coordinates

1. To find a system of coordinates for visualise a system of equations

Given a system of equation (and its inverse): A = \frac{\alpha + \beta}{2} B = \sqrt{\alpha \beta} \alpha = A + \sqrt{A^2-B^2} \beta = A - \sqrt{A^2-B^2} Which is the best system of coordinates (not necessarily orthogonal) that represents graphically these equations? OBS: A is a real...
2. Calculate Area of Ellipse using Elliptic Curvilinear Coordinates

The question is for an ellipse in the form of ((x^2)/(a^2))+((y^2)/(b^2))=1 where a,bâ‰¥0 are constants. Use the elliptic coordinates of the form vec(r)=(x,y)=(p*cosh(u)cos(v),p*sinh(u)sin(v)) where uâ‰¥0, 0â‰¤vâ‰¤2Ï€, p>0 to find the area of the ellipse. (HINT: (In the question) Assume a>b and...
3. Polar coordinates for volume using the double integral

1.) Using polar coordinates, set up the double integral to find the volume of the region above z = 0, below z = x, between y = \sqrt{4-x^2} and y = |x|. \displaystyle \int_0^{2\pi} \int_{-2}^2 \left(\sqrt{4-x^2}\right) r\ dr d\theta \displaystyle \int_0^{2\pi} \int_{-2}^2...
4. Finding line intersect coordinates - where am I going wrong?

Hey guys, Got a couple of questions here asking about line intersecting points. I have had a go at part (a) but when I checked my answer using a graph drawing tool, the second coordinate of the intersect is not what I found :confused: Can anyone help me see where I've gone wrong?
5. Converting Polar to Cartesian Coordinates

Hi there, I'm currently stuck on a problem, and have no idea where to start on it. I've tried converting it to rectangle form, then trying to solve it from there, but I'm still confused. r=\frac{4}{2\cos( \theta )-3\sin( \theta )}
6. Find coordinates on a, b, c, d such that AB=BA

Hi all, Kind of stuck here...Setting the matrices equal to each other, but am not sure of what to do next. Thanks in advance! Matrix A = 1 1 0 1 Matrix B = a b c d AB = (a+c) (b+d) (c) (d) BA = (a) (a+b) (c) (c+d) a + c = a b + d = a + b c =...
7. Expressing already known surface area element in spherical coordinates.

Hi. I'm trying to find the surface area of the shere xÂ² + yÂ² + zÂ² = 8Â², that lies over z = 1. I'm having trouble finding the surface area in polar coordinates. G(x, y, z) = xÂ² + yÂ² + zÂ² - 8Â² = 0 the normal of the surface is the gradient of G = n = 2x i + 2y j + 2z k. dS = |n| dx dy =...
8. How to find the coordinates of the endpoints?

I am going to write down a problem below. (ex) Consider the parabola, y = x^2 + 1. Suppose that there is a horizontal line segment parallel to the x-axis and whose endpoints are on the parabola. Find the coordinates of these two endpoints if the line segment is 6 units long. Could...
9. ODE system (solving using polar coordinates)

Hi all, I'm having some problems to solve the following system of ordinary differential equations (one must turn it into polar coordinates): \left\{\begin{matrix} \dot{x} = (1-x^2-y^2)x - y& & \\ \dot{y} = x + (1-x^2 - y^2)y& & \end{matrix}\right. I must verify if it has...
10. how to find next coordinates of x and y axis if given two points.

hi, i have coordinate of two points with which i can make a line. i want to find out next point of coordinate on the any scale, so that i can extend the line, mathematically with out using graph. yours sincelrey.
11. How to find coordinates from a known position given length and angle?

I have two points A and B represented as coordinates xA,yA and xB,yB respectively. Point A is fixed but B position is variable along it's current trajectory. This can be visualised as below where B may move along the the line or may move away from A as if the line was projected further...
12. right isosceles triangle

Hi, I am writing the code for a program that calculates the coordinates of point C which satisfies the following: BC is perpendicular to the line AB BC=AB In summary, the user enters x and y coordinates of point A and B and my program has to calculate coordinates of R, which create a right...
13. finding coordinates

Hi all - Please help me to get the correct formula for this equation. Area (width = 1920, height = 1080) Coordinates (x = 1102, y = 666) If I reduced the width to 500 and height to 400. What will be the new x,y coordinates?
14. Converting between polar and cartesian coordinates (No calculator)...

I have been reading a book and one of the exercises involves converting between polar and Cartesian coordinates but without a calculator so when x = 4 and y = 3 then the answer is r=5 and Î¸ = tan^-1 (3/4) which is fine but then for some of the answers you know what the values are so when x = -1...
15. Cartesian to spherical coordinates

Given the equation: f(x,y,z)=c*((x^2+y^2+kz^2+2b^2)/(a^2+2b^2)) Where c, k, a and b are just constants. Transform this from cartesian to spherical coordinates. I know the general equations, but I can't figure out how to apply them to this problem. Please help.
16. Function for linking many coordinates

So i have like 100 of (x,y) coordinates, and I need algorytm that would make smooth function that links/connects these coordinates. :furious:
17. Get coordinates of every point inside an ellipse and detect intersection of 2 ones.

1. Get coordinates of every point inside the ellipse. 2. Detect intersection of 2 ellipses. You can assign your own variables, the next is just an example: (x, y) = coordinates of the common system. (a1, b1) = width and height of the ellipse 1. r1 = radius of the ellipse 1. (a2, b2) = width...
18. Use coordinates to make a formula

Coordinates: x -11, -6, -1, 0, 2, 4, 6, 10 y 1.997, 1.876, -2, -6, -30, -126, -510, -8190 Is it possible to find the formula? If so, how? Thanks for help Edit: You can also gimme a link with a lesson perfect for this problem.
19. N [60, 4, 4, 32, 2, 3, 1]Â° To coordinates, How?

Hello! I have tried to figure which category this goes, but i dont know so i put it here. This is too difficult to me so if somebody can solve this it would be great! Hint is Chain Burglar Chapter and one word means something helpfull, maybe Chain? Too difficult to me. N [60, 4, 4, 32...
20. Geometry question involving spherical coordinates and longitude and latitude.

Hi, I'm almost completely stuck on this question: http://i.imgur.com/SpUJYCm.png [1] I realize that p must be equal to the earth's radius if the point is on the surface of the sphere. My strategy, for now, is to first find the values for theta and psi for both Melbourne and London. From there I...