.J ..I' L! 1. (5 marks). There are two coloured pencils: red and blue. The tip of the red pencil is moving along the :r-axis and the tip of the blue pencil is moving along the y-axis. The locations of the tips of the red and blue pencils at time t are given by differentiable functions r(t) and Mt), respectively. We know that t) = sin(t) 2. However} we know only that the tip of the blue pencil moves along the positive y-axis with 11(0) = 3(0) = 1. We are interested in the areas of the triangles made by the two tips of the pencils and the origin. Let's denote such an area at time t by A(t). For example, at t = 0 the area is equal to 21(0) = 1. (Check this to make sure you understand the question!). (a) (2 marks) Find the formula for A(t) in terms of r(t) and Mt). You may want to make sure that your formula gives Am) = 1. (b) (3 marks) Find the rate of change of the area when t = I]