Cubic Definition and 415 Threads

Homework Statement X-intercepts: (-1.57,0) , (0.65, 0) , (2.83, 0) Y-intercept: 11.33 Homework Equations I've got to convert that information into an estimated cubic function. The Attempt at a Solution I tried subbing the y-intercept in; although that didn't work. 11.33...

[SOLVED] cubic reciprocity? I would like to prove the following conjecture: If p \equiv 2\ (mod\ 3) is a prime, then the cubing function x \mapsto x^3 is a permutation of \mathbb{Z}_p . I've tried to find a contradiction to the negation by assuming that if n \neq m\ (mod\ 3), but n^3...

I am completely stuck on working out cubic sequences.. i know its sumthing along the lines of an3+bn2+cn+d but i don't know what each part means as in what does a = b= c= and d=?. And how to go about working it out. I have this sequence which i would like to work out : 1,4,10,20,35

I'm programming some commands in a graphic application, and once again my extremely limited mathematical knowledge has found me rather stumped. Here is my cubic bezier function, written in JavaScript syntax(this is not actually JavaScript, though): function getBezier(percent,p1,cp1,cp2,p2) {...

Hi The curve C has equation y = f(x) and the point P(3,5) lies on C Given that f'(x) = 3x² - 8x + 6 The point Q also lies on C, and the tangent to C at Q is parallel to the tangent to C at P Find the x-coordinate of Q So if there parallel the gradients are equal but i...

Factorising cubic equation Anyone here know how to factor this equation? Homework Statement a^{3}c-a^{3}b+b^{3}a-b^{3}c+c^{3}b-c^{3}a The Attempt at a Solution I tried factoring by grouping but ended up getting nowhere. If anyone can factor this equation, please tell me step by...

1. A cubic polynomial is given by (f)x = x3 + x2 - 10x + 8 1) i) Show that (x -1) is a factor of f(x) ii) Factorise f(x) fully iii) Sketch the graph 2. Factor theorem? 3. Attempt at solution i) I know that f(1) = 0, so (x - 1) is a factor of (f)x = x3 + x2 - 10x + 8...

I don't understand this question at all. But since my Professor gave it to me I'm guessing it relates to the chapter of structures and types of solids. What is the coordination number of an atom in a primitive cubic structure? What the hell is this question asking for?

Calculate the lattice constant of a body-centered cubic iron crystal using the molar mass of iron, the density of iron and the Avogadro number.

I am working on a paper to find the equation of the inverse function of a cubic function. The function is f(x) = x^3 + 6x^2 +12x +7 I have already graphed the function and its inverse. I have found the inflection point of (-2, -1). I found the 3 roots (1 real & 2 complex). The real...

f(x)= x^3-2x^2-11x+52 ----> Find all of the zeros of the function I just need some advice/direction on how to start solving this. It is not in the textbook and my brain is just kinda farting when I look at it. I think i need to get it in an (x-a)(bx^2+cx+d) form or something, but I don't know.

Hi. I know how to find the coefficients of a quadratic with a data set using least sqaures. I now would like to do with to find a polynomial to the 3rd and 4th term. Could someone help me with this? The data set I am using: (-4.5,0.7) (-3.2,2.3) (-1.4,3.8) (0.8,5) (2.5,5.5)...

The question I am looking at states: Prove that the elliptical function x^2 + 3y^2=b is orthogonal to the cubic y=3ax^3. I'm thinking they want me to prove if the functions are orthogonal when they intersect. If I am correct that would just lead to; For the ellipse, 2x+6y(m1)=0...

I still remember how to extract a square root without a computer but could somebody remind me the technique to find a cubic root just with the pencil and paper?

Homework Statement Find an integer c such that the equation 4x^3 + cx - 27 = 0 has a double root. Homework Equations Ax^3+Bx^2+Cx+K = 0 Sum of Roots = -B/A Product of Roots = (-1)^n * k/a etc. The Attempt at a Solution I tried using P/Q with synthetic division to find a...

