3. One might reason since , then cos = COS COS 12 6 12 Is this statement true? Show work to support your answer.Use the Law of Cosines to solve. 6. Two flying drones leave an airport at the same time. The heading of the first is 120 and the heading of the second 320. If the drones are traveling at 80 and 50 mph respectively, how far apart will they be after 1 hour?Exploration 4.6.1: Building a Roller Coaster An established company, the Thrill Ride Roller Coaster Company, has asked your group to help design a roller coaster track. The Thrill Ride Company wants to build a roller coaster subject to a set of con- straints. You are told that the company has several engineers who could design a blueprint and build the track if only they knew the functions whose graphs would define the desired curve of the track. According to a company spokesperson, her people can easily "fit" a curve to a set of points; however, the resulting curve does not necessarily satisfy constraints involving slopes, concavity, extreme values, smoothness, updateability, etc. Furthermore the company's engineers must first build a scaled-down test model, and thus they need the function description for the scale model. Hence your task is to define a piecewise function, that is a function defined in pieces over the interval [0,15], whose graph satisfies the following con- straints for the roller coaster track (each unit represents 10 meters). 1. The entrance onto the track is at the point (0,10) and the exit is at (15,0). There are just two local extreme values, a minimum at (4,2) and a maximum at (8,8). (You do not have to consider designing the stairs leading to the entrance.) 2. The slope of the curve at the entrance and exit points must be zero in order to facilitate getting on and off the roller coaster car.Question 5 12 pts In Exploration 4.5.2 Question 3, cos * - cos resulted in a negative answer. Why is it impossible for cos 12 to be negative? O T is bigger than , therefore it has to be a positive answer. O It is impossible for any trig function to result in a negative answer. O 12 is a positive angle, therefore the cosine of any positive angle must be positive as well. O 12 is in the first quadrant and x values are positive in the first quadrant, therefore cos 12 must be positive.Question 6 12 pts Why is the Law of Cosines a stronger statement than the Pythagorean Theorem? @I The Law of Cosines only works for acute and obtuse triangles. The Pyihagorean Theorem only works for right triangles. O The Law of Cosines works for acute, obtuse, and right triangles. The Pyihagorean Theorem only works for right triangles. O The Law of Cosines has an ambiguous case while the Pythagorean Theorem does not. Q The Law of Cosines uses trigonometry. Question 7 12 pts In Exploration 4.5.3 Question 6, how far apart will the drones be after 1 hour? (Round your answer to the nearest tenth).Question 8 12 pts When you built the Roller Coaster for Exploration 4.6.1, you ended up with three sections. Select the correct equation for the middle section to satisfy the requirements in the exploration. O Section 2 = 5 + 3 cos (2 -4) ) if 4