• necronatural

    image

    this entire scene is one of the funniest scenes in @phantomrose96's A Breach of Trust to me I read the entire fic when MP100 Season 3 first started and I've been stewing on how good the whole chapter is ever since

  • quantummindclassicalheart

    Fun fact: you can actually integrate this, since it's a separable equation (i.e. you can write it as f(x) dx = g(t) dt). In the fic, the characters analyze the shape of dx/dt as a function of x and reason qualitatively that it's a parabola, like below:

    A parabola that opens down. It hits the x axis at two points, around x=0.4 and x=4.6.ALT

    The characters first reason that if your starting value of x at t=0 is between the two places where the graph hits the x-axis, then the rate of change of power is positive, corresponding to regenerating power over time.

    They also conclude that if your starting value of x at t=0 is less than where the graph hits the x-axis on the left, then the rate of change is always negative for t>0, so power drains to zero.

    Both these conclusions are true, but it might be nice if we could find an exact solution! It turns out you get a hyperbolic tangent, so that power regeneration looks something like this:

    A curve that slopes up and then flattens out as a function of t.ALT

    and draining looks like this:

    A curve that slopes down and asymptotes to a value of zero.ALT

    Keep reading

  • phantomrose96

    Hi I love you so much for this

    • #mp100 #abot
    1,580 notes