# B 6 points after wading through frosting for hours

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(b) (6 points) After wading through frosting for hours, you are at the point (1 , - 2) when you spot a candle at the point (7 , 6). What is the initial rate of change of thickness of the frosting as you begin running toward the candle?
Math 230 Final Exam Solutions! Fall Quarter 2012 Page 13 of 17 Question 10. (c) (5 points) Later, your dream becomes a nightmare when the Cookie Monster begins eating the giant cake. In order to save yourself, you need to move in the direction in which the thickness of the frosting is decreasing fastest. If you are at the point (3 , 1), in which direction should you begin moving in order to save yourself from the voracious Cookie Monster? What is the rate of change of frosting depth in that direction? 13
Math 230 Final Exam Solutions! Fall Quarter 2012 Page 14 of 17 Question 11. Park Seon-yeong has set up her recording equipment on top of a 20 m cliff. She is close to her life’s goal: to capture incontrovertible evidence of the existence of the monster or monsters living in Cheonji Lake. There! Is it—? No, only a shadow. And there? It is! She sees the monster! There is no time to lose. The monster is 10 m away horizontally and is swimming away from her at a rate of 2 m/s . She reaches for the tracking device at her belt and throws it directly horizontally toward the monster. (a) (9 points) Assume that acceleration due to gravity is 10 m/s 2 downward and that wind resistance is negligible. What initial speed should she throw the tracking device with in order to hit the monster?