Rectangular Definition and 451 Threads

  1. U

    TE Waves in Rectangular Wave Guide

    Hi guys I'm having difficulty understanding why the boundary conditions lead to dX/dx = 0. Why must Bx = 0 at x = 0 and x = a?
  2. L

    Convolution of a linear and rectangular function

    Hi everyone Homework Statement I want to to calculate the convolution of the following two functions h(t)=\left\{\begin{array}{ll} t, & 0 \leq t \leq 10 \\ 0, & otherwise\end{array}\right. and the function x(t)=\left\{\begin{array}{ll} A, & 0 \leq t \leq 10 \\ 0, &...
  3. S

    Couple calculations Polar to Rectangular Form

    Homework Statement I need to find i1+i2 Homework Equations for i1=0.092<-98.86 i2=-4i1-j10/25=-4i1-0.4 i1=0.092<-98.86 x=rcosθ=0.092cos(-98.86)=-0.0142 y=rsinθ=0.092sin(-98.86)=-0.0909 i1=-0.0142-j0.0909 Therefor...
  4. karush

    MHB Convert r = 5sin(2θ) to rectangular coordinates

    convert $$r=5\sin{2\theta}$$ to rectangular coordinates the ans to this is $\left(x^2+y^2\right)^{3/2}=10xy$ however... multiply both sides by $r$ to get $r^2=5\cdot r \cdot \sin{2\theta}$ then substitute $r^2$ with $x^2+y^2$ and $\sin{2\theta}$ with $2\sin\theta\cos\theta$ and divide each...
  5. B

    Load Impedences - Rectangular to Polar

    Homework Statement Can you simplify rectangular expression 1/j30 + 1/10 + 1/(15-j25) The answer is .134 angle(28.07) Homework Equations The Attempt at a Solution I got = 1/j30 + 1/10 + 1/(15-j25) = -j.03+.1+.06+j.04 = .16 + j.01 = .16 angle(3.57) The...
  6. M

    Nyquist frequency for a system with rectangular pixels

    hey everyone, so i know to calculate the nyquist frequency for a system (for digital imaging in PET and SPECT in this example) given the pixel size its just f = 1/ 2 * pixel size but for pixels that are rectangular and have a larger and smaller dimension, which one should be used here...
  7. F

    Rectangular Waveguide With Dipole in it

    Hi, I know that to receive or inject a signal into a rectangular waveguide (I'll just call it a waveguide from now on with the assumption that I mean rectangular waveguide), you can get a dipole of some sort, and poke it into the waveguide. What I'm wondering about is, if I got a dipole...
  8. S

    Chemical Engineering Computation - Rectangular Matrix Formulation

    Hello all, I've got a somewhat mixed concept question from a Chemical Engineering computational methods class. I'm completely lost with this question, as I do not fully understand what it entails. The question (and data) is this: Homework Statement Data Set Given X Y 0.00 -2.17...
  9. R

    Rectangular function & Inequalities

    Note: I think I solved this while writing this topic, did not want to scrap it! if you think its wrong let me know! I am trying to manipulate the rectangular function with different arguments and came across a confusing one Trying to show: \prod (x^2) = \prod (\frac{x}{\sqrt{2}}) Recall that...
  10. J

    Spherical cylindrical and rectangular coordinates

    Homework Statement Suppose that in spherical coordinates the surface S is given by the equation rho * sin(phi)= 2 * cos(theta). Find an equation for the surface in cylindrical and rectangular coordinates. Describe the surface- what kind of surface is S? Homework Equations The...
  11. K

    TM waves in a rectangular waveguide

    Homework Statement Having trouble understanding why it is that inside a waveguide sides x=a,y=b propagating in z, subject to b.c. E parallel= 0 and Bperp=0... that for TE Bz=Bcos(pinx/a)cos(pimy/b) but for TM Ez=Esin(pinx/a)sin(pimy/a)? Homework Equations E parallel= 0 and Bperp=0 For...
  12. A

    Finding the Fourier Series of a periodic rectangular wave

    Homework Statement The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave. Homework Equations The file called "solution" presents a detailed solution to the...
  13. H

    Possible Rectangular Potential Barrier Transmission Problem

    1. The Problem Statement An electron of effective mass m* = 0.2me and energy E = 0.1 eV hits a barrier of height 0.4 eV and width t = 5 nm. What is the probability of transmission through the barrier? Use the simplest estimate which is an exponential function. Homework Equations I think...
  14. A

    Torsion of rectangular cross section rotated at an angle?

