ACT (Enhanced)MathematicsMedium
A civil engineer is designing a new bridge. The maximum stress (S) a beam can withstand is inversely proportional to the square of its length (L). If a beam of length 10 meters can withstand a stress of 500 kPa, what stress can a beam of length 20 meters withstand?
- A125 kPa
- B2000 kPa
- C1000 kPa
- D250 kPa
Show answer & explanationAnswer & explanation
Correct answer: A. 125 kPa
Inverse proportionality means S = k/L^2. First, find the constant of proportionality (k) using the given values. Then, use k to find the new stress for the new length.
Why the other options are wrong
- B. This is a result of directly proportional to the square of the length, which is incorrect.
- C. This is a result of directly proportional reasoning, not inverse.
- D. This would be the result if stress was inversely proportional to length, not length squared.
Inverse Square Proportionality
A relationship where one quantity is inversely proportional to the square of another quantity.
- Represented as y = k/x^2, where k is the constant of proportionality.
- As x increases, y decreases rapidly.
- Common in physics (e.g., gravitational force, light intensity).
Memory trick: Inverse square, strength decreases with distance, beware!