Power = Work / Time = 500 J / 10 s = 50 W.

Power is calculated as work done divided by time taken. Here, Power = 500 J / 10 s = 50 W.

Useful work output can be calculated using the formula: Useful Work = Efficiency * Input Energy. Here, Useful Work = 0.8 * 1000 J = 800 J.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 5 m = 490 J. Then, P = W/t = 490 J / 2 s = 245 W.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 5 m = 490 J. Then, power is P = W/t = 490 J / 5 s = 98 W.

First, calculate the work done: W = mgh = 10 kg * 9.8 m/s² * 2 m = 196 J. Then, power is P = W/t = 196 J / 4 s = 49 W, approximately 50 W.

The work done against gravity is W = mgh = (50 kg)(9.8 m/s²)(2 m) = 980 J. Power is P = W/t = 980 J / 5 s = 196 W, approximately 200 W.

The work done is W = mgh = 50 kg * 9.8 m/s^2 * 2 m = 980 J. Power is W/t = 980 J / 5 s = 196 W, approximately 200 W.

Work done = Force × Distance = 100 N × 2 m = 200 J. Power = Work / Time = 200 J / 4 s = 50 W.

Taking the cube root of both sides, a = 27^(1/3) = 3.

Since 27 = 3^3, we have a = 3.

Substituting a = b^k into a^x = b^y gives (b^k)^x = b^y, leading to kx = y, hence x = ky.

From a^x = b^y, taking log_a on both sides gives log_a(b^y) = x, hence y * log_a(b) = x, thus log_a(b) = y/x.

Since 1000 = 10^3, log_10(1000) = 3, thus x = 3.

x^3 = 8 => x = 2

Taking the cube root of both sides, x = 8^(1/3) = 2.

Taking the fourth root, x = 81^(1/4) = 3.

Efficiency is calculated as (Output Power / Input Power) * 100%. Here, efficiency = (1800 W / 2000 W) * 100% = 90%.

Output power can be calculated using the formula: Output Power = Efficiency * Input Power. Here, Output Power = 0.8 * 500 W = 400 W.

Power in an electric circuit is given by P = V * I. Here, P = 12 V * 3 A = 36 W.

Power in an electric circuit is given by P = V^2/R. If V is doubled, P becomes (2V)^2/R = 4V^2/R, which is quadrupled.

4^(x+1) = (2^2)^(x+1) = 2^(2(x+1)) = 2^(2x+2).

Using the power of a power property, (a^m)^n = a^(m*n), we get (x^2)^3 = x^(2*3) = x^6.

Power is defined as the product of force and velocity in the direction of the force, given by P = F * v.

In an electrical circuit, power is given by the formula P = VI, where P is power, V is voltage, and I is current.

Power is defined as the rate at which work is done or energy is transferred. The SI unit of power is the Watt (W), which is equivalent to one Joule per second.

Using the property of exponents, (2^3) * (2^2) = 2^(3+2) = 2^5.

4^2 * 4^3 = 4^(2+3) = 4^5 = 1024

Using the power of a power property, (x^2)^3 = x^(2*3) = x^6.

Using the property of exponents, 2^(3x) * 2^(2x) = 2^(3x + 2x) = 2^(5x).