sin(90°) = 1, so θ = 90°.

sin(30°) = 1/2, so θ = 30°.

sin(45°) = 1/√2, so θ = 45°

tan(45°) = 1, so θ = 45°.

Energy of a wave is proportional to the square of the amplitude. If amplitude is doubled, energy increases by (2^2) = 4 times.

The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.

Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Length CD = |10 - 5| = 5.

Using point-slope form: y - 5 = 1(x - 5) => y = x.

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.

The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.

The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.

Power is proportional to the square of the current (P = I²R). If I is tripled, P increases by 3² = 9 times.

Circumference = πd; C = π * 20 ≈ 62.83 cm.

F = E * q = 1000 N/C * 5 × 10^-6 C = 0.005 N.

Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.

Xl = 2πfL; if f is doubled, Xl also doubles.

Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.

The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.

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.

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.

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.