Digital SATMath: Advanced MathEasy
A photographer is adjusting the settings on her camera. The relationship between the aperture setting (A) and the depth of field (D) is inversely proportional. If an aperture setting of 8 results in a depth of field of 1.5 meters, which equation represents the relationship between A and D?
- AD = 1.5A + 8
- BD = 12/A
- CD = A/8
- DD = 8A
Show answer & explanationAnswer & explanation
Correct answer: B. D = 12/A
Inversely proportional means D = k/A, where k is the constant of proportionality. Using the given values, 1.5 = k/8, so k = 1.5 * 8 = 12. Thus, the equation is D = 12/A.
Why the other options are wrong
- A. This represents a linear relationship, not an inverse proportion.
- C. This would mean 1.5 = 8/8 = 1, which is incorrect.
- D. This represents direct proportionality, not inverse.
Inverse Proportionality
Two quantities are inversely proportional if their product is constant. As one quantity increases, the other decreases proportionally.
- Represented by y = k/x, where k is the constant.
- The graph is a hyperbola.
- Used to model relationships where one factor diminishes as another grows.
Memory trick: Direct is 'D'ivide, Inverse is 'I'nverse 'I'nstead of 'D'ivide.