Question

suppose that some substance has a melting - point of - 47.82°c and a boiling - point of 279.72°c. what is the range of temperatures in degrees fahrenheit for which this substance is not in a liquid state? (hint: c = 5/9(f - 32)) express the range as an inequality. let f represent the temperature in degrees fahrenheit. what is the range of temperatures for which this substance is not in a liquid state? (type an inequality or a compound inequality. simplify your answer. use integers or decimals for any numbers in the expression. round to three decimal places as needed.)

Explanation:

Step1: Convert melting - point to Fahrenheit

We use the formula $C=\frac{5}{9}(F - 32)$. Rearranging for $F$ gives $F=\frac{9}{5}C+32$. For the melting - point $C=-47.82^{\circ}C$, then $F_1=\frac{9}{5}\times(-47.82)+32$.
\[

$$\begin{align*} F_1&=\frac{9\times(-47.82)}{5}+32\\ &=\frac{-430.38}{5}+32\\ &=- 86.076+32\\ &=-54.076 \end{align*}$$

\]

Step2: Convert boiling - point to Fahrenheit

For the boiling - point $C = 79.72^{\circ}C$, then $F_2=\frac{9}{5}\times79.72+32$.
\[

$$\begin{align*} F_2&=\frac{9\times79.72}{5}+32\\ &=\frac{717.48}{5}+32\\ &=143.496 + 32\\ &=175.496 \end{align*}$$

\]

Step3: Write the inequality for non - liquid state

The substance is not in a liquid state when $F\leq - 54.076$ or $F\geq175.496$.

Answer:

$F\leq - 54.076$ or $F\geq175.496$