The time for a swing to move forward and backwards is determined by this formula.

T=2pi sqrt L/9.8. T is the time, in seconds,taken for the swing to move through one complete cycle. L is the length of rope supporting the swing.

Determine the length of the rope supporting a swing that takes 3.4 seconds to move through one cycle. Round to nearest tenth of a metre.

Please help thank you

To determine the length of the rope supporting the swing, we can rearrange the formula to solve for L. The formula is given as:

T = 2π √(L/9.8)

We are given that T = 3.4 seconds. Substituting this value into the formula:

3.4 = 2π √(L/9.8)

To solve for L, we need to isolate L. First, divide both sides of the equation by 2π:

3.4 / (2π) = √(L/9.8)

Next, square both sides of the equation to eliminate the square root:

(3.4 / (2π))^2 = L/9.8

Now, multiply both sides of the equation by 9.8 to solve for L:

9.8 * (3.4 / (2π))^2 = L

Using a calculator, perform the calculations:

L = 9.8 * (3.4 / (2 * 3.14159))^2

L = 9.8 * (3.4 / 6.28318)^2

L = 9.8 * (0.54022)^2

L = 9.8 * 0.29236

L = 2.866 km

Therefore, the length of the rope supporting the swing that takes 3.4 seconds to move through one cycle is approximately 2.9 meters (rounded to the nearest tenth of a meter).

just plug in your numbers:

3.4 = 2π√(L/9.8)

Just solve for L