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anonymous

  • 5 years ago

Solve kjackson's problem by double integrals. A rectangular prism planter is filled with potting soil. It has a length of 3 feet and a width of 8inches and a height of 8 inches. How much potting soil can it hold?

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  1. anonymous
    • 5 years ago
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    Alright, I prefer doing these with triples, but it was good to think about these again. integral(from 0 36) integral(0 8) (8dA) integral(from 0 36) 8x|(0 to 8) integral(from 0 36) 64dz 64z|(0 36) 2034

  2. anonymous
    • 5 years ago
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    \[\int\limits_{0}^{3}\int\limits_{0}^{8}8dxdy\] The outer integral would be the length (or y) and the inner one would be width(or x) and the inside is 8 because the height (z) is 8 it would just simplify to 8 * 3 * 3 (which is the volume equation)

  3. anonymous
    • 5 years ago
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    Except 3 would be 36, otherwise proper. Do you see why I prefer triples though? It seems more logical, but perhaps thats just me. Same thing is being accomplished, just with triples I see where its coming from.

  4. anonymous
    • 5 years ago
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    Great, I was trying to figure out what f(x,y) would be. Now I know.

  5. anonymous
    • 5 years ago
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    Have you gotten to triple integrals yet chag?

  6. anonymous
    • 5 years ago
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    No. Haven't got to triples yet.

  7. anonymous
    • 5 years ago
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    Ok, well they are the same idea. Its just it seems clearer to do volume problem in them: In this problem z = 36, y = 8, x = 8. Just makes more sense to me, but I also like using overkill math techniques to figure out simple stuff like this like you do. I am very fun at parties! \[\int\limits_{0}^{z} \int\limits_{0}^{y} \int\limits_{0}^{x} f(x,y,z) dx dy dz\]

  8. anonymous
    • 5 years ago
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    Great. You're invited to my next soiree.

  9. anonymous
    • 5 years ago
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    I don't understand why z is 36..... z is just the height of the box, which is 8 the triple integral would just be \[\int\limits_{0}^{3}\int\limits_{0}^{8}\int\limits_{0}^{8}1dzdydx\] again, giving you 8 * 8 * 3 = 192

  10. anonymous
    • 5 years ago
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    I think they slipped in 3 ft and 8 inches

  11. anonymous
    • 5 years ago
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    Z is 36 because the 3 is in units feet.

  12. anonymous
    • 5 years ago
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    oops i didn't see that i have people that mix units :x i stand corrected! scot's right

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