Quadratic Definition and 965 Threads

Homework Statement Solve the equation 2cos^2\theta + 5cos\theta - 3 = 0\ for\ \frac{3\pi}{2}<\theta<5\pi Homework Equations quadratic equation, power reduction formula: cos^2\theta = \frac {1+cos2\theta}{2} The Attempt at a Solution First I tried using the quadratic...

Homework Statement Basically I have to fill out this ax^2+bx+c using the given numbers -8,-4,-3,1,2,5,6,7,9 The solution must be the one provided So it works like this (example is just with regular addition) 1 2 3=5 8 9 = 18 Here is the problem...

Let F be a field. Suppose f(x)=ax^2+bx+c is an element of F[x] with (2a) a unit in F, and set delta=b^2-4ac. Prove the following version of the quadratic formula. Hint: for (a) and (b) use the identity 4a x f(x)=(2ax+b)^2-delta. (a) If there is a k in F such that k^2=delta, then (-b plus or...

Hi all, I am trying to generalize a geometric concept found on page 7 from Steven Weinberg's "Gravitation and Cosmology" from 2 to 3 dimensions. At the end I am stuck with the following set of equations: 1: a1+a2z32+a3z3z4+a4z42=0 2: b1+b2z32+b3z3z5+b4z52=0 3: c1+c2z32+c3z3z6+c4z62=0...

Homework Statement Consider the general quadratic function f(x)=ax2+bx+c with a>0. By calculating the minimum value of this function, show that f(x)\geq0 for all x if and only if b2-4ac\leq0 Homework Equations The Attempt at a Solution I know that the min for a quadratic equation...

Hello everybody. I found this example online and I was looking for some clarification. Assume 32 = \alpha\beta for \alpha,\beta relatively prime quadratic integers in \mathbb{Q}[i]. It can be shown that \alpha = \epsilon \gamma^2 for some unit \epsilon and some quadratic \gamma in...

Homework Statement Jillian is getting ready to send a holiday package in the mail. The rectangular package has a square base and the sum of all the edges of the package measures 140 cm. What dimensions will produce a package with the largest possible surface area? Homework Equations...

We have two unknown vectors x,y with real non negative values. We can assume ||x||=||y||=1. There are m known nxn matrices with real values. We have m equations of the form: yTA1x=0 ... yTAmx=0 What are the conditions for the existence of solutions for x,y? What is the minimal number m...

Homework Statement Ok, the problem is you have a 30cm wire, you cut it in two and you make one into a square. The second part is a rectangle with a 2:1 side ratio. I need to find the perimeter of each of the two shapes if the outcome sum of areas were to be a minimum. The Attempt at a...

Hello PhysicsForums! I had posted a question earlier today in another thread and I had a follow up question to it (the question in nature isn't extremely related, but the link can be found https://www.physicsforums.com/showthread.php?p=2964009#post2964009"). In the previous example, it was...

In the Searle's 1971 book Linear Model, page 57, has a formula for the Variance of Quadratic form: var(Y^{T}AY)=2tr(A\SigmaA\Sigma)+4\mu^{T}A\SigmaA\mu The proof of this showed on page 55 was based on MGF. I'm looking for proofs are less complicated. Some thing that is similar to show the...

Ive got a few questions id like checking please but i start with the one I got no clue about :S 1)Slove the equation x(x-2)=2-x So i asumme i slove it to zero, x^2-x-2=0 B)Use the solution to part A and the illustrated grapg to write down the solutions of I) X(x-2)<2-x II)X(x-2)>0...

Homework Statement The problem is 3^2x+3^(x+1)-4=0 I know I had to solve it by substitution Homework Equations The Attempt at a Solution I had u = 3^x I put it in: (u )(u ), but I was not sure how to get the middle term 3^(x+1)

Hello PhysicsForums! I was reading up on UFD's and I came up with a few quick questions. 1. Why don't the integers of Q[\sqrt{-5}] form a UFD? I was trying to tie in the quadratic integers that divide 6 to help me understand this, but I am stuck. 2. Why is Z a UFD? 3. Assuming Q[\sqrt{d}] is...

Homework Statement I have to show a proof that if a is odd, b is even, and c is even but not divisible by 4. a,b,c are int coefficients ax2 + bx + c = 0 has no rational solutions Homework Equations all letters here are integers. So i have, a = 2d + 1 b = 2f c = 2g, but c...

MAJOR EDIT: I fixed my position integral and got the answer to 1.ii) Homework Statement A parachutist jumps from a helicopter that's not moving. The mass of the person is 80kg, the quadratic drag is f = -Cv^2 where C = 3,52. Neglect the Earth's rotation effect. The parachute is opened as soon...

