How should you arrange 7 water fountains in a mall to minimize the longest possible walk?

The video tutorial explores the optimal arrangement of water fountains in a circular mall to minimize the maximum walking distance. Initially, the problem is simplified using three fountains, leading to a mathematical approach involving radius and arc calculations. The solution is extended to seven fountains, where a central fountain and six perimeter fountains are used. The tutorial concludes with a discussion on the complexity of the problem and references to further exploration.

What is the main objective when arranging the water fountains in the mall?

• To ensure fountains are evenly spaced

• To minimize the maximum walking distance to a fountain

• To maximize the number of fountains

• To minimize the cost of installation

When simplifying the problem to three water fountains, what is the maximum distance someone would have to walk?

• 1.5 kilometers

• 0.866 kilometers

• 1.12 kilometers

• 0.5 kilometers

What is the smallest radius needed to cover the entire mall with three disks?

• 1 kilometer

• 1.12 kilometers

• 0.5 kilometers

• 0.866 kilometers

How many degrees of the mall's perimeter must each disk cover when using three disks?

• 180 degrees

• 120 degrees

• 90 degrees

• 60 degrees

What is the optimal radius for covering the mall with seven water fountains?

• 0.434 kilometers

• 1 kilometer

• 0.5 kilometers

• 0.866 kilometers

Why can't a radius less than 0.5 kilometers be used for seven water fountains?

• It would be too expensive

• It wouldn't cover the center of the mall

• It would cover too much of the perimeter

• It would require more than seven fountains

What geometric shape helps determine the placement of the water fountains?

• Pentagon

• Square

• Triangle

• Hexagon