5(x - 1) gives y = 5x - 3.

The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.

The distance from the focus to the directrix is 4, so the equation is y = (1/4)(x - 0)^2 + 0, which simplifies to x^2 = 8y.

The distance from the focus to the directrix is 6, so p = 3. The equation is y^2 = 4px = 12y.

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.

f'(x) = 2x + 2. At x = 1, f'(1) = 4. The point is (1, 3). The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.

f'(x) = 2x + 2. At x = 1, f'(1) = 4. The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.

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 ratio of the concentration of products to the concentration of reactants, each raised to the power of their coefficients in the balanced equation. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).

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.

The equilibrium constant Kc is given by the ratio of the concentration of products to reactants, raised to the power of their coefficients.

The equilibrium constant K is given by the expression K = [C]/([A]^2[B]) for the reaction 2A + B ⇌ C.

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

1 liter is equal to 0.001 cubic meters.

R_eq = 1/(1/10 + 1/5) = 3.33Ω.

R_eq = 1/(1/6 + 1/3) = 2Ω.

For resistors in series, R_eq = R1 + R2 = 10 ohms + 5 ohms = 15 ohms.

R_series = 10Ω + 10Ω = 20Ω. R_parallel = 1/(1/20 + 1/5) = 4Ω. Therefore, R_eq = 4Ω.

The equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2 = 1/10 + 1/10 = 1/5. Therefore, R_total = 5Ω.