Question

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:

Answer 1

The answers are:

• Part A: The slope of AB and BC are the same.
• Part B :The initial value is 60 m and the slope is 40 m/min.

What is the triangles about?

Note that the graph depict the depth, y, in meters, of a shark that moves from the surface of an ocean for a given amount of time, x, in minutes.

So:

Part A :

We  look at the two right triangles:  Δ ABD and Δ BCE, and where D(2,100) and E(1,60) points.

Since the  triangle are the same and thus, the slope of line segment AB: tan θ = AD/BD

= 140 - 100 / 2 - 1

= 40

Since the the slopes of line segment BC will be:

tan a = BE/CE

= 100 - 6 / 1 - 0

= 40

So, θ = α and the slope of AB and BC are similar.

Part B :

Using the graph, one can see that  the initial value of the graph is 60 m and it stands for the initial position of the shark

e.g.  at point t = 0 min, the shark was seen at a depth of 60 m from the water surface.

So therefore, since the slope of the graph is 40 it implies that the rate of change of distance from the Ocean surface of the shark in regards to the  time in minutes have to be 40 m per min.

Therefore, The answers are:

Part A: The slope of AB and BC are the same.

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

Learn more about triangles from

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