Parametric Functions and Rates of Change Practice Test

A particle moves along a curve given by $x(t)=\cos t$ and $y(t)=\sin t$, where $t$ is in seconds and coordinates are in meters. The instantaneous slope is $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}$. Determine the rate at which $y$ changes with respect to $x$ when $t=\pi/4$.​

A particle moves with $x(t)=2t+1$ and $y(t)=t^2-4t$, where $t$ is in seconds. The slope of the path is $dy/dx=(dy/dt)/(dx/dt)$. Determine the rate at which $y$ changes with respect to $x$ at $t=2$.