Cube Definition and 593 Threads

Show that $$ \begin{align*} \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{(-1)^n}{4^{3n}} &= \frac{\Gamma\left(\frac{1}{8}\right)^2\Gamma\left(\frac{3}{8}\right)^2}{2^{7/2}\pi^3} \tag{1}\\ \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{1}{4^{3n}}&= \frac{\pi}{\Gamma \left(\frac{3}{4}\right)^4}\tag{2}...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem. Here is the question: Suppose a cube is oriented before you so that from your point of view there...

If a distant observer were to observe a large cube made of strong material approach a black hole, what would he see? ISTM that if one of the faces of the cube were to be the nearest approaching portion, he would see the four edges of the face become shorter and curved, and he would see the...

Homework Statement Find the area of the plane y=3x enclosed within the cube formed by the planes x=y=z= \pm 5 Homework Equations The Attempt at a Solution Using the equation y=3x, I found two points (x,y)=(5,1.66) and (x,y)=(-5,-1.66), then by plugging these points in the distance...

Homework Statement Use Newtons method to compute the cube root of 5. Do the first 10 iterations. x_{(0)}=1 determine the fixed points of the iteration and determine whether they are repelling/attracting. if attracting, then determine if the convergence is linear or quadratic. draw the...

Homework Statement Consider four point charges q1, q2, q3 and q4, located at r1, r2, r3 and r4, respectively. (a) Calculate the electric flux piercing a cube (with side a and centered at r0 = (0, 0, 0) that contains all of these charges. (b) Calculate the electric field of the four charges...

"A cube of wood of side 4cm floats in fresh water with 1:4 showing above the surface. Calculate a) the water pressure on the base of the cube and b) the density of the wood" All I can work out is that the density of fresh water is 1000kgm^-3 and the area of the base is 1.6 x 10^-5 m...

Homework Statement A cube of side a has a cube of side a/2 centered within it. The inner cube has a total charge Q that is uniformly distributed over its surface. A) For the surface of the outer cube, find: ∫s E * dA B) Is this sufficient information to find the electric fields at...

Homework Statement A cubical Gaussian surface is placed in a uniform electric field as shown in the figure to the right. The length of each edge of the cube is 1.0 m. The uniform electric field has a magnitude of 5.0 * 10^8 N/C and passes through the left and right sides of the cube...

A cubic box of side a = 0.410 m is placed so that its edges are parallel to the coordinate axes, as shown in the figure. There is NO net electric charge inside the box, but the space in and around the box is filled with a nonuniform electric field of the following form: E(x,y,z) = Kz j + Ky k...

Flux through sphere Homework Statement Given \vec{F}=\frac{\vec{r}}{r^2} and unit sphere, find the flux through the surface of the cube. Homework Equations Surface Integral of F dS=volume integral of Div. F d^3r The Attempt at a Solution After the above formula, I do not have...

Hello, If I have a rigid cube rotated about an axis with dimensions L x W x H centimeters, how can we find the moment of inertia? Thank you.

Homework Statement A point charge q is located at the corner of a cube with edges of length L. Find the electric flux through the shaded face at y = L.Homework Equations Gauss's Law; flux = ∫E\bulletn dA = qenc/ε The Attempt at a Solution Here's what I'm thinking. In the problem statement...

Homework Statement Asymmetrical Cube - Determine the equivalent resistance between points A and C’ of the circuit below. Homework Equations U = R.i The Attempt at a Solution This problem was my professor that created. I know how to solve it, but I would like to know if other...

Is there any relationship between the surface area of a cube and the surface area of the cube's inscribed sphere? Jean~

Hi, I know how to rationalize a denominator when it is a square root monomial or a square root binomial (through conjugation). For example, for a square-root monomial: 5/√25 = [5(√25)]/ [(√25)(√25)] = [5(√25)]/25 = (√25)/5 = 1 or -1and, for a square-root binomial: 5/(5 + √25) = 5(5 -...

