Cubic Definition and 415 Threads

I am attempting to derive the formula for the variance of a continuous uniform distribution where f(x) = \left\{ \begin{array}{ll} \frac{1}{b-a} & \mbox{$a \leq $x$ \leq b$};\\ 0 & \mbox{otherwise}.\end{array} \right. I was successful, but only after using Wolfram Alpha to...

y = a(x-b)^3 + c I'm not sure what it's called, my book doesn't mention on how it's derived.

Homework Statement An electron is trapped in a cubic 3D infinite well. In the states (nx,ny,nz) = (a)(2,1,1), (b)(1,2,1) (c)(1,1,2), what is the probability of finding the electron in the region (0 ≤ x ≤ L, 1/3L ≤ y ≤ 2/3L, 0 ≤ z ≤ L)? Homework Equations My normalized wave function in the...

If i have let's say have 1 cubic meter of water at a temperature of 23 degree, in a closest system connected to a 1 cubic meter of air of 20 degree, how long time does it take for the heat to balance out, the surface between the two a 1 square meter.

I'm trying to get my head around indexing x-ray diffraction patterns and this thought experiment stumps me. Let's say I have a crystal with a simple cubic lattice structure: http://ecee.colorado.edu/~bart/book/sc.gif I align a narrow x-ray beam incident on the crystal so that the x-ray...

So long story short, I have a friend who wants me to help her learn how to factor cubic polynomials. Normally I would just fess up and say I don't remember but it's something I'd like to review myself and lessons online aren't the clearest. Here's one of the questions: 2x3+3x2-8x+3 I...

Question: Find the cubic polynomial, which take the following values: y(0) = 1, y(1)=0, y(2)=1 and y(3)=10 Hence obtain y(4).

If I have cubic lattice and need to calculate sum \frac{1}{N}\sum_{\vec{k}}\frac{1}{\sqrt{1-\gamma^2(\vec{k})}}coth\frac{6SI\sqrt{1-\gamma^2(\vec{k})}}{2T} where \gamma(\vec{k})=\frac{1}{3}(cosk_xa+cosk_ya+cosk_za) I must go from sum to integral...

Hey guys, new member here. I've decided to join this forum since I am a current Calculus student, and will be taking Physics next semester. Anyways, I do have a question about one of my homework problems. Homework Statement Consider the function: f(x) = -2x^(3) + 6x^(2) - 3. Find its...

what is the best formula for elephants toothpaste not using yeast using potassium iodine and hydrogen-peroxide(30%) and of course soap. how much reactants would i need to fill let's say... 100m cubed (im not going to do that much but its easier to work with) * how long would the reaction take...

Hello. Supose that we have a cantilever beam. For a small force P applied at the free side of the beam, we can find an expression for the maximum deflection: \delta=\frac{P l^3}{3 E I} If we want to use this beam as a string, we can find its equivalent stiffnes noting that P=K_{eq} \delta, so...

In the book of the Dr. Ronald Askeland the problem about x-ray diffraction use the next planes indices to calculate the interplanar distance, but I don't understand why to use such planes indices? Are these planes all of planes in a cubic structure? (111) (200) (211)...

Homework Statement Find the inverse of the function. f(x)=2x^{3}+5Homework Equations Possibly the quadratic equation.The Attempt at a Solutionf(x)=2x^{3}+5 y=2x^{3}+5 -2x^{3}=-y+5 x^{3}= \frac{-y+5}{-2} x= \pm\sqrt[3]{\frac{-y+5}{-2}} y= \pm\sqrt[3]{\frac{-x+5}{-2}}So the solution is two...

One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg at 25°C. Determine the mass of 3.5 m3 of wa One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg at 25°C. Determine the mass of 3.5 m3 of water at 25°C. How i can solve this question ?

Hi Everyone, so I am having a small situation with cubic bezier curves and I must be missing something. I have generated a program in c# that allows a user to create curves over time and to edit them with control points as they see fit. I have gotten to the point where I am trying to export the...

Homework Statement Consider the motion of particle moving on the inside surface of a smooth cone of half-angle α, subject to the gravitational force. Although this problem does not involve a central force, certain aspects of the motion are the same as for a central-force motion. Show that the...

