Squares Definition and 400 Threads

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...

Here is the question from the book: ------ Let n\geq1 and let a_1,...,a_n and b_1,...,b_n be real numbers. Verify the identity: \left(\sum_{i=1}^n{a_ib_i}\right)^2 + \frac{1}{2}\sum_{i=1}^n{\sum_{j=1}^n{\left(a_ib_j-a_jb_i\right)^2}} =...

Homework Statement X mod m is the remainder when x is divided by m. This value is called a residue. Find all perfect squares from the set of residues mod 16. The Attempt at a Solution There was a suggestion that this would become clearer when the definition of perfect square was...

Hi all, I think this sounds like a really simple and trivial question, but I've no clue as to where i should start: true or false? between any two different positive rational numbers lies the square of a rational number. while i can't provide a construction of such a number, i somehow...

I was reading through a proof of the summation formula for a sequence of consecutive squares (12 22 + 32 + ... + n2), and the beginning of the proof states that we should take the formula: (k+1)3 = k3 + 3k2 + 3k + 1 And take "k = 1,2,3,...,n-1, n" to get n formulas which can then be...

Hello i need help with a question, other people tried to help me, i just cannot get it! its driving me crazy Two positive numbers have sum n. What is the smallest value possible for the sum of their squares? so i have n=x+y x>0 y>0 y=n-x we want to minimize S S=x^2+y^2...

I am curious as to whether this pattern will always hold true: Let's say we take the prime numbers: 2,3,5,7,11,13,17,19,23...primes and we take the square(individually) minus 1 3,8,24,48,120,168,288,360,528...p^2 - 1 Then starting with the third p^2 - 1 (24), all of the p^2 - 1 can be...

Which squares are expressible as the sum of two squares? Is there a simple expression I can write down that will give me all of them? Some of them? Parametrization of the pythagorean triples doesn't seem to help.

Suppose X is a set consisting of squares with the property that any addition with elements of X (where no two are the same) gives a square (might not be in X). How many elements can X have?

Greetings, I'm curious if "magic squares" have been found to be useful in mathematical or scientific endeavors apart from an "oddity" or "game"

This has to do with the 2nd order recursive sequence \{...a, b, c ...\} where a,b,c are any three sucessive terms and c = 6b-a + 2k. I found that it has the following property. 8ab - (a+b-k)^2 = 8bc - (b+c-k) That is eight times the product of two adjacent terms always equals the square of...

How do you go from \sum_{n = 1}^n i^2 to \frac{n(n + 1)(2n + 1)}{6}?

We all know the least squares method to find the best fit line for a collection of random data. But I wonder if it is the best method. Suppose we have two random variables y and x that appear to have a linear relation of the type y = ax+b. What we want is, given the next type x signal to...

Hi, I was working on a problem and I can't figure out what I'm supposed to do. It reads, find the vector in subspace S that is closest to v; write v as the sum of a vector in S and a vector in S^a; and find the distance from v to S. S spanned by {(1,3,4)} v = (2,-5,1) Ok, what I did was...

Question states Consider the vector space C[-1,1] with an inner product defined by <f,g> = the integral from 1 to -1 of f(x)g(x) dx a) Show that u1(x)= 1/(2^.5) u2(x)= ((6^.5)/2)x form an orthonormal set of vectors b) Use the result from a) to find the best least squates...

a number n when factorised can be written as a^4*b^3*c^7.find number of perfect square which are factors of n.a,b,c are prime >2. I have no idea how to start? please help.

A figure contains five equal squares in the form of a cross. Can you show how to divide this figure into four equal parts which will fit together to form a square

It seems to me that Linear Regression and Linear Least Squares are often used interchangeably, but I believe there to be subtle differences between the two. From what I can tell (for simplicity let's assume the uncertainity is in y only), Linear Regression refers to the general case of fitting...

ok, i need to derive a forumla that will add the consecutive squares of n numbers. for example 1^2 + 2^2 + 3^2 + ... + (n-2)^2 + (n-1)^2 + (n)^2 I have worked on this problem for quite some time and haven't been able to come up with anything. I do know that the sum of consecutive...

