Quadratic Definition and 965 Threads

Homework Statement Find the minimum value of ## x_1^2+x_2^2+x_3^2## subject to the constraint: ## q(x_1,x_2,x_3)=7x_1^2+3x_2^2+7x_3^2+2x_1x_2+4x_2x_3=1 ## Homework EquationsThe Attempt at a Solution I am not really sure how to think about it. I have seen the opposite way but have not seen this...

Hi, I'm looking for the real solutions to the system \begin{array}{rcl} 1 & = & v_1+v_2+v_3+v_4+v_5 \\ 1 & = & v_1^2+v_2^2+v_3^2+v_4^2+v_5^2 \end{array} Background: I'm looking at a Newton's cradle with 5 balls, each of mass ##m=1##. The first ball is pulled away and let go such that it hits...

Homework Statement How many points of intersection does the line y = x have with the parabola y = 6x − x2 −10 ? A) none B) one C) two D) three E) more than three Homework EquationsThe Attempt at a Solution x = 6x - x^2 - 10 -x^2+5x - 10 Used b^2 - 4ac to check the number of intersections. The...

I have a doubt... Look this matrix equation: \begin{bmatrix} A\\ B \end{bmatrix} = \begin{bmatrix} +\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\ +\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} \begin{bmatrix} X\\ Y \end{bmatrix} = \begin{bmatrix}...

Homework Statement (x2+3x+3)1/3 + (2x2+3x+2)1/3 = 6x2+12x+8 2.Relevant equationsThe Attempt at a Solution (x2+3x+3)1/3 -1 +(2x2+3x+2)1/3 -1 = 6x2+12x+6 (x2+3x+2)/((((x2+3x+3)1/3)2 + (x2+3x+3)1/3 +1) + (2x2 +3x+1)/((((2x2+3x+2)1/3)2)+(2x2+3x+2)1/3 +1) -6(x+1)2=0 then x=-1 or...

Hi! I am trying to build a better understanding of quadratic functions. So I had this idea of trying to fit a quadratic function to two arbitrary points, but I am not sure how this really works. Given the points (-4,1) and (12,1) on a Cartesian plane, how can a quadratic function be defined...

Hi I'm having trouble visualizing why in a function such as 1/(1-x2) linear approximation of 1/(1-u) where u = x2 is the same as quadratic approximation of 1/(1-x2) The linear approximation is 1+u or 1+x2 Quadratic approximation is the same, 1+x2 Can someone explain to me why this happens...

$\alpha$ and $\beta$ are the roots of the equation $2{x}^{2}-5x+c=0$. If $4\alpha-2\beta=7$, find the value of $c$. I did the following: $\alpha+\beta=-\frac{-5}{2}=\frac{5}{2}$ $\alpha\beta=\frac{c}{2}$ $\frac{c}{2}=\frac{7+2\beta}{4}\cdot\frac{-7+4\alpha}{2}$...

Homework Statement if x1 and x2 are solutions to 1) x² + x + 1 = 0, then 2) y1 = ax1 + x2 and 3) y2 = x1 + ax2 are solutions to which quadratic equation? Homework Equations ax² + bx + c = 0 x1∕2 = (−b ± √(b² - 4ac))/2a The Attempt at a Solution Well, firstly i solved for x1 and x2 getting...

How do I get D by itself? This one's got me baffled [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)

Homework Statement Show that all ##n \times n## unitary matrices ##U## leave invariant the quadratic form ##|x_{1}|^{2} + |x_{2}|^{2} + \cdots + |x_{n}|^{2}##, that is, that if ##x'=Ux##, then ##|x'|^{2}=|x|^{2}##. Homework Equations The Attempt at a Solution ##|x'|^{2} = (x')^{\dagger}(x')...

Homework Statement Show that all ##n \times n## (real) orthogonal matrices ##O## leave invariant the quadratic form ##x_{1}^{2} + x_{2}^{2}+ \cdots + x_{n}^{2}##, that is, that if ##x'=Ox##, then ##x'^{2}=x^{2}##. Homework Equations The Attempt at a Solution ##x'^{2} = (x')^{T}(x') =...

Homework Statement Homework Equations Not Sure. The Attempt at a Solution For the first question I know you have to multiply the conjugate of the denominator so it would be (2 - √5)/(1−2√5) x (1−2√5)/(1−2√5) but I'm not sure how to actually do that. For the second question. I have that...

Homework Statement Calculating the roots of a quadratic with complex coefficients Homework Equations x^2 - (5i+14)x+2(5i+12)=0 The Attempt at a Solution I tried the quadratic solution but it gives too complicated solutions. I have no idea on how to do this...

