Please scroll down and try to answer all parts until you get to "END OF THIS QUES'ON". You and your friends Grace and Haz are studying the formulas for the lengths of planar curves. You read that if a curve C is described parametrically by C = {($(t),y{t}] : a g t g )8}. then its length I, is / a) a) In particular, for a polar curve r : 116], 60 g 6 g 61. a parametric representation is given by 12(6) : 1(6) cos[6) and yo?) = r-(Q) 5111(6). One can show in this case that the length 5 is 52/9? T2+(%) d9. {a} Now. you and your friends are ready to test your understanding. Consider the polar curve r- : 41:05.6{3/6]. 0 g 6' 3 2w. Grace says that the length I: of this curve is 211' E =f0 4cosn(6/6)d9 for some positive integer n. Compute the value of n and provide it in the box below' =| @I'u [b] Meanwhile, Haz is studying the polar curve r2 : 6cos 26. with ?r/4 g 9 g \"/4. Hafiz showed that one can write .2+ )2_ d9 _..2' for some positive integer K. Enter the value of K in the box below. K= .123 Hence. nd the area A of the surface formed when the polar curve is rotated about the yaxis and provide the value of A in the box below. A: .1? yntax advice: Enter your answer as an exact value using Maple syntax. For example. type Pi for 7r. sqrt (2) for \\/ and sqrt {2) *Pi for at