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.

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.

RMS current I_rms = I0/√2 for a cosine function.

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.

The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.

In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.

The time period T is the reciprocal of frequency f, T = 1/f. Therefore, T = 1/440 ≈ 0.00227 s.

Wavelength (λ) is inversely proportional to frequency (f) when speed (v) is constant: λ = v/f. If f is doubled, λ is halved.

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.

Inductive reactance Xl = ωL, so if frequency is doubled, Xl halves.

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

The reactance of an inductor is given by XL = ωL. If frequency is doubled, reactance also doubles.

F is inversely proportional to r². If r is doubled, F becomes F/4 = 20 N / 4 = 5 N.