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1 Pure Mathematics

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Question 1017

A chemical reaction produces a foam whose volume VVV (in cm3\text{cm}^3cm3) changes at a rate V′(t)V'(t)V′(t) where t t\,t is the time in seconds since the start of observation, for t>0t > 0t>0.

Given that

  • V′(t)=(t−9)2ttV'(t) = \dfrac{(t - 9)^2}{t\sqrt{t}}V′(t)=tt​(t−9)2​
  • the observation point P(4,10)P(4, 10)P(4,10) lies on the curve V=g(t)V = g(t)V=g(t)
a.

(i) Find the value of the gradient of the curve at PPP.

(ii) Hence find the equation of the tangent to the curve at PPP, giving your answer in the form at+bV+c=0at + bV + c = 0at+bV+c=0, where aaa, b b\,b and c c\,c are integers to be found.

[4]
b.

Find g(t)g(t)g(t), simplifying your answer.

[5]
Markscheme

1 Pure Mathematics Questions

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