Mathematics

Given 3 points in 3D space as cartesian coordiantes (a triangle) I need to calculate the normal for a 3D graphing program I am making. I haven't done any calculus that might help with this and I don't know about linear algebra so Wolfram's solution is of no help: Can anybody please translate this into an algebraic solution for me? Thankyou.

I'm trying to find: [math]\int_{0}^{12}12x^{\frac{1}{2}}-x^{\frac{3}{2}}\cdot dx[/math] Which I thought was [math][12\times \frac{1}{1/2} x^{\frac{2}{3}} - \frac{1}{3/2} x^{\frac{5}{2}}]_0^{12}[/math] Which I simplified to [math][24x^{\frac{2}{3}}-\frac{2}{3}x^{\frac{5}{2}}]_0^{12}[/math] Which comes to aprox. 207. But my textbook tells me that the awnser should be around 133. Can anyone spot where I went wrong?

I have a proposition to prove FLT See attachement Fermat_Theorem1.doc

Hello, I have been away form SFN since Feb 7th. I have been busy working on things. But I am trying to do a math contest on my site. It is free and I am not selling anything. I just want to share ideas. See www.constructorscorner.com for more information. It runs from May 1st to July 30th Hope to see you there.

What is college math like? I have a few questions. 1, Why is my favorite high school olympiad math contents not here? For example, where's number theory? Where's solid geometry? Where's trigonometry? Where's.....? Do they just disappear in college? 2, this is a much more important question. I FALL FOR HIGH SCHOOL MATH OLYMPIAD PROBLEMS. I enjoy the beauty of problem solving there. Am I likely to fall for college math too? You might say "Sure!" But I've read some college math books--they really look quite different. I suppose that every problem solving fan has a BRAIN LIMIT, and she will only feel comfortable when she's solving problems within that limit. No matt…

I'm attempting to create a quiz with the first 8 answers with the possible answers of any of up, down, left, and right... From doing research, I understand this is possible for graph sketching. Is this true? I would like to make a believeable college level simple quiz/test that has these answer possibilities for the first 8 question. Please let me know, thanks.

O My God. The Golden Ratio. Its quite an interesting subject. Its defined as: [1+(Sqaure root of 5) ]/2. In words, 1 plus root 5, all over 2. In symbols, the value is represented by the greek letter, phi. Lets cut to the chase, I just recently attained a calculator that computes to 5011 digits. The value of the golden ratio is 1.618033988749894848204586834366 to 30 decimal places. Anyway, I noticed that the recipricol, or phi^(-1), is phi - 1. Yes, 0.618033988749894848204586834366. And its not a coincidence to 30 decimal places, wen computed to 5011 decimal places, same result, phi^(-1) =phi - 1. Can anyone explain why or how..or what ever.

Hi hmm...i think i have solved this problem but neither of my 2 answers look like a Laguerre polynomial..... problem: my solutions: :S Sarah

Hi all, would anyone be able to give me a bit of help with this problem: this is what i have done so far (i am now stuck ): thanks Sarah

(Dy)² = (a-y²) with y(0) = 0 How do you solve this? Matlab gives these solutions: syntax: dsolve('(Dy)^2 = (a-y^2)','y(0) = 0') y=tan(t)*(a/(tan(t)^2+1))^(1/2) and y=-tan(t)*(a/(tan(t)^2+1))^(1/2) But these solutions are periodic if you look at the diff. equation: when y²=a then y should stay constant (not periodic) can anyone help?

Has anyone studied Differential Geometry from Do Carmo's book, Riemannian Geometry? I am trying to work problem 4 page 57, but I don't even know how to start. I will scan the problem and post it laer.

There is a new theory that may end the endless debate about 1=0.999... the whole theory can be found in this link http://www.geocities.com/humood_theory here is a Quote about cracking the famouse proof: Proof (A) x=0.999... 10x= 9.999... 10x-x=9.999... - 0.999...=9 9x=9 x=1 All the theory and results can be seen in the link: http://www.geocities.com/humood_theory For comments please write it here in this forum or send it to the e-mail said_yam@yahoo.com

I'm in the middle of revision for my final GCSE maths exam. So far its been alright but today I've come across something that is not covered in any of the books I'm using. I'm assuming its an A* question (since "Introduction to modelling" comes up right at the end of one of the revision textbooks.) Here's the question - d = av + bv^2 Find the values of a and b co-ordinates on the expotential graph - (40,120) (60,240) I know the answer is (because they are provided in a separate booklet) a = 1 b= 1/20 Whats the methodology? I know that for a straight line - finding the gradient would give me the answer. I've tried rearranging the equat…

I need to express blood pressure in terms of kPa. The conversion is 1kPa - 7.5mmHg, or .133 kPa - 1mmHg, but how would this be expressed? Just kPa subsituting mmHg, ie kPa/kPa?

I learned to use this way instead of the others an+1/an so when the ratio get smaller and smaller for n>1 does that mean it is decreasing? and not increasing nor decreasing when the ratio stay same for all n>1 like (x^2+2x)/(x^2+2x+2).

Suppose I have x number of items. I am instructed to put them in groups of y items, such as groups of two or groups of three. Is there an equation that I can plug these variables into to figure out all possible combinations? Thanks.

how do I find the upper and lower bound of this sequence? (2^(n-1))/(n+1)!

Addition is an axiom of mathematics, or am I wrong? I heard that the Peano Axioms can prove 1+1=2, but I don't really know why or how. Can any of you more advanced students dechiper this? (I'm only a freshman in high school, remember, and it's frustrating to not be educated higher in math.) So, if anyone can relate this to me, I'd be grateful.

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.