Mathematics

I need to write a function to find the largest square factor of a number so it can be taken out of a radical. I hope there is a known solution to this. The most efficient aproach I can think of is: set total to 1 for (each prime less than square root of n) { while (n is divisble by prime^2) { divide n by prime^2 multiply total by prime } } "total" should then be a square factor of n. The problem with this is that it is very slow. Is there a faster method?

Well, on my final today for AP Calc. BC, I was able to solve all the integrals except this one... It's bugging me because I feel like I'm missing something obvious, and my teacher put them in order from easiest to hardest and this was somewhere toward the middle. The test is over so it doesn't matter now, I'm just curious as to how it should have been solved (without a calculator). [math]\int{x^{5}\ln{(3x)}dx}[/math] Edit: Corrected version of problem (I wrote it wrong, I'm a loser ) [math]\int x^{5}\ln(x+3)dx[/math]

1. A, B and C are points on the circumference of a circle, centre O, and ∠BAC=115°. Calculate the number of degrees in ∠OBC. I drew a diagram but could not come up with anything primarily because ∠BAC and centre O lie on opposite sides of chord BC (draw a quick diagram if you don't know what I mean). 2. ABCD is a quadrilateral inscribed in a circle and AB = CD. Prove that AC = BD. This is pretty simple I think, if AB = CD, then BC = DA (do I need to say why?). Then just use Pythag to prove the diagonals are equal.

My school only offers AP Calc AB.. I would like to have AP Calc BC credit if I can but I wonder how hard they are. Share your opinion here. Thanks.

I have been working with my friend in economics (always fun ) and we are trying to find polynomial roots using summations. The reason I ask is because we are modelling an economy as a system of equations, and if there is a surplus product then it becomes a polynomial. For example, we have an economy of two sectors (wheat and coal). We have the relationship 280 qr. Wheat + 12 t. coal --> 575 qr. Wheat 120 qr. Wheat + 8 t. coal --> 20 t. coal We then set up the value per unit Wheat as X and value per unit coal as Y, giving us: [Math]\frac{(1+r)(280X + 12Y)}{(1+r)(120X+8Y)} = \frac{575X}{20Y}[/Math] thus by reduction of the rate of profit ("1+r"), we m…

I thought to put this thread in the challenge area but it is math and all that stuff seems like philosophy. So here goes. I apologize for the pseudo-code but I do not have latex. Challenge 1: Prove that if n+1=(m+1)(s+1) then sum(a^k,k=0..n)=sum(a^[k*m+1],k=0..s)*sum(a^k,k=0..m) Challenge 2: Show that if n is odd then limit(a->infinity, ln[a](sum(a^k,k=0..n))-ln[a](sum(a^2k,k=0..[n-1]/2))) = 1 Challenge 3: Define an invertible function psi taking the set {limit(a->infinity,ln[a](sum(a^k,k=0..n))), limit(a->infinity,ln[a](sum(a^2k,k=0..[n-1]/2)))|n=1...infinity} to the natural numbers. Challenge 4: Explain wh…

Lets have a nice(and easy) question on my first post Find all [math]x[/math] such that [math]x^2+2[/math] is a prime number.

I'll probably be taking math class at local college in my senior year. I know that the best way to choose class is to contact with the college's math department but I wonder what you guys think will be a good class to take. I know some NT, combinatorics, algebra, trig, geometry, and hopefully be able to learn some graph theory/invariant sometime in future before my senior year. I personally do not like calculus much so good tip? Also, if I take class at local college, will this go as a part of my regular transcript or count as "AP" type credit? Thanks.

Hey, i am little puzzled by this question.... i get that none of the sets (a,b or c) are orthogonal when taken over -infinity to infinity. am i doing something wrong, i would have thought at least one of them would be orthogonal...??? this is the problem in question: the inner product i think i am meant to be using is: <f|g> = ?f*g where the thing on the left (f*) is complex conjugate of f. the combinations i tried were: (a) cos(x) & 3sin(x) (b) 1 & (-x+1) © x * 4x^{3} i would have thought that cos(x) & 3sin(x) would be orthogonal...?? or is it that i am not meant to be integrating from -infinty to infinity? (that is …

any suggestions? I think have to use partial fraction decomposition but I don't seem to get anywhere...

Hey everyone, i am having a bit of trouble trying to do this question. how do i show that they are linearly dependent ? i tried using the wronskian but this doesnt work does it? (because just because the wroskian is 0 on the interval it doesnt neccessarily mean that the two functions are dependent, right?) this is what i have done so far: (a) for 0<t<1 |t| = t so f(t) = t^2.t = t^3 = g(t) therefore f(t) and g(t) are linearly dependent on 0<t<1 for -1<t<0 |t| = -t so f(t) = t^2.-t = -t^3 = -g(t) therefore f(t) and g(t) are linearly dependent on -1<t<0 for -1<t<1 because f(t) is a different mult…

I hope I am not bothering you guys with too many questions and post I am clueless, tried changing it to csc^2(x)csc(x) but doesn't help neither does csc(x)(1+cot^2(x))

hey all, just having a bit of trouble with this problem... i have done a little bit on it, just thought i'd let you guys look at it first, because i havent been able to type up my solution yet. Cheers guys & gals Sarah

this problem, I don't even have a clue where to start...

