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 = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s

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

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

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 Coulomb's law, F = k * |q1 * q2| / r^2 = (9 × 10^9) * (2 × 10^-6) * (3 × 10^-6) / (0.5)^2 = 0.24 N.

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 force on a current-carrying conductor in a magnetic field is given by F = BIL sin(θ), where θ is the angle between the conductor and the magnetic field.

The force on a charge moving in a magnetic field is maximum when the angle θ between the velocity vector and the magnetic field is 90°, as sin(90°) = 1.

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

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

In a parallel RLC circuit, the total current is calculated using I = V/(1/R + 1/X), where X is the total reactance.

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

The average power consumed in an AC circuit can be expressed as P = VI, P = V²/R, and P = I²R.

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

The total impedance in a parallel circuit is given by 1/Z = 1/Z1 + 1/Z2 + 1/Z3.

Frequency f = number of oscillations / time = 30 / 60 = 0.5 Hz.

Frequency = 1/Period = 1/0.01 s = 100 Hz.

Frequency (f) = Number of vibrations / Time = 256 / 2 = 128 Hz.

Frequency f = 1/T = 1/0.01 s = 100 Hz.

Frequency f = 1/T = 1/0.1 s = 10 Hz.

Frequency (f) is the reciprocal of the period (T). Therefore, f = 1/T = 1/0.2 s = 5 Hz.

Frequency (f) = 1/Period (T) = 1/0.5 s = 2 Hz.

Frequency (f) = speed (v) / wavelength (λ) = 300 m/s / 3 m = 100 Hz.

Frequency (f) is given by the formula f = speed / wavelength. Here, f = 340 m/s / 2 m = 170 Hz.

g = G * M / r² = (6.67 × 10^-11) * (100) / (10²) = 6.67 × 10^-10 N/kg

Weight = mass * g = 50 kg * 9.8 m/s² = 490 N

Weight W = m * g = 50 kg * 9.8 m/s² = 490 N.