# Avoiding fracture of a ship moving through temperature gradient

Posted 9 years ago
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 As everyone?, Hope someone can help me solve this problem because I could not solve it. I have made some attempts but nothing.Any help is welcome, thanks in advanceThe captain Raul has difficulties near the sunny side of Mercurio.La temperature hull of the ship when it is at position (x, y, z) is given by T (x, y, z) = E ^ (x ^ 2-2y-3z ^ 2 ^ 2), where x, y, z are measured in meters. Currently he is in (1,1,1).A) In what direction should move faster to lower the temperature? If the ship travels to E ^ 8metros per second, how quickly decrease the temperature, if it moves in that direction?C) Unfortunately, metal hull fractured if cooled at a rate higher than Sqrt [14] E ^ 2 degrees per second. Describe the set of possible solutions that you can move to lower the temperature at a rate not more than that.
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Posted 9 years ago
 Another hint: Since your answer to the first question seems to indicate that the path you are going to take is fairly simple and since your velocity is fairly simple and since the outside temperature is a fairly simple function of position...could you imagine any way that you might be able to write down the outside temperature as a function of time? or of distance from your original location? With or without using Mathematica.If you can do that and if doing that makes sense to you then spend a little time thinking about why you would not have considered doing that yourself. The answer to that question might be helpful for other problems in the future.
Posted 9 years ago
 Now I present my solution to a)grad = -D[E^(x^2 - 2 y^2 - 3 z^2), {{x, y, z}}] /. {x -> 1, y -> 1,    z -> 1}indicating that you should move in the direction  {-(2/E^4)i,4/E^4 j,6/E^4 k}.To paragraph b), we first calculate a unit vector to the vector gradient obtained above, then multiply by e ^ 8normgrad = #/Norm@grad & /@ gradLater multiply normgrad by {e^8,e^8,e^8}I think I'm doing something wrong, please correct me because I'm confused, Greetings
Posted 9 years ago
 The forum posting software does some very odd things when it tries to desktop publish what you type. I can't offer any advice or explanation about why that is. Sorry.but there is advice, go under People to Moderation Team: they offer two links with hands-on how to write and format posts here ... and here is the spoiler: If nothing goes ahead, klick the Source button (below the infamous Spikey) and you will see what you get ...
Posted 9 years ago
 Thank you, Udo, we think you mean this post:How to type up a post: editor tutorial & general tips Luis, Bill - have you seen that? Going to "Source" mode is a good idea.Luis you can make a bullet or number lists using editor interface.Emoticons are part of editor code
Posted 9 years ago
 You're welcome, possibly you can link this How to type up a post: editor tutorial & general tipsbehind Help on the top of  page, showing then Dashbord | Groups | People | HelpQuite often problem owners copy code into the text making the code as wells as the text more or less unreadable; because they want an answer, they would proably have a look into a help if they could find it.
Posted 9 years ago
Posted 9 years ago
 I refer to paragraph b, does not know why the emoticon that goes when write b) capitalized
Posted 9 years ago
 hi, Bill, thanks for the answer but I want some steps to solve this problem, try to resolve it without success, paragraph in particular left me confused and I've read several times but still do not know what to do, I hope you have an idea, greetings
Posted 9 years ago
 insinuar quizá gradiente cálculo?http://reference.wolfram.com/mathematica/ref/Grad.htmlPido disculpas por mi falta de conocimiento de la lengua
Posted 9 years ago
 For those of you who are not up on your French, Bill's reply Google-translates as,    "perhaps hinting gradient calculation?   I apologize for my lack of knowledge of the language"  (Yes, I know it's not French.)