Question

3. (05.05 MC)

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:
Distance vs. Time
180
160
120
Distance
from Ocean 100
Surface
(m)
C
80
60
40
20
y
0
C
B
1 2 3 4 5
Time (min)
Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the lame as the sla
Part B: What are the initial value and slope of the graph and what do they represent? (6 points)

Answer 1

The slope of AB and BC are the same.

The initial value is 60 m and the slope is 40 m/min.

Explanation:

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes.

See the graph attached.

Part A :- If we consider two right triangles one Δ ABD and Δ BCE, where D(2,100) and E(1,60) points.

Now, those triangle are similar and hence the slope of line segment AB will be tan θ = AD/BD = 140 - 100 / 2 - 1 = 40

Again, the slopes of line segment BC will be tan a = BE/CE = 100 - 6 / 1 - 0 = 40

Hence, θ = α and the slope of AB and BC are the same. ( Answer )

Part B :- From the graph, it is clear that the initial value of the graph is 60 m and it represents that initial position of the shark i.e. at t = 0 min, the shark was at a depth of 60 m from the water surface.

The slope of the graph is 40 means the rate of change of distance from the Ocean surface of the shark with respect to time in minutes will be 40 m per min. ( Answer )