Math Sample

In this year’s school musical production of The Little Mermaid, Arial needs to be lifted and flown around the stage while performing. The stage crew is responsible for the actors’ safety as well as the production quality.

A fly system is a theatrical system of ropes and pulleys that helps the stage crew move equipment such as drapery, electrical lighting – and sometimes people – quickly and quietly during a stage production.

The stage crew has two types of rope available to move the props and the people: manila hemp rope and wire rope. Both ropes are ½ inch in diameter. The weight W (in pounds) that can safely support the diameter d (in inches) of the different types of rope is found by solving the quadratic inequalities shown here:

Manila Hemp Rope

W ≤ 1480d²

Wire Rope

W ≤ 8000d²

Both of these expressions are quadratic inequalities. How do we know? Think about it, then click Show Me to see if you are correct.

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Quadratic comes from the Latin word quadratum, which means square; so, we know these are quadratic because they contain at least one term that is squared. We know they are inequalities because they contain ≤, which is an inequality sign.

The graphs for each inequality are shown below. The weight, W, is represented on the y-axis and the diameter, d, is represented on the x-axis. The point when d=½ is labeled on each graph. Since it is unclear exactly which value W is when d=½, solving the inequalities will yield the correct weight.

Manila Hemp Rope

W ≤ 1480(1/2)²

W ≤ 1480 1/4

W ≤ 370

Wire Rope

W ≤ 8000(1/2)²

W ≤ 8000 1/4

W ≤ 2000

How much weight can each type of rope support?

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The manila hemp rope can support 370 pounds or less and the wire rope can support 2,000 pounds or less.