Quadratic Definition and 965 Threads

Could someone please explain how to go about putting an equation into quadratic form. e.g: Q(x,y,z)=7x^2-2y^2-40z^2-14xz+20yz. I know it equals 7(x-z)^2 -2(y-5z)^2 +3z^2. dnt know how to get there though.

Could somebody explain what exactly a "piecewise quadratic approximation" is? Problem Statement Find a piecewise quadratic approximation P(x) of f(x), where f(x)=\sin{4x}\; on \; [0,\pi] Plot f(x) and P(x) on [0,\pi]. What is the maximum value of the following: |f(x)-P(x)| \...

Could somebody explain what exactly a "piecewise quadratic approximation" is? Problem Statement Find a piecewise quadratic approximation P(x) of f(x), where f(x)=\sin{4x}\; on \; [0,\pi] Plot f(x) and P(x) on [0,\pi]. What is the maximum value of the following: |f(x)-P(x)| \; on \;[0,\pi]...

Homework Statement Prove that for all real values of a and b , the roots of the eqn : ax^2-(2a+b)x+b-5a=0 are real and different roots Homework Equations discriminat=b^2-4ac where a is the x^2 coefficient and b is the x coefficient and c is the absolute term The Attempt at a...

Homework Statement Find all values of x for which x^2-5x+6<0 Homework Equations (x-2)(x-3)<0 The Attempt at a Solution When I draw the graph the solution is clearly 2<x<3 However, if I approach it mathematically (x-2)(x-3)<0 This implies either 1. (x-2) is positive and (x-3) is...

Homework Statement The Quadratic Equation. I am looking for an example of the quadratic equation being used in any form of engineering, or physics. I am supposed to give an example for my algebra class, but I really don't want to do the "two trains left a station," or "sally jumped off a...

Hello, I am revising eigenvalues in matrices and I've come across a part where i need to factorise the following quadratic equation; let lander = x 36-36x+11x^2-x^3 = 0 I know that the answer is (x-2)(-x^2+9x-18), but i don't know how he got to it. Ive look through google but i can't find any...

P.S. I'm not sure where to post this question, in particular I can't find a number theory forum on the coursework section for textbook problems. Please move this thread to the appropriate forum if this is not where it should belong to. Thanks!

Homework Statement Consider an object that is coasting horizontally (positive x direction) subject to a drag force f = -bv - cv^2 . Write down Newton's second law for this object and solve for v by separating variables. Sketc the behaviour of v as a function of t. Explain the time dependence...

Homework Statement Which of the following converge quadratically and which converge linearly? a) 1/n^2 b) 1/2^(2n) c) 1/sqrt(n) d) 1/e^n Homework Equations All I've got in my lecture notes is: The sequence converges with order a if there exist constants a and C and integer N such...

Homework Statement Given a real symmetric matrix A, prove that: a) A is positive definite if and only if A = (B^T)B for some real invertible matrix B b) A is positive semidefinite if and only if there exists a (possibly singular) real matrix Q such that A = (Q^T)Q Homework Equations...

Homework Statement Let f(x)= 125x-6x2 find the maximum value of f to four decimal places graphically Homework Equations (x)= 125x-6x2 The Attempt at a Solution Homework Statement attempt solution: x=-b+\sqrt{}b2-4ac/2a x=-125+\sqrt{}1252-4(-6)(0)/2a x= 0/-12=0...

Hello, I am sorry for removing the template but it is not an actual problem that I need help with. Well it is, but it should be pretty quick and straight forward. The problem is located here: http://www.cdli.ca/courses/math3103/unit05_org01_ilo04/images/3-less9.gif (It's a bit difficult...

x2 + 3x + 2 = 0 (x + 1) (x + 2) so x = -1 or -2 Is that right?

Homework Statement .002x - .000001x^2 = .50 Homework Equations -b+-sq.rt.((b^2)-(4ac))/2a [b]3. The Attempt at a Solution Plugging a=-.000001, b=.002, and c=-.5 does not get the the correct answer. x is supposed to be 292.89. I can't remember any other way of going about...

Homework Statement Determine the largest value of x_{1}^2 + x_{2}^2 + x_{3}^2 when x_{1}^2 + 2x_{2}^2 + 2x_{3}^2 + 2x_{1}x_{2} + 2x_{1}x_{3} + 2x_{2}x_{3} = 1Homework Equations Not sufficiently relevant to produce the expected answer.The Attempt at a Solution Completing the square, we get...

