Question

the formula for converting fahrenheit temperature, f, to celsius temperature, c, is $c = \frac{5}{9}(f - 32)$. if the celsius temperature ranges from $10^\circ$ to $40^\circ$, inclusive, what is the range for the fahrenheit temperature? use interval notation to express the range for the fahrenheit temperature. select the correct choice below and fill in the answer boxes to complete your choice. (type integers or decimals.) \\(\bigcirc\\) a. $\square ^\circ\text{f},\square ^\circ\text{f})$ \\(\bigcirc\\) b. $(\square ^\circ\text{f},\square ^\circ\text{f})$ \\(\bigcirc\\) c. $\square ^\circ\text{f},\square ^\circ\text{f}$ \\(\bigcirc\\) d. $(\square ^\circ\text{f},\square ^\circ\text{f}$

Explanation:

Step1: Solve for F when C = 10

We start with the formula \( C=\frac{5}{9}(F - 32) \). Substitute \( C = 10 \) into the formula:
\[
10=\frac{5}{9}(F - 32)
\]
Multiply both sides by \( \frac{9}{5} \) to isolate the term with \( F \):
\[
10\times\frac{9}{5}=F - 32
\]
\[
18=F - 32
\]
Add 32 to both sides:
\[
F=18 + 32=50
\]

Step2: Solve for F when C = 40

Substitute \( C = 40 \) into the formula \( C=\frac{5}{9}(F - 32) \):
\[
40=\frac{5}{9}(F - 32)
\]
Multiply both sides by \( \frac{9}{5} \):
\[
40\times\frac{9}{5}=F - 32
\]
\[
72=F - 32
\]
Add 32 to both sides:
\[
F=72+32 = 104
\]
Since the Celsius temperature range is inclusive (from \( 10^\circ \) to \( 40^\circ \), inclusive), the Fahrenheit range should also be inclusive. So we use square brackets in interval notation.

Answer:

C. \([50^\circ\text{F}, 104^\circ\text{F}]\)