# Chloe's equation

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"This [problem] has been particularly frustrating, and yet Chloe ... she solved it in a minute flat. Whatever alien influence she's under, it's studying this ship."
Nicholas Rush[src]

Chloe's equation was the first mathematical problem that Chloe Armstrong, under the influence of the Nakai pathogen, solved for Dr. Nicholas Rush. (SGU: "Pathogen")

The problem, with its accompanying solution, is:

$-\int g \sin\gamma \,dt = -\ddot{r}t \sin\gamma.$

## NotesEdit

In integral calculus, it is trivial that

$\int f(x) \,dt = t \cdot f(x)$

$\frac{d}{dt}\left[t \cdot f(x)\right] = f(x).$

Dr. Rush, having completely mastered calculus, should have realized that

$-\int \lambda \sin\gamma\,dt = -\lambda t \sin\gamma.$

Thus, it is assumed that the solution to Chloe's equation is dependent on the fact that

$\lambda := \ddot{r}.$

However, during integration, constant variables should be ignored. Thus, it is assumed that the presence of $t\!$ somehow allowed for $g \mapsto \ddot{r}$.