A hiker is standing beside a stream on the side of a mountain, examining her map of the region. The height of land in kilometres) at any point (x, y) is given by 20 h(x, y) = 3 + x2 + 2y2' where x and y (also in kilometres) denote the coordinates of the point on the hiker's map. The hiker is at the point (3,2). (a) What is the direction of flow of the stream at (3, 2) on the hiker's map? How fast is the stream descending at her location? y hop, 7 (b) Find the equation of the path of the stream on the hiker's map. (c) At what angle to the path of the stream (on the map) should the hiker set out if she wishes to climb at a 15° inclination to the horizontal? (d) Make a sketch of the hiker's map, showing some curves of constant elevation, and showing the stream

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