Given that y varies inversely as the square of x. If x = 3 when y = 100, find the equation connecting x and y.

Analyze the question: "y varies inversely as the square of x" means y is proportional to 1/x².

Concept: Inverse variation with the square of x is written as

y = k/x², which can be rearranged to yx² = k

Solution:

1. Substitute x = 3 and y = 100 to find k: 100 = k/3² 100 = k/9 k = 100 × 9 = 900

2. Put k back into the equation: y = 900/x², or yx² = 900

Check: If x = 3, then yx² = 100 × 9 = 900 ✓

Why the other options fail:

• A: yx² = 300 would need k = 300, which comes from wrongly multiplying 100 × 3.
• C: y = 100x/9 is a direct variation, not an inverse one.
• D: y = 900x² is a direct variation with x², not an inverse one.

Exam tip: For inverse variation, find k by multiplying the two quantities, y × x² = k. Always remember to square x before multiplying. "Inversely" means the product stays constant.