Cartesian Definition and 549 Threads

Homework Statement Let A be the set that contains all rational numbers, but not zero. Let (a,b),(c,d) \in A×A. Let (a,b)\tilde{}(c,d) if and only if ad = bc. Prove that \tilde{} is an equivalence relation on A×A.Homework Equations The Attempt at a Solution The solution just needs to show...

Homework Statement Homework Equations The Attempt at a Solution my only problem curently is in finding the angle θ. I do get the equation x^2 + y^2 =1 however am confused whether this would be a semi-circle on the positive axis or a full circle. because my teacher has notes that...

Hello how can Convert Cartesian coordinates to spherical with shape? for clear my question i explain a way to convert my coordinates in different spherical. for example i use this diagram to convert Cartesian coordinates to Cylindrical(with image to axises) for example: now how can i do...

- Hi guys, I'm new to this forum and was just wondering if I could receive some help on this question. I'm really struggling to complete it. Consider the plane in R3 with the Cartesian equation x + 7y − 2z = 0. (You may assume that this is a subspace of R3.) (a) Find a vector equation...

I basically am looking for an efficient way to implement the following: I have ten inputs, {A,B,C,D,E,V,W,X,Y,Z}. I have twenty-five outputs that I need to implement: {AV,AW,AX,AY,AZ, BV,BW,BX,BY,BZ, CV,CW,CX,CY,CZ, DV,DW,DX,DY,DZ, EV,EW,EX,EY,EZ}. Obviously, a brute force way to do this would...

I am pretty much satisfied with the example of a rotating shell example 5.11 pg 367 griffiths electrodynamics.on many ocassions he chooses cartesian coordinates before integration (see 5.10 too) , integrates and finds w×r along y direction .then he manipulates w×r, and writes it down in...

Let f be a continuous function from R to R and let A be a subset of R^2. Define A={(x,y): y<f(x)}. Can you express A as a cartesian product of two open sets? I tried RxU alpha_x where alpha_x = {y:y<f(x)}. But that didn't work, i need to change something about R.

Homework Statement "You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine...

Homework Statement A curve is defined by the parametric equations: $$x=tan(t-1)\ \ \ \ \ \ \ y=cot^2(t+1)$$ Homework Equations The Attempt at a Solution I think rearranging the first equation for t gives: $$t=tan^{-1}(x)+1$$ However that doesn't help me as I don't know how to...

Homework Statement Evaluate the appropriate determinant to show that the Jacobian of the transformation from Cartesian (this is a typo, they mean spherical) pψθ-space to Cartesian xyz-space is ρ2sin(ψ).Homework Equations The Attempt at a Solution Uhm, I am lost. I'm supposed to prove that when...

Homework Statement Suppose that A and B are finite sets. What is |P(AxB)|? Meaning what is the cardinality of the power set of a cartesian product of the sets A and B. Homework Equations |AxB|=|A| * |B| since A and B are finite sets Power set of a set is the set of all subsets of...

Homework Statement Plot the following point: B(-2,3,5) The Attempt at a Solution If I were to plot (-2,3,5), when I make my first movement of -2, it does not move anywhere on the y-axis correct and when I am moving on my Y axis, There is no movement in the z axis?

Homework Statement Prove the La Placian of V(x,y,z)=(zx^{2})/(x^{2}+y^{2}+z^{2}) in Cartesian coordinates is equal to that in Spherical coordinatesHomework Equations \nabla^{2}V=0 The Attempt at a Solution I have attempted to calculate all the terms out, and there were A LOT. I was hoping...

Homework Statement Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat. Homework Equations r-hat=cos(phi)x-hat+sin(phi)y-hat phi-hat=cos(phi)y-hat-sin(phi)x-hat, The Attempt at a Solution I have been working on this for a really long time, and I keep getting a...

Homework Statement It's given that absolute permitivity is a coordinate function: ε (x, y, z) = Asin(x)cos(y), where A=const Homework Equations We need to find an electrostatic field potential function \varphi in Cartesian coordinate system. The Attempt at a Solution I tired to solve, but...

Homework Statement If the line "l" is given by the equations 2x-y+z=0, x+z-1=0, and if M is the point (1,3,-2), find a Cartesian equation of the plane. a) passing through M and l b) passing through M and orthogonal to l Homework Equations (r-r0)n=0The Attempt at a Solution I expanded the...