Hello I am working on this integral \[\int \frac{\sqrt[3]{x}}{(\sqrt[3]{x}+1)^{5}}\]I have tried using a substitution, I did: \[u=\sqrt[3]{x}+1\] and I got that the integral becomes: \[3\cdot \int \frac{(u-1)(u-1^{2})}{u^{5}}du\]I moved on from there, got a result, however it was not...

Homework Statement Twelve resistors of equal resistance are connected so as to form a cube ABCDEFGH shown. Equivalent resistance between points A and G is 5/3 ohm. If a battery of voltage 100 V is connected across the points A and G, find the current (in ampere) flowing through the...

To add to the oq - Is the "center" of an object an entirely logical construct? I draw a circle, find it's center and mark a point there. This point, no matter how small I mark/draw it takes up space (both physically and visually in my mind). Anything that takes up space has a center point...

Homework Statement I am working through a couple of revision sheets and have questions about the following two questions: 1) A)An ice cube of mass 0.03 kg at 0C is added to 0.2 kg of water at 20C in an insulated container. (a) Does all the ice melt? (b) What is the final temperature of the...

I saw this video a long time ago and just assumed it was fake, but I just saw it again and honestly don't know how this is possible. Wouldn't the ice cube just instantly melt? https://www.youtube.com/watch?v=aLwaPP9cxT4

Homework Statement A cube is positioned with its vertices at the following points: A=(0,0,0) C=(1,1,0) E=(0,0,1) G=(1,1,1) B=(1,0,0) D=(0,1,0) F=(1,0,1) H=(0,1,1) What is the angle of intersection of the planes formed by the triangles EBC and ECD Homework Equations AB=ABcosθ...

is this means that torque is proportional or inversely proportional to the cube of speed the problem says The torque of a load driven by a 385-V, Dc shunt motor varies as the cube of the speed. The current taken by the motor is 51A at a certian speed. Calculate the additional resistance...

Does anyone know what this guy is on about? I understand some of the basics of group theory and I know there's a connection between Galois theory and the solving of a Rubik's cube, but I'm not sure what law he is even trying to disprove here. I'm assuming something with regards to symmetry or...

Homework Statement A homogeneous cube, each edge of which has a length \ell, is initially in a position of unstable equilibrium with one edge in contact with a horizontal plane. The cube is then given a small displacement and allowed to fall. Find the angular velocity of the cube when one face...

Homework Statement When is the net flux for a cube 0 and when is it not? Homework Equations ∫EdA= Q/8.85E-12 The Attempt at a Solution if you have no test charge then the flux of a cube is zero. but if you have a test charge then the net flux is the charge divided by 8.85E-12...

I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices. Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite...

Homework Statement Derive cube root formula using Newton-Rhapson's method. x - y^3 = 0. Homework Equations xn + 1 = xn - f(xn)/f'(xn) The Attempt at a Solution I know that the solution is (2y + (x/y^2))/3 I tried using implicit differentiation and stuff but I can't get this out...

Homework Statement F(x,y,z) = xyzi+xyj+x^2yzk Surface is the top and four sides of cube with vertices at <+/-1,+/-1,+/-1> Homework Equations ∫∫curlF * ds = ∫F*dr The Attempt at a Solution At Z = 1, I broke up the surface into 4 lines, parameterized them and combined...

Hypothetically, if the Earth were a cube, would walking to the corners(vertices etc.) feel like you were going uphill or would it feel flat?

A 10 nC point charge is at the center of a 2.0m x 2.0m x 2.0 m cube. What is the electric flux through the top surface of the cube? related equations: gauss's law -- Qin/e0 e0 = 8.85 x 10 ^-12 C^2/Nm^2 my attempt: 10 x 10^-9 C ________________________ = 1129.94 C/Nm^2 8.85 x 10...

Homework Statement Evaluate the triple integral for the function \int\int\int y dV over that part of the cube 0 \leq x,y,z \leq 1 lying above the plane y +z = 1 and below the plane x+y+z = 2 Homework Equations The Attempt at a Solution This is the first attempt at a triple...

I was watching a Walter Lewin lecture on Newton's laws (which was great, by the way), and at the end, he presented this problem; There's a string hanging from the ceiling (actually not the ceiling, it was just a surface), and a cube is hanging from that string. There is another string, attached...

