question a street light is at the top of a pole that has a height of 17 ft. a woman 5 ft tall walks away…

Explanation:

Step1: Set up similar - triangles

Let $x$ be the distance of the woman from the base of the pole and $y$ be the distance from the base of the pole to the tip of her shadow. By similar triangles, we have $\frac{17}{y}=\frac{5}{y - x}$. Cross - multiplying gives $17(y - x)=5y$. Expanding, $17y-17x = 5y$, and then $12y=17x$, so $y=\frac{17}{12}x$.

Step2: Differentiate with respect to time

Differentiate both sides of $y=\frac{17}{12}x$ with respect to time $t$. Using the chain rule, $\frac{dy}{dt}=\frac{17}{12}\frac{dx}{dt}$.

Step3: Substitute the given value of $\frac{dx}{dt}$

We know that $\frac{dx}{dt}=8$ ft/s. Substituting this into the equation $\frac{dy}{dt}=\frac{17}{12}\frac{dx}{dt}$, we get $\frac{dy}{dt}=\frac{17}{12}\times8=\frac{34}{3}$ ft/s.

Answer:

$\frac{34}{3}$