More word problems

Q:  The equation for the time of one swing of a pendulum is T = 2 π √(L/32), where T is the time in seconds and L is the length in feet.  Find the length of a pendulum that makes one swing in 3 seconds.

A:  Start with our equation T = 2 π √(L/32) and we know that T = 3.

T = 2 π √(L/32)

3 = 2 π √(L/32)

Divide both sides by 2 π

3 / (2 π) = √(L/32)

Square both sides:

[3 / (2 π)]² = [√(L/32)]²

9 / (4 π²) = L / 32

Multiply both sides by 32:

32 * 9 / (4 π²) = L

288 / (4 π²) = L

72 / π² = L

The length is 72 / π² ≈ 7.295 feet