Recent content by Kork

Homework Statement Let D be the set of points (x,y) in R^2 for which 0 is ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find a function g: R^2 --> R for which: ∫_0^1 ∫_0^1 h(x,y)dxdy = ∫_0^1∫_0^1 h(y^5, x^3) * g(x,y)dxdy is true for all functions h: D--> R integrable over D In the question before this I...

Homework Statement Determine the field lines of the vector field f: R^3 --> R^3 defined by f(x,y,z) = (x/(1+z2) , y/(x2+y2) , 0) Homework Equations The Attempt at a Solution I know that my vector field is: F(x,y,z) = (x/((1+z^2)*(x^2+y^2))*i + (y/((1+z^2)*(x^2+y^2))*j + 0k I choose...

I am also asked to: let D be the set of points (x,y) in R^2 doe which 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find a function g: R^2 --> R for which ∫10∫10 h(x,y)dxdy = ∫10∫10 h(y5, x3*g(x,y)dxdy is true for all functions h: D --> R integrable over D

Okay, thank you. But I have another question, what is the difference between the Jacobi Matrix and the Jacobi determinant?

So if I do like this: z*2 = ((12/25)x - (6/25)y+4/5) * 2 it can be concidered a valid answer?

Homework Statement The transformation f is defined by: R^2 --> R^2 and is defined by: f(x,y) = (y^5, x^3) Find the jacobi matrix and its determinant Homework Equations f(x,y) = (y^5, x^3) The Attempt at a Solution I would start by differentiating y^5 with respect to x and then y, then...

D is a set of all points (x,y) in R2 distinct from (0,0). I have the funtion f: D --> R which is defined by: f(x,y) = (2xy)/(x2+y2 Im asked to find the equations (in plural) of the tangelnt plane and the normal line to the graph of the function at (1,2) My attempt: I use the tangent plane...

Thank you very much!

I don't think I quite understand the buoyancy part. If I tak a cointainer with water and take out an imaginaray area then the forces on the area would be the buoyancy and the gravitationa pulling down? Right?

Hi :) When I have a container with water and put a piece of metal down in the water while it's hanging on the string, I know that there will be two forces pulling it upwords: B = δVg and the string force T But the force pulling it down, is that the gravitation? Or is it a force that...

Or is this correct: In the start I have that: E = mgh + 1/2mv^2 What about when it hits the ground?

Hi again! So, this time I have a ball with a mass m that I throw down from some point with a height h. I want to write the kinetic and potentiel energies that the ball has in the start and in the end for this ball that is falling to h=0. What I have thought of is that the ball must...

Thank you guys very much. This has helped a lot!

Im danish :) Sure I will hang on, I have confused myself completely.

Du er svensk :)