Squares Definition and 400 Threads

Substitute each of the capital letters in this 3x3 square by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subsquares is equal to 6*E. A B C D E F G H I What will be the arrangement(s), if keeping all the other conditions unaltered, the...

I am doing a calculation involving taking three or more temperature measurements and then plotting them against another quantity (dependent). I get a relationship that is pretty linear, so I take the line of best fit to obtain an equation with a slope and an intercept. Now, my question is...

Hello everybody, I have two questions on conditional expectation w.r.t (Polynomial) OLS: Let X_t be a random variable and F_t the associated filtration, Vect_n{X_t} the vector space spanned by the polynomials of order {i, i<=n }, f(.) one function with enough regularity. I am wondering how...

Hi, does anyone know how many squares of side 1 millimeter can fit in a big square of side 1000.25 millimeters ? Cheers, Aaardvark.

All - Given a set of data {(xi, yi)| i = 1,2,...,m} and the regression equation f(x) = ax + b, I want to use the simplex method to minimize the equation Sigma [(yi - f(xi))/f(xi)]^2. However, I am stuck on how to initially organize the problem. I am not sure whether the equation, Sigma [(yi -...

I'm kind of lost on this one. Could someone please help me. Two equally big squares with the sides 12 cm partly covers each other as the figure shows. One of the squares corner is in the other squares center. Decide the area of the shadowed part...

Homework Statement Find A: A2 = (4/5)(18292 + 12982) in about 3min, because this comes at the end of a rather difficult geometry problem with 6 min for the entire question. (edit: Yes, calculators weren't allowed because it was a competition. I have verified that everyone comes to this step...

Least squares regression of Y on A-D based on sample size of 506. Reported results with standard errors are: Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d =...

Least squares regression of Y on A-D based on sample size of 506 Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d = coefficient on D null: D ~ N(0, 0.006) Pr(d...

Least squares regression of Y on A-D based on sample size of 506 Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d = coefficient on D null: D ~ N(0...

Hey guys, long time lurker, first time poster! Just having some trouble with something..Im probably just looking at it the wrong way, but I was wondering if anyone could help me with this.. Im trying to prove that by choosing b0 and b1 to minimize...

the proof in my text starts with what's called a telescoping sum (1+i^3)-i^3 what is the relevence of this to i^2

Hi i was just wondering if someone could tell me how one can find the phase shift and the number of squares to move the graph over by from an equation?. We are doing cosine and sine graphs and my teacher has been away for a few days so the supply teachers haven't been really that great in...

Hello, I am a first year undergraduate university student majoring in Engineering and Computing Sc. One of my courses is Linear Algebra. We have been given an assignment in which question no. 2 is out of syllabus. It is on Least Squares Regression Analysis. This has not been taught to us. We...

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...

Each of CEM, NOVE, UM and ZERO is a decimal perfect square. Each letter represents a different decimal digit from 0 to 9, but the same letter always denotes the same digit. None of the four numbers can contain any leading 0. What numbers do CEM, NOVE, UM and ZERO represent?

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,...) | \Sigmaxi < \infty} we have d(x,y) = \sqrt{\Sigma (xi-yi)^2} I need to show that this is a metric, starting by showing that if...

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...