Frequency (f) = (1/2π)√(k/m). If mass (m) is doubled, frequency decreases.

Efficiency (η) = Work done / Input heat = 300 J / 500 J = 0.6 or 60%.

Probability = Number of winning tickets / Total tickets = 2/10 = 1/5.

Probability = Number of winning tickets / Total tickets = 3/10.

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.

Y = 1/R + j(ωC - 1/ωL); calculate Y for given values.

Quality factor Q = (1/R) * √(L/C) = (1/50) * √(0.2/50e-6) = 2.

In a purely capacitive circuit, the current leads the voltage by 90°.

In a purely capacitive circuit, the current leads the voltage by 90 degrees.

Average rate = Δ[A]/Δt = (0.8 - 0.4) / 20 = 0.02 M/min.

For a first-order reaction, if [A] is halved, the rate also halves.

If the rate decreases to one-fourth when concentration is halved, the reaction is second-order.

According to Le Chatelier's principle, if the concentration of products increases, the system will shift to the left, decreasing the rate of the forward reaction.

According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left to counteract the change.

According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left to counteract the change.

According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right to favor the formation of products.

According to Le Chatelier's principle, if the concentration of reactants is increased, the equilibrium will shift to the right to favor the formation of products.

For a second-order reaction, t₁/₂ = 1 / (k[A₀]) = 1 / (0.05 * 0.1) = 200 s.

f0 = 1 / (2π√(LC)) = 1 / (2π√(0.1 × 100 × 10^-6)) = 159.15 Hz.

Resonant frequency f₀ = 1 / (2π√(LC)) = 1 / (2π√(0.1 * 100e-6)) = 159.15 Hz.

If inductive reactance (XL) is greater than capacitive reactance (XC), the circuit is inductive.

Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.

Resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1*100e-6)) ≈ 159Hz.

When light reflects off a denser medium, a phase change of π occurs, leading to destructive interference for certain path differences.

For a zero-order reaction, the rate is constant and does not depend on the concentration of reactants. The unit of the rate constant (k) is mol/L·s.

In a zero-order reaction, the rate is constant and does not depend on the concentration of the reactants.

Inductive reactance (XL) = 2πfL = 2π(60)(0.2) ≈ 75.36Ω.

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

The impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36 ohms.

Real power P = V * I * power factor = 120 * 10 * 0.8 = 960 W.