I'm volunteering in a summer school for year 12 students in my area, and have to teach them a few topics. I've been struggling to get the parametric equations from this. Sketch: |z| = \arg(z) So I thought that the obvious way to explain it to them would be to say: "that as the magnitude of...

Find the Cartesian Form of r(1+sinθ)=a I understand that: x=rcosθ y=rsinθ and r2=x2+y2I can get quite far to the point I end up with x2=a2-2ay I'm struggling to eliminate "a"...

If we were to consider a nucleon-nucleon interaction: We know that the incident wave (plane wave) is ψ= Ae^{ikz}, propagating in z direction But for some mathematical facilities, we tend to use spherical coordinates, the wave becomes = \frac{A}{2ik}[e^{ikr}/r - e^{-ikr}/r] How come...

Problem Solution answer For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.

Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...

There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant. Question...

Let $AB$ be the distance between the two points $A(x_{1} ~ x_{2})$ and $B(x_{2}, ~ y_{2})$ -- e.g. $AB = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$. Why is the point $P$ which divides $AB$ in the ratio $\lambda:\mu$ given by $\displaystyle ~~ \bigg(\frac{\lambda x_{2}+\mu x_{1}}{\lambda+\mu}, ~...

Homework Statement Change the Cartesian integral to an equivalent polar integral and evaluate ∫∫dydx The bounds of the first integral (The outermost) are -5 to 5, and the bounds of the second (inner) are 0 to \sqrt{ 25-x^{2}}Homework Equations ∫∫dydx == ∫∫r(dr)(d\Theta) x^{2}+y^{2}=r^{2}...

Homework Statement Let A = {1, 2}, B = {3, 4}, C = {3} What is (A x B) - (B x C)? Homework Equations The Attempt at a Solution (A x B) - (B x C) = {(1, 3), (1, 4), (2, 3), (2, 4)} - {(3, 3), (4, 3)} = {(1, 3), (1, 4), (2, 3), (2, 4)} Since there where no elements in (B x...

Hi, everyone. I'm practicing Cartesian products and wanted to see if I was doing this correctly. Here's the problem Let A = {x, y, z}, B = {a, b}, C = {1, 3}, Find B x (C x A) (the x denotes multiplication) Now wouldn't B x (C x A) = B x C x A? Then we would have: B x (C x A) = B...

Homework Statement I'm trying to get to grips with Godel's 1949 Paper on Closed Time-like Curves (CTCs). Currently I'm trying to confirm his transformation to cylindrical coordinates using maple but seem to keep getting the wrong answer. Homework Equations The line element in cartesian...

Hi all, I was wondering how would one go about converting a displacement vector in cartesian coordinates to cylindrical. I am getting a bit confused on how to deal with the unit vectors; converting a point in space is a simple task, but when it's a vector it just confuses me. I am specifically...

Imagine I have a set of discrete points equally spaced out and indexed from 1 to n (a 1D grid). On a cartesian grid if the spacing, dx, is constant the index can be obtained simply by: i = floor(x/dx) That was pretty simple, now if the cartesian grid is stretched (i.e. dx is not constant)...

Homework Statement Here is the problem and solution but I am confused as to part B http://gyazo.com/e77d05fc67cb6ac266ff021ef88052dc The Attempt at a Solution I understand the first part, but I am totally lost on how they reached their cartesian answer for part B. Firstly why did they...

Homework Statement Hi The expression for the magnetic field from an infinite wire is \boldsymbol B(r) = \frac{\mu_0I}{2\pi}\frac{1}{r} \hat\phi which points along \phi. I am trying to convert this into cartesian coordinates, and what I get is \boldsymbol B(x, y) =...

Just curious, does anyone know what are the equations for the displacement-time graph of a Keplerian orbit? The horizontal displacement-time graph should be somewhat sinusoidal, the vertical one cosinusoidal, or vice versa.

If A and B are vector spaces over ℝ or ℂ show that a sequence (a_n, b_n) in A×B converges to (a,b) in A×B only if a_n converges to a in A and b_n converges to b in B as n tends to infinity. To me this statement sounds pretty intuitive but I have been having trouble actually proving it...

Homework Statement I need to isolate the expressions for ellipsoidal coordinates (see below)... I'm given: x2=\frac{(a^2+\lambda)(a^2+\mu)(a^2+\nu)}{(a^2-b^2)(a^2-c^2)} y2=\frac{(b^2+\lambda)(b^2+\mu)(b^2+\nu)}{(b^2-a^2)(b^2-c^2)}...

