Consider the two functions yi = 2 - = x .
(a) Sketch the two graphs on one set of axes, labeling the graph carefully. (b) Calculate the points of intersection, showing all your working out. (c) Calculate the area bounded by the two functions.
Question 2
X: 1'2 4 Find the equation of the normal to the ellipse — += =1 when x =1 and r > 0. Give the result in 9
general form, ie ax + by = c .
Question 4
011 Is bubbling to the surface of the water from a broken undersea pipe. If the oil stain on the surface is increasing in radius by 3 km per hour, in a circular shape, find the rate of increase of the area of the spill after 3 hours.
Question 5
The little known' Quinn-Rathore mechanism translates rotational motion to straight line motion along the x axis. A particular mechanism, which is being used to train cats not to chase moving objects, causes the position of a mouse-like toy to be given by the expression x(t) = 3 + 2 cos(2t) , where x is measured in centimetres. For this function, find:
(a) the frequency,
(b) the period, (c) the amplitude, and (d) sketch the graph for 2 periods (e) find the first time when the x position is 4 cm.
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