22 leaves a remainder of 2 when divided by 5, but it is not possible for 22 to leave a remainder of 2.

The smallest number that satisfies both conditions is 14 (14 % 10 = 4 and 14 % 3 = 2).

If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.

The smallest number that satisfies both conditions is 23 (23 % 9 = 5 and 23 % 5 = 3).

The new number is (original number - 3) = (10k + 7 - 3) = 10k + 4, which gives a remainder of 4.

The new number is (original number - 3), which gives a remainder of (7 - 3) = 4.

15% of 25 grams = 0.15 * 25 = 3.75 grams, rounded to 4 grams.

200 mg per serving * 3 servings = 600 mg.

The correct form is 'A pair of shoes was left at the door.' 'Pair' is singular, so the verb should be 'was'.

Energy U = 1/2 C V^2. Initial U = 1/2 * 5 × 10^-6 * 10^2 = 0.025 J; Final U = 1/2 * 5 × 10^-6 * 20^2 = 0.1 J. Change = 0.1 - 0.025 = 0.075 J = 75 µJ.

Capacitance C is inversely proportional to the distance d between the plates. If d is halved, C doubles, so the new capacitance is 10μF.

The electric field E between the plates of a parallel plate capacitor is given by E = V/d, where d is the separation between the plates.

1/3 of 12 = 12 / 3 = 4 members are from the ruling party.

Fraction from ruling party = 3/15 = 1/5.

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

The third force can be determined by vector addition of the first two forces to ensure the net force is zero.

Angular velocity ω = v/r.

The tangential speed v is given by v = rω.

The tangential speed v is given by v = rω.

Centripetal acceleration a_c = v²/R.

L = mvr = 4 kg * 3 m/s * 2 m = 24 kg·m²/s.

Angular momentum L = mvr, if v is doubled, L also doubles.

The angular momentum is constant because the particle's velocity and distance from the point are constant.

Angular momentum L = mvr, where v is the linear speed and r is the radius of the circular path.

Angular momentum L = mvr, where r is the perpendicular distance from the line of motion to point O.

Using the equation v = u + at, where u = 3 m/s, a = 2 m/s², and t = 5 s, we get v = 3 + (2 * 5) = 3 + 10 = 13 m/s.

Angular velocity ω = v/r = 6 m/s / 3 m = 2 rad/s.

Circumference = 2πr = 20π m. Period T = distance/speed = 20π m / 5 m/s = 4π s.

Centripetal acceleration (a_c) = v²/r = (5²)/10 = 2.5 m/s².

Time period T = 2πr/v = 2π(10 m) / (5 m/s) = 4π s.