Quadratic Definition and 989 Threads

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! 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 the...

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 The first part is to find a quadratic parametric curve f(t) = (p1(t),p2(t)) which passes through the points (0,0) (1,1) and (2,1). (hint: find two interpolating polynomials, one for x and one for y) Second part is to find the control points for the curve( ie. change...

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...

While a problem, this is more for me to learn to help my kid with her own homework. I used to be great at this sort of thing but for some reason I just can't get my head around this one. -125 = 39.1t - 4.9t^2 I need to find the value for t. It should be approx 10.4. I would just like to...

Homework Statement Solve the following equation for Z, find all solutions. z2 -2z + i = 0 Homework Equations [-b(+/-) sqrt(b2-4ac)]/2a The Attempt at a Solution Using the equation above, z = [2 (+/-) sqrt( (-2)2 - 4 (1) (i)) ]/ 2(1) =[2 (+/-) sqrt ( 4 - 4i)]/2 =...

Homework Statement Solve (a/2)x^2+vx-d=0 for x. Homework Equations Quadratic factoring, quadratic formula (?) The Attempt at a Solution I have no idea where to start with this question. It is probably the variables that are throwing me off, and as such I have no idea what I'm doing...

Homework Statement Factor. 2x^{2}+5x-12 I just took a semester off from school and I feel dumb. My recommendation to anyone reading is don't do that. Anyways, back to gr. 10 math :cry: Normally if I was going to factor this I would try to eliminate the coefficient of x^{2} but it...

Homework Statement consider a*z - b*conj(z) + c = 0 where a,b,c are unknown complex constants. find a formula for z in terms of a, b, c answer should be in the form "z = ..." where the ... does not contain any z or conj(z)Homework Equations I multiply the whole equation by z z*(a*z -...

[b]1. Solve: l2x^2+7x-15l<10 [b]3. I split it up into two cases and got: 2x^2+7x-25<0 and 2x^2+7x-5>0 With the quadratic formula I got: x= [-7+/- (249)^(1/2)]/4 and x= [-7+/- (89)^(1/2)]/4 These clearly are the answers, but I am confused about the inequality from this...

Hi guys, I'm currently on holiday and my exam starts right after holidays. I bought this book to do some exercise but they only provided answers without solutions. So i wonder if you guys could help me :) 1. If 3 + \sqrt{3} is a root of the equation 2x2 + 3ax + 3b = 0, where a and b are...

Hi! I have this Math 11 problem. I do my math through Distance Ed. and there are no examples like this one in the supplied lessons. If anyone could help me with this question, that would be great! Homework Statement Find the equation of the quadratic function with a vertex at (1,3) passing...

Hi guys what's up. I just have a small question i wish to ask. If you are given vertex(-2,3) and it passes through point(2,5) how do you determine its equation? Its been around 6 months since i last did some math so i am having a hard time remembering. I am not asking you guys to solve it but...

hey guys, could u use the quadratic formula; x = -b +/- sqrt (-b2 - 4ac) 2a for the following questions; y = 4x2 - x y = 4x2 -1 y = x2 + 4 and y = -2x2 + 4x i ask this as there is no value for (c)...

I know this is probably really easy, but i just can't figure it out.. Homework Statement Find values of k for which (5 + 4x - x^2 = k) has equal roots. I know the answer is k = 9 but i don't know how to get there.. Homework Equations ax^2 + bx + c = 0 Discriminant = b^2 - 4ac...

Homework Statement Find the roots and the vertex for 3x^2 + 5x - 2 Homework Equations ax^2 + bx + c a(x - h) + k The Attempt at a Solution OK, this is what I attempted. 3x^2 + 5x - 2 = 0 3x^2 + 6x - x - 2 = 0 3x(x+2) - 1(x+2) = 0 x = 1/3 and x = -2 OK, so I found the roots...