"order" of a mod m & quadratic residues 1) Definition: Let m denote a positive integer and a any integer such that gcd(a,m)=1. Let h be the smallest positive integer such that ah≡ 1 (mod m). Then h is called the order of a modulo m. (notation: h=em(a) ) ================ Now, why do we need to...

Here is a quadratic equation along with its solution. There's only 1 thing I don't understand. In the brackets how do we know that the values are - 4 and - 5 as opposed to + 4 and + 5. Why are they both negative when the quadratic contains both a negative and a positive expression? x2 - 9 +...

Hi, I have three questions about the application of quadratic approximation, what it is & when to use it. It ties in with a question about linear approximation also, I'll give an example first of what I'm talking about, just for you to evaluate if I'm wrong in the way I see the whole process, I...

Homework Statement i have quadratic form x^2-xy+y^2 how can I check if this form has always same sign (+ or -)?

Homework Statement A sprinter accelerates from rest to a top speed with an acceleration which magnitude is 3.80 m/s^2 . After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is 50 m long. If the total race is run in 7.88 s, how far...

1. Hi everyone. I'm looking for help with converting this function to quadratic form. 2. The function is f(x1,x2)=(x2-x1)^4 + (12*x1*x2) - x1 + x2 - 3. The quadratic form I need to convert to is: f(x)=(1/2)x'Qx - x'b + h where x is a vector=[x1 x2]', '=transpose, Q and b are...

Consider a one dimensional gauge theory where the field has mass. The term, m^{2}A^{\mu}A_{\mu} is the conventional mass term. What if you find terms in your Unified Field Theory lagrangian of the form M_{\mu\nu}A^{\mu}A^{\nu} [SIZE="4"]? In this case M_{\mu\nu} is constant...

The graph of y=(5-2x)^2+1. What are the transformations that have occurred from y=x^2. Im really confused with the transformations here.

Hey guys, This is my first post on PhysicsForums; my friend said that this was the best place to ask questions about math. Anyways, I have to find the Quadratic Variation of a Poisson Process. My professor doesn't have a class textbook (just some notes that he's found online), and...

Homework Statement These two questions are very similar: 1) Let c be a constant. If a and b are the roots of the equation x^2 + 2x - c = 0 then 2b-a^2 = ? 2) Let k be a constant. If a and b are the roots of the equation x^2 - 3x + k = 0 Then a^2 + 3b = ? Homework Equations...

Homework Statement Find the value of m and n, where m and n are integer, so that P(x) = x3 + mx2 – nx - 3m and Q(x) = x3 + (m – 2) x2 –nx – 3n have common quadratic factor. Homework Equations The Attempt at a Solution Is m = n = 0 one of the solution? If m = n = 0,then : P(x)...

Homework Statement Let U1, U2, and U3 be independent random variables uniform on [0,1]. Find the probability that the roots of the quadratic U1x2+U2x+U3 are real. Homework Equations The Attempt at a Solution So we need to find P(U22>4U1U3), which involves evaluating some...

Homework Statement How would you solve this problem: x^2 - 5x >= 0 Homework Equations The Attempt at a Solution I think it might be something to do with the Quadratic Formula?

Homework Statement 1 {(1-x)^1/2+1} +1{(1+x)^1/2-1}=1/x The Attempt at a Solution I can't got any clue how to solve it! I tried to multiply the terms with the LCM of the denominator but bit doesn't help. Please give me a clue!:frown: Thank you.

Homework Statement (a)2 + a · b - c = 0 a and b are vectors which (in general) with different directions while c is a scalar. How to solve for a? The Attempt at a Solution (a)2 + a · b - c = 0 (a + (1/2)b)2 - (1/4)b2 - c = 0 (a + (1/2)b)2 = (1/4)b2 + c In...

I actually have two questions, both are in the complex plane. Homework Statement Q1: Express 962 as a sum of two squares (Hint: 962 = (13)(74) Q2. Given z,a belong to C (complex). Find a such that the roots of the equation z^2 + az + 1 = 0 have equal absolute values (or modulus)...

