a2 = b2 + c2 - 2bc * cos(θ)
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 It's probably because you said ∏=3.1415926535(etc)406286 instead of ∏=3.1415926535(etc)406286... Anyways... Do you have any tricks to calculate the probability of an event? [Quote] [Link]
 Sophrosyne Administrator3142 Posts12 Ineo 0:3 - 5.20.23623.387 days ago The ACT really isn't a knowledge test. It's more logic. I got high scores on it without a calculator. [Quote] [Link]
 Yes, by all means lurkstick around until someone is wrong so you can jump up and point it out. [Quote] [Link]
 Sophrosyne Administrator3142 Posts12 Ineo 0:3 - 13.45.86622.974 days ago ...? [Quote] [Link]
 I feel like everybody is just out to make me look stupid. I mean I was identified as a genius! I sat 6th chair at state orchestra as a sophomore! Cut me some slack! [Quote] [Link]
 I hope you're joking. [Quote] [Link]
 Nips13651 Posts12 Ineo 0:3 - 15.73.89622.86 days ago I think he is. Or she. I really don't know or care. [Quote] [Link]
 Total Dirken said:I feel like everybody is just out to make me look stupid. I mean I was identified as a genius! I sat 6th chair at state orchestra as a sophomore! Cut me some slack! So you're used to dealing with mundanes and can lord it over them with your mighty intellect? It's not going to happen here. Get used to it. Here any slight defect in your posts can and usually will be pointed out. There is no malice involved. You can use that response as an opportunity to improve your precision, or you can go and sulk in a corner. Your call. [Quote] [Link]
 I was never really that good at math anyway. I like the arts better. Puzzles are fun too I guess. [Quote] [Link]
 f(x) = x3 + xlog(x) - x, g(x) = x4+x How would I go about proving that f(x) = O(g(x)) using the definition of Big-O? f(x) may not be O(g(x)) but from looking at it I think it is. I just don't know how to prove it. [Quote] [Link]
 Hydrogen777 Administrator5988 Posts12 Ineo 1:0 - 10.55.5620.12 days ago For x ≥ 1, x3 + xlog(x) - x ≤ x4 + x(x) + x4 ≤ x4 + x4 + x4 ≤ 3x4 ≤ 3(x4 + x). Thus f(x) is O(x) with witnesses N ≥ 1, k = 3. [Quote] [Link]
 How do you come up with the (x)+x4 in the second part of the first inequality and why do you do that? [Quote] [Link]
 Hydrogen777 Administrator5988 Posts12 Ineo 1:0 - 10.98.31620.098 days ago There are three terms in the expression for f(x): "x3", "xlog(x)", and "-x". We want to show that the sum of these terms is less than or equal to another expression which we can trivially show is O(g(x)). The easiest way to do that is to show that each of the terms is less than or equal to x4, for x ≥ 1, and combine them. Note that since both x and log(x) are ≤ x for x ≥ 1, we have that xlog(x) ≤ x(x) ≤ x4. As for the right term, it should be apparent that -x ≤ x4 for x ≥ 1. And the same holds for the first term. Edit: Fixed a "≤". [Quote] [Link]
 Do you have to do anything special when the bases are different? Like f(x) = log3n and g(x) = log2n [Quote] [Link]
 Hydrogen777 Administrator5988 Posts12 Ineo 1:0 - 12.72.71620.011 days ago logbx is lower order than x, regardless of the value of b. [Quote] [Link]
 Blake Webmaster2082 Posts12 Ineo 1:0 - 16.41.37619.827 days ago More specifically, it's because to change a base of a logarithm, you simply divide by the logarithm of the new base, which is a constant term. logbx = logax / logab logab is a constant and so it doesn't matter to big O. [Quote] [Link]
 Gotcha. Okay last one and I have to use limits for this one. f(x) = n2 and g(x) = nlogn. Should I use L'hopital's Rule or is there a better way? [Quote] [Link]