Wikipedia:Reference desk/Archives/Mathematics/2008 January 28

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January 28

measurements

What is 15 Spiritual Cubits in measurement? —Preceding unsigned comment added by 68.23.169.220 (talk) 06:46, 28 January 2008 (UTC)

A google search for "spiritual cubit" indicates that a "spiritual cubit" is equal to three normal cubits, which would make 15 of them 45 cubits, or 67.5 feet (20.6 m). However, I have no clue where the term "spiritual cubit" comes from. --Evan Seeds (talk)(contrib.) 07:45, 28 January 2008 (UTC)

The Google hits are from the Conflict of Adam and Eve with Satan, second book, Chapter XI.  --Lambiam 12:09, 28 January 2008 (UTC)

Multiples of two but not quite

Is there a name for this specific series of numbers: 2, 4, 8, 16, 32, 64, 128, 256, etc.? It's not multiples of two because six isn't in that list. It's just two to various powers but I was wondering if there's a specific name for the series. Dismas|^(talk) 09:17, 28 January 2008 (UTC)

Technically this is a sequence, and not a series. You could simply call it the powers of two, but it is also a geometric progression. 134.173.92.17 (talk) 09:26, 28 January 2008 (UTC)

Great! Thanks! Dismas|^(talk) 09:56, 28 January 2008 (UTC)

Should have just said powers of two... —Keenan Pepper 14:19, 28 January 2008 (UTC)

See also the OEIS sequence OEIS:A000079. 14:41, 28 January 2008 (UTC) —Preceding unsigned comment added by PrimeHunter (talk • contribs)

Not understanding these calculus problems

I've been self-teaching calculus, so I'm not sure if I have covered the material required for these problems with sufficient depth yet:

f is a polynomial, integrate by parts: 0ƒπ f(x)sinx dx

(that's a definite integral from 0 to pi; I can't figure out how to display it right)

I'm stuck at f(pi)*cos(pi)- ƒ(cos*f'); it keeps looping around from f(x)sinx to f'(x)cosx and so on and so forth.

Is there anything else I need to do, or am I just missing something? Any help would be appreciated.

And I have no idea what's going on here:

g is defined for 0 ≤ x ≤ r by g(x) = qx(r-x), verify:
g(0) = g(r) = 0
g(x) > 0 for 0 < x < r
max g(x) = g(r/w) = qr²/4 = p²/4q

Is r special, or is it just a second variable? What about q? Where did p come from? Pointers to what I need to teach myself, useful pages, or perhaps a walkthrough of a similar type of problem would be most helpful.

Many thanks,
147.129.97.137 (talk) 10:11, 28 January 2008 (UTC)

For the first, I'll give a hint - when you do integration by parts, you differentiate one of the functions and integrate the other. You have done it twice - the first time you have differentiated the polynomial, which is good, but in the second time you have chosen to integrate it, so you end up back where you started. Try differentiating the polynomial both times and continue from there (in fact you will have to do it several times).

For the second - r is just a constant, you can treat it as if it was a number. It looks like the question is missing information about w and p, but it looks like w is supposed to be 2 and p is supposed to be qr, which also happens to be equal to $g'(0)\;\!$. -- Meni Rosenfeld (talk) 10:22, 28 January 2008 (UTC)

For the statement g(x) > 0 to be true, q has to be positive. In general you should not encounter free variables like p in the statements you are required to prove unless they have been introduced in what is given; it suggests that the material was prepared in a sloppy way. Where did you find this material?  --Lambiam 19:27, 28 January 2008 (UTC)