Q48. The ruler postulate suggests tha... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 1: Q48. (page 16)

The ruler postulate suggests that there are many ways to assign coordinates to a line. The Fahrenheit and Celsius temperature scales on a thermometer indicate two such ways of assigning coordinates. A Fahrenheit temperature of $32 掳$ corresponds to a Celsius temperature of $0^{鈭�}$ . The formula, or rule for converting a Fahrenheit temperature F into a Celsius temperature C is $C = \frac{5}{9} (F 鈭� 32)$ .
a. What Celsius temperatures corresponds to Fahrenheit temperature of $212^{鈭�}, 98 {.6}^{鈭�}$ ?
b. Solve the equation above for F to obtain a rule for converting Celsius temperature to Fahrenheit temperatures.
c. What Fahrenheit temperatures correspond to Celsius temperatures of $鈭� 40^{鈭�}, 2000^{鈭�}$ ?

Short Answer

Expert verified

a. In Celsius $C = 100^{鈭�}$ and $C = 37^{鈭�}$ respectively.

b. The equation to convert the Celsius to Fahrenheit temperature is $F = \frac{9 C + 160}{5}$ .

c. The Fahrenheit temperature is $F = - 40 掳$ and $F = 3632 掳$ respectively.

Step by step solution

a. Step 1- Check the figure.

Consider the figure.

a. Step 2- Apply the concept of ruler postulate.

The Ruler Postulate suggests that there are many ways to assign coordinates to a line. The Fahrenheit and Celsius temperature scales on a thermometer indicate two such ways of assigning coordinates. A Fahrenheit temperature of $32 掳$ corresponds to a Celsius temperature of $0 掳$ .

a. Step 3- Step description.

A Fahrenheit temperature of $32 掳$ corresponds to Celsius temperature or $0 掳$ . The formula for converting a Fahrenheit temperature F into Celsius temperature C is $C = \frac{5}{9} (F 鈭� 32)$ .

Substitute value of $F = 212^{鈭�} 鈥塱苍鈥� C = \frac{5}{9} (F 鈭� 32)$ .

$\begin{array}{l} C = \frac{5}{9} (212 鈭� 32) \\ 鈥夆赌夆赌夆赌夆赌� = \frac{5 脳 180}{9} \\ 鈥夆赌夆赌夆赌夆赌� = 5 脳 20 \\ C = 100 \end{array}$

Substitute value of $F = {98.6}^{鈭�} 鈥塱苍鈥� C = \frac{5}{9} (F 鈭� 32)$

$\begin{array}{l} C = \frac{5}{9} (98.6 鈭� 32) \\ 鈥夆赌夆赌夆赌夆赌� = \frac{5 脳 66.6}{9} \\ 鈥夆赌夆赌夆赌夆赌� = 5 脳 7.4 \\ C = 37 \end{array}$

Hence, in Celsius, the temperature is $C = 100 掳$ and $C = 37 掳$ respectively.

b. Step 1- Check the figure.

Consider the figure.

b. Step 2- Apply the concept of ruler postulate.

b. Step 3- Step description.

From the equation

$\begin{array}{l} C = \frac{5}{9} (F 鈭� 32) \\ 9 C = 5 (F 鈭� 32) \\ 9 C = 5 F 鈭� 160 \\ 5 F = 9 C + 160 \end{array}$

Solve the obtained equation further as follows:

$F = \frac{9 C + 160}{5}$

Hence, the value of the above expression is $F = \frac{9 C + 160}{5}$ .

c. Step 1- Check the figure.

Consider the figure.

c. Step 2- Apply the concept of ruler postulate.

c. Step 3- Step description.

From part (b) the equation is $F = \frac{9 C + 160}{5}$ .

Substitute value of $C = 鈭� 40^{鈭�}$ in the equation $F = \frac{9 C + 160}{5}$ .

$\begin{array}{l} F = \frac{9 脳 (鈭� 40) + 160}{5} \\ 鈥夆赌夆赌夆赌夆赌夆€夆€夆€� = \frac{鈭� 360 + 160}{5} \\ 鈥夆赌夆赌夆赌夆赌� = \frac{鈭� 200}{5} \\ F = 鈭� 40 \end{array}$