Arranging the numbers: 2, 3, 5, 7, 11, 13. Median = (5 + 7) / 2 = 6.

Finding the derivative f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. Evaluating f(0) = 16, f(2) = 0, and f(-2) = 0, the minimum value is 0.

Mode is the number that appears most frequently, which is 4.

The modulus of resilience is the energy per unit volume stored in a material up to the yield point.

The moment of inertia of a composite body can be calculated using the parallel axis theorem.

The moment of inertia of a hollow cylinder about its central axis is I = MR^2.

The moment of inertia is calculated by summing the mass of each particle times the square of its distance from the axis of rotation: I = Σ(m_i * r_i²).

The slopes can be found by solving the quadratic equation in terms of m, yielding slopes -1 and -2.

The discriminant of the quadratic equation is positive, indicating two distinct real roots.

The product of the slopes of the lines is given by m1*m2 = c/a = 1/2 = -2.

Factoring gives (2x - 3y)(2x - 3y) = 0, indicating the lines are coincident.

The discriminant of the quadratic equation is positive, indicating two distinct real roots.

The discriminant of the quadratic equation is negative, indicating imaginary lines.

Rearranging gives (x-2)^2 + (y-2)^2 = 0, which represents two intersecting lines.

To determine the nature of the lines, we can rewrite the equation in the form of (x - a)^2 + (y - b)^2 = r^2 and analyze the discriminant.

Rearranging gives (x-2)^2 + (y-3)^2 = 0, which represents a single point, hence the lines are coincident.

To determine the nature of the lines, we can find the slopes from the equation. The product of the slopes will help us conclude if they are perpendicular.

The given equation can be factored as (x - 2y)(x - 2y) = 0, indicating that the lines are perpendicular.

Since the coefficient of (x - 2)^2 is negative, the parabola opens downwards.

The phenomenon of a liquid rising in a narrow tube is called capillarity.

Capillary action occurs due to the combination of surface tension (which pulls the liquid up) and adhesion (which attracts the liquid to the walls of the tube).

The phenomenon of liquid rising in a narrow tube is called capillarity.

Surface tension arises from cohesive forces between liquid molecules.

The potential energy U of a system of two point charges is given by U = k * q1 * q2 / r.

The power factor is defined as the ratio of real power to apparent power.

The product of the roots is given by c/a = 10/1 = 10.

Using Vieta's formulas, the product of the roots is k = 10. Thus, k = 17.

z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - i^2 = 2 + 1 + i = 3 + i.

The discriminant is 0, indicating one real root (a repeated root).

For both roots to be negative, the sum of roots (4) must be positive and the product (k) must be positive, hence k > 0.