Quadratic Definition and 965 Threads

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...

Homework Statement A sphere of radius 0.2 cm is fired straight up with speed v0. What is its speed when it hits the ground? (Include quadratic air resistance but ignore linear air resistance.)Homework Equations Quadratic air resistance: FR = cv2 c = 0.5CpA = 4.05 x 10-6The Attempt at a...

Homework Statement Let F(x, y, z) be a quadratic form and A its associated matrix. The inertia of A, denoted in(A), is defined as the triple in(A) = (n1, n2, n3) where n1, n2, n3 denotes the number of positive, negative, and zero eigenvalues of A respectively. Prove the following: If...

Homework Statement Classify the quadratic surface: 2x^2 + 4y^2 - 5z^2 + 3xy - 2xz + 4yz = 2 Homework Equations A quadratic form is a second degree polynomial equation in three variables which has the form F(x,y,z) = ax^2 + by^2 + cz^2 + 2dxy + 2exz + 2fyz where coefficients a...

Homework Statement Let the quadratic form F(x,y,z) be given as F(x,y,z) = 2x^2 + 3y^2 + 5z^2 - xy -xz - yz. Find the transitional matrix that would transform this form to a diagonal form. Homework Equations A quadratic form is a second degree polynomial equation in three...

An object accelerates at the rate of 1.30 m/s^2 over a displacement of 11.8m, reaching a final velocity of 7.00 m/s. For what length of time was it accelerating? Explain the answers. NOTE: Actually, when I first was about to post this, I finally had gotten the answer I needed. However, I cannot...

Okay, this is something that's been bugging me for a while. A lot of the polynomials with higher powers can't be solved using algebraic methods and must be estimated. So my idea was to take these answers and find a way to convert them into an exact form, such as quadratic irrationals/surds...

I seem to have forgotten the rule to find a Turning point in a quadratic graph. Can anyone help me?

Let P^ + ,P^ - ,I,Q \in R^{n\times n}, K\in R^{n\times 1}, M\in R^{1 \times n}, and assume that Q is positive definite, P^ - is positive semidefinite whence (MP^ - M^T + Q)^{ - 1} exists (where T denotes transpose). In what sense does K = P^ - M^T(MP^ - M^T + Q)^{ - 1} minimize the quadratic...

Hello PF, Ok so here is my problem. I have an array of data points which are the chi^2 values for a fit I have performed. I wish to calculate the 1-sigma error for this fit, so I figure I could find the lowest chi^2 value, and the two points either side that value, and fit a quadratic...

Homework Statement It Costs a bus company $225 to run a minibus on a ski trip, plus $30 per passenger. the bus has seating for 22 passengers, and the company charges $60 per fare if the bus is full. For each empty seat, the company has to increase ticket price by $5. How many empty seats...

Homework Statement A company sells running shoes to dealers at a rate f $40 per pair if fewer than 50 pairs are ordered. If a dealer orders 50 or more pairs (up to 600), the price per pair is reduced at a rate of 4 cents times the number ordered. What size order will produce the maximum...

Homework Statement A light bulb is wired in series with a 144Ohm resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4W. What is ther resistance of the light bulb? Note that there are two possible answers. Homework Equations P = I^2R...

[b]1. A farmer grows orange trees. He has 20 trees/hectare with 300 oranges/tree. When adding another tree to a hectare, the amount of oranges decreases by ten. What is the max yield of trees. (They want to know how many trees they should have in a hectare to maximize their orange production.)...

[b]1. Suppose y = bx^2 +cx + a a.) in terms of a, b, and c, what values of x make y=0? b.) if a=3.1, b= -2.2 and c=-4.3 evaluate those solutions to 3 significant digits: Homework Equations [b]3. I am not really sure how to solve for what the question is asking for in part...

Homework Statement Identify the vertex and x-intercept(s) of the quadratic function algebraically. Homework Equations f(x) = 1/2x^2 - 4 1/2 Is the coefficent if its not clear. The Attempt at a Solution Ok I do not need help finding the vertex I have already got that, I...

Homework Statement I have a probability distribution function (PDF) going fromi 0 to a on the y-axis and 0 to 30 on the x-axis. The function describing the PDF is the quadratic equation f(x) = a+bx+cx^2 I have to find a, b, and c. Homework Equations The Attempt at a Solution...

Hi all, I need to construct the Casimir op. of group SU(3). I have these relations; T2=\sum C_{i}_{j}T_{i}T_{j} i,j=1,2...,8 ...eq1 [Ti , Tj]= \sum f_{i,j,k} T_{k} ...eq2 [T2 , Ti]=[\sum C_{i}_{j}T_{i}T_{j} , Ts]=\sum C_{i}_{j}T_{i}[T_{j}, T_{s}] + \sum C_{i}_{j}[T_{i}...

Homework Statement Y(s)=(s^2+s-6)/(s^2-2s+5) The Attempt at a Solution I tried splitting up the bottom into the form (s-1)^2+4, but I can't get the top to factor correctly to make that work. I'm not sure where to go from here, since I can't do partial fractions with the top and bottom...

k so i used x-xo= Vo t + 1/2 at^2 plugged in all my values then moved everything to one side and used the quadratic formula here is my question. when i solve for it i get t=40.28 and t= 40.58 So which t is my time?

Q- A number is a quadratic residue modulo m if it takes the form x^{2} mod m for some integer x. List the quadratic residues modulo 3, 4, 5, and 7. What patterns, if any, do you notice? modulo 7 0^2=0, 1^{2}=1, 2^{2}=4, 3^{2}=2, 4^{2}=2, 5^{2}=4, 6^{2}=1 modulo 5 0^2=0, 1^{2}=1, 2^{2}=4...

the curve points are: a) (25, 43) b) (28, 46) c) (32, 47) d) (35, 45) would i use y=mx+b i think that's a straight line