Lesson 09.08 Parametric, Polar, and Vector-Valued Equations Discussion-Based Assessment Assigned Problems NO CALCULATOR IS ALLOWED FOR THIS ASSIGNHENT 1. The graphs orthe polar curves r = 3 and r = 3 + 2sina are shown. Part A: Find where the two curves intersect. Show the work that leads to your answer. Part B: Let R be the shaded region that is inside the graph of r = 3 + 2sina and outside the graph of r = 3. as shown in the graph. Write an expression involving an integral and solve for the area of R. Part C: A satellite's path orbiting a stellar object moves along the polar curve r= 3 + 2sina for 04:91:. The satellite's distance to the center of the stellar object increases at a constant rate of 2.5 units per second. Find the rate at which the angle 9 changes with respect to time at the instant when the position of the satellite corresponds to 9-%. Include your units or measurement in the nal answer. 2. A particle moves in the coordinate plane with position vector (rm. y{t))such that X(t) = t2 4t + 3 and y(t) = 4 5t + 3t2 in the time interval 0 5 ts 4. Part A: Find the equation of the tangent line to the path of the particle when 1': 4. Part B: At what time (if any) is the particle at rest? Justify your answer. Part C: Is the speed of the particle increasing or decreasing when 1': 4? Justify your answer. Part D: Write an expression for the total distance traveled by the particle on the interval 0 s t s 4