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    Exponentials Problem

    I have ln((V+v)/(V-v)) = 2ctV, and I've checked this is right. But how do I go from here to v = V((e^Vct - e^-Vct)/(e^Vct+e^-Vct))? The solutions just give them as successive lines. (I appreciate that's not the easiest thing to read, it's taken from the 2004 MEI specimen paper for A-level...
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    Normal Subgroups

    I'm working on introductory group theory and am stuck on this proof. I don't even know where to start, so I'd appreciate any help at all! "A subgroup H of a finite group G is said to be a normal subgroup if, for each element h ∈ H and each element g ∈ G, the element g^1hg ∈ H Prove that if...
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    Direction vector of a line

    How would I find the direction vector of a line given in the form ax + by + cz +d =0? Thankyou.
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    Finding the speed of a bullet

    I'm doing this without a teacher, so this isn't really a homework question, but this still seemed the most appropriate forum. I have the following question: A square board, of side 2a and mass M, is to be used to estimate the speed of bullets. It is freely hinged about one horizontal edge...
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    Infinite series of complex numbers.

    I have the two series: C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx I have to express, in terms of x, the sum to infinity of these two series. Here's what I've done so far: Let z represent cosx + jsinx C + jS = z^0 +...
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