Prove that the square of an odd integer is always of the 8k + 1, where k is an integer. Any help would be appreciated.

Hi, I am having some difficulty with this problem: what would be Y^h^a^t if s_y_/_x = 439, n = 24 and 95% confidence interval estimate for the average Y given a particular value of X is 1125 and 1695. ----------------- I know Y^h^a^t = b_o + b_1x but I am not sure how I can use the...

I have a statistics test coming up and we were given two really hard problems to figure out. I don't quite know what they are asking, and we are kinda on our own to solve it. Any help would be greatly appreciated. 1. Given that the equation for the sum of the squares is SS = x2 - (x)2/n...

Start with a 8 by 8 board of squares (for instance, a chessboard) and take away the top-left and bottom-right corner squares so that there are 62 squares left. Take some dominoes that are the same size as two squares of the chessboard. Can you cover the 62 squares of the board with 31 such...

How do I factor this equation x^3-1

Greetings friends, I have come across an argument on cancelling the squares on either side of an equation. For example if the equation is (a-b)^2=(c-b)^2 my argument is that i can cancel the squares by taking the square root of both sides as to get (a-b)=(c-b) and hence a=c. But others says...

\begin{array}{c} {{A_n}={\sqrt{\sum _{z=1}^{n}{z^2}}} } \\ {{A_1}=1 } \\ {{A_{24}}=70}\end{array}\ Is there a proof that only for n =1 or n=24 that An is an integer quantity?

Magic Square Hello, Don't know, which forum, so i put it to general... Yesterday i saw something like an magician on an exposition, showing some math to angle for attention. He asked the audience to give him a number between 41 and 100. So he got the 47. He worked out a magic...

How do I find out if a number is a perfect square modulo a? For example, is 4 (mod 10) a perfect square?

Compute the following: \sum_{n=1}^{+\infty} \frac{1}{n^{2}} =...?? \sum_{n=1}^{+\infty} \frac{1}{n^{4}} =...?? .LINKS TO WEBPAGES WITH SOLUTIONS ARE NOT ALLOWED! :-p Daniel.

Construct the normal equations for the linear polynomial least squares to fit the data x = [1 0 -1], y=[3;2;-1]. (a) Find the parameters of the linear regression u1, u2 using QR decomposition, and plot the data and the fit curve in a graph (paper and pencil). (b) Calculate the eigenvalues of the...

urgent! finding co-ordinates in squares A(7,2) and C(1,4) are vertices of a square ABCD. equation BD is y=3x-9 midpoints AC: (4,3) find the co-ordinates of B and D i just don't understan how to get the co-ordinates, I've tried plotting a graph but to no avail. i found the midpoints...

First I'd like to say that I'm getting back into college after several years out in the job market. Unfortunately, I need to complete several more upper division math courses before I can complete my CS degree. Before I go back and start taking my classes again, I've been trying to self-study...

A little while ago I noticed a pattern in the sums of the digits of perfect squares that seems to suggest that: For a natural number N, the digits of N^2 add up to either 1, 4, 7, or 9. ex: 5^2 = 25, 2+5 = 7 In some cases, the summation must be iterated several times: ex: 7^2 = 49...

I'm getting confused and can't seem to wrap my head around this problem. Prove that the sum of the squares of any 3 consecutive odd numbers when divided by 12 gives a remainder of 11. I'm not sure how to set this up or proceed I figured that (n^2 + (n +2)^2 + (n+4)^2)/12 = x + 11...

perfect square? hello everyone! i have come across an on-going research onDETERMINING A PERFECT SQUARE GIVEN A DIFFERENCE . However, I have a feeling that this was not an original one. the researcher used the Pythagorean theorem to arrive at his so called "theorem". would anyone give...

Greetings, I suppose all of us have at one time or another been fascinated by "magic squares" My question is: has the relationship of numbers in a magic square been found to be useful in the mathematical sciences in any advanced analytical work? Or is is just a mathematical curiousity?