Author Topic: Math Sucks, Again  (Read 2173 times)

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Offline Bobboau

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thanks, it's nice to know I still remember this stuff.
this has reawakened my desier to get that damned moment of inertia tensor for the POF header figured out.

now this is a man's math problem :)
intigrateing along a volume defined by the volume under three points, intigrate the following six formulie:
y^2+z^2
x^2+z^2
x^2+y^2
x*y
z*x
z*y

this might not seem like that hard a problem but it isn't realy the intigrand (is that the right termonology? the formula getting integrated) that bites you in the ass, it's the volume of intigration
the first step shows this, you have to intigrate the volume under the plane defined by the normal of the polygon (N) and one of the points (P). after useing the plane forumla to get a height function pln(x,y), you have to integrate along z from z=0 to z = pln(x,y), doesn't seem to nasty untill you realise that pln(x,y)=(Nx*x-Ny*y+Nx*Px+Ny*Py+Nz*Pz)/Nz. (NOTE Px means the x component of the vector P not P*x, the variables x and y are only in that function once respectively, the rest of those are more or less constants, unfortunately they are constants who's value we do not know)

doing the first step of intigration will yeild an slightly more complicated equasion, pln(x,y)*I(x,y) so long as you are not integrateing any of the elements with a z in them, if you do integrate one of the z elements, you get an unholy beast of a horably unnatural equasion of doom! so horrable I'm not even going to try to type it out, and it still needs to be integrated two more times! along the area on the xy plane defined by the polygon's three points, and each of these intigration must be done in two parts!

I'm thinking a Jacobian transformation might posably make this problem solveable, too bad they just skimmed over that in my Calc 3 class. :doubt:
« Last Edit: April 18, 2005, 10:45:51 pm by 57 »
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Offline adwight

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Jesus Christ, I don't even want to try and begin to do something like that.  I barely understand this normal Calc.
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Offline BlackDove

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Quote
Originally posted by Bobboau
bah, this isn't hardly even calculus 1, give me some 4th dimentional gradients integrated along a hellixical volume, that'd be a bit of fun there:)


You are the only man I know of that put "helixical volume" and "fun" in a same sentence.

 

Offline Taristin

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And you should be shot for doing so. You sick, sick man.
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Offline Night Hammer

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Stop... Hammertime :hammer:

 

Offline Dark RevenantX

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As I am only in 7th grade Algebra, all I can tell you is to get a few equations to fit into the rate of change equation, and do the math from there.  Of course, as I am only in Algebra, I could be mistaken.  Also, I am too tired to read all the posts to see if this has been resolved, so forgive me if I am posting like an idiot.

 

Offline Bobboau

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don't worry too much Algebra is probly the hardest you'll have to deal with, exept maybe trig.
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Offline Dark RevenantX

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Are you saying Eighth Grade will be easier than what I'm doing now?  Riiight...

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Offline adwight

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Seriously, Geometry was cake compared to my first crouse in Algebra.
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Offline adwight

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Yay another problem that I can do half of, but I can't seem to figure out the first half.

The rate of fuel consumption, in gallons per minute, recorded during an airplane flight is given by a twice differentiable and strictly increasing function R of time t.  The graph of R and a table of selected values of R(t), for the time interval 0 <= t <= 90 minutes, are shown below.

(don't have graph, but you could make one from this info positive concavity from 0 to 50, negative concavity(but still increasing) from 50 to 70, and positive concavity from 70 to 90.  Looks like a demented W.  )

Table              
t(mins)    R(t)(galls/min)
0              20
30            30
40            40
50            55
70            65
90            70

Use Data from the table to approx. for R'(45).  Show computation and units of measure. (I still can't do derivatives with no equation... :()

The rate of consumption is fastest at time t = 45 minutes.  What is the value of R''(45)?  Explain reasoning.

There, I can do the rest, I just don't know how to find the derivative when I don't have the equation for it...

You can use a calculator.  I promise this will be like the last one... I swear.
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Offline WMCoolmon

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What does the ' and " mean?
-C

 

Offline adwight

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' = 1st derivative
'' = 2nd derivative
Neo-Terra Victorious

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Well, if you've got a TI Graphical Calculator, put all the values for R in L1, then do y1=nDeriv(L1). You can find nDeriv under Math, option 8. Not sure if this will work, don't think you'll get a proper graph.

Otherwise, you need to create a formula/equation for R(t). And I'll be damned if I know how.
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Offline tom

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Quote
The rate of consumption is fastest at time t = 45 minutes.

right

=> maximum of the rate of consumption = max(R'(t))
=> the function R'(t) has a maximum at t=45
=> R''(t) = derivation of R'(t)
=> R''(t=45) = 0