Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 162: 24

$-614$ knots. (decreasing)

Step 1. Identify the given quantities: $\frac{dx}{dt}=442$ knots, $\frac{dy}{dt}=481$ knots, $x=-5, y=-12$ Step 2. $AB^2=AO^2+BO^2=12^2+5^2=169$, $s=AB=13$ Step 3. $s^2=x^2+y^2$, differentiate $2s\frac{ds}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}$; thus $\frac{ds}{dt}=\frac{-5(442)-12(481)}{13}=-614$knots. (decreasing)