Homework Statement This is probably an easy question, but using the rational zero theorem I have not found any roots for this cubic polynomial. Factor the Following 6x^3-37x^2-8x+12 Homework Equations The Attempt at a Solution I have used all my knowledge of factoring and...

In an essence, using normal straightedge and compass construction, we can add, subtract, multiply, divide and find a square root. This means that we can find the real roots of a quadratic equation with rational coefficients because the quadratic formula consists of only these operations. The...

Linear Algebra -- Cubic Equation from Given Points Homework Statement Find the equation to the third polynomial that flows through the given points: (0,1); (1,0); (-1,0); (2, -15). Homework Equations f(t) = a + bt + ct^2 + dt^4 Need to find a, b, c, and d. The Attempt at a...

Homework Statement I've been given the following quartic equation in a question: x = (1 + 2a + a^2)x - (2a + 3a^2 + a^3)x^2 + (2a^2 + 2a^3)x^3 - a^3x^4 and need to show that two of the solutions (that aren't 0 and 1) can be given by: x= \frac{(2+a) \pm \sqrt{a^2 - 4}}{2a} 2. The attempt...

gas flow rate has units of "sccm" that standard cubic centimeter per minute. what does "standard" means here? how is derived? if there is gas flow of 1 sccm then how much gas flows in cubic meters?

find the cubic spine of f(x)=sin(x^2) i have two formulas one for the M's the other for the sums S_i but i need a table of points to know what indexes to put and when here i don have it?

Homework Statement My cubic function is y=(x-6)(x-1)(x-9) or y=x^3-16x^2+69x-54 I need to find the tangent at the point x=2.5Homework Equations The Attempt at a Solution All that I have managed to do is work out the y value for x=2.5, that is y=34.125 Please help someone!

Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...

Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the equation are dependent on x only, except M is dependent on x and t. En, Ep, N and h are constants. i know...

Homework Statement Find the solution to the ODE via the power series: y = \Sigma_{i=0} a_j x^{2j + m} Homework Equations y' - y^3 = 0 The Attempt at a Solution I get \Sigma_{i=0} a_j (2j+m) x^{2j+m-1} - \Sigma_{i=0} (a_j)^3 x^{3(2j + m)} = 0 I don't know how to deal with the cubic...

CUBIC BLOCK Make 10 ft sided cubic block (1000 cu ft) of concrete, rebar, and sand, on a barge. Then use 2 barges and pulleys perhaps to drop such block 2000 ft (10 secs?), which might penetrate 100 ft(?) into muck. Drop it slightly off target, so that sub-mud surface conduit collapses shut...

The total electric field is given as Etotal = E0 +E1 +E2 +E3 Where E0 is the applied field, E1 is the depolarization, E2 is caused by polarization of a hypothetical sphere while E3 is the one dependent on lattice geometry... How come E3 is zero for cubic symmetry? Can I picture this as...

Suppose one is to find the stationary states of a particle in an infinite cubic well. Inside the box the time independent SE is: - \frac{\hbar}{2m} \big( \frac{\partial ^2 \psi}{\partial x ^2 } + \frac{\partial ^2 \psi}{\partial z ^2 } + \frac{\partial ^2 \psi}{\partial z ^2 } \big)= E\psi...

I am feeling stupid over this one but I cannot remember how to solve it. I have the following cubic equation: 4x^3 - 32x = -12 I get the solution of x = -3 but not the other two. I initially had it factored as: 4x(x^2 - 8) = -12 Did 4x = -12, got x = -3 But then I could not get the other two...

What is the volume of atom/volume of cell?

Hey guys, I got this assignment last week and have been doing every bit of research I can to try to figure out what I am supposed to be doing. I have found a lot of cubic spline interpolation (csi) write-ups including one on here but we don't have a book in this class to help understand how to...

\phiHi all, I would like to make band structure calculations with tight binding method and I start reading about this method from Ashcroft - Mermin, Chapter 10: The Tight Binding Method and try to solve the problems at the and of the chapter. In problem 2 a. As a consequence of cubic...

