GroupHomework #8 Put group member names here

A tank consists of a circular cylinder lying on its side. If this tank has water of height h in it, it will gather at the bottom as seen in the picture 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Fdcs;$!1@;a,R*f/"!#:$"21nA'y*)oX8FdcsAssume the tank has radius R and the water is at height h. a) Show that the width of the water at height h is NiMqJiIiIyIiIi0lJXNxcnRHNiMsJiokKSUiUkdGJEYlRiUqJCksJkYsRiUlImhHISIiRiRGJUYxRiU=.b) Show that the cross-sectional area of the water is NiMsJiomKSUiUkciIiMiIiItJSdhcmNjb3NHNiMqJiwmRiZGKCUiaEchIiJGKEYmRi9GKEYoKiZGLUYoLSUlc3FydEc2IywmKihGJ0YoRiZGKEYuRihGKCokKUYuRidGKEYvRihGLw==.

The area in a sector of a circle is given by NiMqJiomJSZ0aGV0YUciIiIqJCklIlJHIiIjRiZGJkYmRiohIiI=, where NiMlJnRoZXRhRw== is the angle of the sector. Find the area in the sector and subtract off a triangle.

c) A tank with length 3 m and radius 2 m is being filled at a constant rate of NiMqJiIiIyIiIiokKSUibUciIiRGJUYl/min. At what rate is the height increasing when the the tank one quarter full (with respect to volume)?

A hurricane is traveling at due north at a speed of 20 knots (knots = nautical miles per hour). A boat with a maximum speed of 12 knots is located 10 nautical miles north and 5 nautical miles east of the hurricane. Its heading is measured in terms of degrees clockwise from due north. a) If the boat takes a heading of NiNJJnRoZXRhRzYi, find how close the hurricane gets to the boat and the time when the minimum distance ocurs. These will both be functions of NiNJJnRoZXRhRzYi. b) The captain of the boat wants to maximize this minimum distance. What heading should be chosen so that the minmium distance between the hurricane and the boat is maximzed?c) Suppose that the location of the boat is NiMmSSJ5RzYiNiMiIiE= nautical miles north and NiMmSSJ4RzYiNiMiIiE= nautical miles east of the hurricane. What is the heading which will maximize the minimum distance between the boat and the hurricane? How does this answer depend on the starting point NiM2JCZJInhHNiI2IyIiISZJInlHRiZGJw== ?