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Show all work. Draw a diagram Where applicable; introduce notation. Put a around your nal answer. 1. (5 pts.) Function y(x) is given implicitly: 3 + 2x = sin(x - y4). Find the derivative y '(x) . 2. (5 pts.) A snowball melts so its surface area decreases at a rate of 1cm2/s. Find the rate at which the diameter decreases when the diameter is 10 cm. 3. (5 pts.) Two small planes approach an airport, one flying clue west at 120 mi/hr, and the other flying clue north, at 150 mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180 mi from the airport and the northbound plane is 225 miles from the airport? (Round your answer to the nearest whole number of miles/hr.) 4. (5 pts.) An oil rig springs a leak and oil spills in a circular patch around the rig. If the radius of the oil patch increases at a rate of 30 meters per hour, how fast is the area increasing when the radius is 100 m