4MA1/2HR Jan 2022, Question 20: Proportion to Powers of x
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Using two proportional relationships, y inversely proportional to √x and x directly proportional to T³, with y = 8 at T = 25, determine the exact T when y = 27.
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Solution · 4 marks
- 1y is inversely proportional to √x, so y = k/√x
- 2x is directly proportional to T³, so x = pT³
- 3Putting them together, y = c/√(T³) for a constant c
- 4y = 8 when T = 25, so 8 = c/√(25³)
- 5√(25³) = 5³ = 125, so c = 8 × 125 = 1000
- 6The rule is y = 1000/√(T³)
- 7When y = 27: √(T³) = 1000/27, so T³ = (1000/27)²
- 8T³ = 1000000/729, so T = 100/9
Answer100/9
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