Hi, I've been trying to solve this equation for hours no, hoping somebody here can help. I have the equation: -2m2w3 + 15Bmw2 - 27B2 = 0 where m, B are unknown constants and I'm trying to solve for w. Is there a general formula for solving cubic equations? Thanks in advance.

S= \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} for simple cubic I= \begin{bmatrix} -\frac{a}{2} & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & -\frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & -\frac{a}{2} \end{bmatrix}...

How would you go about solving ax^3+bx^2+cd+d=0 for x. Please step by step! Thanks!

Homework Statement My problem is that whenever I have to use cubic functions - whether it's finding the roots (when dy/dx kis a cubic function) or finding the x-intercepts... With quadratic functions I usually use the quadratic formula. I try to figure out how to factor these equations in my...

This is not a homework question, per se, because I'm not a student. But it is a problem I found in a book. Actually, the problem doesn't involve what I'm going to ask, but it did present an opportunity for me to explore the subject. I have the graph of f(x)=x^{3}+3x^{2}-9x+3. I know the x...

Homework Statement The equation x3 − 3x2 + px + 4 = 0, where p is a constant, has roots α −β , α and α + β , where β > 0. (a) Find the values of α and β . (b) Find the value of p. how do i start off? all i know is that sigma a= -b/a and ab= c/a and ab(gamma) = -d/a . Would this be one of...

Homework Statement Doing my vector mechanics dynamics homework and I cannot believe I am stuck on this part. trying to factor t^3 - 6t^2-36t - 40 = 0 Homework Equations The Attempt at a Solution I honestly do not remember where to begin. I remember there is a formula for perfect...

Homework Statement 2) Given a cubic equation y = (x+5)(ax^2 + bx - 2). Give conditions on a and b for the equation to represent the following curve. The curve is attached to the email. http://img35.imageshack.us/img35/8246/question2o.png Homework Equations The Attempt at a Solution...

20 Liters per cubic meter of rain? A weather report for Chiclayo Peru said we received 20 liters per cubic meter of rain yesterday. How many inches of rain would a New York weather report say we received? Thanks. Tom

Homework Statement Write the equation of the cubic function with a y-intercept at 1, a local minimum of (3,1) and through point (2,5) Homework Equations The Attempt at a Solution I know that d= +1 and that's about it. I am really stuck and needs to know this for my summative on...

Homework Statement The figure shows the graph of a cubic polynomial. The function graphed is f(x)= Hint: You may write the function as f(x) = a(x-b)(x-c)(x-d) where b, c, and d, are integers and a is a fraction. Homework Equations The Attempt at a Solution I'm lost...

Homework Statement I think I saw another thread answer this question, but I was a little lost whilst reading it. I have just recently learned of the rational root theorem and was using it quite happily; figuring out what possibly answers went with cubic and quartic polynomials gave new...

Homework Statement Not so much a homework problem, but a problem that is annoying me because of its simplicity. Not all cubic polynomials with rational coefficients can be factorized by the rational root theorem (or is this false?). What I am finding hard to comprehend is how a cubic with...

The proof of the quadratic formula was so simple, I moved to the proof of the cubic formula with supreme confidence. And found myself awash in as and cs and cubic roots. Can you turn this equation into a cubic? x=-\frac{b}{3a}...

So I found the characteristic equation of a matrix, and I know the roots of the equation are supposed to be the eigenvalues. However, my equation is: \lambda^3-2\lambda^2 I have double checked different row expansions to make sure this answer is correct. So don't worry about how I came to get...

x3 - 12x + 1 = 0 How does one solve for x?

Cubic equation f=a x+b x^2+c x^3 Solving: A=\frac{-(a b+9 c f)+\sqrt{(a b+9 c f)^2-4 \left(b^2-3 a c\right) \left(a^2+3 b f\right)}}{2 \left(b^2-3 a c\right)} G=a+2 b A+3 c A^2 H=a A+b A^2+c A^3-f F=G^3-27cH^2 B=\left\{F^{1/3}\,,-(-1)^{1/3} F^{1/3}\,,(-1)^{2/3}F^{1/3}\right\}...