Squares Definition and 383 Threads

Homework Statement We have the following x, y values x ||| y 1.0 -0.15 1.5 0.24 2.0 0.68 2.5 1.04 3.0 1.21 3.5 1.15 4.0 0.86 4.5 0.41 5.0 -0.08 How can you find the equation y(x) = ax^2 + bx + c by least squares? The Attempt at a Solution I know how to...

Homework Statement In the least squares method the vector x* that is the best approximation to b statisfies the Least squares equation: A^T A x^*= A^T b Prove that there's always a solution to this equation. Homework Equations - The Attempt at a Solution I distinct 2...

Homework Statement If C^2 = ab and the greatest common divisor of a and b is equal to 1, prove that a and b are perfect squares Homework Equations I know that if (a,b)=1, then there exists integers u and v where 1=au+bv (even though i don't think this is necessary in this proof)...

n=p1r1...pkrk In order for p to be a perfect square, r must be even. Therefore n=p12h1...pk2hk taking the square root of both sides I'm just left with n=p1h1...pkhk Does this work as a proof that n is a perfect square if r is even? It's a homework problem and I'm not sure if this...

Homework Statement x^2 = 2/11x + 99/121 Homework Equations The Attempt at a Solution x^2 = 2/11 x + 99/121 x^2 - 2/11x - 99/121 = 0 x^2 - 2/11x =99/121 I understand that (b/2)^2 must be added to each side to become a perfect square trinomial...But HOW I do it...

Determine all possible positive decimal integer(s) of the form aaabbb, each with no leading zeroes, that becomes a perfect square when 1 is added to it. What are the positive nondecimal integer base(s) S, with S<=16, such that S admits at least one valid solution in conformity with the given...

Homework Statement graph the following Homework Equations 9x^2+4y^2+36x-8y+4=0 The Attempt at a Solution I think I need to get it into \frac{(x-x0)^2}{a^2}+\frac{(y-y0)^2}{b^2} but I'm not sure. I have \frac{9x^2}{-4}-8x+y^2-2y=1 and now I'm stuck

hi all I need some help with this question Let (a,b)=1 and ab=c^2. Show that a and b are perfect squares. Thank you

Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation: (PQR)2 + (STUQ)2 = (SVWX)2 Note: None of P and S can be zero.

3x3 magic squares * updated http://en.wikipedia.org/wiki/Magic_square#Types_of_magic_squares_and_their_construction given a 3x3 block with 3 numbers inserted e.g. |2|_|_| |_|_|6| |_|3|_| How would I solve this magic square? Is there a pattern for this? The method in wikipedia...

prove that for any integer n, n^{2} \cong 0 or 1 (mod 3), and n^{2} \cong 0,1,4(mod 5)

Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.

Hi, I am trying to learn some numerical algebra. Now I don't understand the following. I'm finding the solution to the Linear Least Squares problem min||A\lambda-y||_{2}, which turns out to be (1,1). I did this by doing a QR factorization using Givens rotations. with: A= \[...

Does a http://en.wikipedia.org/wiki/Tikhonov_regularization" solution for least squares have to be iteratively solved? Or is there a way to perform regularization via linear algebra, the way linear regression can be done by solving the (XTX)B=XTy normal equations?

Does anyone know where to find source code for a simple and fast least squares solver written purely in C++?

Hm, is this the right place to ask this? It's kind of a topology question, I guess. Let's say I've got a square. It's got four sides. ______ | 1 | |2 3| | 4 | ------ And I want to tile this over and over on the plane. ________________________ | 1 | 1 | 1 | 1 | |2 3|2 3|2...

Hi everybody :smile: I'm currently reading Burton's Elementary Number Theory (almost done!) and in the chapter about Lagrange's Theorem about the sum of four squares, there is a supposedly easy question which I can't solve for some reason :blushing:. I'd really appreciate a hint or two...

Dear all, Apologies if this is in the wrong forum. I have a bit Nonlinear least squares fit problem. I have a pair of parametric equations (see attached, fairly nasty :frown: ). in it, a b c x0 y0 z0 are all constant, and they are the values I want to determine from a nonlinear least...

