Using the lens formula, the image distance is calculated to be -16.67 cm.

Using the mirror formula, 1/f = 1/v + 1/u, where f = -10 cm (concave mirror), u = -30 cm. Solving gives v = -15 cm, which means the image is formed 15 cm in front of the mirror.

Using the mirror formula, 1/f = 1/v + 1/u. Here, f = -5 cm (concave mirror), u = -10 cm. Solving gives v = -10 cm.

Tension T = mg/cos(θ) to balance the vertical component of weight.

In a conical pendulum, T = mg/cos(θ) where θ is the angle with the vertical.

The vertical component of tension balances the weight: T cos(θ) = mg, thus T = mg/cos(θ).

The vertical component of tension balances the weight: T cos(θ) = mg.

As the angle increases, the vertical component of tension must increase to balance the weight.

Tension T provides the centripetal force and balances the weight, T = mg/cos(θ).

Tension provides the vertical component to balance the weight: T cos(θ) = mg.

Tension T = mg/cos(θ) to balance the vertical component of weight.

Power (P) = 1/f (in meters). f = 0.15 m, so P = 1/0.15 = +6.67 D.

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

Using the lens formula 1/f = 1/v - 1/u, we find v = 60 cm.

Using the lens formula 1/f = 1/v - 1/u, where f = 20 cm and u = -40 cm, we find v = 20 cm. The image is formed at 20 cm on the opposite side.

Power (P) = 1/f (in meters). f = 20 cm = 0.2 m, so P = 1/0.2 = 5 D.

Resistance (R) = ρ * (L / A) = 1.68 x 10^-8 * (100 / 1 x 10^-6) = 1.68 Ω.

The total flux through the cube is Q/ε₀, and since there are 6 faces, the flux through one face is Q/6ε₀.

The total flux through the cube is Q/ε₀, and since the charge is at one corner, the flux through one face is Q/(12ε₀).

The charge at one corner contributes 1/8 of its flux to the cube. Thus, total flux = (1/8)Q/ε₀ = Q/(12ε₀).

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

The direction of the force on a current-carrying conductor in a magnetic field is given by the right-hand rule.

Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 10² = 50 m.

Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 8² = 32 m.

Using the formula: distance = ut + 0.5at². Here, u = 0, a = 2 m/s², t = 10 s. Distance = 0 + 0.5 * 2 * 10² = 100 m.

Kinetic Energy = 0.5 × m × v² = 0.5 × 70 kg × (10 m/s)² = 3500 J. Power = Work / Time = 3500 J / 5 s = 700 W.

Work done = Change in Kinetic Energy = 0.5 × mass × (final velocity² - initial velocity²) = 0.5 × 75 kg × (15 m/s)² = 843.75 J.

Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 75 kg × (15 m/s)² = 8437.5 J.

Weight = Work / Height = 300 J / 5 m = 60 N; mass = Weight / g = 60 N / 9.8 m/s² ≈ 6.12 kg.

Power can be calculated using P = F * v. Here, F = 100 N and v = 5 m/s. Thus, P = 100 N * 5 m/s = 500 W.