    I want to use a rectangular cross section to act as a torsion spring that can be adjusted. The idea is that the adjustment would be made via rotating the rectangular cross section about it's center at an angle theta. I've used parallel axis theorem before, but I don't think that is applicable...
  15. O

    The moment of inertia of a rectangular plate about its diagonal

    Homework Statement Find the moment of inertia of a rectangular plate of mass m, sides 2h and 2k , rotates about its diagonal. Homework Equations I= Ʃmr^2 The Attempt at a Solution I=Ʃ m(x^2 +y^2) , let 2h parallel to x-axis, 2k parallel to y-axis. I= m(x cosθ)^2 + m (y cos ∅)^2 where...
  16. Philosophaie

    Formulating x^n Coordinate System for Non-Rectangular/Spherical Riemann Manifold

    I want to be able to formulate x^{n} coordinate system. x^{n} =(x^{1}, x^{2}, x^{3}, x^{4}) How do you do this when the Riemann Manifold is not rectangular or spherical? Also how do you differentiate with respect to "s" in that case. \frac{dx^n}{ds}
  17. L

    Complex numbers rectangular form

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...
  18. K

    Analytical solutions for electric field of finite rectangular sheet

    Hi, I have been trying to find analytical solutions for a finite rectangular sheet, say, in the xy plane, with dimensions a and b. Assume it is uniformly charged. An excellent (and short) description of the problem is here. The three integrals for Ex(x,y,z), Ey(x,y,z) and Ez(x,y,z) given on...
  19. A

    Confused about vectors into rectangular components

    So, i have been learning about forces, vectors and such. I know many times for convience we break vector forces into rectangular components...fx=Fcostheta, fy=Fcostheta. It is easier to do regular alegbra verus vector alegrba My question is both fx and fy are scalars, but then they can be...
  20. B

    Uniqueness of identity elements for rectangular matrices

    Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the identity matrix and it is unique. The proof follows from the monoidal properties of multiplication of square matrices. But if the matrix is not square, the left and right...
  21. F

    A Beam of rectangular cross section 200mm deep and 100mm wide

    Homework Statement Please visit my flickr link for a scanned image of the problem statement. http://www.flickr.com/photos/93763273@N05/8815418518/lightbox/ Homework Equations M/I = σ/y = E/R This is the flexure or bending formula. The Attempt at a Solution a) = 8.333 kN...
  22. S

    Projection of a distance in rectangular coordinates

    My problem is that I believe I have a wrong concept somewhere, and I can't find what I'm doing wrong exactly. For this problem let's suppose what I want to do is find the rectangular coordinates of BC. I had two "possible solutions" I tried to achieve this, . First the correct one: (I...
  23. M

    Laplace's Equation: Steady-State Temperature in a Rectangular Plate

    Homework Statement A long rectangular metal plate has its two long sides and top at 0°. The base is at 100°. The plate's width is 10cm and its height is 30cm. Find the stead-state temperature distribution inside the plate. Homework Equations ∇2T = 0 T(x,y) = X(x)Y(y) X(x) = Acos(kx) +...
  24. Saitama

    Velocity of end points of rectangular frames

    Homework Statement (see attachment, ignore those marks done with the pen) Homework Equations The Attempt at a Solution I think this has to do with calculating torques and forces but I don't know about which point to calculate torque about. I know this is a very less attempt...
  25. MarkFL