Can someone explain to be in detail what is quadratic inequality? It's rather confusing. Thank you

Homework Statement How to solve this kind of inequality? x²-4x+3≤(3x+5)(2x-3)Homework EquationsThe Attempt at a Solution :[/B] I'm confused. Should I factor the left side or should I FOIL the right side then equate it to zero to find the critical numbers? Help pleaasee.

Fundamental theorem of calculus: \int_a^b \frac{df}{dx} dx = f(b) - f(a) All right? Everybody knows... BUT, BUT, exist some analog of the FTC for this case: \int_a^b \left( \frac{df}{dx} \right)^2 dx = ? Hum?

m^4+4m^3+8m^2+8m+4=0

Homework Statement [/B] A baseball of mass m is thrown straight up with an initial velocity v0. Assuming that the air drag on the ball varies quadratically with speed (f = cv^2), show that the speed varies with height according to the equations. Where x_{0} is the highest point and k = c/m...

Homework Statement [/B] As attached Homework EquationsThe Attempt at a Solution [/B] The answer is stated as option A. However, my solution is -6≤x≤3; I can seems to find an option that fits the solution.

Let $$ f(x)$$ and $$ g(x)$$ be quadratic functions such as the inequality $$ \left| f(x) \right| \ge \left| g(x) \right| $$ is hold for all real $$ x$$ . Prove that $$ \left| \Delta_f \right| \ge \left| \Delta_g \right|$$. For quadratic function $$ f(x)=ax^2+bx+c $$, then $$ \Delta=b^2-4ac. $$...

I heard that proportionality of kinetic energy with square of velocity, ##E_k\propto v^2##, can be derived with help of quadratic forms. It goes like: we guess that ##E_k\propto v^2## and we assume that momentum ##p\propto v##, then equation is valid in another inertial system. And so on. The...

$$\cos\left({4x}\right) =8\sin^4\left({x}\right) -8\sin^2\left({x}\right) +1$$ I thought this would break down nice from the quadratic but it didn't.

Is possible classify the quadric equation Axx + Bxy + Cyx + Dyy + Ex + Fy + G = 0 how straight, hyperbola, circle, ellipse, parabola, etc, in the same way that is did in the phase plan: https://upload.wikimedia.org/wikipedia/commons/3/35/Phase_plane_nodes.svg...

Hi, This is not coursework, just private study. Ok, I understand that q is a quadratic residue MOD n if x^2 = q MOD n What I don't understand is how to figure this out? I read a paper that states "8 is a quadratic residue mod 17, since 5^2 = 8 MOD 17", fair enough. It then goes on to state...

Homework Statement Hello! One of the easiest rules (when possible to apply) to factor a quadratic is to find both x-s by x1 + x2 = b x1 * x2 = c Homework Equations Please, take a look at what is written in the book. I can't grasp why x1 = -2 and x2 = 3, and not, as I thought, x1 = -3 and x2...

Homework Statement Find diagonal shape of next quadratic form ( using eigenvalues and eigenvectors) Q(x,y)= 5x2 + 2y2 + 4xy. What is curve { (x,y)∈ ℝ| Q(x,y)= λ1λ2, where λ1 and λ2 are eigenvalues of simetric matrix joined to quadratic form Q. Draw given curve in plane. The Attempt at a...

Homework Statement Given a series of mathematical statements, some of which are true and some of which are false. Prove or Disprove: 1. A sufficient condition that ax2+bx+c=0 (a≠0) have a real root is that b2-4ac>5. 2.A necessary condition that ax2+bx+c=0 (a≠0) have a real root is that...

A train travels a distance of 480km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train. Represent this situation in the form of quadratic equation. So I have been trying this but couldn't find...

Im to solve ##(k+l)^{2}e^{-ila}-(k-l)^{2}e^{ila}=0##, for ## k##, The solution is ##k=l(e^{ial}-1)/(e^{ial}+1)=il tan(al/2)## FIRST QUESTION So it's a quadratic in k, should be simple enough, my working so far using the quad. formula is ##k= (4l^{2}(e^{-ila}+e^{ila})\pm...

Homework Statement If a and b are both quadratic residues/nonresidues mod p & q where p and q are distinct odd primes and a and b are not divisible by p or q, Then x2 = ab (mod pq) Homework Equations Legendre symbols: (a/p) = (b/p) and (a/q) = (b/q) quadratic residue means x2 = a (mod p) The...

Basic question, I think, but I'm not sure. It is a step in a demonstration, so it would be nice if it were true. True or false? Why? If A is a real, symmetric, nonsingular matrix, then xTAx≠0 for x≠0.

Not homework but given the question it probably fits here best Given the following equation $$x^2+138x+317=y^2$$ How do you find the integer solutions? For example wolframalpha has the solutions. but I cannot see how they are derived http://www.wolframalpha.com/input/?i=x^2+138x+317=y^2 By...

