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  1. Q

    Showing a vector field is imcompressible

    Do I treat the non-bold r as a constant? If sub in bold r, I get: G = [(x^2 + y^2 + z^2)^0.5 ] / 4*pi*r^3
  2. Q

    Showing a vector field is imcompressible

    Homework Statement Homework Equations The Attempt at a Solution As you can see, the solution is shown just below the question. Essentially, I don't understand how the x, y and z component of the vector field has been separated because the numerator of the vector field's fraction is: (x^2...
  3. Q

    How to work out expected frequency from normal distribution

    How is the expected frequency column worked out for each interval of trains? 2) My attempt Take the first interval, 60 - 62, I thought about doing this: (62 - mean) / standard deviation (62 - 67.45) / 2.92 = - 1.866 using Z score < - 1.886, from the normal distribution table, I get: 1 -...
  4. Q

    Determining the forces in a framework

    The framework is attached below. I've tried going to each joint and resolving the forces vertically and horizontally. I've got to joint B and I'm stuck, because I have three unknown members there. And its the same if I go to joint J. what do I do?
  5. Q

    Ground water flow question

    'head' is simply stress (or pressure) mulitplied by depth for total head is the total pressure as it were
  6. Q

    Ground water flow question

    Its attached below. I don't understand how you work out the total head. Can someone explain how you do it? I'm really struggling. I know how to do the elevation, which is just the height above/below the datum level. And I've checked the solutions as well, it seems like you're supposed to work...
  7. Q

    Determining forces in members of a structure

    Theres no rebuilding, I've built the thing, and now I've got to analyze it as it is (terrible situation I admit). The whole structure is supported at its two ends. One is shown on left of my diagram, hence there is a 4KN arrow, and the other is the right hand side of the structure which isn't...
  8. Q

    Determining forces in members of a structure

    This is actually half pf a complete structure (which I have designed and built), so I have omitted the rest of the right hand part in my diagram, but lets assume that we know the forces in the other members (caused by the applied loads). What I want to ask is, whether theres a way to work out...
  9. Q

    Determining forces in members of a structure

    Homework Statement I want to find the force in the vertical purple member. Assuming I know the forces in all the other members, theres a problem with working out the force in the purple member. (Bear in mind, I'm using the method where I assume equilibrium at each joint in the...
  10. Q

    Directional derivative question

    Sorry about that, what I meant to get across, was that I understood the method in a sort of algorithmic way, but didn't understood the reason behind steps due to not understanding some basic stuff like 'level curve'. Anyway its sorted now.
  11. Q

    Directional derivative question

    Thanks a lot!!! I understand whats going on now. Before I was just plugging in the numbers without knowing the concepts properly.
  12. Q

    Directional derivative question

    I've done the first part, but I'm stuck on the second paragraph of the question. Maybe I'm being stupid, I don't even understand exactly what is meant by, 'the level curve'. I also don't quite understand the whole concept of directional derivative. When it says, 'the gradient in the...
  13. Q

    Use of guassian elimination to find the determinate of a matrix

    the matrix I posted in the pic inb my 1st post was for matrix A, not (A - I*lamda) I've done what you've suggested, by writing down A - I*lamda, its basically the same as matrix A, except for the three values in the central diagonal, they each have '- lamda' I'm trying to calculate the...
  14. Q

    Use of guassian elimination to find the determinate of a matrix

    seems like a decent method, never come across it before though is there any significance to the values next to each of 'a' in the matrix shown in your first link?
  15. Q

    Use of guassian elimination to find the determinate of a matrix

    but theres two values in row 3 that I need to get to zero I can't make a subtraction that would get them both to zero, because they're not the same values sorry I can't see why
  16. Q

    Use of guassian elimination to find the determinate of a matrix

    The three values I was referring to, are the ones in the matrix: A - I*lamda they're located in the same positions are the three values I've circled for matrix: A I know I have to get them to zero, right?
  17. Q

