Rectangular Definition and 477 Threads

Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?

Homework Statement Given that: Write an equivalent integral in spherical coordinates. Homework Equations (Triple integral in spherical coordinates.) (Conversions from rectangular to spherical coordinates.)(What spherical coordinates entail) The Attempt at a Solution The region...

Is the Fresnel-Kirchhoff formula (FKF) valid also for gaussian beams? I a book starting from the gaussian intensity: U_0(x,y)=\sqrt{\frac{2}{\pi\omega_0^2}}\exp\left(-\frac{t^2+s^2}{\omega_0^2}\right) it said that using the FKF in free space the gaussian beam spreads (in far-field assumption)...

Homework Statement Determine the dimensions of a rectangular box, open at the top, having volume 4 m3, and requiring the least amount of material for its construction. Use the second partials test. (Hint: Take advantage of the symmetry of the problem.) Homework Equations The...

Homework Statement r(u,v)=u i +v j +(1/2)v k Homework Equations The Attempt at a Solution x=u : y=v : z=(1/2)v because x=u and y=v, x & y are the parameters so r(x,y)=x+y+(1/2)y=x+(3/2)y but the answer says it is y-2z=0. What am I not seeing correctly?

Homework Statement If an electron is in an infinite rectangular prism well, with sides of length a, b, and c where c is the shortest and (b^2)*c=a^3, for what value of the d=b/c is the first excited state of the electron minimized? This isn't the complete problem but it's the part that's...

Homework Statement change from rectangle to spherical coordinate : z^2 = x^2 + y^2 I know that : z = pcos(phi) x = psin(phi)cos(theta) y = psin(phi)sin(theta) there fore z^2 = x^2 + y^2 in spherical coordinate is p^2cos(phi)^2 = (psin(phi)cos(theta))^2 +...

A horizontal hollow rectangular mild steel tube 30mm x 50mm with 4mm wall thickness and 350mm long, which is part of a frame has 2 lengths of studding 300mm long , 180mm apart and equidistant from the ends, welded to the 50mm face of the tube. A total perpendicular load of 400Kgs is...

Dear all, I am trying to solve a simple model with Comsol to find the pressure drop in a rectangular channel W=5mm, h=0.6mm, L=10mm. When i try to set the inlet velocity to 0.5m/s the solver shows the error message "Maximum number of Newton iterations reached". The solver works fine if i set...

Homework Statement Homework Equations n/a The Attempt at a Solution I set up the intgral at integral from 0 to 5 of integral from 0 to 5y of 8e^(y^2)dxdy I solved it as an iterated integral so I solved the first part, then ended up with integral from 0 to 5 of 40ye^(y^2)...

Homework Statement A uniform rectangular plate of width d, height h, and weight W is supported with its top and bottom edges horizontal. At the lower left corner there is a inge, and the upper right corner there is a cable. For what angle \theta with the vertical will the tension in the cable...

Homework Statement The figure shows a metallic block, with its faces parallel to coordinate axes. The block is in a uniform magnetic field of magnitude 0.020 T. One edge length of the block is 25 cm; the block is not drawn to scale. The block is moved at 2.8 m/s parallel to each axis, in turn...

The Basis of this question is that: * Rockets launched at an angle follow the path of a rectangular hyperbola when thrust greater than their mass is produced. * That rockets fall in the path of a parabola when thrust is no longer produced, this only applies when the rocket has both x and y...

Hi guys I am currently using Comsol to model a single rectangular channel, a typical one found in a fuel cell (with symmetry boundary). Dimension of the inlet and outlet area is of the order 10e-3 and the length of the pipe is 0.1 m. I am having difficulty getting the expected result. The...

Homework Statement Draw a picture to illustrate the two-dimensional drumhead in the x-y plane. Label the coordinates of the sides of the drumhead. Use this picture to illustrate the "modes" of vibration.Homework Equations \frac{\partial^{2}Z}{\partial x^{2}} + \frac{\partial^{2}Z}{\partial...

Homework Statement The hyperbola y = 1/x in the first quadrant can be given the parametric definition (x, y) = (t, 1/t), t>0. Find the corresponding parametric form of its evolute, and sketch both curves in the region 0<x<10, 0<y<10 Homework Equations Curvature formula...