Homework Statement I am working on a little project in which I analyze a video I found online and try to determine if it is real of a hoax. The video I am analyzing includes a man throwing a football off of a football stadium (at the very top) and making it into a basketball hoop at field...

Hello, I'm having some trouble on this question, and I'd imagine it's just because I'm looking at it incorrectly. The problem statement is: The quadratic function f(x) = p + qx - x2 has a maximum value of 5 when x = 3 (i.e. vertex at (3, 5), right?) Find the value of p and the value of q...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] Hi, I'm having difficulty solving the following quadratic equation x^2-(660/x-5)-91=0. The fact that the middle term has an x-5 rather than just an x that is throwing me Can anyone please...

This may be a bit vague but can anyone explain this sentence to me http://en.wikipedia.org/wiki/Quadratic_residue:"Modulo 2, every integer is a quadratic residue. Modulo an odd prime number p there are (p + 1)/2 residues (including 0) and (p − 1)/2 nonresidues." If this is to vague I apologize.

So this problem was a 2 part question. The first part goes as such. 1. A gun is fired straight up. Assuming that the air drag on the bullet varies quadratically with speed, show that the speed varies with height according to the equations: v2 = Ae-2kx - (g/k) (upward motion) v2 = (g/k) -...

Homework Statement Hi everyone, I am doing a lab currently (and it looks like a few other people on here have had similar questions...) and I'm having trouble with one of the concepts. I had to drop a ball from a height and measure the movement with a motion sensor, which was graphed with the...

I understand how to solve these equations when the square is on this side of the equal sign: x2 + 8x + 7 = 27 But when the square is on the other side, I am thrown. Like this one... x2 = 14x - 33 The solutions manual shows the next step as the following, but what do you do to get to this...

Solve (x+3)^2 = 4x+17 where did i go wrong? (x+3)(x+3 )= 4x+17 x^2 + 3x + 3x + 9 = 4x+17 x^2 + 6x + 9 = 4x + 17 x^2 + 6x + 9 - 4x - 17 = 0 x^2 + 2x - 8 = 0 (x-2)(x+4) <-- USING THE CROSS METHOD x= -2, 4 is my cross method working incorrect or something? do explain my mistake

Homework Statement The Attempt at a Solution Looks like the graph would be a parabola? And since it's a>0 it would be upward and therefore a minimum. Not sure what that would be. Unsure how to solve the rest[/B]

Homework Statement Dear Mentors and PF helpers, Here's the question: The roots of a quadratic equation $$3x^2-\sqrt{24}x-2=0$$ are m and n where m > n . Without using a calculator, a) show that $$1/m+1/n=-\sqrt{6}$$ b) find the value of 4/m - 2/n in the form $$\sqrt{a}-\sqrt{b}$$ Homework...

I'm going through an explanation in a number theory book about Tonelli's algorithm to find the square roots of a quadratic residue modulo ##p## where ##p## is prime, i.e. I want to solve ##x^2 \equiv a \pmod{p}## with ##(\frac{a}{p}) = 1##. The book goes as follows: Let ##p - 1 = 2^s t##, where...

I mainly just need some clarification here. I was doing my homework and then browsing the web to find an answer to my problem and came across mathewarehouse' definition of Standard form and then I looked at my homework and went..."huh?" I don't understand if my homework is listening this wrong...

Find constants $P,\,Q,\,R,\,S, a,\,b$ such that $P(x-a)^2+Q(x-b)^2=5x^2+8x+14$ $R(x-a)^2+S(x-b)^2=x^2+10x+7$

Homework Statement Dear Mentors and PF helpers, I saw this question on a book but couldn't understand one part of it. Here the question: Solve the following inequality I copied the solution as belowHomework Equations The Attempt at a Solution I don't understand why the numerator in step...

Homework Statement A Stark effect experiment is performed on the rubidium D1 line ##(5p \ {}^2P_{1/2} → 5s \ {}^2S_{1/2})## at 780.023 nm. Given that the polarizabilities of the ##5p \ {}^2P_{1/2}## and ##5s \ {}^2S_{1/2}## levels are ##6.86 × 10^{−16}## and ##2.78 × 10^{−16} cm−1 m^2 V^{−2}##...

Homework Statement A player hits a volleyball when it is 4 ft above the ground with an initial vertical velocity of 20 ft/s (equation would be h = -16t2 + 20t + 4). What is the maximum height of the ball? Homework Equations quadratic formula The Attempt at a Solution t = -20 ±√202 - 4(-16)(4)...

hi! i don't quite know how to start solving for this. i understand the problem and what it's asking for but i have no idea how to start solving for it. In a volleyball game, a player from one team spikes the ball over the net when the ball is 10 feet above the court. The spike drives the ball...