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Clear[x, y, z, f, r, s, t]; f[a_] 3-2 sin [2 s]; x[r_, s_, t_] = r f[s] sin [s]

ID: 3009384 • Letter: C

Question

Clear[x, y, z, f, r, s, t]; f[a_] 3-2 sin [2 s]; x[r_, s_, t_] = r f[s] sin [s] cos [t], y[r_, s_, t_] = r f [s] sin [s] sin [t]; z[r_, s_, t_, ] = r f[s] cos[s]; skin=paranetrieplot 3D [[x[3, s, t], Y [3, s, t], z [3, s, t]}, (s, 0, pi), (t, 0, 2pi), Plotpoints rightarrow [30, 30], Boxed rightarrow False, Box Ratios rightarrow Automatic, viewpoint rightarow CHView, PlotRange rightarrow All, AxesLabel rightarrow (-x-, 'Y', -x-)}; |clear[gradx, grady, gradr, vxyx]; gradx [x_, s_, t_] = [D[x[x[r, s, t], r], D [x [r, s, t], s], D [x[r, s, t], t]}; grady [r_, s_, t_] = {D [Y [r, s, t], r] D [Y[r, s, t], s], D [Y[r, s, t], t]}, grad x[r_, s_, t_] = [D[z{r, s, t], r], D [z[r, s, t], D {x[x[r, s, t], t]}; vxyx [r_, s_, t_] = Factro [TrigReduce [Det: [{grad x [r, s, t], grady [r, s, t], grad z][r, s, t]}]]] -r^2 (30 cos [s] - 30 cos [3 s] - cos [5 s] + cos (7 x]-45 sin {s] - 9 sin [3 s] + 9 sin [5 s]) You have enough information to give a relatively painless calculation of the volume measurement of the solid whose outside skin is plotted above. SET UP the integral for this volument measurement. You do NOT need to solve this integral.

Explanation / Answer

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