Final answer:
Attempting to solve for the second time after the hottest day of the year when the temperature reaches 20°C using the provided function results in an impossible cosine value, indicating a typographical error in the model or question. A correct model is needed to find the solution.
Step-by-step explanation:
To find the second time after the hottest day of the year when the daily high temperature is 20°C in Santiago, Chile, we use the given temperature model T(t) = 7.5 cos(t) + 365 - 21.5. We set this equal to 20°C and solve for t in radians:
20 = 7.5 cos(t) + 365 - 21.5.
To simplify, we subtract 365 and add 21.5 to both sides:
-323.5 = 7.5 cos(t).
Next, divide both sides by 7.5:
-43.13 = cos(t).
The value on the right side of the equation is not possible since the cosine function ranges from -1 to 1, suggesting there may have been a typo. Assuming the actual equation should omit the "+ 365", we solve:
20 = 7.5 cos(t) - 21.5
41.5 = 7.5 cos(t)
5.5333... = cos(t)
This value is also outside the range, hinting at a possible typo in the original equation or question. We would need a correct model to solve for t, the second time after the hottest day of the year when the temperature is 20°C.