Homework Statement i need to find the laplace transform of this equation by using the partial fraction. it is an irreducible quadratic factor that i don't really know how to solve it. Homework Equations [(s+1)^2 + 6]/[(s+1)^2 +4]^2 The Attempt at a Solution please help me, thanks. =)

Homework Statement Skydiver #1 from the University Skydiving Club steps out of a plane when it is 1 miles above the ground and 10 seconds later skydiver #2 steps out of a plane (at the same height). They both want to land on the ground at the same time. To make an estimate assume that...

Homework Statement Given that: f(x) = 2(1-x) for 0 < x < k ...0 for otherwise sketch the graph of f(x) and find: (i) the value of k, (ii) the median of x Homework Equations The Attempt at a Solution (i) I sketched the graph and got a line from (0,2) to...

Homework Statement A block of mass m slides on a horizontal surface that's been lubricated with a heavy oil so that the block suffers a viscous resistance that varies as the 3/2 power of the speed. If the initial speed of the block is Vo at x=o, show that the block cannot travel further...

Homework Statement If one of the roots of the quadratic equation, ax^2+bx+c=0 is m+ni, show that the other root is m-ni. Homework Equations The Attempt at a Solution How do i actually show this? I mean it's a well known fact and a direct outcome of the quadratic formula. Is this...

Homework Statement Given that for all values of x: 3x^2 + 12x + 5 = p(x +q)^2 + r a) find the values of p, q and r b) solve the equation 3x^2 + 12x + 5 = 0 The Attempt at a Solution I'm completely lost here but here's my attempt at a solution - I'm pretty sure that I did it...

Homework Statement The solution of the quadratic equation x2 - 11x + 22 = 0 are x = 3 or x = 6. What is the base of the numbers? Homework Equations Knowledge of how to convert from a generic base to decimal? The Attempt at a Solution I tried to just place r in where I would...

Homework Statement For the function y= |x2-4x+3| a. Sketch the function b. Is the function continuous? Explain. c. Is the function differentiable everywhere? explain d. find gradient of curve at the point where x = 3/2 Homework Equations chain rule, differentiating... The...

Homework Statement ......49ac-12b2 (4α-3β)(3α-4β) =------------------------ .......a2 Deduce that, If 12b2< 49ac< 49b2/2 then β lies between 3α/4 and 4α/3 Homework Equations α+β = -b/a αβ = c/a The Attempt at a Solution

Homework Statement 2n=n2 Homework Equations The Attempt at a Solution I know the solution is 2 and 4. But I have no idea how to solve it without guessing...

Hello, I'm looking to derive the error of a quadratic equation as a function of x. y=ax2+bx+c y is measured and variables a,b,c have an associated error Da,Db,Dc To solve for x you complete the square. x=&\pm\sqrt{\dfrac{y-c}{a}+\dfrac{b^{2}}{4a^{2}}}\mp\dfrac{b}{2a} If the variables y,c...

Homework Statement How do I simplify the transformation of this equation? y=-2[-1/3(x+2)]^2-4 Homework Equations af(k(x-d))+c The Attempt at a Solution If this was a linear equation I would simply distribute the -1/3 into (x+2) and then distribute -2 into the (-1/3x -2/3)...

Do know anybody explicit form of variation action quadratic in Riemann tensors (for general dimension)? Link to internet sources? Or computer program for symbolic and tensors algebra, which the variation tell me (preferably open-source)? Thx

Hi, I'm slowly reading through the book What is Mathematics which asks the following question at the end of its quadratic residues section. I'm not sure how to begin it really, so any hints/suggestions would be greatly appreciated. Homework Statement We have seen that x^{2} \equiv (p -...

Need help solving some. I'll put up one for now. a/b-x + b/a-x = 2 I'm just looking for how to solve it, because I always reach 2x^2 - 3ax - 3bx + a^2 + b^2 + 2ab = 0 and get stuck. Please show me your steps. Thanks!

How can I found out in which p-adic fields a quadratic form represent 0? For example in which p-adic fields does the form 3x2+7y2-15z2 represent zero?

I am trying to write this program, it runs fine but I can't get the imaginary numbers to print correctly. I have been trying this for a few hours now and can't figure it out. Here is the code, I am running Force 2.0. Thanks in advance for the help. Program Quad Implicit None...

Hi everyone, For some reason I can't put this together in my head. I have a series of equations that can be solved directly, but my resulting equation is of the form: Ax^2 + Bx + Cx^(-1) + D = 0 Obviously the C/x term is the one throwing the wrench in the works here. Could anyone...

Homework Statement Given that the quadratic equation (m^2-3m-4)x^2+(m^2+2)x+12=0 has real roots a and b .Find the set of values of m such that a<-1<b Homework Equations The Attempt at a Solution By using the fact this equation has two real roots ,b^2-4ac>0.That's all i can see...

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