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Hi. I'm trying to do part b. The min drag that I have is 0.006U^2+1.5833(W^2/U^2).

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  • $\begingroup$ I've tried 12000 <= w <= 20000 n = length (w) for i = 1 : n u (i) = (263.8833*w (i)^2)^(1/4) fd (i) = 0.006*u (i)^2 + 1.5833*(w (i)/u (i))^2 Plot[u, fd] $\endgroup$ – Kassidy Moy Apr 3 at 21:36
  • $\begingroup$ This looks like a homework question. Please edit your question and add the WL code you have tried. The code in your comment is not valid WL code. $\endgroup$ – Rohit Namjoshi Apr 3 at 23:08
  • $\begingroup$ The one i tried was Plot[0.006U^2+1.5833(W^2/U^2){x,0,580}] $\endgroup$ – Kassidy Moy Apr 3 at 23:18
  • $\begingroup$ There are two independent variables U and W so you will have to use ContourPlot or some other way to visualize the function. The range argument to Plot has to use the same symbol as the independent variables. Try ContourPlot[0.006 u^2 + 1.5833 (w^2/u^2), {u, 0, 580}, {w, 12000, 20000}]. $\endgroup$ – Rohit Namjoshi Apr 4 at 0:57
  • $\begingroup$ It looks really strange with multiple lines and different colors $\endgroup$ – Kassidy Moy Apr 4 at 1:43
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Can probably find your answer using a parametric plot.

(* Create the function *)
fd[u_, w_, sigma_ : 0.6] := 0.01 sigma u^2 + 0.95/sigma (w/u)^2
(* Minimum is at fd'\[Equal]0, which turns out to be a simple \
function of w *)
D[fd[u, w], u]
(* Solve fd'\[Equal]0, inspection indicates Last answer is real *)
soln = Last@Solve[D[fd[u, w], u] == 0, u]
(* Make a function out of that *)
u[w_] := u /. soln
(* Visualize sensitivity *)
ParametricPlot[{u[w], fd[uf[w], w]}, {w, 12000, 20000}, 
 AspectRatio -> 1, AxesLabel -> {"U", "FD"}]

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