Chapter 5.4, Problem 54E

a.

To determine

To calculate: Wind speed for $B=0$ and $B=3$ .

Answer to Problem 54E

Wind speed when $B=0$ is $0.16\text{ miles per hour}$

Wind speed when $B=3$ is $10.8\text{ miles per hour}$

Explanation of Solution

Given information:

The Beaufort numberb can be modeled by,

  $B=1.69\sqrt{s+4.25}-3.55$

where sis the wind speed in miles per hour.

The following table:

  

Calculation:

When $B=0$ ,wind speed is calculated as:

  $\begin{array}{l}B=1.69\sqrt{s+4.25}-3.55[\text{Given]}\\ 0=1.69\sqrt{s+4.25}-3.55[\text{Substitute]}\\ 1.69\sqrt{s+4.25}=3.55[\text{Add 3}\text{.55 to both sides]}\\ \sqrt{s+4.25}=\frac{3.55}{1.69}[\text{Divide both sides by 1}\text{.69]}\\ \sqrt{s+4.25}=2.10059[\text{Simplify]}\\ s+4.25=4.41[\text{Raise both sides to the second power]}\\ s=0.16[\text{Subtract 4}\text{.25 from both sides]}\end{array}$

When $B=3$ , wind speed is calculated as:

  $\begin{array}{l}B=1.69\sqrt{s+4.25}-3.55[\text{Given]}\\ 3=1.69\sqrt{s+4.25}-3.55[\text{Substitute]}\\ 1.69\sqrt{s+4.25}=6.55[\text{Add 3}\text{.55 to both sides]}\\ \sqrt{s+4.25}=\frac{6.55}{1.69}[\text{Divide both sides by 1}\text{.69]}\\ \sqrt{s+4.25}=3.88[\text{Simplify]}\\ s+4.25=15.05[\text{Raise both sides to the second power]}\\ s=10.8[\text{Subtract 4}\text{.25 from both sides]}\end{array}$

b.

To determine

To write: An inequality that describes the range of the wind speeds represented by the Beaufort model

Answer to Problem 54E

An inequality that describes the range of the wind speeds represented by the Beaufort model can be written as:

  $0\le B=1.69\sqrt{s+4.25}-3.55\le \text{12}$

Explanation of Solution

Given information:

The Beaufort number b can be modeled by,

  $B=1.69\sqrt{s+4.25}-3.55$

where s is the wind speed in miles per hour.

The following table:

  

Calculation:

Since the Beaufort model ranges from $0$ to $\text{12}$ , and is given by,

  $B=1.69\sqrt{s+4.25}-3.55$

An inequality that describes the range of the wind speeds represented by the Beaufort model can be written as:

  $0\le B=1.69\sqrt{s+4.25}-3.55\le \text{12}$