Mathematics

Problem

A particle moves in the plane so that its coordinates satisfy

x(5)=4

and

y(5)=10

. At time

t=5

, the rates are

\dfrac{dx}{dt}=3\text{ units s}^{-1}

and

\dfrac{dy}{dt}=-2\text{ units s}^{-1}

. Let

s(t)=\dfrac{y(t)}{x(t)}

. What is

\dfrac{ds}{dt}

t=5

? a)

-\dfrac{19}{2}

\dfrac{19}{8}

-\dfrac{19}{8}

-\dfrac{2}{3}