    Use of guassian elimination to find the determinate of a matrix

    Homework Statement I have to find that the characteristic polynomial for a 3x3 matrix A, which is effectively the same as finding the det(A - I*lamda) matrix A is: the problem is that when I've written out 'A - I*lamda' in matrix form, the three values at the bottom left of the matrix...
  18. Q

    What evidence supports the big bang theory?

    off the top of my head: - isotropic microwave radiation corresponding to 3.73K blackbody curve - hubble's law - red shift of galaxies - 3:1 ratio between hydrogen and helium, and the relative abundance of them is there any more? and also, can someone explain the hydrogen-helium ratio thing...
  19. Q

    Confusion about the accelerating expansion of the universe and Hubble

    so if hubble's constant has stayed the same through all time, then the expansion of the universe would indeed be accelerating? and when you say its been declining as % growth rate, that means the actual constant value is still increasing, right? so that means the constant isn't staying the...
  20. Q

    Confusion about the accelerating expansion of the universe and Hubble

    My school textbook says that discovery of the 1a supernova was what led to the understanding that the universe expansion is accelerating but doesn't hubble's equation already suggest that the universe would expand at an accelerating rate? V = Hd (V = velocity, H = hubble's constant, d =...
  21. Q

    Why do geosynchronous satellites have to orbit above the Equator?

    but can't you have a geosynchronous satellite orbiting in a non-latitude plane?
  22. Q

    Why do geosynchronous satellites have to orbit above the Equator?

    I get that they have to be at the same position relative to the earth but why is it that they have to be specifically above the equator? thats the sense I get from the textbooks, they all seem to emphasize the satellite being above the Equator can't you have a geosynchronous satellite...
  23. Q

    Show how gravitational potential varies between the earth and the moon

    so at the point where the two masses' gravitational field strength cancel, say if the gravitatiional potential due from one mass was -60MJkg-1 and the gravitational potential due from the other mass is -40MJkg-1, the resultant potential at this point would be -100MJkg-1?
  24. Q

    Show how gravitational potential varies between the earth and the moon

    Homework Statement gravitational potential at surface of the earth = -63MJkg-1 gravitational potential at surface of the moon = -2MJkg-1 The attempt at a solution I thought gravitational potential was a scalar, so in which case, you would surely just add up the potential due from both...
  25. Q

    Single slit width change, how would fringes differ?

    slightly different from my original question, but what if I had a double slit and I wanted to compared the difference between two wavelengths of light would the longer wavelength of light produce wider maximas and have greater separations between them?
  26. Q

    Single slit width change, how would fringes differ?

    just to be clear, this is single slit diffraction of light if the slit width is made narrower, this would lead to more diffraction, so the fringe width would be wider, yeah? but I'm a bit confused, because is this basically the same as saying the fringe separation would be wider?
  27. Q

    Young's fringes experiment, interference fringes

    Oh, because I wasn't totally sure about what I observed was true. Glad to know that though, it makes sense now. Really? I have another similar one in my textbook as well, I thought it was pretty common. Surprised you haven't come across a diagram like that, since you've probably been around...
  28. Q

    Young's fringes experiment, interference fringes

    You said that if w = 1λ then the entire screen is filled with the central bright fringe, which I understand because from your formula, this means that the first order dark fringes would be at 90 degrees as you've pointed out. But if w = less than one wavelength, how would this look? is just like...
  29. Q

    Young's fringes experiment, interference fringes

    so what I said about the single slit pattern appearing within the central fringe is correct? isn't this like single slit pattern within a single slit pattern? because the central fringe comes from a single slit pattern and I didn't realise this before you mentioned it, so usually the slit...
  30. Q

    Young's fringes experiment, interference fringes

    I haven't come across the formula 'I ~ cos2(πdsinθ/λ' nor 'Fraunhofer diffraction', I'm still in high school and this was a question from my textbook. I'm using only high school level knowledge here so I may have completely misunderstood you, can you tell me if I've got the right idea from your...
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