\begin{tabular}{l} The average daily minimum temperature for Pablo's hometown can be modeled by the function $$ f(x)=15.3 \sin \left(\frac{\pi x}{6} ight)+44.1 $$, \ where $$ f(x) $$ is the temperature in $$ { }^{\circ} \mathrm{F} $$ and $$ x $$ is the month. \ $$ x=0 $$ corresponds to January. \ What is the average daily minimum temperature in June? \ Round to the nearest tenth of a degree if needed. \ Use 3.14 for $$ \pi $$. \ Enter your answer in the box. \ $$ \square^{\circ} \mathrm{F} $$ \ \hline\end{tabular}

Question

\begin{tabular}{l} The average daily minimum temperature for Pablo's hometown can be modeled by the function $$ f(x)=15.3 \sin \left(\frac{\pi x}{6}ight)+44.1 $$, \ where $$ f(x) $$ is the temperature in $$ { }^{\circ} \mathrm{F} $$ and $$ x $$ is the month. \ $$ x=0 $$ corresponds to January. \ What is the average daily minimum temperature in June? \ Round to the nearest tenth of a degree if needed. \ Use 3.14 for $$ \pi $$. \ Enter your answer in the box. \ $$ \square^{\circ} \mathrm{F} $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

To find the average daily minimum temperature in June, we need to substitute $$ x = 6 $$ into the given function $$ f(x) = 15.3 \sin \left(\frac{\pi x}{6}ight) + 44.1 $$ and calculate the value.

Given:
$$ f(x) = 15.3 \sin \left(\frac{\pi x}{6}ight) + 44.1 $$
$$ x = 6 $$ for June

Substitute $$ x = 6 $$ into the function:
$$ f(6) = 15.3 \sin \left(\frac{\pi 	imes 6}{6}ight) + 44.1 $$

Simplify the expression:
$$ f(6) = 15.3 \sin (\pi) + 44.1 $$

Since $$ \sin(\pi) = 0 $$, the expression simplifies to:
$$ f(6) = 15.3 	imes 0 + 44.1 $$

Therefore, the average daily minimum temperature in June is $$ 44.1^{\circ} \mathrm{F} $$.
The average daily minimum temperature in June is $$ 44.1^{\circ} \mathrm{F} $$.

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