9. the side profile of a bridge is overlapped with the coordinate axes such that (x, y) represents a point…

9. the side profile of a bridge is overlapped with the coordinate axes such that (x, y) represents a point on the arc that is x meters horizontally from one end of the bridge and y meters vertically above the road. the bridge meets the road at coordinates (0, 0) and (200, 0). pedestrians are able to climb the full arch of the bridge. find the average steepness of the climb over the interval 0, 20. average steepness = enter your next step here

9. the side profile of a bridge is overlapped with the coordinate axes such that (x, y) represents a point on the arc that is x meters horizontally from one end of the bridge and y meters vertically above the road. the bridge meets the road at coordinates (0, 0) and (200, 0). pedestrians are able to climb the full arch of the bridge. find the average steepness of the climb over the interval 0, 20. average steepness = enter your next step here

Answer

Explanation:

Step1: Recall slope formula

The average slope (steepness) of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b=20$. We need to find the $y$-values at $x = 0$ and $x = 20$ from the graph. At $x = 0$, $y=0$. From the graph, at $x = 20$, $y\approx40$.

Step2: Calculate average steepness

Using the formula $\frac{f(b)-f(a)}{b - a}$, we substitute $a = 0$, $b = 20$, $f(0)=0$, and $f(20)\approx40$. So the average steepness is $\frac{40 - 0}{20-0}$. $\frac{40}{20}=2$

Answer:

$2$