First of all, I searched the forums and couldn't really find one on how to approach a quadratic equation that has brackets. Here is the equation: y=(x+1)2 - 2 My teacher told me to factorize by sight in pairs and i used this equation for it: ax2+bx+c. I think c=-2 but I don't know how to get...

I understand how the discriminant, b^{2}-4ac, comes from in the quadratic equation ax^{2}+bx+c=0, but how does it come from the general quadratic equation ax^{2}+bxy+cy^{2}+dx+ey+f=0 ?

The general quadratic equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 How is this derived? How does the discriminant, B2 – 4AC determine the class of the conic section?

Homework Statement An object falls from height h from rest. If it travels .50h in the last 1.00 s, find (a) the time and (b) the height of its fall. Explain the physically unacceptable solution of the quadratic equation in t that you obtain. Homework Equations Pretty much any free...

Quadratic equation and absolute value... Consider equation |x2-2x-3|=m, m belongs to R If the given equation has no solution then find the interval in which the m lies. 2. Homework Equations -Given in question 3. Since this equation is in modulus there would be two equations...

can someone pls tell me how you can get the value of 'a' or the gradient in a quadratic equation by analysing the quadratic graph as a reminder the equation is y=ax^{}2+ bx + c

Homework Statement A baseball of mass 0.145kg and radius 0.0366m is dropped from a tower 381m high. Homework Equations The Attempt at a Solution Work=integral(from 0 to 381): c(2) (terminal velocity)^3*(tanh(t/(characteristic time)))^3 with respect to time. Gets me really...

Homework Statement Lets say you have Ax + Bx^2 + C = 0 Usually I would use the Quadratic formula in this situation. But what if you do this x( A + Bx ) + C = 0 x( A + Bx ) = -C Couldn't you then say x = -C and A + Bx = -C x = (-C - A) / B ?

Homework Statement Integrate: (x-1) / (X^2 - 4x +5) The attempt at a solution Normally I would try to factor this into something like (x-1) (x+3) (That's an example completely unrelated to this problem.) However, as no easy factors quickly occurred to me I did a run through of the...

A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R = -40c^2 = 720c describes the relationship between the cost of tickets, c dollars, and the amount of...

Homework Statement 2iz^2 - (3-8i)z -6 + 7i Homework Equations z = \frac{-b +/- \sqrt{b^2 - 4ac}}{2a} The Attempt at a Solution Right, here goes... a = 2i b = -3 + 8i (is this correct? Or would it be better to leave it as 3-8i?) c = (-6 + 7i) so using these: z =...

Homework Statement Solve the equation ax2 + bx + c = 0. The following are the given information: (a) a = 1 (b) One root is twice the other root. (c) c = 2 You are NOT required to solve the problem but to decide whether: 1) The given information is all needed to solve the problem. In...

I've been having trouble understanding why my answers are always different to the solutions and I found that there's two equations: {-b ± SQRT(b^2 - 4ac)}/2a and {-b ± SQRT(b^2 -ac)}/2a I don't know when to use either equation, always having used the first, and for someone at my level to...

If a(12a+5b+2c)>0 and the equation ax^2+bx+c=0 has roots y and z , then find out the range of the roots of the equation ...

Homework Statement If x is real and p = \frac{3(x^{2}+1)}{2x-1}, prove that p2 - 3(p+3) \geq 0. Homework Equations ax2 + bx + c = 0 x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} Nature of the Roots of a Quadratic Equation: If b2 - 4ac is positive, quadratic equation has two real &...

Hi everybody, I'm trying to minimize a function with multiple variables. My goal is to approximate on the L2 norm a matrix by the outer product of 2 vectors (or is it called tensor product ?). So I have to determine a vector y = (y1,...,yn) and a vector x = (x1,...,xm) such that their...

I'm not sure how you apply the rules of a derivative on a quadratic form. I've been trying to find the solution on google but no luck: Basicallly: J=\frac{1}{2} (z-X \theta)^T (z-X \theta) and \frac{ \partial J}{\partial \theta}= -X^T z +X^TX\theta I can't for the life of me...