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1.7.19 Parametric and implicit differentiation (A-level only)

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Question 76

A chemical reaction's rate RRR (measured in units/s) and the concentration CCC of the substrate (measured in mmol/L) are related by the equation

R3+5C2−30RC=0 R^3 + 5C^2 - 30RC = 0 R3+5C2−30RC=0

The graph of this relationship for C,R≥0C, R \ge 0C,R≥0 forms a loop in the first quadrant with a stationary point at PPP, where the rate of change of RRR with respect to CCC is zero.

a.

Show that at the point PPP, the rate RRR satisfies the equation

R2(R−45)=0 R^2(R - 45) = 0 R2(R−45)=0
[5]
b.

Hence, find the coordinates of PPP in the form (C,R)(C, R)(C,R).

[3]

1.7.19 Parametric and implicit differentiation (A-level only) Questions

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