    MHB Convert 7sqrt5 cis(tan−1 (2)) to Rectangular Form - Yahoo! Answers

    Here is the question: Here is a link to the question: Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  26. E

    Triple Integration from Rectangular to Spherical Coordinates

    Homework Statement Convert the integral from rectangular coordinates to spherical coordinates 2 √(4-x^2) 4 ∫ ∫ ∫ x dz dy dx -2 -√(4-x^2) x^2+y^2 Homework Equations x=ρ sin∅ cosθ y=ρ sin∅ cosθ z=ρ cos∅ In case the above integrals cannot be understood: -2...
  27. Petrus

    MHB What is the Result of Raising a Complex Number to a Power?

    Hello MHB, calculate $$\left(\frac{1}{2}+i\frac{\sqrt{3}}{2} \right)^{100}$$ in the form $$a+ib$$ progress: I start to calculate argument and get it to $$r=1$$ (argument) then $$\cos\theta=\frac{1}{2} \ sin\theta=\frac{\sqrt{3}}{2}$$ we se it's in first quadrant( where x and y is positive)...
  28. C

    A uniform rectangular block of length 37.0 cm is placed so that its ce

    Homework Statement A uniform rectangular block of length 37.0 cm is placed so that its centre of mass is a distance of 1.50 cm away from the edge of the table. Since its centre of mass is still over the table (i.e. not sticking out past the edge), the block is stable. An identical block is...
  29. C

    A force F is exerted on the top right corner of a rectangular plate at

    Homework Statement A force F is exerted on the top right corner of a rectangular plate at an angle 60o above the horizontal, as shown below. The magnitude of the torque of the force F about point A, the lower left corner is given by See picture please ...
  30. S

    Fair to say there are twice as many square matrices as rectangular?

    Fair to say there are "twice" as many square matrices as rectangular? Is it fair to say that there are at least twice as many square matrices as there are rectangular? I was thinking something like this... Let R be a rectangular matrix with m rows and n columns, and suppose either m < n...
  31. K

    How to Calculate Heat Transfer Rate in Rectangular Fin Design?

    Homework Statement A straight, rectangular fin made from 2024 aluminium has a thickness of t = 3mm and length L = 20mm. Base temperature is 100 °C and it is exposed to a fluid at 20 °C. h = 60 W/m^2-K k = 185 W/m-K (a) Determine the heat transfer rate from the fin to the fluid per unit...
  32. G

    Will a rectangular truck fit into a half circle formed tunnel when

    A truck with a width of 2,40 and height of 3,41 is driving through a tunnel that is formed like a half circle and has the radius of 3,60. Will it work? Now, this is a very pathetic question because this is junior high level geometry. I could blame the incapacity to solve this question on...
  33. S

    MHB Triangular prism on top of rectangular prism in the shape of a house......

    What formula would you use to calculate the area (excluding the base)? What formula would you use to calculate the volume? What would its longest side be?
  34. E

    Transformations of Double Integrals with Rectangular Domains in the 1st Quadrant

    Suppose we have the double integral of a function f(x,y) with domain of integration being some rectangular region in the 1st quadrant: 0≤a≤x≤b, 0≤c≤y≤d. Would the following transformation generally be acceptable? (I've quickly tried it out several times with arbitrary integrands and domains...
  35. I

    I need to find a low deflection rectangular steel tube

    What I need is a 1"x.5" rectangular tube .065" wall and 84" long steel tube that will have the least or very low deflection. I have been trying to educate myself today on the different grades of SS which would be preferable for rust resistance. If I understand things correctly 304 SS is the...
  36. S

    Thermodynamics: Heating a Rectangular Box

    Homework Statement This question is from a thermodynamics test from a previous science olympiad competition that I am using to study from for a future test. "Consider two neighboring rectangular houses built from the same materials. One of the houses has twice the length, width, and height...
  37. A

    Eliminate T to Show SHM of a Rectangular Plate

    Q:A rectangular plate of sides a and b is supended from a ceiling by two parallel strings of length L each(Fig). The Separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute SHM. Find the time period...
  38. M

