Osmotic pressure (π) can be calculated using the formula π = iCRT. For NaCl, i = 2, C = 0.5 M, R = 0.0821 L·atm/(K·mol), and T = 298 K, resulting in approximately 24.6 atm.

The magnetic field at the center of a circular loop of radius R carrying a current I is given by B = μ₀I/(2πR).

The magnetic field at the center of a circular loop is given by B = μ₀I/(2R).

The magnetic field B at a distance r from a long straight conductor carrying current I is given by B = (μ₀I)/(2πr).

The magnetic field B at a distance r from a long straight wire carrying current I is given by B = (μ₀I)/(2πr).

The equation xy = c represents a family of hyperbolas with varying constant c.

The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with semi-major axis a and semi-minor axis b.

The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.

The equation y = e^(kx) represents a family of exponential functions where 'k' determines the growth rate.

The equation y = k/x represents a family of hyperbolas with varying asymptotes depending on the value of 'k'.

Using the formula m1*T1 + m2*T2 = (m1 + m2)*Tf, we find Tf = (200*90 + 300*30) / (200 + 300) = 70°C.

Using the chain rule, f'(x) = 2e^(2x).

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.

For a concave lens, the focal length (f) is negative. The virtual image distance (v) is -20 cm. Using the lens formula 1/f = 1/v + 1/u, we can find f. Since v = -20 cm, we can assume u is at infinity, thus 1/f = 1/(-20) + 0, giving f = -20 cm.

The focal length of a concave lens is negative, so it is -15 cm.

Power (P) = 1/focal length (f). Therefore, f = 1/P = 1/(-2) = -0.5 m.

Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.

Using the mirror formula 1/f = 1/v + 1/u, where u = -30 cm and v = -10 cm, we find f = 15 cm.

Using the mirror formula, 1/f = 1/v + 1/u; here, v = -15 cm (real image) and u = -30 cm. Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = 10 cm.

Using the lens formula 1/f = 1/v - 1/u, where v = 30 cm and u = -15 cm, we find f = 20 cm.

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/(-15) - 1/(-10) = -1/15 + 1/10 = -1/30, thus f = -30 cm.

Using the lens formula, we find the focal length to be -12 cm.

For the image to be at infinity, the focal length must be equal to the object distance, hence f = 60 cm.

Using the lens formula, 1/f = 1/v - 1/u. Here, v = -20 cm (virtual image), u = -10 cm. Solving gives f = 5 cm.

Using the lens maker's formula for a plano-convex lens, f = R/2 = 30 cm / 2 = 30 cm.

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (9 × 10^9) * |2 × 10^-6 * -3 × 10^-6| / (0.5)^2 = -1.08 N.

The force experienced by a charge q in an electric field E is given by F = qE.

The magnetic force on a charge moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity and the magnetic field.

The force experienced by a charge q moving with velocity v in a magnetic field B is given by the Lorentz force law: F = q(v × B), which can be expressed as F = qvB sin(θ), where θ is the angle between the velocity and the magnetic field.

The force experienced by a current-carrying conductor in a magnetic field is known as the Lorentz force.