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    nightbaneZ

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    [–] Can someone help me understand why this square root and squared exponent don't automatically cancel eachother out? nightbaneZ 1 points ago in askmath

    Because sqrt(r2 - x2 ) = sqrt((r - x)(r + x)) can't be further simplified. If you're thinking of (r - x), then it's incorrect because (r - x)2 = r2 + x2 - 2rx.

    [–] Probability of finding (n)Length sequence of digits in the first million digits of pi nightbaneZ 0 points ago in askmath

    That depends on the number of distinct sequences of length n in the first million digits of pi, say x. Also, for a random sequence of length n to be equal to a specific sequence, the probability is 1/(10n ). So the required probability is min(x/10n , 1).

    [–] Why do absolute values shift to the left when you add (within the parentheses)? nightbaneZ 1 points ago in askmath

    I think you're confused here. Only x becomes -3 when f(x + 3) = 0. f(x + 3) becomes 3 when x = 0.

    [–] Why do absolute values shift to the left when you add (within the parentheses)? nightbaneZ 1 points ago in askmath

    Oh I see. That is a result of a standard graph transformation of the form y = f(x + k) where the graph of y = f(x) is shifted k units in the negative x-direction, i.e. shifted left. If k is negative then it will be shifted towards the right. To understand this intuitively you can think of it this way: every x-value of the f(x + 1) graph must be 1 unit smaller than every x-value of the f(x) graph to get the same y-value.

    [–] Why do absolute values shift to the left when you add (within the parentheses)? nightbaneZ 1 points ago in askmath

    If |x| = 0, x = 0 and thus |x + 1| = |1| = 1. Unless you're talking about solving the equation |x + 1| = 0 which implies x + 1 = 0 and thus x = -1.

    [–] rate my lvl 150 pure mage build + advice? nightbaneZ 1 points ago in AdventureQuest

    Thanks for the suggestions. Love Potion controls the monster for 1 more round in addition to Vamp so wouldn't it make sense to keep it? Also I use Staff Master Emblem for Zealot's Wrath which is my most powerful weapon.

    [–] rate my lvl 150 pure mage build + advice? nightbaneZ 2 points ago in AdventureQuest

    Yeah I was trying out Werewolf but realised Vampire is better for mages, so I'm going to change that.