Help with math functions
[From: ] [author: ] [Date: 11-07-04] [Hit: ]
volume = length*width*height = x*2x*3x = 6x^3.let w be width, and using w = 2x, rearrange, x = w/2.then volume = 6*(w/2)^3 = .......
So, given that height = x
width = 2x
and length = 3x
we have D(x) = sqrt(x^2 + (2x)^2 + (3x)^2) = sqrt(x^2 + 4x^2 + 9x^2) = sqrt(14x^2)
D(x) = sqrt(14x^2) can be simplified a bit more, though...
D(x) = x*(sqrt(14))
And that's it!
Hope this helps.
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1. volume = length*width*height = x*2x*3x = 6x^3.
let w be width, and using w = 2x, rearrange, x = w/2. then volume = 6*(w/2)^3 = .75w
so now write v(w) = .75w
2. use Pythagoras. let d be the diagonal, h be height, l length, and w width.
first get the diagonal for one face, call it b, b^2 = l^2+w^2 (or any combination of two edges).
then d^2 = b^2 + h^2 = l^2 + w^2 + h^2 = 9x^2 + 4x^2 + x^2 = 14x^2.
like before, note that h = x, so write d(h) = (14h^2)^.5
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Hiii ,you can see the Step by Step ,detailed and explained solution of the above questions at:
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Not really sure about the first but the second thing... My idea is that the diagonal cuts the rectangle into two triangular prisms.
