Basics of polar coordinates & parametrized curves

only explain 18,19,20, and just solve everything else no need to explain.

9. The area of all petals of r = cos(20) is given by: .271 7 / 4 3 cos?(20 ) do II. - cos2 (20) de III. - cos2 (20) do 2 2 A. I only B. II only C. III only D. II and III E. I and III F. none of the above10. Represent the area using one or more integrals of the region inside the graph of r = 2 cos(30). A . " ( 2 cos (30 ) ? de B. 2 (2 cos (30) ) 2 de C. =(2 cas(30) )2 do D. (2 cos(30))? do E. none of the above 11. The area inside the flower r = 2 sin(30) is A. B. C. D. E. 27 F. none of the above12. The area enclosed by the curve r = 2 - 2 cos(0) is A. 67 B. 87 C. 97 /2 D. 97 /4 E. 9 F. none of the above 13. Which of the following definite integral gives the area enclosed by the inner loop of r = 1 - 2 sin 0? A . (1 -2 sin 0)2 do 6 B. (1 - 2 sin 0)2 de 6 C. (1 - 2 sin ()2 do 6 D. (1 - 2 sin 0)2 do E. none of the above14. Which of the following definite integrals gives the area enclosed by the inner loop of r = 3 + 6 cos 0? 4 7 A. 2 (3 + 6 cos 0)2 de 2 71 3 2 10 B. 2 (3 + 6 cos 0)2 de 0 2 1T 3 C. (3 + 6 cos 0)2 de 2 1 D. (3 + 6 cos 0)2 de 2 TT E. (3 + 6 cos 0)2 do F. none of the above15. Which of the following definite integrals gives the area enclosed by the outer loop of r = 4 - 8 cos 0? A . 2 (4 - 8 cos 0)2 de 3 B. (4 - 8 cos 0)2 do C. NIH (4 -8cos0)2 do TT D. NIH (4 - 8 cos 0)2 do .2 71 E. (4 - 8 cos 0)2 de F. None of the above16. Set up the polar integral which represents the area of the region on the right half of the plane bounded by x2 +y? =144 and x =6V2 A. (144 - 72 sec2 0) do 7 1 B. NIK (144 - 72 sec2 0) de C. (144 - 72 sec2 0) de D. NIH (144 - 72 csc2 0) de E. (144 - 72 csc2 0) do F. None of the above17. Express the curve x(t) = 2et, y(t) = e3t - 4 by an equation in terms of r and y: A. x = 2y - 4, y > 0 B. y = 2x3 - 4, r > 0 C. y = - -4, x > 0 (cr - 4)3 D. y = ,1>0 8 (x + 4)3 E. y ,1>0 8 F. none of the above 18. Find a parametrization x = x(t), y = y(t), te [0, 1] for the line segment through (2,6) and (6,3). A. x(t) = 2 - At, y(t) = 6 + 3t B. x(t) = 2 + 4t, y(t) = 6+3t C. x(t) = 2 - 4t, y(t) = 6 - 3t D. x(t) = 2 + 4t, y(t) = 6 -3t E. x(t) = 6 - 3t, y(t) = 2+ 4t F. none of the above19. Find a parametrization of the ellipse given by 25x2 + 4y2 = 100. x(t) = 2 cos(t) (t) = 5 cos(t) I(t) = cos(t) x(t) = 4 cos(t) x(t) = 10 cos(t) A. y(t) = 5 sin(t) B. y(t) = 2 sin(t) C. y(t) = 5 - sin(t) D. y(t) = 25 sin(t) E. y(t) = 5 sin(t) 0