Q48. Hypothermia and hyperthermia are... [FREE SOLUTION]

Chapter 1: Q48. (page 45)

Hypothermia and hyperthermia are similar words but have opposite meanings. Hypothermia is defined as a lowered body temperature. Hyperthermia means extremely high body temperature, both conditions are potentially dangerous and occur when a person鈥檚 body temperature fluctuates by more than $8 掳$ from the normal body temperature of $98.6 {}^{鈭�}F$ . Write and solve an absolute value inequality to describe body temperatures that are considered potentially dangerous.

Short Answer

Expert verified

The potentially dangerous body temperatures are $t 鈮� 106.6 {}^{鈭�}F$ or $t 鈮� 90.6 {}^{鈭�}F$ .

Step by step solution

– Description of step.

A normal body temperature of a person is $98.6 {}^{鈭�}F$ . When person鈥檚 body temperature fluctuates by more than $8 掳$ from normal body temperature, the conditions hyperthermia and hyperthermia can occur.

Let $t$ be the person鈥檚 body temperature.

– Description of step.

Write an absolute value inequality to describe potentially dangerous body temperatures using the information in step 1.

$|t - 98.6| 鈮� 8$

– Description of step.

$|t - 98.6| 鈮� 8$ is equivalent to $t - 98.6 鈮� 8$ or $t - 98.6 鈮� - 8$ . Consider $t - 98.6 鈮� 8$ . Add $98.6$ on each side of the inequality.

$\begin{array}{l} t 鈭� 98.6 + 98.6 鈮� 8 + 98.6 \\ t 鈮� 106.6 \end{array}$

– Description of step.

Consider $t - 98.6 鈮� - 8$ . Add $98.6$ on each side of the inequality.

$\begin{array}{l} t 鈭� 98.6 + 98.6 鈮� 鈭� 8 + 98.6 \\ t 鈮� 90.6 \end{array}$

Therefore, the potentially dangerous body temperatures are $t 鈮� 106.6 {}^{鈭�}F$ or $t 鈮� 90.6 {}^{鈭�}F$ .

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