Rectangular Definition and 477 Threads

Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...

The volume of a rectangular prism can be represented by the polynomial V(x)=2x^2+9x^2+4x-15 a. The depth of the tank is (x-1) feet. The length is 13 feet. Assume the length is the greatest dimension. Which linear factor represents the 13 ft?This is probably a really easy question but I am so...

How do you convert this to Spherical Components? Spherical Convention = (radial, azimuthal, polar) ##\vec r = |\vec r| * \cos{(\theta)} * \sin{(\phi)} * \hat x +|\vec r| * \sin{(\theta)} * \sin{(\phi)} * \hat y +|\vec r| * \cos{(\phi)} * \hat z## Is this correct? ##\vec r =\sqrt{(x^2 + y^2 +...

Say you have a rectangular channel with a width, w (m), and a height, h (m) and an infinite length. The channel itself is fixed and none of the sides can move with respect to one another. If you know the volume flow rate, V (m3/s) of fluid through the channel, how do you calculate the shear rate...

$\tiny{s10.03.25}$ $\textsf{Write complex number in rectangular form}$ \begin{align*}\displaystyle z&=4\left[\cos\frac{7\pi}{4} + i\sin \frac{7\pi}{4} \right]\\ \end{align*} $\textit{ok from the unit circle: $\displaystyle\cos{\left(\frac{7\pi}{4}\right)}=\frac{\sqrt{2}}{2}$}\\$ $\textit{and...

Hello. I'm not sure if this question is to project-specific, but I will try to explain as best that I can. I am working with a system such as this one, with only a few differences: http://www.sciencedirect.com/science/article/pii/S0168583X1400706X it is a cryogenic stopping cell. The part I am...

Homework Statement Convert from rectangular to spherical coordinates. (-(sqrt3)/2 , 3/2 , 1) Homework Equations We know the given equations are ρ = sqrt(x^2 + y^2 + z^2) tan theta = y/x cos φ = z / ρ The Attempt at a Solution My answer was (2, -pi/3, pi/3) It should be a simple plug and go...

Hello, and thanks in advance for taking a look at my question. Generally, I am trying to make a railgun force model. Since railguns depend on the magnetic field created around the rails (and the resulting Lorentz force) I need to model the magnetic field created by the current that flows...

Homework Statement Solve for support reactions of a rigid, rectangular steel frame sitting on rubber pads at the four corners (See attached), when a shear force and a moment is applied at some point on the frame. All the known variables are shown in black while the unknown are in red. It is a...

$\textrm{write polar to rectangular coordinates}$ $$r=5\sin{2\theta}$$ $\textit{Multiply both sides by $r$}$ $$r^2=5r[\sin{2\theta}] =5\cdot2[r\cos(\theta)r\cos(\theta)]$$ $\textit{then substitute $r^2$ with $x^2+y^2$ and $[r\cos(\theta)r\cos(\theta)$ with $xy$}\\$ $\textit{then}\\$...

Hello everyone! I want to design a rectangle vacuum chamber (12x12x72) out of 1/2 steel. I would be welding the sides together to form a seal. Would this work? any suggestions on what I could do? Thx! (I not great at this stuff so your help is much appreciated!)

Homework Statement Given the Z component of E inside a rectangular wave guide, Find the ratio of the maximum charge density on the plane x = 0 to the maximum charge density on the plane y = 0. Additionally, Find the ratio of the maximum surface current on the x = 0 plane to the maximum surface...

What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?

Homework Statement Homework Equations Magnetic flux = integral(B dot dA) line integral(B dot ds) = (u_o)(i_enc) (Ampere's Law) The Attempt at a Solution I can't see how Ampere's law applies because all of the magnetic field vectors along the loop will be perpendicular to that stretch of...

Homework Statement In a rectangular waveguide, b = a/2, find the section, if exists, in which the magnetic field is circularly polarized (TE10 mode). Homework Equations Rectangular waveguide equations for TE10 mode (referencing Pozar book). Circular polarization (π/2 out of phase and same...