Homework Statement Hello, the problem ask you to pass this integral \displaystyle\int_{-2}^{2}\int_{-\sqrt[ ]{4-x^2}}^{\sqrt[ ]{4-x^2}}\int_{x^2+y^2}^{4} x {dz}{dy}{dx} to sphere coordinates, but I don't really know how Homework Equations Well, I know the basics formulas...

A rectangular block has dimensions 2.9cm x 3.5cm x 10.0cm. The mass of the block is 615.0 g. What are the volume and density of the block? how do you do it?

Homework Statement A rectangular loop of wire lies in the same plane as a straight wire, as shown http://i30.tinypic.com/347fupw.jpg". There is a current of 2.5 Amperes in both wires. Determine the magnitude and direction of the net force on the loop. Homework Equations Not sure. I am...

Problem: Evaluate (leave in rectangular coordinates): \int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz\,dy\,dx

Homework Statement Suppose you have an a x b rectangular array of distinct integers (think of it as a matrix if you would like). Now suppose we first move across the columns and take a permutation of the entries in each column. Informally, we can imagine the integers in the array as cards, and...

Hi, I have got a simple problem which makes me struggle. I have a rectangular thin conductive sheet (2D) of width w, height h and conductivity suspended in air. I would like to calculate with COMSOL/Femlab the electrical resistance between one of the corners of the conductive sheet and any...

So I know x=(r)cos(theta) and y=(r)sin(theta) As well as r^2 = x^2 + y^2 And (theta)=tan^-1 y/x or sin^-1 y/r or cos^-1 x/r If I want to convert the polar coordinates (7.6 , 285(degrees)) to rectangular coordinates, to the nearest hundredth, what would I do? And also...

Homework Statement Hey i know that we can change it by using r^2=X^2+y^2 and tan(theta)=y/x; but finding some problems in converting the area surrounded by X=0; Y=0; x+y=1; x+y=2 to polar coordinates . yr of course you can convert X=0 to theta=pi/2 and Y=0 to theta=0; But i...

r= (15)/(3-2cos(theta)) I'm lost! Please Help! :confused:

Hi, I have the fields for a rectangular waveguide in terms of cartesian components, that is, Ex, Ey, Hx, Hy. I need to convert these to polar components in terms of r and theta. I've done this the other way around, converted a circular waveguide field which was written in terms of r and theta...

Homework Statement For an air-filled waveguide rectangular wave guide with the top and bottom made of PEC and the left wall made of PMC and the right wall of PEC. The dimensions are a=5cm b=3m. Find the dominant mode propagating in this wave guide (a is length and b is the height) Homework...

Homework Statement F(w) is the Fourier transform of f(t). Write down the equation for F(w) in terms of f(t). A rectangular pulse has height H and total length t0 in time. Show that as a function of w, the amplitude density is propertional to sinc(wt0/2). Homework Equations F(w) =...

hi, I have a question on determining whether rectangular matrices are singular. \left[1 0 0 1 0\right] \left[1 0 0 0 1\right] \left[0 1 0 1 0\right] \left[0 1 0 0 1\right] \left[0 0 1 1 0\right] \left[0 0 1 0 1\right] The book says it's singular. But the explanation isn't very...

hello again folks, this is the last problem that I haven't gotten in this week's homework. see attached image. Homework Statement Two rectangular pieces of glass (see attached image, I painstakingly made it with a very fussy/crash-ey program) are laid on top of one another on a plane surface...

I am told in the problem that i am to minimize the amount of cardboard needed to make a rectangular box with no top have a volume of 256 in^3? I am to give dimensions of box and amount of cardboard needed. Can anyone help

Homework Statement The rectangular and polar coordinates of a point are (x,y) and (r, Theta ) and theta equals 67 degrees Homework Equations ?? The Attempt at a Solution I know nothing about this does anyone know an equation or anything PLEASEE thanks.

Homework Statement can anyone please send me the link to calculate the moment of inertia of cuboid,rectangular and triangular lamina ??(along with figure) Homework Equations The Attempt at a Solution

Hello everyone; here is the problem that I’m currently working on: =============================================== a- Find the principal moments of inertia of a flat rectangular plate (mass = 30g, a = 80 mm, b = 60 mm) that rotates about a diagonal with velocity ω = 15 rad/s. b- What are...

