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Avoiding fracture of a ship moving through temperature gradient

Posted 10 years ago
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 advance

The 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?
emoticon 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.
POSTED BY: Luis Ledesma
10 Replies
Posted 10 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 BY: Bill Simpson
Posted 10 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 ^ 8
normgrad = #/Norm@grad & /@ grad
Later 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 BY: Luis Ledesma
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 BY: Udo Krause
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 emoticon
POSTED BY: Moderation Team
You're welcome, possibly you can link this 

How to type up a post: editor tutorial & general tips

behind Help on the top of  page, showing then Dashbord | Groups | People | Help

Quite 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 BY: Udo Krause
Posted 10 years ago
Everything I've written about this, above and below, are only hints. I'm not doing your homework problem for you, just poking you in the right direction. No pun intended.

The definition of the gradient is a vector function that points in the direction of the most rapid increase in a function.

To help understand this you might think of some really simple functions of x,y,z, simpler than your actual problem, where you are fairly sure you know which direction to move from a point to most rapidly increase the function. Then by hand and with Mathematica calculate the gradient and see if it matches what you think the answer should be.

Then you need to think how you might apply this understanding to your first question.

You can even try checking the answer for this. To do that move in some other direction and see if the result is not as good. Move in almost exactly the same direction as you calculate using the gradient and see if the result is very close, but still not quite as good.  You are doing this to convince yourself you understand the gradient and you have the right answer.

Then for the second question you want to think of all the information you have and compare that with exactly what you need. What kind of thing would you have to have to get from what you have to what you need? When you know that then you might be able to think of a way of constructing it.

The final question I haven't thought about enough to offer any suggestion.

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.
POSTED BY: Bill Simpson
Posted 10 years ago
I refer to paragraph b, does not know why the emoticon that goes when write b) capitalized
POSTED BY: Luis Ledesma
Posted 10 years ago
hi, Bill, thanks for the answer but I want some steps to solve this problem, try to resolve it without success, paragraph emoticon 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 BY: Luis Ledesma
Posted 10 years ago
insinuar quizá gradiente cálculo?

http://reference.wolfram.com/mathematica/ref/Grad.html

Pido disculpas por mi falta de conocimiento de la lengua
POSTED BY: Bill Simpson
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.)
POSTED BY: Bruce Miller
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