Total Mechanical Energy = Kinetic Energy = 0.5 * m * v² = 0.5 * 5 kg * (10 m/s)² = 250 J.

Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 5 kg × (3 m/s)² = 22.5 J

Momentum p = mv = 5 kg * 3 m/s = 15 kg·m/s.

Using F = ma, we find a = F/m = 20 N / 5 kg = 4 m/s².

In series, R_eq = R1 + R2 = 5Ω + 10Ω = 15Ω.

Power P = V²/R = (10V)² / 5Ω = 100 / 5 = 20W.

Using the formula for parallel resistors: 1/R_eq = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_eq = 2Ω.

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.

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Power (P) = V²/R = 9²/3 = 27W. Energy (E) = P * t = 27W * 10s = 270J.

Power (P) can be calculated using P = V²/R = (9V)² / 3Ω = 81 / 3 = 27W.

The voltage drop across the resistor is equal to the battery voltage, which is 9V.

a^3 = 2^3 = 8 and b^3 = 3^3 = 27, so 8 + 27 = 35.

cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.

a^2 = 9 and b^2 = 16, so 9 + 16 = 25.

a^2 = 9 and b^2 = 16, so 9 + 16 = 25.

A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.

a^2 = 16 and b^2 = 4, so 16 + 4 = 20.

B × A = |i  j  k| |-1  3  0| |4  2  0| = 0, hence A · (B × A) = 0.

Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.

A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.

The intersection A ∩ B includes elements that are in both A and B. Here, A ∩ B = {2}.

The prime numbers less than 10 are 2, 3, 5, and 7. Therefore, A = {2, 3, 5, 7}.

The union A ∪ B includes all even numbers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Total marbles = 4 + 6 = 10. Probability of yellow = 6/10 = 3/5.

Total marbles = 4 + 6 = 10. Probability of green marble = 4/10 = 2/5.

The body experiences centripetal acceleration directed towards the center of the circular path.

A body moving in a circular path experiences centripetal acceleration directed towards the center of the circle.

Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.

Kinetic Energy (KE) = 0.5 × mass (m) × velocity² (v²). KE = 0.5 × 1000 kg × (20 m/s)² = 200,000 J.