Need help with this multi-part question on derivatives. Please fill out the 3 charts. Variable r is the radius and variable P is the perimeter. I'll give helpful rating :)

Advancing Oil Slick Because ofa recent accident on an offshore rig, an oil slick is spreading across the surface of Isaac's Bay. The prevailing winds cause the slick to take on a wedge-like shape heading eastward, threatening the ecosystem of the Newton's Island Wildlife Refuge, 30 miles away. Satellite imaging has confirmed that the area of the wedge is growing at the steady rate of 50 square miles per day. It has been determined that the size of the vertex angle of the wedge is dependent upon the speed of the prevailing winds. Specically, the vertex angle 90f the wedge is a function of w, the speed of the prevailing wind (in miles per hour) modeled by the formula 0(w) = wl'ao . Yourjob is to determine the rate at which the oil slick will be advancing and how long it will take before the oil slick makes landfall on the island. You have also been asked to estimate how many miles of absorbent boom will be needed to contain the slick as it advances, should the leak not be stopped, and how rapidly the perimeter of the slick will be growing. Isaac's Bay Newton's Island A Wildlife Refuge You are given that the oil slick is in the shape of a sector of a circle with central angle 6, express the area ofthe oil slick in terms of0 and r. Assuming the prevailing wind holds steady at the indicated values, complete the chart below by providing: - the size ofthe angle 9 for each wind velocity w given 0 (w) = "112130 - an accurate estimate ofthe area ofthe oil slick at the moment it makes landfall on the island (Le. when r = 30 miles) - an accurate estimate of the number of days until the slick makes landfall based on the fact that the area of the slick grows steadily at 50 square miles per day x, J Font Sizes The Isaac's Bay Oil Slick Area and Estimated Arrival at Newton's Island Wind velocity Wedge angle 0 Area when r = 30 Days until impact 0 mph 130 1413.7 sq. miles 28.3 days 10 mph 20 mph 30mph 40 mph Characters used: 219 / 15000 Suppose an effort is made to surround the oil slick with containment boom. Use the fact that the area of the sector is increasing at a constant rate of 50 square miles per day, find an expression for dr/dt, the rate at which the leading edge of the slick will be advancing. Part A Suppose the leak goes unchecked and that the wind holds steady at 10 mph. Complete the chart below by providing: I the radius of the oil slick for each day the leak goes unchecked I the rate at which the radius is growing at that moment I the total perimeter of the oil slick at the end of each day the rate at which the perimeter is growing at that moment B I Q X' XZJFontSizes 3'1-.- The Isaac's Bay Oil Slick Size and Rate of Growth of Radius and Perimeter (wind steady at 10 mph) Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 A 50 100 150 200 250 300 350 400 450 r 7.98 dr/dt 3.99 P 28.49 dP/dt 14.25 Characters used: 278 / 15000 Part B Construct a similar chart based on the assumption of a steady 20 mph prevailing wind. BIU X XZ Font Sizes A - A wur - E V Isaac's Bay Oil Slick Size and Rate of Growth of Radius and Perimeter (wind steady at 10 mph) Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 A 50 100 150 200 250 300 350 400 450 9.77 dr/dt 4.98 P 29.78 dP/dt 14.89 Characters used: 274 / 15000