Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.

Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.

Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.

Energy required = mass * latent heat = 0.5 kg * 2260 kJ/kg = 1130 kJ.

Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).

Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.

Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).

Setting y = 0 in the equation gives 3x + 12 = 0, thus x = -4.

Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).

Rearranging gives y = (3/4)x + 3. The slope of the line is 3/4, so the slope of the parallel line is -3/4.

Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.

Rearranging to y = -7/2x + 7 shows that the slope is -7/2.

The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength. Therefore, if the magnetic field strength is doubled, the force also doubles.

The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength. Therefore, if the magnetic field strength is doubled, the force also doubles.

The force on a current-carrying conductor is directly proportional to the magnetic field strength, so if the field strength is doubled, the force also doubles.

The force on a current-carrying conductor is directly proportional to the magnetic field strength, so if the magnetic field strength is doubled, the force also doubles.

Average induced EMF (ε) = -ΔΦ/Δt = -(0.5 Wb - 0.2 Wb) / 2 s = -0.3 Wb / 2 s = -0.15 V. The absolute value is 0.15 V or 150 mV.

Average induced EMF = -ΔΦ/Δt = -(0.5 Wb - 0.2 Wb) / 2 s = -0.15 Wb/s = 150 V.

Density is defined as mass per unit volume, so the unit of density is kg/m³.

F ∝ m/r²; if m is tripled and r is halved, F = 3m/(1/4) = 12m, so it increases by a factor of 9.

Gravitational force is directly proportional to mass. If mass doubles, force also doubles.

Perimeter = 4 × side, so side = 40/4 = 10 cm.

pH = 3 means [H+] = 10^-3 M = 0.001 M.

For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.

The angle θ can be found using cos(θ) = power factor. Thus, θ = cos⁻¹(0.8) ≈ 36.87°.

According to Boyle's Law, P * V = constant at constant temperature, so if P increases, V must decrease.

The product of the roots gives k = (-2)(-3) = 6.

Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.

Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.

Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².