ACT (Enhanced)MathematicsMedium
A civil engineer is calculating the maximum stress a support beam can withstand. The stress (S) is directly proportional to the applied load (L) and inversely proportional to the square of its thickness (T). If a beam with a thickness of 0.2 meters can withstand 100 Pascals with a load of 500 Newtons, what stress can a beam with a thickness of 0.4 meters withstand with the same load?
- A25 Pascals
- B50 Pascals
- C400 Pascals
- D200 Pascals
Show answer & explanationAnswer & explanation
Correct answer: A. 25 Pascals
Establish the proportionality relationship S = k * L / T^2. Use the given values to find the constant k. Then, use k and the new thickness with the same load to find the new stress.
Why the other options are wrong
- B. Incorrect. This would be true if the relationship was inversely proportional to T, not T^2.
- C. Incorrect. This implies a direct proportionality to T^2.
- D. Incorrect. This implies a direct proportionality to T^2, or an inverse proportionality to T (then doubled).
Combined Proportionality
Combined proportionality describes how one variable relates directly, inversely, or jointly to two or more other variables, often involving powers.
- Direct proportionality: y = kx.
- Inverse proportionality: y = k/x.
- Combined: y = k * (direct_vars) / (inverse_vars).
Memory trick: Balance the 'Constants' with 'Variables' to find the 'Relationship'.