I not sure which maths forum to stick this in so I'm putting it here I don't mind if it gets moved though. I was thinking about this earlyer and its been bugging me for a while now. Say you have two numbers 1 and 2 isn't there an inifnate amount of numbers between them? Like 1.999' So how can we ever get from one to the other? Does that make sense I'm going crazy here!

Hey, I'm currently struggle with these two proofs, if anyone can help me I would be very thankful. 1. prove that one of the roots of x^3+ax^3 +bx + c = 0 is the negative of another if and only if c=ab. 2. Prove that if the diagonals of a quadrilateral divide it into four triangles of equal area, then the quadrilateral is a parallelogram.

I have a assignment due by Friday and ive done most of it but a few problems are really killing me and I was wondering if I could get some help and by help I mean the answers lol to some problems if u can help me I will be greatly apprciative. 3. Find the length of arc S, if r= 10 and its like a 0 with a line in the middle = pie over 6. 4. Find the area A of the sector if the 0 with the line in the middle = pie over 4 and r = 6 5. If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the eaquator? (use pie = 3.1416) please can some one help me its a matter of life and death lol.

From now on, I will use this thread to inquire my math questions that I have. I don't want to create a new thread for everytime when I have a single, small math question. Waste of time in my opinion. Also, to let everybody know, those math questions will never be my homework. They are just some bogus math questions that I see around or on the Internet. IT'S NOT MY HOMEWORK. Awhile ago, I just found this old Fermat Competition booklet in my bedroom that I entered last year (A Canadian National Math Contest), and I have this question. When [math]a=\frac{1}{2}[/math] and [math]b=\frac{2}{3}[/math], what what does [math]\frac{6a + 18b}{12a + 6b}[/math] equals? I…

how to solve this: sin(z)= i where z =x+iy. (or if we have sin(z) = ni where n belongs to N(natural number) in general. It's a question of a quiz and I don't know what kind of equation it is) Thanks in advance

Hi all, i am having a lot of trouble trying to do this problem, as my textbook does not discuss circuits and it is only covered in 3 very brief lecture slides. if anyone would be able to point me to some good websites on how to do these type of problems or be able to help me in any other way that would be great! Thanks guys & gals! -Sarah

Hello, Recently I stumbled across a math problem, that I hope you can help me with. It is really about defining a planetary orbit from very little data, but since all orbits are ellipses I might as well post it here too (it has also been posted in the astronomy subforum). I'm building a simple 2D program that simulates gravitiational attraction between celestial bodies. The program is strictly Newtonian - it calculates all movement using F = G*(M+m)/d^2 - but I'd like to calculate backwards so to speak and find the details about any orbit's eccentricity, orbital period, orbit centre and foci ect ect. All the data I have is: -body's velocity vector length …

terrence mckenna derived the FRACTAL TIMEWAVE out of the KING WEN sequence of the I CHING. i have looked at his math and it is very complicated and i do not understand, plus I know nothing about FRACTALS except that they relate to the structure of CRYSTALS. it is my theory that the universe is really just one big giant CRYSTAL and i think terrence mckenna went a long way to prove that with the timewave. he says that history is feeding back on itself and that time resonates over and over again and that these resonances are increasing and will reach infinity in THE YEAR 2012 WHICH IS THE END OF TIME. he does not explain what happens in 2012 but says that man…

Hi I hope someone can help me. Are there any good websites for learning logic? I've just been trying to figure out antecedents and consequents and the two valid ways and the two invalid ways of arguing them. I'm confused by the following sets of propositions: If I buy the correct ticket then I'll win the Lottery. I'll win the Lottery only if I buy the correct ticket. The consequents and antecedents are reversed from one the the other, yet one of them can be a true statement and the other not?

if y_1 and y_2 are the answers of this equation: (d^4 y/dx^4) + 4 y = f(x) then what's y_2 - y_1? I used laplace Transform! Thanks in advance

I'm currently in a linear algebra class and we are doing a massive amount of proofs, something that is foreign to me. Every time I'm asked to do a proof my effort turns into a narrative argument, and my problem isn't knowing why something is true or not. I piece it together in my mind and can argue it, and if I had to teach somebody whether or not something is true I have faith in my abilities to do so, but I'm having difficulty providing any type of valid mathematical proof. What's lost on me appears to be the logic behind the language of proofs and what assumptions can be made when doing them. A lot of proofs make perfect sense to me when I read them, but somet…