1.

Captain Picard is hiding in a square arena, 50 meters on a side, which is protected by a level-5 force field. Unfortunately, the Cardassians, who are firing on the arena, have a death ray that can penetrate the force field. The point of impact of the death ray is exposed to 10,000 illumatons of lethal radiation. It requires only 50 illumatons to dispatch the Captain; anything less has no effect. The amount of illumatons that arrive at point ( x, y) when the death ray strikes one meter above ground at point ( x ₀ , y ₀) is governed by an inverse square law, namely

The Cardassian sensors cannot locate Picard's exact position, so they fire at a random point in the arena.

1. Use contour to display the arena after five random bursts of the death ray. The half-life of the radiation is very short, so one can assume it disappears almost immediately; only its initial burst has any effect. Nevertheless include all five bursts in your picture, like a time-lapse photo. Where in the arena do you think Captain Picard should hide?

2. Suppose Picard stands in the center of the arena. Moreover, suppose the Cardassians fire the death ray 100 times, each shot landing at...