Problem 1. A hiker Visiting a state park is descending a mountain as night falls, decreasing Visibility. Their altitude is given by the function 5(3: + y) Way) : $2+y2+1 based on their geographical coordinates (3:, y), in miles to the east and north of the park entrance in the southwest. (a) If the hiker is currently 4 miles north and 5 miles east of the park entrance, in which direction should they head to descend the mountain most quickly? (b) How steep is the descent in this direction? (c) Is this in the direction of the park entrance? Problem 2. The temperature in Lake Charlotte is given by Haw=&w3 (in degrees Celsius) with (0, 0) representing the center of the lake. To stay warm, you swim in a circle along the path described by 113(15) : cos (10%) ,y(t) : sin (10%), where t is in seconds. (a) Find the rate of change of temperature as a function of time using the chain rule. (b) Conrm your answer in part (a) by writing T as a function of t and then differentiating with respect to t