Direct and Inverse Proportion

Illumination \(I\) lux is inversely proportional to the square of distance \(d\) metres from a lamp. At \(2\) m, illumination is \(180\) lux.

1. Find \(I\) in terms of \(d\).

2. Find the illumination at \(6\) m.

3. Find the greatest distance at which illumination is at least \(45\) lux.