sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

sin(60°) = √3/2 ≈ 0.866, so θ = 60°.

sin(90°) = 1, so θ = 90°.

sin(90°) = 1, so θ = 90°.

sin(90°) = 1, so θ = 90°.

sin(30°) = 1/2, so θ = 30°.

Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - (1/√2)²) = √(1/2) = √2/2

sin(45°) = 1/√2, so θ = 45°

tan(45°) = 1, so θ = 45°.

The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.

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 carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.

Magnetic flux (Φ) is given by the product of magnetic field (B) and area (A). If the area is doubled and the magnetic field remains constant, the magnetic flux also doubles.

Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled and the magnetic field (B) remains constant, the magnetic flux also doubles.

Capacitive reactance XC = 1/(ωC). If capacitance C increases, XC decreases.

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; 31.4 = 2 * π * r; r = 5 cm.

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.

According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.

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.

Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).

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

Slope = (5-1)/(5-1) = 4/4 = 1

Distance CD = |10 - 5| = 5.

Length CD = |10 - 5| = 5.

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

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