Chapter 6, Problem 8QC

(a)

To determine

Write compound inequalities for the wind speeds of category 3 and category 4 hurricanes.

Answer to Problem 8QC

Compound inequalities are: $111\le x\le 130\text{and}131\le x\le 155$

Explanation of Solution

Given:

  

Concept Used:

Category 3: The wind speed 111 − 130 $\Rightarrow 111\le x\le 130$

Category 4: The wind speed 131 − 155 $\Rightarrow 131\le x\le 155$

Thus, the compound inequalities for the wind speed of category 3 and 4 are: $111\le x\le 130\text{and}131\le x\le 155$

(b)

To determine

Find the intersection of the two graphs of the inequalities you found in part a.

Answer to Problem 8QC

No Intersection: Ø

Explanation of Solution

Given:

  

Concept Used:

Category 3: The wind speed 111 − 130 $\Rightarrow 111\le x\le 130$

Category 4: The wind speed 131 − 155 $\Rightarrow 131\le x\le 155$

Category ends at 130 mph and category starts from 131mph.

Category 3: $\Rightarrow 111\le x\le 130$ on the number line.

  

Category 4: $\Rightarrow 131\le x\le 155$ on the number line.

  

So, there is no intersection.

Thus, there is no intersection of the two graphs of the inequalities we found in part a.