Homework Statement In a 6 x 4 grid (6 rows, 4 columns), 12 of the 24 squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let be the number of shadings with this property. Find the remainder when is divided by 1000. There is a...

1) Suppose that a and b are relatively prime natural numbers such that ab is a perfect square (i.e. is the square of a natural number). Show that a and b are each perfect squares. a=(a1^p1)(a2^p2)(a3^p3)...(a_n^p_n), a_i distinct primes b=(b1^q1)(b2^q2)(b3^q3)... (b_m^q_m), b_j distinct...

I need help with these: 1. Charles was married once before, & he and his first wife had a child who suffers from cystic fibrosis. His current wife Elaine's brother died of cystic fibrosis. What is the probability that Charles & Elaine will have a baby with cystic fibrosis? Let's say A=...

You must have used it couple of times while solving an engineering problem. For example in line fitting, why do we have to square? Can't we just pass the line thru the max number of points. Can someone explain. Thanks in advance.

Homework Statement I have an equation as a function of time. (eq1) C(t) = Css + a(e^.5t) + b(e^.9t) t>0 Where, Css is a constant. then I have 6 data points of time and C (Concentration of a liquid) 1. I have to find an equation to find the maximum time and contains a, b and Css...

If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...

Homework Statement So, L2 is defined to be the set of all infinite sequences of real numbers, s.t. the sum of their squares converges: L2 = {x=(x1,...,xn,...) | \Sigmax[SIZE="1"]i < \infty} we have d(x,y) = \sqrt{\Sigma (xi-yi)^2} I need to show that this is a metric, starting by showing...

Hi, Forgive me if the subject of this post is not accurate, I'm not quite sure what the correct terminology would be for what I'm trying to figure out. Currently I am using linear least squares via SVD to find the coefficients of a ten term polynomial, say f. This model allows me to...

Prove that if n is a perfect square, then (2^n) -1 is not prime. All I can get is that 2^n is some even number. I can't work in the perfect square part.

Let u_n be a sequence of positive real number. If \sum_{n=1}^{\infty}u_n^{2} finite + (condition??) then \sum_{n=1}^{\infty}u_n finite. I want to find the condition.Please help me.

I'm looking for patterns and if you can add to things I noticed before working it out, that would be good :-] 1. (a+b+c)(a+b-c)=a^2+b^2+c^2+2ab I noticed that b+c and b-c compensated for each other. 2. (a+b+c)(a-b-c)=a^2-b^2-c^2-2bc a+b and a-b compensated for each other and the fact that...

Homework Statement The infinite series defined by \Sigma a_{n}, with a_{n}>0 are convergent. If then the series defined by \Sigma a_{n}^{2} coverges, prove it! Homework Equations The relevant equations has been stated above. The Attempt at a Solution Since every term in the first...

Homework Statement Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.) Homework Equations The Attempt at a Solution a^2+b^2=4n+3=3 mod 4 is impossible if you look at the possibilities of a^2 and b^2. I did not use the fact...

I am currently working on a lab report for my physics class. During the lab, we used air tracks, gliders, and a photogate to measure the value of 'g'. Basically, we would raise one end of the air track to a certain height and let the glider slide down the frictionless track and the timer would...

I took a short break from the rudin-crunching. I'm now doing reimann's integral. Anyhow here's a question I've having trouble with. Does f^2 is integrable imply that f is integrable? -No, take f=1 on rationals, f=-1 on irrationals on [0,1]. Does the integrability of f^3 imply that f...

Homework Statement A square is divided into 81 smaller squares by lines parallel to its sides. The numbers 1, 2, ..., 81 are entered in an arbitrary fashion, one in each square. Show that, however the numbers are entered, it is possible to find two small squares with an edge in common whose...

My google search just turns up results telling me that one of the assumptions I have to make is that each Y is normal. My question is why do I have to assume its normal. Why does it follow that it has to be normal as opposed to some other distribution? Hope that makes sense. Edit: I thought...