Homework Statement In the equation x^3+ax^2+bx+c=0 the coefficients a,b and c are all real. It is given that all the roots are real and greater than 1. (i) Prove that a<-3 (ii)By considering the sum of the squares of the roots,prove that a^2>2b+3 (iii)By considering the sum of the cubes of...

Here's an interesting question. I'm aware of closed forms of cubic polynomials that go through 1 or 2 specific (x,y) points. Are there closed form versions for 3 or 4 points? 1 pt: y = a(x-x_0)^3 + b(x-x_0)^2 + c(x-x_0) + y_0 2 pt: y = a(x-x_0)^2(x-x_1)\ +\ b(x-x_0)(x-x_1)^2 \ +\...

Attached below are two cubic spline tutorials: 1. Explanation of the classic tri-diagonal cubic spline formulation. Included are 2 example problems. 2. Extension to parametric cubic splines. Included are 2 example problems . :smile:

Homework Statement To solve the following equation 3x^3 + x^2 + 15x + 27 = 0 Homework Equations The Attempt at a Solution {(x-> 1/9{-1 - 134/(-3079+27Sqrt.(16305)^(1/2) + (-3079+27Sqrt.(16305)^(1/3)} {x-> -1/9 + 67(1+iSqrt.3)/9(-3079+27Sqrt.(16305)^(1/2) -1/18...

Does anyone know whether the graphical solution of cubic equations with real roots by means of intersecting a circle and a parabola or hyperbola (or just a parabola and hyperbola) is known or not? That solution has to give the equations for the circles, parabolas and hyperbolas involved and not...

Hi! Who knows: can any cubic root like \sqrt[3]{x} with x real be written as a form in which only square roots (real or complex) are involved?

L.S. I am looking for detailed information on the subject of cubic equations. Problem is that I cannot find anything but the most basic properties of such equations. For example, if given an arbitrary cubic equation with roots x(i),where to find the equation like with roots y(i) = x(i) - x(j)...

Does anyone have a chart of what a straight pipe flows in cfm? Like 3 inch inside diam.? 4 inch? Etc? Thanks:)

I'm using a bézier curve in a Computer Game I'm working on that has four points: p0 (start point) p1 (directional helper for p0) p2 (directional helper for p3) p3 (end point) I nabbed the drawing formula from Wikipedia and it works fine. I have some problems though. I really need...

If one would make no assumtions to try to simplify, except for just assuming OH- were negligible in a solution of weak diprotic acid, H2A, we can create four equations to represent concentrations for : H2A == H + HA- HA- == H + A- Each of those has a K value for equilibrium constant...

Hi, I was wondering in a cubic equation such as x³ - 5x = 2x - 1 can be rearranged to x³ - 7x + 1 = 0 is that 0 the y value, and +1 where the line crosses the y axis? Is - 7x the gradient or is x³ - 7x the gradient? Thankyou

Has anyone shopped for an air compressor lately? It's amazing how far retailers will go in providing exaggerated/skewd/completely misleading info on these things. Due to this, I have a question: -Is there a simple formula for working with cubic feet per minute (cfm) and PSI? Ex: If you...

Homework Statement Show that for negative c (a,b,c - real) equation x^3+ax^2+bx+c=0 has at least one positive root. 2. The attempt at a solution Considering the equivalent form of the equation above for large |x|: x^3(1+\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3})=0 we can conclude that there...

Homework Statement Hi,i came across this problem in a past exam paper and i got a bit stuck on it,can anyone enlighten me please?im prob just missing something really obvious and basic... A spherical air bubble at the bottom of a lake,10m below the surface,has a radius of 1mm. The...

Considering the case of cubic polynomials with integer coefficients and three real but irrational roots. Is it true that it's impossible that all three roots can be in the form of simple surd expressions like r+s \sqrt{n} (where r and s are rational and sqrt(n) is a surd). The argument is that...

Hi. I am a bit lost as to how to factorize a cubic function. Would anyone be able to help me out? Thanks, Dan.

Even though it is uncommon to see questions asking for an analytical solution to equations of degree 3 or 4, they have been asked on the forum. It's also good to know how, in any case. Cubic : http://www.karlscalculus.org/cubic.html Quartic : http://www.karlscalculus.org/quartic.html...

