Question

(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y2 = 9, and its height is 4. (a) Give a parametric equation, r(t) for the rim, C. r(t) with <t< (For this problem, enter your vector equation with angle-bracket notation: <f(t), g(t), h(t) >.) (b) If S is oriented outward and downward, find 's curl (-6yi + 6xj + 7zk)·da. Ss curl (–6yi + 6xj 7 7zk)·dA =

Answer 1

The solid and Z=1 > Solution: s given to us in cylindrical in shape. The side of a given by x+y = 9 In cylindrical coordinate system, * = roost), yursinct) we have s9 = = 3. as the height of the cylinder Z= 4 viser 2-4 and tE[0, 2P3] TCE) = crcosct), rsinct), >. tE[0, 28, 10 YCH)=<3C03 (!), 38717(), 43 and t E Co, Lps] t E (0,211] Sarlstoy; +6x) +72 k) d A and b) we nud to find Now, Curl(-bys +683 + 7 2x ) = میں d da I by be 72 = 3(0-0) - ; (0-0) + (6 + 6) = 0.0 x 12k 12k are given that sin oviented outwards and downwards.

2 da = -kds Scuril-ogg +625+ 7 ZdA S 12K) (*)ds -35-12ds ds=rardt, r Eto, uy and t E Co, 2TJ Se-by? +688 +7 Z kdA Now curl =SSirds an u rdret - - 12 - 128 0 0 2 T -- = -12 dt 2 S (16-oldt -oldt 2T - 6) Ibat 2T = -96 s dt -96 [ty =-96[2T-o 9-192 T Souri ( by; +65 +7 Zk/dA =-1925