Question

I just need help on part A

Answer 1

Part A) see the explanation

Part B) The initial value is 60 meters and the slope is 40 m/min (see the explanation)

Explanation:

Part A) see the attached figure with letters to better understand the problem

we know that

If two triangles are similar then the ratio of its corresponding sides is proportional

In this problem

triangles ACD and ABE are similar by AA Similarity Theorem

so

`(AE)/(AD)=(BE)/(CD)` ----> equation A

Remember that the slope is equal to divide the change in the y-value by the change in the x-value

so

The slope AB is equal to
`(AE)/(BE)`

The slope AC is equal to
`(AD)/(CD)`

Rewrite the equation A

`(AE)/(AD)=(BE)/(CD)`

`(AE)/(BE)=(AD)/(CD)`

therefore

The slope of AB is equal to the slope of AC

Part B)

Let

x ---->the amount of time in minutes

y ----> the depth in meters

Find the initial value

we know that

The y-intercept or initial value is the value of y when the value of x is equal to zero

In this context the y-intercept is the depth of the shark when the time is equal to zero, so is the initial depth of the shark

Looking at the graph

For x=0

y=60 meters

therefore

The initial value is 60 meters

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

Take two points from the graph

C(0,60) and B(1,100)

substitute

`m=(100-60)/(1-0)`

`m=40\ m/min`

That means ---->The depth of the shark increases at the rate of 40 meters per minute