Question

A whale descends 382.5 feet in 45 seconds. Write an expression that can be used to find the average elevation change of the whale during its descent in, in feet per second.

Answer 1

Answer:

Part a) The expression is  $y=-8.5x$

Part b) -51 feet

Step-by-step explanation:

The complete question is

A whale descends 382.5 feet in 45 seconds.  

The whale's elevation changes at a constant rate.

Part a) Write an expression that can be used to find the average elevation change of the whale during its descent in feet per second

Part b) What is the elevation change of the whale after 6 seconds?

Part a)

we know that

Find out the unit rate

To find out the unit rate divide the total elevation by the total time

Remember that

The sea level represent the level zero

If a whale descends, then the elevation is negative (below the sea level)

so

$\frac{-382.5}{45}\ \frac{ft}{sec}=-8.5\ \frac{ft}{sec}$

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form

$y/x=k$ or $y=kx$

Let

x ----> the time in seconds

y ----> the elevation in feet

In this problem we have a proportional relationship, because the line passes through the origin (For x=0, y=0)

so

$y=kx$

The value of the constant of proportionality k is equal to the unit rate or slope of the linear equation

$k=-8.5\ \frac{ft}{sec}$

substitute

$y=-8.5x$

Part b) For x=6 sec

substitute in the linear equation

$y=-8.5(6)$

$y=-51\ ft$