Applying it to -x2 - bx +c = 0 I would have thought it to be (b +- (b2+4c)0.5) /-2 = (-b +- (b2+4c)0.5) /2 But Anytime I try and graph a function like it the roots are (b +- (b2+4c)0.5) /2 I can't see why this is? Thanks

Homework Statement Here the the word problem: Genelle and Eljen can paint a room together in 4 hours. Working alone, Genelle can paint the room in two hours less than Eljen can. Find how long it takes Eljen to paint the room alone. Homework Equations Maybe, this problem can be solved using...

Here is an interesting problem I came up with during my research. I first present a slightly simplified version. Let us the define component-wise the following bilinear symmetric form, returning a vector: a_i(u,v) = \frac{1}{2} (u^T A_i v - d_i) \;\;\; i=1 \ldots m where u,v \in V = R^n...

Hey there! I just want to know that this problem (t-2)^2=36 can be solved by squaring t-2 so we have the answer as t=8 ,-4 but suppose if I rather do like this that I square root 36 and remove the power on t-2 then or t- 2= 6 or t=8 here also i get the 8 result but i don't...

Please. Need help with quadratic word problem! [SIZE="5"]PLEASE HELP WITH THIS! An object is launched upward at 9.8 meters per second (m/s) from a 39.2-meter tall platform. a)write an equation representing this path b) What is the height of the object after 3 seconds c) For what time span is...

Homework Statement This is a real world problem and not a problem in a book, so if you feel I am missing some information just let me know. A ball is flying at 25 m/s The wind is blowing perpendicular to the trajectory at .44704 m/s \rho = \frac{1.17 kg}{{m}^3} Cd = 1/2...

How do you explicitly solve for x in terms of y using this quadratic formula? y = 2x2 + x I need to solve for x in order to find the inverse fxn. I know how to factor, but after that I'm stuck. Any suggestions? ~Jules~ * And what about polynomials of a higher order, like x3 +...

For a second order differential equation, is it necessary to derive a weak form if quadratic interpolation are used?

I couldn't figure out what to do with this type of integration \int (a x^{2}+ bx +c) ^{\frac{m}{n}}dx here m, n are integer numbers. Integration limit -∞ to +∞. Will Binomial expansion work? Please give me some clue.

Homework Statement Simplify \frac{-2\pm\sqrt{-56}}{30} \frac{-2\pm 2i\sqrt{14}}{30} \frac{-1\pm i\sqrt{14}}{15} Is this correct?

Homework Statement Here are two, unconnected example problems, having to do with quadratic inequalities. I'm confused b/c I understand how to solve them with an = sign, but as inequalities the book shows extra steps where signs get reversed and a total of ~ 4 possible answers come up instead...

Using the quadratic formula, solve the distance: x= distance needed to solve (also our y value in the formula) A= .5*k B= -m*g*sin(30) C= -m* g* d*sin(30) Where: k= 3000 m= 5 g=9.81 d=1.3 I get 48.13, but it says that I am wrong. what does everyone else get?

Homework Statement 2x^2 + 7x - 5 = A(x-1)^2 + Bx + C Homework Equations N/a The Attempt at a Solution This is an interesting equation as regardless of the whether I substitute x = 0 or x = 1 i still encounter the problem of not be able to make the calculation any easier. I...

Homework Statement For the function y = 1 / ((x-1)^2) what is: a) the sign of slope b) change in slope (increasing or decreasing) for the interval x > 1 Here is the graph: http://img7.imageshack.us/img7/3204/12491454.jpg Homework Equations None The Attempt...

Homework Statement By substituting y for 9x^2 solve 81x^4 - 63x^2 + 10 = 0 Homework Equations The Attempt at a Solution My attempt at a solution is: y^2 - 7y + 10 (y-2)(y-5) therefore y = 2 y = 5 Can someone double check this? Cheers

Let Q: R3 \rightarrow R be the quadratic form given by Q(x) = 2x1x2 + 2x1x3 + 2x2x3 where x = (x1x2x3)t How do I write down the matrix A of the quadratic form Q in the standard matrix E. and how do I find the numeric values for \lambda

Now what? Quadratic equation! Homework Statement A cannon having a muzzle speed of 1000 m/s is used to destroy a target on a mountaintop. The target is 2000m from the cannon horizontally and 800m above the ground. At what angle, relative to the ground, should the cannon be fired? Ignore air...

Homework Statement In the time interval from 0.0 s to 10.8 s, the acceleration of a particle traveling in a straight line is given by ax = (0.1 m/s3)t. Let to the right be the +x direction. The particle initially has a velocity to the right of 10.0 m/s and is located 4.8 m to the left of the...