Answer:
-9ft/y
Step-by-step explanation:
At the origin, the equation of the circle the jogger is running about is simply
[tex]x^2+y^2=65^2[/tex].
Differentiating with respect to t yields
[tex]2x\frac{dx}{dt}+ 2y\frac{dy}{dt}=0[/tex]
The problem stated that at the point (39,52), [tex]\frac{dx}{dt}=12 ft/s[/tex]. Plugging these values into the equation directly above, we obtain
[tex]2(39)(12)+ 2(52)\frac{dy}{dt}=0[/tex]
We are required to solve for [tex]\frac{dy}{dt}[/tex]. We see that:
[tex]936+ 104\frac{dy}{dt}=0\\104\frac{dy}{dt}=-936\\\frac{dy}{dt}=-\frac{936}{104}\\\frac{dy}{dt}=-9 ft/y[/tex]
Hey y coordinate is changing at a rate of -9ft/y.
