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January 27[edit]

Continued Fractions As Nested Radicals of Order -1[edit]

Are there any meaningful or interesting insights arising from this simple observation ? Any books or articles, preferably online, which highlight this link between continued fractions and nested radicals, and discuss its possible implications ? (I know of at least one source that mentions it, but then it just stops there, and doesn't go any "deeper" into it). — 79.118.185.51 (talk) 03:59, 27 January 2014 (UTC)[reply]

Interesting question, but I have no idea. Sławomir Biały (talk) 13:43, 28 January 2014 (UTC)[reply]

Can someone help me solving a equation?[edit]

The equation is:

440*(2^(y/x))=432, y<0, x>12,

What would be the value of X and Y assuming both are intergers.

Well there are many solutions problably, so pick the one with the smallest X.
201.78.130.241 (talk) 11:12, 27 January 2014 (UTC)[reply]

There are no exact solutions in integers. Dmcq (talk) 13:59, 27 January 2014 (UTC)[reply]

The nearest integer approximations I can find are y = -9 and x = 340 (But it's not exact, as Dmcq says above. The RHS comes out as 432.00049 on my calculator.) Dbfirs 22:28, 27 January 2014 (UTC)[reply]

Simplifying, we get

2^y == (54/55)^x

You can obviously see that it is unlikely to have integer solutions for x and y. 202.177.218.59 (talk) 01:56, 28 January 2014 (UTC)[reply]

Further simplification

2^y == ( (2*3*3*3)/(5*11) )^x

2^y == ( (2^x) * 3^(3 x) ) / ( 5^x * 11^x )

202.177.218.59 (talk) 02:01, 28 January 2014 (UTC)[reply]

Take the logarithm of 440*(2^(y/x))=432 to get log(440)+log(2)*(y/x)=log(432). Solve to get y/x=(log(432)−log(440))/log(2)≃−0.0264722. Expanding as a continued fraction gives the rational approximations

y/x≃−1/38≃−0.0263158

y/x≃−4/151≃−0.0264901

y/x≃−9/340≃−0.0264706

y/x≃−40/1511≃−0.0264725

. . .

Bo Jacoby (talk) 10:39, 28 January 2014 (UTC).[reply]

(Yes, the fourth approximation is much better than mine. I didn't use continued fractions, but just noticed that the reciprocal of 0.0264722 was approximately 37.77... which I recognised as 37 and seven ninths.) Dbfirs 11:06, 28 January 2014 (UTC)[reply]

Math (pouring from a cylinder)[edit]

Hi, I really need help with this q for my exam tomorrow, so here it is. Luke is pouring a glass of water, from a cylinder cup. The diameter is 12cm, and the height is 18cm. The relationship between the volume of the water in the cup, and the time (in seconds) can be represented by V=-15+2034.72 a)how long will it take for the glass to be approx. half filled? b)quarter filled? c)empty? 207.219.69.242 (talk) 21:39, 27 January 2014 (UTC)[reply]

I've removed the duplicate of your question. It doesn't make sense because there is no time in your equation. I assume that it should have been: Volume = 2034.72 - 15t (with pi approximated at 3.14) and that he is pouring into one cup from another identical cup. You need to know the formula for the volume of a cylinder. What would the volume be when the height of the water is half of 18cm? Dbfirs 21:48, 27 January 2014 (UTC)[reply]

Step 1. Calculate Radius from Diameter

Step 2. Calculate the Area in the base of the cylinder

Step 3. Calculate the Volume using "base times height" 202.177.218.59 (talk) 02:08, 28 January 2014 (UTC)[reply]

I've improved on your original pourly worded title. :-) StuRat (talk) 02:47, 28 January 2014 (UTC) [reply]