Total energy E = 1/2 kA^2, where A is the amplitude.

Total mechanical energy in SHM is E = 1/2 kA^2, where A is the amplitude.

The SI unit of electric charge is Coulomb (C).

The SI unit of energy is Joule (J).

The SI unit of pressure is Pascal (Pa), defined as one newton per square meter (N/m²).

The SI unit of pressure is Pascal (Pa), defined as one newton per square meter (N/m²).

(1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2.

Using the power of a power property, (a^m)^n = a^(m*n), we get (x^2)^3 = x^(2*3) = x^6.

Using the right triangle definition, cos(tan^(-1)(x)) = adjacent/hypotenuse = 1/√(1+x^2).

Since 32 = 2^5, log2(32) = 5.

Since 32 = 2^5, log_2(32) = 5.

Using the right triangle definition, sin(tan^(-1)(x)) = opposite/hypotenuse = x/√(1+x^2).

sin^(-1)(-1) corresponds to the angle whose sine is -1, which is -π/2.

Since π/4 is in the range of sin^(-1), sin^(-1)(sin(π/4)) = π/4.

sin^(-1)(√3/2) corresponds to the angle whose sine is √3/2, which is π/3.

tan^(-1)(√3) corresponds to the angle whose tangent is √3, which is π/3.

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at (±3, 0).

Maximum possible weight = Measured weight + Absolute error = 10 + 0.1 = 10.1 kg.

True weight range = Measured value ± Absolute error = 200 ± 5 = 195 g to 205 g.

The work done in moving a charge in an electric field is equal to the change in electric potential energy.

Using Newton's second law, the net force is (3 kg * 9.8 m/s²) - (2 kg * a) = (2 kg + 3 kg) * a. Solving gives a = 1.2 m/s².

Using Newton's second law, the net force is (3 kg - 2 kg) * g = 1 kg * 9.8 m/s². The total mass is 5 kg, so a = F/m = 9.8 N / 5 kg = 1.96 m/s², approximately 2 m/s².

For capacitors in series, the equivalent capacitance C_eq is given by 1/C_eq = 1/C1 + 1/C2. Thus, 1/C_eq = 1/2 + 1/3 = 5/6, so C_eq = 6/5 = 1.2μF.

The equivalent capacitance of capacitors in series is given by 1 / (1/C1 + 1/C2).

Relative speed = 50 km/h + 70 km/h = 120 km/h = 33.33 m/s. Time = Distance/Speed = 200 m / 33.33 m/s = 6 seconds.

Relative speed = 50 km/h + 70 km/h = 120 km/h = 33.33 m/s. Time = Distance / Relative speed = 200 m / 33.33 m/s = 6 seconds.

Relative speed = 70 + 50 = 120 km/h. Distance apart after 2 hours = 120 × 2 = 240 km.

Relative speed = 40 + 60 = 100 km/h. Distance apart after 1 hour = 100 km.

Relative speed = 70 + 50 = 120 km/h. Distance apart after 2 hours = 120 * 2 = 240 km.

At the midpoint, the electric fields due to both charges cancel each other out, resulting in a net electric field of 0.