Let f(x) = ax3+bx2+cx+d and let f have x-intercepts x1, x2, and x3. How can I show that the expression for f(x) becomes f(x) = a(x-x1)(x-x2)(x-x3) ?

I need to find b, c and d in a cubic equation of the form y=x3+bx2+cx+d (ie. a=1 if a is the coefficient of x3). I've been given three points (-2,-13), (-1,0), (1,2). If I had a fourth piece of data i could solve the equation I suppose, but with only three I've really struggled. Here's what...

Find a cubic function f(x) = ax^3 - bx^2 + cx - d that has a local maximum value of 40 at x = 1 and a local minimum valud of -68 at x = 4 Since x = 1 and x = 4 are the max and min, respectively, then f'(x) must equal 0 at x = 1 and x = 4. Therefore f'(x) = (x-1)(x-4) = x^2 - 5x +4 Using...

How does one find the roots of an equation, for instance: r^4 + r^3 - 7r^2 - r + 6 = 0 ...completely by hand. Is there some type of non-lengthy process or trick to find special circumstances for easy solving? Thanks.

A 3rd degree polynomial is called a cubic, and a 2nd degree is a quadratic. But quad implies 4. Why is a 2nd degree called quadratic?

Construct a free cubic spline to approximate f(x) = e^ -x , by using values for x = 0 , 0.25, 0.75, 1 now i know i have to contstruct something like this ss_{j} = a_{j} + b_{j} (x - x_{j}) + c_{j} (x-x_{j})^2 + d_{j} (x- x_{j})^3 also we know from the initial conditions that a0 = f(0), but...

With my buddies TI-83 I've plotted a cubic function but am wondering how I can find the x value for a given y value.

Hai, I have a question solving a cubic equation. I have a function y=ax*x*x+bx*x. I want to get a solution for the value of a and b. From reference, I found that a=(xtan(Theta)-2y)/(x*x*x) and b=(3y-xtan(Theta))/(x*x) [Theta] is an angle or tangent of each point x along a cubic curve or...

The determinate of the following 3x3 matrix 1-y, 2 , 3 2 , 4-y, 5 3 , 5 , 7-y gives a cubic that simplifies to, y^3 - 12*y^2 + y + 1 = 0. Now, apparently the teacher picked random numbers for the original matrix, making the problem delve into other realms of mathematics...

volume of a cone is 10 cubic cm... Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper. Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3. I think you solve this...

Just when I thought I understood the concept of planes and miller indices, I got stuck on a 'test your understanding' Q in my book. I can't understand that there can be two or more (110) planes in a crystal lattice? I thought there can be only one such plane. The question asks me to find the...

Hi, all, I'm studying the superconducting qubit based on current-biased josephson junction. The system can be considered as a particle in a washboard well, or a cubic well. The two states |0> and |1> are the ground and the first excited ones. But How to quantize the cubic well. Could anyone...

Maths urgent help If there is a cubic log with a mass "M" and edges which have a length "2a" and is kept on top of a table,and there is a hole dug inside it right in between two parraral faces of this cube. This hole starts from the middle of one top edge(A) and leads on to the bottom of the...

On mathworld's discussion of the cubic formula he has that "determining which roots are real and which are complex can be accomplished by noting that if the polynomial discriminant D > 0, one root is real and two are complex conjugates; if D = 0, all roots are real and at least two are...

Hi, A cubic equation has at least one real root. If it has more than one why are there always an odd number of real roots? Why not an even number of real roots? Can someone help me to prove this? Thx! LMA

Hi, A cubic equation has at least one real root. Can someone help me to prove this? Thx! LMA

Hello, I tried to consider one-dimensional anharmonic (cubic) oscillator in second quantization formalism. And I found that energy difference between the first excited state and the ground state (as well as energy difference between the second excited stated and the the first one) as...

1. Find the equation of a cubic relationship given that the graph has only two x intercepts, one at point (3,0) and the other at (-1,0). It is also known that the graph passes through the point (4,-10) and has a y-intercept of (0,-18) 2. Write down the exact co-ordinates of the two turning...