Recent content by Anoonumos

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    Force on air column in a solar updraft tower

    Homework Statement For a solar tower compare the total force on the air column in the tower (i) by calculating the pressure at its bottom and top (ii) from Archimedes’ Law. Hint: there is a temperature difference between top and bottom of the tower. I have to estimate height...
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    The order of all elements of (Z/ 7161 Z)* divide 30

    Hi, Homework Statement Show that for every x in (Z/ 7161 Z)*, the order of x divides 30. Homework Equations (Z/ 7161 Z)* is the group of units of Z/ 7161 Z. The Attempt at a Solution I factorised 7161: 7161 = 3 * 7 * 11 * 31 I used the Chinese remainder theorem to show that (Z/...
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    Capacitance concentric spherical shells

    Hi, I'll ask if they could have meant equal charges instead of equal densities. I'll let you know. Thank you for your time.
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    Capacitance concentric spherical shells

    Homework Statement Given two concentric spherical metal shells, with radii a and b (a < b), and surface charge densities Sa and Sb. Find the capacitance if Sa = - Sb. Homework Equations C = Q/V The Attempt at a Solution I would know how to solve this if the absolute values of the...
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    Two Variable Limit: Solve xy²/(sin(x²+y²))

    I think I've solved it. (xy²)/(sin(x² + y²) = (x² + y²)/(sin(x² + y²) * (xy²/(x²+y²)) And I know both these limits (1 and 0).
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    Two Variable Limit: Solve xy²/(sin(x²+y²))

    Hi, Homework Statement lim (xy²)/(sin(x² + y²)) (x,y) -> (0,0) The Attempt at a Solution I think the answer is 0, but I don't know how to get rid of the sin (x² + y²). I thought about using taylor series but I'm not sure if that works with two variables. Can someone help me out?
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    Maximum number of transpositions required to make all permutations.

    Hi, Homework Statement Can all permutations of {A,B,C,D} be made by multiplications of transpositions (AB), (BC), (CD)? And by multiplications of transpostion (AB) and 4-cycle (ABCD)? What is the maximum number of multiplications needed in both cases? Homework Equations All...
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    Constructing a sequence in V converging to sup V

    I understand. I have one final question. Nevermind, thanks :)
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    Constructing a sequence in V converging to sup V

    Sorry for the double post, but I came across another problem when writing it down. v(i+1) doesn't have to exist right? And there doesn't have to be a smallest v(i+1). So how would one formulate the sequence? v_{i+1} \in [v_1, sup V) perhaps? Or is it enough to state v(i+1) exists and v(i+1)...
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    Constructing a sequence in V converging to sup V

    Thanks!
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    Constructing a sequence in V converging to sup V

    Hi, Homework Statement V is a non-empty, upper bounded subset of R. Show that a sequence (v_n)_{n \geq 0} in V exists such that: 1)v_0 \leq v_1 \leq ... and 2) the limit of the sequence is sup V. (Hint: use a recursive construction) Homework Equations The Attempt at a Solution...
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    Two images of a dot in a half-silvered glass sphere

    I've calculated the distance from the image created by the mirror to the mirror. It is to the right side of the mirror. Let's call the distance x. I now want to calculate the distance to the flat side of the sphere. I think I should use: (1/n * R) + x, because that image is not in glass anymore...
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    Two images of a dot in a half-silvered glass sphere

    I see, thanks. One final question just to check: the other image would be affected by this as well right? (Image created by mirror looks closer) and both images would be virtual.
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    Two images of a dot in a half-silvered glass sphere

    Well, we're looking at the dot with a zero degree angle, so there wouldn't be any refraction right? I guess the mirror refracts some light as well, which could explain a second image. Thank you for your response.
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    Two images of a dot in a half-silvered glass sphere

    Hi, http://imageshack.us/photo/my-images/141/optica.png/ The sphere in the picture is made of glass with n = 1.60. The curved side of this sphere is a mirror. The question is why we see two images of the black dot. Homework Equations Snells law? The Attempt at a Solution One...
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