Quadratic Definition and 990 Threads

Hi: I want to know the quadratic covariation of Brownian motion B(t) and poisson process N(t).Is it B(t)? Thanks !

For the theorem that states that in quadratic field Q[sqrt d], if d is congruent to 1 mod 4, then it is in the form (a + b sqrt d)/2 and if it's not, it's in the form a + b sqrt d where a and b are rational integers, is it saying that if a and b are rational integers and the quadratic number are...

Homework Statement 4n^2+9m^2-240n-720m+18000=0 Find n+m Homework Equations The Attempt at a Solution I try to express the equation in the form of a(n+m)^2-b(n+m)+c=0 but i couldn't find a way to do so .

Quadratic "Proof" Homework Statement Show that if a>0, then ax^2 + bx + c \geq 0 for all values of x if and only if b^2 - 4ac \leq 0 http://www.math.toronto.edu/~drorbn/classes/0405/157AnalysisI/HW2/HW.html Homework Equations I believe I'm supposed to be working only with basic...

FUN solving Quadratic equations :) Homework Statement Marnie can walk 1km/h faster than Jon. She completes a 20 km hike 1 hour before him. Write an equation ans solve it and find their walking speeds. Homework Equations speed= distance/time the quadratic equation The Attempt at a...

Homework Statement What I'm supposed to do is to rearrange the this formula -16t^2+Vt+h and solve it for V. V= Initial Velocity t= time (throwing the ball in a parabolic arc) h= height I know what the height is and it is 6ft. I also have the time which is 2.03 seconds. How do I rearrange...

express the following in terms of alpha1 x beta1 and alpha2 x beta2 alpha1 x alpha 2=beta1 x beta2

Homework Statement What are the meanings of each of the parameters in the Y = At^2 + Bt + C equation? example: A = -4.8 B = 21.9 C = -23.8 I know that B is suppose to represent the initial velocity, but not sure about the other 2. Is A supposed to represent acceleration?

Homework Statement The quadratic equation x^2 + kx + 2k = 0 where k is a non-zero constant, has roots \alpha and \beta. Find a quadratic equation with roots \frac{\alpha}{\beta} and \frac{\beta}{\alpha}. {one is meant to be inverted - the code isn't working properly :( } Homework...

Okay so this seems like a very simple problem to me but I can't figure it out so I definitely need some help. I'm not a mathematician but a programmer and in this case I need to figure out how to get the curve that passes through 3 points. I know this can be done easily with substitution but...

Homework Statement The quadratric equation x^2 - 5x + 7 = 0 has the roots α and β. Find the quadratic equation with roots α^3 and β^3. Homework Equations N/a The Attempt at a Solution u = α^3 α = u^(1/3) u^(2/3) - 5(1/3) + 7 = 0 u^(1/3)[u - 5] = -7 --- minus 7 off each...

I am trying to derive an equation of motion for a simple electrostatic potential well. Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space). In 1 dimension, the...

Homework Statement Make a change of variable that transforms the quadratic form with no cross-product term: 9x1^2 - 8x1x2 = 3x2^2 Homework Equations A = PDP^-1 Q = y^TDy The Attempt at a Solution I know the answer. This is a question regarding concept. The eigenvalues for...

Homework Statement Find the time required for a train to reach 100m if V0=20m/s and acceleration is 0.5m/s2 Homework Equations s=v0t+(1/2)at2 The Attempt at a Solution i am not sure of how to go about getting s=(20)t+(1/2)0.5t2 into quadratic form for use in the quadratic formula...

Homework Statement 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. Homework Equations The Attempt at a Solution I know it equals 7(x-z)^2 -2(y-5z)^2 +3z^2. dnt know how to get there though

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]...

Hi dudes. I'm studying the paper of Witten: 2+1 Dimensional gravity as an exactly soluble system. Before eq (2.8) the author justifies as a way to find the inner product the fact that in this theory we have the casimir \epsilon_{abc}P^aJ^b. Then he introduce the invariant quadratic form...

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...

This is a general question. When using the optimal method to design a controller, specifically a linear quadratic regulator, you usually have a state-space representation of a system, and a cost function to minimize. The cost function usually takes the (quadratic) form: I don't...

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 Find the matrix that represents the given quadratic form relative to the variables yi. a) q(x_1, x_2, x_3) = 4x_1x_2 - 2x_1x_3 + {x_2}^2 +2x_3x_2 x_1 = y_1 x_2 = -y_1 + y_2 + 2y_3 x_3 = -y_1 + 2y_2 + 2y_3 Homework Equations The Attempt at a...

Homework Statement Suppose that for each v = (x1, x1, ... xn) in Rn, q(v) = XTAX for the given matrix A. For the given basis B of Rn, find the expression for q(v) in terms of the coordiantes yi of v relative to B. a) A =...

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} ? In this case M_{\mu\nu} is constant. When it is...

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.

Can someone please help me out with mass terms in the general case for a lagrangian? It is known that for n scalar fields, any quadratic in these fields will be a mass term. For classical fields \varphi_{j} with the most general possible expression being M^{jk}\varphi_{j}\varphi_{k} , the...

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 Show that the most general two-dimensional quadratic map with a constant Jacobian is the Henon map: xn+1=yn+1-ax2n yn+1=bxn, where a,b are positive constants. [/b] Homework Equations From the general quadratic map, xn+1=f1+a1xn+b1yn+c1x2n+d1xnyn+e1y2n...