Hidden Variables Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
The area formula A=lwA = lw has hidden units. If l=5l = 5 m and w=3w = 3 m, what is AA, and what hidden variable (units) must be tracked?

Solution

  1. 1
    Compute: A=5Ɨ3=15A = 5 \times 3 = 15.
  2. 2
    Hidden variable: units. ll is in metres, ww is in metres, so AA is in square metres: A=15Ā m2A = 15\text{ m}^2.
  3. 3
    If one dimension were in cm and the other in m, the formula would give a wrong answer unless units are first harmonised.

Answer

A=15Ā m2Ā (unitsĀ areĀ aĀ hiddenĀ variableĀ thatĀ mustĀ beĀ tracked)A = 15\text{ m}^2 \text{ (units are a hidden variable that must be tracked)}
Units are a hidden variable in many formulas. Ignoring them causes dimensional errors. Tracking units throughout a calculation is essential for correct answers in applied mathematics.

About Hidden Variables

Quantities or factors that influence a mathematical or real-world situation but are not explicitly included in the current model or expression.

Learn more about Hidden Variables ā†’

More Hidden Variables Examples

Example 1 easy

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Example 2 medium

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Example 4 medium

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