Hello, I just have a question about dot products of different coordinate systems. I was wondering if anyone can explain why unit vector z(rect.) DOT unit vector r(spherical) is equal to cos(theta). As well, I was hoping if anyone could explain z DOT (Theta) = -sin(theta)?

THe following exercise deal with the steady state distribution of the temperature in either 2-dimensional plates or 3-dimensional regions. Problem: A 10X20 rectangular plate with boundary conditions . at the lower side where there is poor insulation the normal derivative of the temperature is...

1. Find the resultant of two forces of 40 lbs. and 50 lbs. acting at an angle of 60○ between them. 2. Three forces of 30 gms, 50 gms, and 60 gms respectively act at an angle of 120○ from each other. Find the resultant by rectangular-resolution (a) by making the 30-gm force lie on the x-axis...

I'm given a complex function in the exponential form: 2.5j e^(-j40*pi) Transforming this into the standard Cartesian form is pretty straight forward, but the extra j multiplying the 2.5 is kind of throwing me off. I don't know if I did it right, but this is what I did: 2.5j...

Homework Statement A particle moves with position as a function of time in seconds given by the vector ~r = (5t^3, 3t − 6t^4)m. What are the rectangular coordinates of the particle’s position at t = 2.5 s? What are the rectangular coordinates of the particle’s velocity at t = 2.5 s...

Homework Statement Convert into rectangular coordinates: r = \frac {1}{1-cos(theta)} Homework Equations The Attempt at a Solution r = \frac {1}{1-cos(theta)} r –r(cos) = 1 (why can't I get a minus sign to display correctly? - I'm trying to show r -...

Homework Statement Convert into rectangular coordinates: r = tan(theta) Homework Equations The Attempt at a Solution r = \frac {sin}{cos} I used r = \sqrt{x^2+y^2} and cos = \frac {x}{r} x = (r)(cos) sin = \frac {y}{r} y = (r)(sin)...

Homework Statement How much force is required to tip an object? Given- It is a rectangular prism 1m tall, .5 m wide, 2m long. The center of gravity is .75m from the ground vertically and otherwise centered. The force can be applied wherever it is easiest to solve the problem. Homework...

COMSOL Rectangular mesh (VERY URGENT) I am trying to modify the mesh of a COMSOL simulation. I need to make my mesh rectangular instead of triangular that COMSOL defined already. Thanks. Engin

Homework Statement A WxH rectangular loop of wire, with resistance R, lies on a table a distance s from a separate long straight wire carrying a current I. If the loop is pulled to the right, parallel to the wire, with the speed v, then what is the magnitude of the current induced on the...

1. I can't seem to find a formula to figure out the area of an upright rectangular glass rod. Can someone point me in the right direction? 2. The Attempt at a Solution

Homework Statement change from polar to rectangular coordinates Homework Equations \cos{theta}+r^2\sin{theta}=\tan{theta} The Attempt at a Solution I got x^2 + y^2 + x + y = \frac{y}{x}\sqrt{x^2+y^2} does that look right?

Homework Statement r^2= 2cos^2 θ+3sin^2θ Homework Equations X= r cosθ y= r sinθ The Attempt at a Solution √r=√2cos^2 θ+3sin^2θ r = 2 cos θ+ 3 sin θ r = 2x + 2 y. I doubt that i even got close to the correct answer so I like to ask anyone who knows how to deal with this...

Homework Statement Hi, I need to calculate the voltage drop in an n by m grid. There are resistors 4 resistors connected to a square; R1 for horizontals and R2 for verticals. There's a voltage applied at point B and point A is grounded. I need to create a MATLAB function that will solve for...

1. A rectangular tank 2.0 m by 2.0 m by 3.5 m high contains gasoline, with a density of 0.68E3 kg/m3, to a depth of 2.5 m. What is the gauge pressure anywhere 1.2 m below the surface of the gasoline? 2. P=Ps + Pl Pl=density (g) (h) 3. I'm sure this is an easy problem, but I...

Homework Statement Find the dimensions of the rectangular box of largest volume that can be inscribed in a sphere of radius 1. Homework Equations v=w*l*h, Set the partials equal to 0, then solve a system, etc. The Attempt at a Solution I'm really just unsure of the constraints that...