Homework Statement I've been given a task to find "A 4-digit perfect square whose digits are all unique, and whose square root is a prime number". That's all. I know that there are about 10 possible answers and I need them all. Thanks a lot for any future help.

Homework Statement why did you use the least squares method for finding m, rather than the standard slope formula? Homework Equations The Attempt at a Solution I am totally confused about why you have to use the least squares method

Homework Statement An open-top box can be formed from a rectangular piece of cardboard by cutting equal squares from the four corners and then folding up the four sections that stick out. For a particular-sized piece of cardboard, the same volume results whether squares of side one or...

how would you do: lim x->3+ of abs(x+3) / x^2 - 9 because if you take the difference of squares of the bottom and divide x+3 / x+3 for the positive abs case you are left with 1/(x-3) with x approaching 3 making the denominater 0 I have since realized that the question was asking for...

[SOLVED] Punnet Squares The allele for dark hair D is dominant over that of red hair d, and the allele for brown eyes B is dominant over that of blue eyes b. A women is red-haired and has blue eyes. Her husband is dark-haired and has brown eyes. a) What are the possible genotypes for the...

Homework Statement An experiment was conducted on a liquid at varying temperatures and the volume obtained at the differing temperatures are as follows: V/cm3 θ/oC 1.032 10 1.063 20 1.094 29.5 1.125 39.5 1.156 50 1.186 60.5 1.215 69.5 1.244 79.5 1.273 90 1.3 99 Assume that V...

Anybody know the math/theory behind linear least squares where the curve is forced to go through the first and last data points?I'm specifically dealing with cubic polynomials. In standard linear least squares formulation (i.e. ATAc = ATy) the curve doesn't, in general, go through any of...

Hello to you all! I've been involved in Magic Squares & Cubes for the last 8-9 years. I've recently developed 3-D models of that, too. What I've observed is a unique relationship between simple Arithmetic Sequence & Magic Squares & Cubes. Combining the two, I've reached a new 3 Dimensional...

[img=http://img527.imageshack.us/img527/9639/96652845hm1.th.jpg] I can do 6.a) and b) but still need to know how to do c). I've done half of the question because I have an example of one where the diagonal adds up to 33, but I can't prove that's the smallest diagonal sum. Dont know where...

Randomly select eight odd integers of less than 1000 a) Determine the remainders when dividing their squares by four, and tabualte your results b) Make a conjecture about your findings c) test your conjecture with at least five larger integers d) Prove of justify the conjecture you make. n...

I'm reviewing material for my exams and I came across this: \lim _{x\rightarrow \infty }\sqrt {{x}^{2}+x+1}-\sqrt {{x}^{2}-3\,x} The only explanation it gives is "By the difference of squares" the solution sheet then jumps to: \lim _{x\rightarrow \infty }{\frac {4\,x+1}{\sqrt...

I have a problem that says to find the least squares solution to \newcommand{\colv}[2] {\left(\begin{array}{c} #1 \\ #2 \end{array}\right)} K x = \colv{2}{2} for K = \left( \begin{array}{cc} 1 & 2\\ 2 & 4 \end{array} \right). Then express the solution in the form x = w + z, where w is in the...

Homework Statement The sum of two numbers is 20. What is the least possible sum of their squares. 2. The attempt at a solution Before I show my work, I'm pretty sure I have the answer. I think it's 200. If you add 10 and 10, you will have 20. If you square 10 you get 100, thus the sum...

Homework Statement I must prove the theorem that if the GCD of a and b is 1, and if p is an odd prime which divides a^2 + b^2, p is of the form 4n + 1. Homework Equations I have seen two proofs that I think might be helpful. 1. If a and b are relatively prime then every factor of...

Can someone help with the folowing? Suppose L1 is the line through the origin in the direction of a1 and L2 is the line through b in the direction of a2. I am supposed to find the closest points x1a1 and b+x2a2 on the two lines. So I am trying to find the equations that would minize...