4 cos 2x The diagram shows the curve y=- 3-sin 2 for x>0, and the normal...
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4 cos 2x The diagram shows the curve y=- 3-sin 2 for x>0, and the normal to the curve at the point (7,0). Show that the exact area of the shaded region enclosed by the curve, the normal to the curve and the y-axis 9 is In+ [10] 2.0) In this question you must show detailed reasoning. 13 A scientist is attempting to model the number of insects. N. present in a colony at time r weeks. When t=0 there are 400 insects and when / 1 there are 440 insects. (i) A scientist assumes that the rate of increase of the number of insects is inversely proportional to the number of insects present at time f. (a) Write down a differential equation to model this situation. (b) Solve this differential equation to find N in terms of t. dN N dr 3988c (ii) In a revised model it is assumed that terms of r (iii) Compare the long-term behaviour of the two models. [1] 141 Solve this differential equation to find N in 161 121 4 cos 2x The diagram shows the curve y=- 3-sin 2 for x>0, and the normal to the curve at the point (7,0). Show that the exact area of the shaded region enclosed by the curve, the normal to the curve and the y-axis 9 is In+ [10] 2.0) In this question you must show detailed reasoning. 13 A scientist is attempting to model the number of insects. N. present in a colony at time r weeks. When t=0 there are 400 insects and when / 1 there are 440 insects. (i) A scientist assumes that the rate of increase of the number of insects is inversely proportional to the number of insects present at time f. (a) Write down a differential equation to model this situation. (b) Solve this differential equation to find N in terms of t. dN N dr 3988c (ii) In a revised model it is assumed that terms of r (iii) Compare the long-term behaviour of the two models. [1] 141 Solve this differential equation to find N in 161 121
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To answer the mathematics problem presented in the first part of the question The given curve is y frac43cos2x frac13sin2x for x 0 and we need to find the exact area of the shaded region enclosed by t... View the full answer
Related Book For
Pearson Edexcel A Level Mathematics Pure Mathematics Year 2
ISBN: 9781292183404
1st Edition
Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran
Posted Date:
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