Homework Statement A rectangular loop of wire with sides H = 22 cm and W = 77 cm is located in a region containing a constant magnetic field B = 0.82 T that is aligned with the positive y-axis as shown. The loop carries current I = 334 mA. The plane of the loop is inclined at an angle θ = 30°...

Is it possible to create a rectangular prism while using only one prism and without repeating any two shapes?

How does the velocity at an elemental height h equates to √(2gh)? My application of Bernoulli's equation is not yielding the result. Please show the process. Thank you

Homework Statement The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the...

I've been trying to come up with wave equations to describe the motion on vibrating rectangular (more specifically, square) membranes. However, most paper I find assume fixed edges. What are the boundary conditions I need to apply to the 2D wave equations in order to have an free boundary in a...

Hello, is there a way to directly use a rectangular wave as input current without using an external circuit in ansoft maxwell? The instructions from ansoft that model a toyota motor just put the sine wave function directly into the winding's current settings, can I put a rectangular wave instead...

Homework Statement Prove that the chord joining the points P(cp, c/p) and Q(cq, c/q) on the rectangular hyperbola xy = c^2 has the equation x + pqy = c(p + q) The points P, Q, R are given on the rectangular hyperbola xy = c^2 . prove that (a) if PQ and PR are equally inclined to the axes of...

So if I have a system of equations: $$x_1+x_2+x_3=1$$ and $$x_4+x_5+x_6=1$$ Then they can be put into a matrix representation \begin{equation*} \begin{bmatrix} 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1\\ \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \\ x_6 \\ \end{bmatrix}...

Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...

Any ideas on how to begin ?

By bending a 16 cm wire a rectangular frame is made. By taking the length as x , write the width in terms of x. If the area of the frame is $11 cm^2$ show that x satisfies the equation $x^2-8x+11=0$ Solve the equation by taking the $\sqrt{5}=2.24$ Ideas on how to begin ? (Happy)

My question is that I have to find the dimensions of a rectangular prism (cuboid), where none of the faces are square that will maximise its volume. The sheet metal I have to build it from is 120 cm by 80 cm. I don't even know where to start, I can do it if I'm given a height, width or length...

Hi, I wish to manufacture a transition tube from 4"x1" rectangular section to 3" OD circular section. The height of the part is 3" and is supposed be around 2 mm (.082") thick. Currently I am planning to manufacture this in a hydraulic press using (custom made ) end forming tools. The forming...

Hello everyone. I have what is probably a relatively simple question. I'm trying to calculate the resistance between two rectangular copper plates submerged in water. I found this thread that briefly discusses it...

Homework Statement [/B] Three conducting loops, all with the same resistance ##R## move towards a uniform and constant magnetic field, all with the same velocity ##v##. Their relative sizes can be identified by the grid. As the loops move into the magnetic field an induced current begins to...

Homework Statement As shown in the figure below, a current I passes through a straight conducting wire located within this page. Rectangular circuit ABCD on the page is moving away from the straight conducting wire with speed v, while side AB remains parallel with current I. The length of side...

How charming! (Photo: ESA/Hubble and NASA) http://www.usatoday.com/story/tech/sciencefair/2016/04/08/star-red-rectangle-nasa-hubble/82796522/

I couldn't get equal graphs one plot 4 leafs the other 2

Homework Statement I have a rectangular coil with length L and the cross-section's sides has length a and b (b>a). A wire is tightly wrapped around N times. Calculate the magnetic field inside the coil. Homework Equations The problem I have is that in class we were taught how to calculate...

I need to mount several rectangular orifices or sections on a wall with those two factors: - 20 Pascals differential pressure (negative pressure inside) - Inlet air speed 1100 feet per minute (5.58 meters per minute) I've got the section of each window, and the air caudal to renovate. I would...

