15. [-/0.12 Points] DETAILS SCALCET9 10.2.055. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin (t), y = 5 cos (t), Osts 4n Compare with the length _ of the curve. L= Need Help? Read It Watch It 16. [-/0.12 Points] DETAILS SCALCET9 10.2.071. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the exact area of the surface obtained by rotating the given curve about the x-axis. x=t', y=t, osts1 Need Help? Read It Watch It 17. [-/0.12 Points] DETAILS SCALCET9 10.TF.001. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Determine whether the statement is true or false. If the parametric curve x = f(t), y = g(t), satisfies g'(1) = 0, then it has a horizontal tangent when t = 1. O True False Need Help? Read It 18. [-/0.23 Points] DETAILS SCALCET9 10.TF.002. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Determine whether the statement is true or false. day If x = f(t) and y = g(t) are twice differentiable, then dt 2 dx 2 d 2 x dt 2 O True O False Need Help? Read It11. [-10.12 Points] DETAILS SCALCET9 1D.2.AE.DOS. 0.1100 Submissions Used MY NOTES ASK YOUR TEACHER Example Video Example-(3) 3' 0 27\" x CD Find the length of one arch of the cycloid x = rm 5in(0)), y = r(1 005(9)) Solution From a previous example we see that one arch is described by the parameter interval 0 s 9 s 21:. Since = and = d0 d9 L=fohll(%)2+(%)2 d0 = f\"(:| )d 211' f if r1(1 2 cosw) + c0320?) + sin1(9)) d9 0 21: ff V 2(1 cos(0)) dB. 0 To evaluate this integral we use the identity sin2(x) = \" cos(2x}) with 6 = 2x, which gives 1 005(9) = 2 sin2( |:| ). Since 0 s 6 s 22:, we have 0 s :| 5 Jr and so sin() 2 0. Therefore 2 f . 2 9 2(1 005(6) = 4 sm (_) = 2 2 = E L = 2r/02\"sin(;)da = ml: l: 4E l = E - Need Help? 12. [-10.12 Points] DETAILS SCALCET9 1D.XP.2.026. 0l100 Submissions Used MY NOTES ASK YOUR TEACHER Find the exact length of the curve described by the parametric equations. x=5+6t2, y=5+4t3, 05:51 : Need Help? 13. [-/0.12 Points] DETAILS SCALCET9 10.2.048. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Find the exact length of the curve. x = et - t, y = 4et/2, Osts 3 Need Help? Read It 14. [-/0.12 Points] DETAILS SCALCET9 10.2.051. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Graph the curve. x = 5etcos(t), y = 5etsin(t), Ostsn 10 10 - X -120 -100 -80 -60 -40 -20 20 -20 20 40 60 80 100 120 -10 -20 -20 -30 - 30 -40 -40 -50 -50- O DO 50 50 40 40 80 30 20 20 10 X - X -120 -100 -80 -60 -40 -20 20 - 20 20 40 60 80 100 120 -10 O -10 DO Find its exact length. Need Help? Read It Watch It