Recent content by Trail_Builder

yeah, I separated the variables in the usual way, to get a solution. but the solution has a constant term and a log(r) term, in addition to the "r^(±α)*sin(αθ), r^(±α)*cos(αθ)" terms they mention. and I am not sure why the qu doesn't have all the term I have :S

Homework Statement Show that Laplace’s equation ∇^2(φ) = 0 in polar coordinates (r,θ) has solutions proportional to r^(±α)*sin(αθ), r^(±α)*cos(αθ) for any constant α. Find the function φ satisfying Laplace’s equation in the region a < r < b, 0 < θ < pi, where φ(a,θ) = (sin(θ))^3, φ(b,θ) =...

right, i think i may have a solution to this problem. can someone please check it for me :) thanks. say that n^3 + 100 is divisible by n + 10. then n^3 + 100 = 0 (mod n + 10) n = -10 (mod n + 10) so (-10)^3 + 100 = 0 (mod n + 10) ... 0 = 900 (mod n + 10) we want to maximise...

Homework Statement Find the largest positive integer n such that n^3 + 100 is divisible by n + 10. Homework Equations The Attempt at a Solution The hint I've been given is to use (mod n + 10) to get rid of the n. but i don't quite see how it would work :S all my attempts...

no specified constaints

thanks for the clarification. I kind just used my intuition before but glad to know how to properly do it, lol :). the answer is no and no then, because there isn't a constaint on x... :S so was I right in saying none?

still don't know :S I know the x^2>9 is equivalent to x<-3 or x>3. so I am guessing that rules out the <=> and if it was the x>3, then I would stick the <= one in. ("only if"). "if" obviously won't work. but don't you have to consider the x<-3 case too? or am I imposing somekind...

Homework Statement Insert either "if", "only if", or "if and only if".. x>2 ... x^2>9 Homework Equations The Attempt at a Solution I don't think any fit :S coonffuuuuuused

so I've factorised it as far as I can? :S if so its a stupid problem lol. wouldve thought it would've given linear factors.

Homework Statement factorise: a^3 + b^3 + c^3 - 3abc Homework Equations The Attempt at a Solution I had a few random attempts and found that (a + b + c) is factor, and then dividing the original equation by (a + b + c) yeilds a^2 + b^2 + c^2 - ab - ac - bc I can't figure...

o rite i see. I think I have the right answers lol cheeers

Homework Statement Find all values of x in the interval 0<=x<=2pi for which 2sin^2(x)+sin(x)-1=0. Homework Equations The Attempt at a Solution I have no idea. I spent awhile trying to figure it out on my graphics calculator but couldn't figure it out. I have only been told...

o sick thanks for help guys :D much appreciated I see it now :)

ooooo yeah I see why L=sqrt(2L+5). I still can't go anywhere from here though :S

Homework Statement shows that the sequence U(n+1) = \sqrt{2U(n) + 5} where U(1) = 3 converges to a limit, u, and find the value of u correct to 2 decimal places. Homework Equations The Attempt at a Solution I only know how to solve convergences when dealing with series lol...