Homework Statement Homework Equations Is my part a correct and am I on the right track for part b? If not please give me some suggestions to get me closer to the right track. Also, how would I even begin c.? We have literally done no examples like this in class. The Attempt at a Solution...

I'd like to know if the diagonal of a rectangular thin foil is an inertial principal axis.I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a symmetry axis, so it shouldn't be a principal axis. Is it correct? So, if I consider that...

Homework Statement An equation is given in spherical coordinates ## \rho sin(\phi) = 8cos(\theta) ## Express the equation in rectangular coordinates a) ## (x-4)^2 + y^2 = 16 ## b) ## x^2 + y^2 + z^2 = 16 ## c) ## x^2 + (y-4)^2 = 16 ## Homework Equations ## x = \rho sin \phi cos \theta, y...

The following code compares my result to the known correct result. Can anyone find where my error is? If you run the octave code you will see that my answer has positive concavity whereas the correct one has negative concavity...I've checked this so many times and can't find my error. I wanted...

Homework Statement Rectangular barrier of width a and height V0 with an E < V0. What is the transmission ratio, T? Homework Equations T = C*C/A*A What am I missing in my attempted solution (variable name = TChip), which is different from the known solution (variable name = TSoln)? The Attempt...

Hi Guys :) I have become interested in producing true random numbers of uniform distribution, and have come across this Numberphile video in my travels: The narration hints at the topic of converting numeric sequences of a curved distribution, inherently more likely to be closer to a mean...

Homework Statement If the area of a rectangular field has length of 110 m and 80 m.If a spaceship is traveling with 0.9c velocity along the diagonal of the field.Then what is the area of the field seen by the astronaut in the spaceship? Homework Equations L=L(initial) Root over (1- (v/c)^2)...

Iam having trouble understanding how one arrives at the transformation matrix for spherical to rectangular coordinates. I understand till getting the (x,y,z) from (r,th ie., z = rcos@ y = rsin@sin# x = rsin@cos# Note: @ - theta (vertical angle) # - phi (horizontal angle) Please show me how...

I need an android calculator app that will convert between rectangular and polar. I need these keys: ->R and ->P

Covert to polar $$y=3 x$$ I got... But it didn't plot on desmos... Can't show polar graph here? $$r\sin\left({\theta}\right)=3r\cos\left({\theta}\right)$$

Prepare a function m-file containing a function that converts polar coordinates in two-dimensional space to rectangular (Cartesian) coordinates. Include a suitable H1 line and some additional comment lines. The input will be 2 vectors, and the output will be 2 vectors. The length of each vector...

Homework Statement Find the volume of the solid region that lies inside the cone φ= pi/6 and inside the sphere ρ=4. Use rectangular coordinates. Homework Equations x=ρ sinφ cos θ y=ρsinφ sin θ z=ρ cos φ ρ^2=x^2+y^2+z^2 x= r cos θ y= r sin θ r^2=x^2+y^2The Attempt at a Solution at first...

Hi all, I am looking for a precise definition of " Crow Flies Distance" on a rectangular grid. I have not found a precise definition yet, but from what I have read, I think it would be the standard Euclidean distance ## d((x_1,y_1),(x_2,y_2)) = \sqrt {( (x_1-x_2)^2+(y_1-y_2)^2}) ## Is this...

Homework Statement The problem I'm stuck on is to come up with an equation which will model the path of the projectile in an xy-plane. We are given: r(t)={ [(v0cos(θ))t], [h+(v0sin(θ))t-(½)gt2] } v0=100 ft/s θ=60° h=4 ft so basically, r(t)={[100cos(60)t], [4+100sin(60)t-16t2]} Homework...

Hello, I have to calculate the air flow through a small rectangular opening with following data: - temperature at one side: 1200°C - temperature at other side: 20°C - pressure at hotter side is 3 mm WC lower than the colder side - the length of the opening is 240 mm - the width of the opening is...