Chapter 2.8, Problem 38PPSE

Solution

$\left(a\right)$

To find: To find the domain for given situation, write an inequality and to find the least time spend on the phone per week and to find the most time spend on the phone per week.

The domain of the situation is $0\le x\le 28$ .

The inequality for the graph given is $x+y\le 28$ .

The least time spent on the phone per week is $0$ hour.

The most time spent on the phone per week is $28$ hours.

Given information:

The graph at the right angle relates the number of hours spend on the phone to the number of hours spend studying per week. Describe the domain and write an inequality for the graph. What is the least amount of time spent on the phone per week and what is the most amount of time spent on the phone per week.

  

Calculation:

From the graph $1\text{unit}\text{=}\text{4 hours on the }x-\text{axis and }y-\text{axis}$ :

Let $x$ be the time spent on the phone per week and $y$ be the time spent on studying per week.

The domain of the situation from the graph is:

  $0\le x\le 28$ .

When $x=0$, $y=28$ from the graph:

Therefore, the boundary line of the graph is $x+y=28$:

Since the boundary line is solid and the region shaded is below the boundary line, the inequality will be:

  $x+y\le 28$ .

The least time spent on the phone per week is when $x=0$ and the most time spent on the phone per week is when $x=28$ :

The least time spent on the phone per week is $0$ hour.

The most time spent on the phone per week is $28$ hours.

$\left(b\right)$

To find: The least time spend on the studying per week and to find the most time spend on the studying per week.

The least time spent on the studying per week is $0$ hour.

The most time spent on the studying per week is $28$ hours.

Given information:

The graph at the right angle relates the number of hours spend on the phone to the number of hours spend studying per week.

  

Calculation:

The least time spent on studying per week is when $y=0$ and the most time spent on studying per week is when $y=28$ :

The least time spent on the phone per week is $0$ hour.

The most time spent on the phone per week is $28$ hours.

$\left(c\right)$

To find: The greatest amount of time spent either on the phone or studying per week.

The greatest amount of time spent either on the phone or studying per week is $28$ hours.

Given information:

The graph at the right angle relates the number of hours spend on the phone to the number of hours spend studying per week.

  

Calculation:

From the graph, the greatest amount of time spent on the phone per week is $28$ hours and the greatest amount of time spent on studying per week is $28$ hours.

Therefore, the greatest amount of time spent either on the phone or studying per week is $28$ hours.