Ok, so a cube and a sphere are both centered at origo. The cube has side lengths L. I need to know the surface area of the part of the sphere that is inside the cube, for all possible r. There will be three different equations, one for 0 < r < L/2, when the entire sphere is inside the cube, one...

Homework Statement A cube, with a volume of 0.78 m3 is submerged in a swimming pool. What is the buoyant force acting on the object if it has a mass of 328 kg? Homework Equations The Attempt at a Solution

Homework Statement A point charge +Q is placed at the center of a cube. What is the electric flux through a face of the cube? Homework Equations Flux = Q/ε The Attempt at a Solution The answer is Q/(4ε), but I thought it should be Q/(6ε) which isn't even an option. I'm I crazy? Since there...

Hey, it is clear for me that \sum_{i=1}^{n} i = \frac{n(n+1)}{2} how to find a formula for \sum_{i=1}^{n} i^2 \sum_{i=1}^{n} i^3 Thanks

Homework Statement A metal box has 6 walls, all insulated from one another. The left and right wall are held at V= V0, which are at y=-d and y=d. All the other walls are grounded. The cube has dimensions where walls run from x=0 to x=2d, z=0 to z=2d, and y=-d to y=d. Homework...

Let's say there is a cube sitting in the first octant. Our F(x,y,z): <ax , by, cz> and Each face of the cube is oriented to outward pointing normal. Can I just calculate the the flux of one face and then multiply this by the number of faces to get the total flux? Will flux in a cube always be...

inverse square vs cube = ? If the electric field falls off at the inverse square ratio, and magnetic at inverse cube, does EM radiation dissipate at 1/r^5 ratio for circularly polarized waves?

Homework Statement Hello, the problem I am working on is: Assume the magnitude of the electric field on each face of the cube of edge L = 1.05 m in the figure below is uniform and the directions of the fields on each face are as indicated. (Take E1 = 31.5 N/C and E2 = 26.5 N/C.) (a) Find...

An E field exists in a region of space and it can be described by: \bar{E} = \hat{i}xy^2 Calculate the flux through a cube of size 1.0m, with one end extending into the positive x,y and z directions. Find the charge enclosed. I have no idea how to start this? can someone point me in...

Hi members of the forum, Problem: Rationalize the denominator of $\displaystyle \frac{1}{a^\frac{1}{3}+b^{\frac{1}{3}}+c^{\frac{1}{3}}}.$ I know that if we are asked to rationalize, say, something like $\displaystyle \frac{1}{1+2^{\frac{1}{3}}}$, what we could do is the following...

Homework Statement Suppose there is a uniformly charged cube with known side length. I then imagine a larger, closed cube surface surrounding it. This larger cube has double the side length and is symmetrical to the smaller cube. Is is practical to use this Gaussian surface to compute the...

been an ice cube maker for many years now :-p and have never seen this happen before. I imagine air was trapped water was starting to freeze and forced the air out at the same time as freezing, but all seems pretty coincidental for two cubes to do this. Anyone know how this happened...

Hey everyone! I have the following question for you guys to settle an argument: If you were an inhabitant of Flatland and a cube decided to visit you like the sphere did, would you be able to see more than 2 sides at a time? My answer is no because Mr. Cube could appear as a point, a square...

My friend has been working on mastering the Rubik's cube lately. He can solve it now and make new designs. One day he asked me for a pattern so, I told him I wanted the red center piece enclosed by the green cubes, and the green center piece enclosed by the red cubes. I think this is...

A cube of osmium with a volume of 166 cm³ is placed in fresh water. The cube's apparent weight is 35.0 N. What is the density of osmium?This is what I did: I converted force to mass by : 35 N / 9.8 = 3.57 kg then changed the 166 cm³ to m³ which is : .000166 m³ After that i divided the mass...

I am working on designing a music visualization system using LEDs. I would like to create an analog design that uses op amps to filter, amplify, and add DC bias to an audio signal so it can be read into the A/D of a 5V microprocessor. The input signal is a +/- 1.5V volt audio signal coming from...