Recent content by mrcleanhands

  1. M

    B Optimisation problem

    Firstly, I'm not even sure how to frame this mathematically, but I'd be curious to know what kind of problem it is and what kind of subjects within maths it requires to be able to solve it. Here's my problem-- I've set it up in excel to help you visualise it. There is a different amount of...
  2. M

    Parameterising a line given by two points

    I'm working on a green's theorem integral and I'm given a line (0,0) to (1,2) which i parameterise as (t,2t) but the answer is actually (1-t, 2(1-t)) and if I use my parameterisation on the integral I get a different answer!
  3. M

    Spherical coordinates

    Yeah, I don't really get why z=1 gives \tan\phi=\pm\sqrt{3} I can get this if I convert to spherical co-ordinates straight away but not by solving the intersection of the rectangular coordinates. Also while there are no negative in spherical co-ordinate radians I get \phi=\pm\frac{pi}{3}
  4. M

    Line integrals in physics

    How is weight not linked to C? to find weight/mass you must take a line integral through that plane, and that line integral is C. What I was confused about is if I take a 3cm wire and position it from (0,0) to (0,3) and then I move it to some other place in the xy plane suddenly it's weight...
  5. M

    Line integrals in physics

    Wasn't sure which section to put this q in. Just reading now that f(x,y) can represent the density of a semicircular wire and so if you take a line integral of some curve C and f(x,y) you can find the mass of the wire... makes sense. What I don't get is that if I then move the wire around the...
  6. M

    Line integrals

    oook so it is actually a curtain area still except this time it's the relevant area under the plane z=2x
  7. M

    Line integrals

    When I think line integral - I understand when I'm taking a line integral for a function f(x,y) which is in 3D space above a curve that the integral is this curtain type space, just like if you had a 2D function and you find the area under the curve, except now it's turned on its side and it's...
  8. M

    Spherical coordinates

    Cool, I see it now. This. x^{2}+y^{2}=3z^{2} \rho^{2}\sin^{2}(\phi)\cos^{2}(\theta)+\rho^{2}\sin^{2}(\phi)\sin^{2}(\theta)=3\rho\cos^{2}(\phi) \sin^{2}(\phi)=3\cos^{2}(\phi) \tan^{2}\phi=3 \tan\phi=\pm\sqrt{3} \phi=\pm\frac{\pi}{3} Ok. I see you've found the intersection using the...
  9. M

    Spherical coordinates

    Homework Statement Find VR_{z}^{2} = \int \!\!\! \int \!\!\! \int_{E} (x^{2} + y^{2})dV given a constant density lying above upper half of x^{2}+y^{2} = 3z^{2} and below x^{2}+y^{2}+z^{2} = 4z. Homework Equations The Attempt at a Solution Why does it say upper half of x^{2}+y^{2} =...
  10. M

    Improving problem solving skills

    I've often been plagued by the thought of being unintelligent and slow compared to others. I seem to take much longer to understand concepts and work out problems. With that said, I do really well at school (but also put in much more time than others). I'm also quite obsessive when it comes to...
  11. M

    Python Trouble understanding recursion (Python)

    I'm trying to understand a function which draws a koch curve using a library which draws (lt = left turn, fd = move forward, t represents an object class). def koch(t, n): if n<3: fd(t, n) return m = n/3.0 koch(t, m) lt(t, 60) koch(t, m) rt(t, 120)...
  12. M

    Algorithm for drawing an arc

    Hi, I'm working through thinkpython and there is an exercise which requires drawing flowers and arcs. I'm having some trouble understanding the arc function. def arc(t, r, angle): """Draws an arc with the given radius and angle. t: Turtle r: radius angle: angle subtended by the...
  13. M

    Center of mass of a lamina

    Homework Statement The boundary of a lamina consists of the semicircles y=\sqrt{1-x^{2}} and y=\sqrt{4-x^{2}} together with the portions of the x-axis that join them. Find the centre of mass of the lamina if the density at any point is proportion to its distance from the origin. Homework...
  14. M

    Trouble taking 2nd deriv of multi variable

    I know what I did wrong and I finally understand the question. I was taking the second derivative of dz/dr and used the product rule but r is independent of \theta so when I treat \theta as a constant I get the same answer as you. Thanks again for helping me out guys! much appreciated.