User:DragoonWraith/Math

$$ r=\sqrt{\left ( 2400 ft + 900 \frac{ft}{s} t \right )^2 + \left ( 700 ft \right )^2} $$

$$ v = \frac{dr}{dt} = \frac{d}{dt} \sqrt{\left (2400 ft + 900 \frac{ft}{s} t \right )^2 + \left ( 700 ft \right )^2} = \frac{d}{dt} \left ( \left ( 2400 ft + 900 \frac{ft}{s} t \right )^2 + \left ( 700 ft \right )^2 \right )^\frac{1}{2} $$

$$ v = \frac{1}{2} \left ( \left ( 2400 ft + 900 \frac{ft}{s} t \right )^2 + \left ( 700 ft \right )^2 \right )^{-\frac{1}{2}} \frac{d}{dt} \left ( \left ( 2400 ft + 900 \frac{ft}{s} t \right )^2 + \left (700 ft\right )^2 \right ) $$

$$ v = \frac{1}{2} \left ( \left ( 2400 ft + 900 \frac{ft}{s} t \right )^2 + \left ( 700 ft \right )^2 \right )^{-\frac{1}{2}} 2 \left ( 2400 ft + 900 \frac{ft}{s} t \right ) \left ( 900 \frac{ft}{s} \right ) $$

The &frac12; and 2 cancel out, and we substitute $$t=0$$ which eliminates a lot of things, so we get:

$$ v = \frac{\left (2400 ft\right )\left (900 \frac{ft}{s}\right )}{\sqrt{\left (2400 ft\right )^2+\left (700 ft\right )^2}} $$

$$ A = w * l $$

$$ P = w + l + w + l = 2w + 2l $$

But one side is taken up by house, so $$ P = 2w * l $$ (choice of width or length is arbitrary and unimportant)