Homework Statement Express the following equation in Cartesian form r = 1 - cos(θ) Homework Equations x = r*cos(θ) y = r*sin(θ) r^{2} = x^{2} + y^{2} tan(θ) = \frac{y}{x} The Attempt at a Solution I have no idea... a hint would be nice thanks! BiP

Homework Statement Rectangular pipe, infinite in the z direction. The sides in the y-z plane (at x=0 and x=a) are held at V=0, while the sides in the x-z plane (at y=0 and y=b) are held at V=V0 Explain why there cannot be a non-trivial solution to this configuration. Homework...

A text I am reading displays the attached image. Can someone explain the general method for obtaining the velocity analogues of those terms (in parentheses) in 1.5? I know the second and third terms in parentheses in 1.6 and 1.7 are the squares of angular velocities, but can a general procedure...

Homework Statement I am stuck at this point where I have to prove that the kronecker delta is isotropic tensor. Homework Equations δij=δji The Attempt at a Solution I know that to prove this I have to show that under coordinate transfor mation it does not change..but it's a bit...

Okay I need to rotate a parabola on a cartesian coordinate system, y=x^2 by 90 degrees about the origin (either direction) without using piecewise, or inverse functions. Basically I am trying to use translations and deformations to accomplish this. Anyone thoughts?

Homework Statement Please see the rotation formula in the attachment. Homework Equations The Attempt at a Solution I understand this formula rotates x,y into x',y' by some angle theta. Problem is, how is this formula derived? I cannot for the life of me visualize the cosine and...

I was given the problem r=2sin(2(θ)). I'm supposed to write the equation in the Cartesian Coordinates. I understand the basics to this but I'm not really sure how I'm supposed to write the equation when I have x=2sin(2(θ))cos(θ) and y=2sin(2θ)sin(θ).

Homework Statement Find the Cartesian Eqationn of the plane containing the points (0,-2,6), (1,8,-2) and (2,0,5). Homework Equations The Attempt at a Solution → OA = 0,-2,6 → AB = 1,10,8 → AC = 2,2,-1 Cross product of AB AC = 6,-15,-18 X - 0 * 6 Y - (-2)...

Homework Statement Prove that A\times(B\capC)=(A\timesB)\cap(A\timesC) In particular what I cannot prove is (A\timesB)\cap(A\timesC)\subseteqA\times(B\capC)Homework Equations The Attempt at a Solution In order to learn how to deal with proofs I am reading How to prove it: a structured...

The solution to a linear differential equation is, y=exp(ax). If a is complex ,say a=b+ic, then the period is T=2pi/c. My question is, if a is in polar form, a=r*exp(iθ), how is the period then T=2pi/θ. Any help would be great, Thank, Will

Hello all, I've got a quick question, I am sure it will be resolved by the first comment, but I'm just looking for a quick answer. I brought home a pipette from my mothers lab last week and made a cartesian diver to show my wife, it worked perfectly for about 3 days, then yesterday...

How would you graph a square of any dimension on the cartesian coordinate system?

Hello, I recently run into a problem. Let's say I have the point (a,b) and (-a,-b). The, I know that θ_1 = atan(b/a) and θ_2 = atan((-b)/(-a)) = θ_1. But, what if I want to go back to Cartesian coordinates? If I assume r = 1, a = cos(θ_1) and b = sin(θ_1) while -a = cos(θ_2) and b =...

1. Find a Cartesian equation to represent the curve r = 9 cosθ 2. I know that rcosθ= x and cos θ= x/r 3. I got (x-9/2)^2 +y^2 = (9/2)^2 but its coming up wrong when I put it into our online homework. Can anyone help me?

Let A={1, 2} and B={∅}. First, I find the power set of A and the power set of B: P(A)= { ∅, {1}, {2}, {1, 2} } P(B)= { ∅, {∅} } I believe the power sets are correct. I'm still new to the concept of power sets. Anyway, my main question is regarding cartesian product of power sets. I'm...

I'm reading through a multivariable calculus book and it starts off with some linear algebra. It defines vector addition as V \times V \rightarrow V. My text describes V as a set and describes the above process as a mapping. I believe the \times may represent a Cartesian product. Could someone...