4(a) Suppose a particle P is moving in the plane so that its coordinates are given...

4(a) Suppose a particle P is moving in the plane so that its coordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t.

x2 y2
(i) By finding a, b ∈ R such that a2 + b2 = 1, show that P is travelling on an elliptical

path. [10 marks] (ii) Let L(t) be the distance from P to the origin. Obtain an expression for L(t).[8 marks] (iii) How fast is the distance between P and the origin changing when t = π/8?[7 marks]

(b) A wire of length 100 centimeters is cut into two pieces. One piece is bent to form a square. The other piece is bent to form an equilateral triangle. Find the dimensions of the two pieces of wire so that the sum of the areas of the square and the triangle is minimized.(25marks)

Expert Solution

milcah answered 2 years ago

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