Answer to Question #124104 in Calculus for Bernadet

Question

4. (a) Suppose a particle P is moving in the plane so that its coordinates are given by P(x, y),
where x = 4 cos 2t, y = 7 sin 2t.
(i) By finding a, b ∈ R such that x2 a2 + y2b2
= 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.

Answer 1

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