    Calculating Weight Savings with Rectangular Section Beam

    Here is the original question, i know the first answer as 182mm A square section cantilever beam, 3 m in length, carries a concentrated load of 10 kN at its free end. If the maximum bending stress is not to exceed 30 MPa determine the minimum dimensions of the section. Ans 182mm, What...
  39. Z

    Solving for the Height of a Rectangular Hyperbola

    Homework Statement An arch is the shape of a hyperbola. IF it s 300m wide at its base and has a maximum height of 100m, how high is the arch 30m from the end ? Note: this is a rectangular hyperbola. Homework Equations (y-h)^2 - x^2 = a The Attempt at a Solution I determined the...
  40. reddvoid

    Identifying Wave-guide modes in rectangular wave guides

    How to identify type of wave-guide mode here, like its TE or TM TE01 , TE10, TM11, TE02, TE20 . .. I read number of half wavelengths in x direction is the m and number of half-wavelengths in y direction is n. . .but I can't figure-out how . . .can somebody please explain
  41. A

    Curvilinear Motion: Rectangular Components

    Homework Statement What is the magnitude of the velocity at t=4.00s? I would like to see if my approach and answer is correct. Homework Equations Position: r = {-30cos(\frac{\pi}{10}t) i + 30sin(\frac{\pi}{10}t) j - (7t) k} ft The Attempt at a Solution I took the first...
  42. O

    Double Integrals, Rectangular Region

    Homework Statement Using ∫∫kdA = k(b-a)(d-c), where f is a constant function f(x,y) = k and R = [a,b]x[c,d], show that 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32, where R = [0,1/4]x[1/4,1/2]. Homework Equations ∫∫kdA = k(b-a)(d-c) 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32 The Attempt at a Solution I tried to...
  43. C

    Magnetic Field above a Rectangular Circuit

    Homework Statement On the XY there lies a conducting wire-rectangle with sides parallel to the axis. The current is given and constant. What is the magnitude of the magnetic field along an axis parallel to the z axis, going through the intersection of the rectangle's diagonals?Homework...
  44. W

    Matrix differential equation for rectangular matrix

    Given a matrix differential equation (system of equations?) of the form: \textbf{X}^{\prime}(t) = \textbf{AX}(t) (where X is a complex matrix, t is real scalar and A is always a square and normal real matrix) I am able to find (e.g. here) that a general solution for square \textbf{X} is...
  45. H

    Forces Concerning a Rectangular Prism

    Homework Statement I'm wondering this for any object with moment of inertia I, but I'll ask this question for a rectangle for simplicity and I'm sure I can extend it to general objects. Say we have a rectangular object (with mass m, height h, and width L) that is attached to a wall by some...
  46. W

    Rate of change of volume of a rectangular box

    Homework Statement How fast is the volume of a rectangular box changing when the length = 6 cm, width = 5 cm and depth = 4 cm and the length and height are increasing at a rate of 1 cm/s and width is decreasing at a rate of 2 cm/s. Homework Equations Volume of a rectangle = l*w*h The...
  47. D

    Optimization of a rectangular window surmounted on a semicircle

    Homework Statement A decorative window has the form of a rectangle surmounted by a semicircle whose diameter is equal to the top of the rectangle. If the TOTAL perimeter of the window 16+pi, then what is the maximum area? A. 25.653 B. 32.148 C. 15.923 D. 38.047 E. 30.018 Correct...
  48. Z

    Vector Question: 3 dimensions inside a rectangular soild?

    Vector Question: 3 dimensions inside a rectangular soild?? Homework Statement Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid along its three edges. a. Calculate the magnitude of the equilibrant of these three forces. b. Determine the angle that the equilibrant...
  49. R

    Trigonometric Methods - Calculating impedance in rectangular and polar forms

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...
  50. K

    Finding the inertia with a thin rectangular sheet

    A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b. Express your answer in terms of given...
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