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JAMB 2012 Mathematics · Question 34

If y varies directly as n\sqrt{n} and y = 4 when n = 4, find y when n = 179\frac{7}{9}

Options

  1. A.17\sqrt{17}
  2. B.43\frac{4}{3}
  3. C.83\frac{8}{3}
  4. D.23\frac{2}{3}

Answer: C. 83\frac{8}{3}

Explanation written with AI and checked against the answer key

Analyze the question: y varies directly as √n, so y = k√n. We find k from the given values, then use it to find y for the new n. Concept: Direct variation means y = k × (the quantity). Here the quantity is √n. Solution: Step 1: Find k. y = 4 when n = 4: 4 = k√4 = 2k, so k = 2. Step 2: Write the relationship. y = 2√n Step 3: Convert the mixed number. n = 1 7/9 = (9 + 7)/9 = 16/9 Step 4: Substitute. y = 2 × √(16/9) = 2 × (4/3) = 8/3 Answer: y = 8/3, which is option C. Tip: When a variation question involves a mixed number, convert it to an improper fraction first. It often turns into a perfect square, as 16/9 did here. Always find k first, then substitute.

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