Ac3
  • Ac3
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1,0,0),(0,2,0),(0,0,3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
IrishBoy123
  • IrishBoy123
steps: find the equation of that plane first. and write it as z = f(x,y). then integrate over that region
Ac3
  • Ac3
alright let me see if I can get this equation.
IrishBoy123
  • IrishBoy123
i make it 6x + 3y + 2z = 6 you should check that though or we will be chasing our tails forever!!

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Ac3
  • Ac3
lol I only have the final answer for this
Ac3
  • Ac3
I think I can see how you got that.
Ac3
  • Ac3
When I first did this problem I thought it was simply.... \[\int\limits_{0}^{1}\int\limits_{0}^{2}\int\limits_{0}^{3}dzdydx\]
IrishBoy123
  • IrishBoy123
no that is for a cube same problem.....we need to the limits of integration right......
Ac3
  • Ac3
so this region is pretty much a rectangular prism
IrishBoy123
  • IrishBoy123
here we have a triangle again, on the xy plane |dw:1449768946933:dw|
IrishBoy123
  • IrishBoy123
|dw:1449768986389:dw|
IrishBoy123
  • IrishBoy123
the shaded area is our region. we are integrating \(z = f(x,y) =\frac{1}{2}( 6 - 6x - 3y)\) over that region
Ac3
  • Ac3
man i'm having a really hard time getting to visualize these
IrishBoy123
  • IrishBoy123
you get used to it. it can hurt to start with, that's normal bigger: |dw:1449769150216:dw|
Ac3
  • Ac3
When I drew it this is what I thought it was.... |dw:1449769209025:dw|
Ac3
  • Ac3
so i thought it would be the little region bounded by all those planes
Ac3
  • Ac3
the "rectangular prism"
IrishBoy123
  • IrishBoy123
the clues they give are: it's in the first octant bounded by the coordinate planes AND bounded by that plane passing through those 3 points we are given i think triangular prism is the correct description...i don't know much geometry anymore
Ac3
  • Ac3
lol maybe that's the problem I need to take a geometry class
Ac3
  • Ac3
but yea I agree the rectangular prism would go On the x-axis from 0-1, on the y-axis from 0-2, and the z axis from 0-3
IrishBoy123
  • IrishBoy123
nah. geometry is for wimps! i got back up to speed on this initially by watching these https://www.khanacademy.org/math/multivariable-calculus/double_triple_integrals/double_integrals/v/double-integral-1 double integrals are not what they seem, they are iterated integrals, and Salman Khan goes to great lengths to show you what you are actually doing with the double integral. fubini's theorem, it might be called. well worth taking the time.
Ac3
  • Ac3
|dw:1449769708422:dw|
Ac3
  • Ac3
alright I'll check that out as well thanks Irish boy
Ac3
  • Ac3
how far are you in math?
IrishBoy123
  • IrishBoy123
any time post grad, applied math i'm actually really crap at proper math, little bit better at applied :-))
Ac3
  • Ac3
sweet then youll be able to help me when i hit math for scientists and engineers
IrishBoy123
  • IrishBoy123
love that stuff your level?!?!
IrishBoy123
  • IrishBoy123
don't have to say BTW if i can't help you, there's are loads other who have helped me out, we will find a way!!!
Ac3
  • Ac3
just finishing up multi-variable calc
IrishBoy123
  • IrishBoy123
coool!
IrishBoy123
  • IrishBoy123
gtg carol service......
Ac3
  • Ac3
later thx again
IrishBoy123
  • IrishBoy123
ciao!!

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