4PM1/02R Jun 2024, Question 5: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
Given F = 3/(20r²) newtons with r in cm, and r growing at 0.7 cm/s, work out how fast F changes in newtons/s at r = 2.8 cm, to 3 significant figures.
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Solution · 6 marks
- 1dr/dt = 0.7
- 2F = (3/20)r⁻², so dF/dr = −2 × (3/20)r⁻³ = −0.3/r³
- 3dF/dt = dF/dr × dr/dt
- 4= −0.3/2.8³ × 0.7
- 5= −0.00957 (3 s.f.)
Answer−0.00957 newtons/s
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