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).\npedestrians are able to climb the full arch of the bridge. find the average steepness of the climb over the interval 0, 20.\naverage steepness = enter your next step here
Answer
Explanation:
Step1: Recall slope formula
The slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the average steepness (average rate of change) over the interval $[x_1,x_2]=[0,20]$, we need to find the $y -$ values at $x = 0$ and $x=20$. From the problem, when $x_1 = 0$, $y_1=0$. We need to estimate the $y -$ value at $x_2 = 20$ from the graph. Let's assume from the graph that when $x = 20$, $y\approx40$.
Step2: Calculate average steepness
Using the slope formula for the average rate of change over the interval $[0,20]$, we have $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{40 - 0}{20-0}$. $m=\frac{40}{20}=2$.
Answer:
2