A research probe measures the atmospheric pressure PPP (in kPa) relative to its horizontal distance ddd (in km) from the center of a stable weather system, modeled by the function P(d)=101−120(d2−25)2P(d) = 101 - \frac{1}{20}(d^2 - 25)^2P(d)=101−201(d2−25)2 for d≥0d \ge 0d≥0.
Determine the equation of the normal to the graph of pressure against distance at the point where d=5d = 5d=5.
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P=101 P = 101 P=101 P=5 P = 5 P=5 d=101 d = 101 d=101 d=5 d = 5 d=5717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.