Jump to content

Wikipedia:Reference desk/Archives/Mathematics/2015 April 16

From Wikipedia, the free encyclopedia
Mathematics desk
< April 15 << Mar | April | May >> Current desk >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


April 16

[edit]

Gross tonnage inverse solution

[edit]

I always thought this would not even be a recognizable special function. However I derived a solution in terms of the Lambert W function, as follows:

Make the substitution . Then:

from which

.

Wolfram Alpha gives ([1]) the simpler . Thus I want to ask: firstly, is my solution equivalent to WA's, and if so, how? If not, what did I do wrong? My answer works after substituting it into the formula for GT, but how does WA's?--Jasper Deng (talk) 04:20, 16 April 2015 (UTC)[reply]

Nevermind. I answered both questions on my own. For the equivalence to WA's solution, multiply the answer by and use the fact that . That last identity also aids in checking the solution by substitution.--Jasper Deng (talk) 06:52, 16 April 2015 (UTC)[reply]

(ec) The Gross Tonnage (GT) is related to the volume (V) by the equation

GT = 0.02 V ln(V)/ln(10) + 0.2 V

So

y = (V+k) ln(V)

where y = 50 ln(10) GT and k=10 ln(10). Take it from here. Bo Jacoby (talk) 07:13, 16 April 2015 (UTC).[reply]