I am not understanding what they did to obtain that result (in the image). My question is not about the actual exercise. My question is about the las 2 steps of the solution. How did they solve fot t? **Temperature Function Analysis**Given the temperature function:\[ T(t) = -9.5 \sin \left( \frac{\pi}{12} t \right) + 77.5 \]**Objective:**Determine how many hours after midnight the temperature first reaches 84°.Since 84° is greater than 77.5°, our answer will fall between 12 and 18 hours because the function \( T(t) \) is less than 77.5 up to 12 hours and then starts increasing, peaking at 18 hours.**Steps to Solve for \( t \) when \( T(t) = 84 \):**1. Set the equation:\[ 84 = -9.5 \sin \left( \frac{\pi}{12} t \right) + 77.5 \]2. Subtract 77.5 from both sides:\[ 84 - 77.5 = -9.5 \sin \left( \frac{\pi}{12} t \right) \]\[ 6.5 = -9.5 \sin \left( \frac{\pi}{12} t \right) \]3. Divide both sides by -9.5:\[ \frac{6.5}{-9.5} = \sin \left( \frac{\pi}{12} t \right) \]4. Calculate the left-hand side:\[ \sin \left( \frac{\pi}{12} t \right) = -\frac{6.5}{9.5} \]5. Take the arcsine (inverse sine) of both sides to solve for \( t \):\[ \frac{\pi}{12} t = \arcsin \left( -\frac{6.5}{9.5} \right) \]6. Divide by \( \frac{\pi}{12} \) to isolate \( t \):\[ t = \arcsin \left( -\frac{6.5}{9.5} \right) \times \frac{12}{\pi} \]7. Solve for \( t \):\[ t \approx 14.878 \]**Conclusion:**The temperature first reaches 84° approximately 14.878 hours after midnight.

Name: I am not understanding what they did to obtain that result (in the ima
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: I am not understanding what they did to obtain that result (in the image). My question is not about the actual exercise. My question is about the las 2 steps of the solution. How did they solve fot t? **Temperature Function Analysis**Given the temper