Cubic Definition and 415 Threads

May i know how to count the coordination number of fcc? i know coordination number is count by the number in contact. i can understand the coordination number of bcc which is 8 , becoz that is 8 number in contact . but why fcc is 12 , not 13? i counted it as 13 if we take one face atom as...

Is it possible to have the reciprocal of a cubic function that does not have any vertical asymptotes?

theta and R are of equal size and contain the points i want to fit to a spline. What really has me perplexed is the coefficients that are produced. How do i interpret these coefficients; I originally assumed that they were the coefficients of a polynomial in standard form, however after...

Homework Statement g(x)= x^4-2x^3-3x^2+2x+2 Homework Equations The Attempt at a Solution After using synthesized division, got x^3-x^2-4x-2 I need help in factoring from here please

Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are \vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z) \vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z) \vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z) Thanks!

I've been looking at some practise exams for the University I would like to apply to, I have to sit the exam on 4th November. We have never done finding the roots of a cubic equation before and I cannot figure it out from looking on the internet, the formulas are all horrible to understand...

Derivative of a sum of functions What would you interperate this as? It is one of the subsections of Differentiation from the syllabus of a University entrance Exam in November but I cannot think what it is referring to. Differentiation: Derivative of xa, including for fractional...

Say I have a monic polynomial, x^3 + ax^2 + bx + c with a=-2.372282, b=1.862273, c=-0.483023 The discriminant is given by a^2 b^2 - 4 b^3 - 4 a^3 c - 27 c^2 + 18 ab c which is < 0, indicating 1 real root and 2 complex conjugates. A method for solving a general cubic using the...

Homework Statement (0.1 - 0.3j)^(1/3) = a + bj, where j is the imaginary number or more specifically sqrt(-1). Does anyone know how to solve for a and b? Homework Equations I've looked at cubic function equations, along with some polar equations. However, the latter requires some angle...

Homework Statement Consider the use of cubic splines to interpolate a set of data. Suppose at some stage in the calculation we arrive at the following spline functions for two consecutive intervals \tilde{f_{0}} = x^{3} + ax^{2} + bx + c over the interval -1 \leq x \leq 1 \tilde{f_{1}} =...

Hello, I am trying to find the equation in the form ax^3+bx^2+cx+d for the curve passing through the origin and (40 sq root 6, -20). How do I find the a, b, c, and d values?

There is a very handy numerical solution for cubic equations like ## x^3+ax^2+bx+c=0## with ##x_i \in R## while a^2-3b \neq 0. Though it makes use of the method of Newton, the starting point for the algorithm gives it a great advantage to the normal algorithm. And you can use MS Excel as an...

The following set of equations is believed to be unknown but it is very hard to become sure of that. If it is really new it might be published in Wikipedia. Does anybody know of a graphical solution of cubic equations that meets this one? I am very interested to hear from you. Given an...

Does x^3 - 3x + 3sqrt(3) = have a constructible root? my solution: suppose a is a constructible root of the equation above. we square both sides to get x^6 - 6x^4 + 9x^2 = 27. since a is constructible, a^2 is constructible as well and we can turn this equation into cubic poly with rational...

I hope somebody will help me with the following problem. Analytical solutions of cubic equations make use of the method of Cardano. Those solutions give roots that are functions of the coefficients of the equations, being functions where cubic roots are involved. Generally speaking cubic roots...

Hello again. :smile: I'm having more trouble with my homewrork, but this one really isn't fair. We haven't done the work in class, and as far as I can tell it isn't on the syllabus, but we're still expected to do it. Homework Statement http://img17.imageshack.us/img17/4379/questions7.jpg...

Homework Statement factor -x^3 + 27 Homework Equations The Attempt at a Solution Nothing, I have no idea how to factor it.

1. Find an equation that best fits the data? Data 2 16.40 3 15.70 4 15.30 5 15.20 6 15.21 7 15.40 8 15.80 9 16.30 10 16.80 11 17.50 12 18.18 13 18.70 14 19.36 15 19.88 16 20.40 17 20.85 18 21.22 19 21.60 20 21.65 I have narrowed it...

Homework Statement An element crystallises in a face-centered cubic lattice with a basis group of two atoms at [000] and [1/4 1/4 1/4]. The lattice constant is 3.55 x 10^-10 m (Q1) How many nearest and second-nearest neighbours does each atom have? (Q2) Calculate the average volume per...

Homework Statement Assuming that each cubic centimeter of water has a mass of exactly 1.00 g, find the mass of one cubic meter of water in kilograms. Homework Equations well i just changed everything from grams to kilograms and cm to m The Attempt at a Solution Well if there is 1g...

Homework Statement Factroise equation Homework Equations The Attempt at a Solution Can anyone help shopw me the best way to factorise cubic equations? I am doing a question on matrices, and have a 3x3 matrix, which ends up giving me a cubic equation: -x^3 +10x^2 - 27x + 18...

Hey, I have a cubic of this form: \\ax^{3}-bx-c=0\\ how do I solve for x?

Homework Statement find a cubic function g(x)=ax^3 +bx^2+cx +d that has a local maximum value of 3 at -7 and a local minimum value 0f -9 at 12. Homework Equations The Attempt at a Solution I know the derivative should equal zero for a max or min to occure. So i got f...

Homework Statement The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the...

How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.

Homework Statement Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 Homework Equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a The Attempt at a...

Homework Statement I am stuck on these two pre-cal problems... can anyone help? Solve By Factoring: 2x^3 + 2x^2 = 4x + 4 This next one I have no idea how to do Find an equation of the cubic function whose graph passes through the points (3,0) and (1,4) and is tangent to the x-axis...

