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3 marksFunctions, Graphs, Equations and Inequalities

CAPE Integrated Mathematics · 2016 · Paper 2 · Question 6(d)(i)

The boundary of a school compound is modelled by f(x) = 30x - x^2 and a fence by g(x) = 2x, bounding a reserve for agricultural activities. Q is the x-coordinate where the line meets the parabola.

Find the value of Q.

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Other parts of this question

  1. 6(a)(i)Determine the integral: int (4x + 7)^6 dx.[3 marks]
  2. 6(a)(ii)Determine the integral: int (5x^3 - 3x^2 + 1) dx.[2 marks]
  3. 6(b)Evaluate the definite integral int_0^(pi/2) (cos x + 2 sin x) dx.[4 marks]
  4. 6(c)(i)Show that P satisfies the equation P(t) = e^(kt + c).[4 marks]
  5. 6(c)(ii)When t = 0, P = 4000. Calculate the value of c.[2 marks]
  6. 6(c)(iii)Given that k = ln 2, determine the population size when t = 3.[3 marks]
  7. 6(d)(ii)Using integration, determine the area reserved for agricultural activities. Give your answer to the nearest whole number.[4 marks]

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