Range = Maximum value - Minimum value = 30 - 15 = 15.

Range = Maximum - Minimum = 30 - 15 = 15.

Range = Maximum value - Minimum value = 8 - 3 = 5.

Range = Maximum value - Minimum value = 20 - 5 = 15.

Range = max - min = 30 - 5 = 25.

Range = Maximum - Minimum = 25 - 5 = 20.

Range = Maximum - Minimum = 15 - 5 = 10.

Range = Maximum - Minimum = 50 - 10 = 40.

Range = Maximum - Minimum = 25 - 5 = 20.

The function is a downward-opening parabola with a maximum value of 4, so the range is (-∞, 4].

The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).

The range of sin^(-1)(x) is (-π/2, π/2).

The range of y = cos^(-1)(x) is [0, π].

The range of y = sin^(-1)(x) is [-π/2, π/2].

The range of the function y = tan^(-1)(x) is (-π/2, π/2).

The rows of A are linearly dependent, hence the rank is 2.

The rank of E is 2 because the rows are linearly dependent (the third row is a linear combination of the first two).

The rank of the matrix is 2, as the rows are linearly dependent.

For a first-order reaction, k = 0.693 / t₁/₂. Here, t₁/₂ = 10 min, so k = 0.693 / 10 = 0.0693 min⁻¹.

The rate law for a reaction is determined by the order with respect to each reactant. For a first order with respect to A and second order with respect to B, the rate law is Rate = k[A][B]^2.

For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.

The rate law expression is derived directly from the rate equation, which is given as rate = k[A]^2[B].

The rate law is determined by the order of the reaction with respect to each reactant. For first order in A and second order in B, the rate law is Rate = k[A][B]^2.

Reactance (X_L) = 2πfL = 2π(50)(0.1) = 31.4 Ω.

The reactance of an inductor in an AC circuit is given by the formula X_L = 2πfL.

The real part of the complex number 4 + 5i is 4.

The real part of 5 - 7i is 5.

The real part of the complex number 7 - 4i is 7.

The real part is 2 * cos(π/3) = 2 * 1/2 = 1.

The real part of z = 4 + 5i is 4.