First, Is there a way to convert a complex number to polar form without using boolean commands? And now, my real question: Do all of viete's formulas hold true when the coefficients of a cubic formula are complex? I wrote a script that finds the roots of a cubic formula with complex...

If 1/a^3+ a^2+ 9=0 , is ''a'' greater than/less than or equal to -1/3. This a GRE question. Thanks!

Homework Statement Suppose a resistor R lies along each edge of a cube (12 resistors in all) with connections at the corners. Find the equivalent resistance between two diagonally opposite corners of the cube Homework Equations \SigmaI = 0 at a node (a junction) \SigmaV = 0...

Find the roots of the equation x^3 - 3x^2 - 10x +24 = 0 I personally, have never done cubic equations so can you please explain what should i do here. Should i try with GCF, even though i don't see one yet, or is there a method to do this?

Homework Statement I have the graph of a function f(x)=(x+1)(x+4)(x+6). I've found the tangent at x=-6, the equation of which is y=10x+60. I then need to algebraically find the equation of another tangent on the curve which is parallel to the first. Homework Equations No idea.The Attempt at...

Hello, Recently,I study about the slip systems of metals which regarding to the material science subject. For face centered cubic(FCC),it slip system is {111}<110>.Hence the number of slip systems is 12.The{111}is the family for (111), (-111), (1-11), (11-1),(sorry！-1 means a bar line on top...

packing fraction of body-centered cubic lattice -- solid state physics Homework Statement This is part of a series of short questions (i.e. prove everything in Kittel Ch. 1, Table 2): Prove that the packing fraction of a BCC (body-centered) cubic lattice is: 1/8 * pi * \sqrt{3}...

Homework Statement Find the solutions of: x^3-3x-2=0 using the Cardano's method. Homework Equations The Attempt at a Solution x=u+v (u+v)^3-3(u+v)-2=0 u^3+v^3+(u+v)(3uv-3)-2=0 3uv-3=0 uv=1 u^3v^3=1 u^3+v^3=2 u^3=v^3=1 Now u=v=\sqrt[3]{1}. I found...

X^3+PX+Q=0 X_0 = A + B (A+B)^3 + P(A+B) + Q = 0 A^3 + B^3 + (3AB+P)(A+B) + Q = 0 The next step is 3AB+P=0 What make Cardano drop 3AB+P? Why it is zero?

Homework Statement I desperately need help, cause I cannot find anything about hermite cubic elements and I need to make fortran program who solves this equation with hermite cubic elements: please explain to me how to solve this equation need answer fast for semestral signature...

Now this is an example in my book that I don't really understand. It says prove that the limit of (4n^(3)+3n)/(n^(3)-6))=4 as n goes to infinity. Basically the definition of a limit of a sequence as n->infinity is as follows. Lim{a}=L For any epsilion>0 there is a N>0 such that n>N=>...

Homework Statement Find a cubic function ax^3 + bx^2 + cx + d whose graph has horizontal tangents at the points (-2, 6) and (2. 0).Homework Equations No idea.The Attempt at a Solution I realize that the trick in here somewhere is to work "backwards". I completed a problem earlier that asked me...

Homework Statement I was just wondering if anyone could give me a quick lesson on solving cubic equations(Ax^3+Bx^2+Cx+D=0), or a good place to go to, if anyone can help thanks alot Homework Equations The Attempt at a Solution

I find complex numbers very fascinating. But i don't understand something. Why does a cubic equation have 3 answers instead of 6? I know that there are 3 cube roots of a complex number, and the imaginary part of the complex number can be either positive or negative, so there should be 6...

Homework Statement Barium metal crystallizes in a body-centred cubic lattice. The density of the metal is 3.50gcm^-3. Calculate the radius(in pm) of a barium atom. M(Ba)=137.3g/mol , NA = 6.022x10^23/mol The Attempt at a Solution For 1 unit cell: m=2x137.3/6.022x10^23...

If you stretch a wire, increasing its length will the number of electrons per cubic metre decrease? Assuming the Cross sectional area stays the same. The number of electrons will surely stay the same, and won't increase just by you stretching it, and the number of cubic metres has increased, so...

Homework Statement I am to calculate the number of states in a 3Dcubic potential well with impenetrable walls that have energy less than or equal to E Homework Equations \ E_n=\frac{\hbar^2\pi^2}{\ 2 \ m \ a^2}\ (\ {n_x}^2 + \ {n_y}^2 + \ {n_z}^2) The Attempt at a Solution We may...

1) Prove that the acute angle whose cosine is 1/10 cannot be trisected with straightedge and compass. ... I worked it out and at the end found out that , if I can prove that the cubic polynomial 40x3 - 30x -1 has no rational roots, then I am done. Now, is there any way to prove (e.g...

Homework Statement A cubic polynomial gives remainders (5x + 4) and (12x -1) when divided by x^2 - x + 2 and x^2 + x - 1 respectively. Find the polynomial. Homework Equations The Attempt at a Solution

Hey I need help with this proof: Consider the cubic function: x^3 + bx^2 + cx + d = 0 . If the two solutions of the cubic function are not equal, ie r != s, but r=-s, then prove that bc=d. Thanks

The quadratic formula is, as you are well aware: ax^2+bx+c=0 x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} What is the cubic formula? ax^3+bx^2+cx+d=0 Thanks.

solve in R (x^2+2)^{1/3}+(4x^2+3x-2)^{1/3}=(3x^2+x+5)^{1/3}+(2x^2+2x-5)^{1/3}

Homework Statement From James Stewart's Essential Calculus Early Trancendentals, p.21 #5. Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0 Homework Equations Used zeros of the function. The Attempt at a Solution I understand that the values of x...