Answer:
September, October, November
Explanation:
When monthly rainfall in centimeters is represented by A(t) = 2.3sin(πt/6)+9.25 and A(0) represents July's rainfall, you want to know the months in which average rainfall is at least 10.5 cm.
Inequality
We want to find the values of t that make A(t) ≥ 10.5:
2.3sin(πt/6) +9.25 ≥ 10.5
2.3sin(πt/6) ≥ 1.25 . . . . . . subtract 9.25
sin(πt/6) ≥ 0.543478 . . . . divide by 2.3
πt/6 ≥ 0.574575 . . . . . . . take inverse sine
t ≥ 1.097
The sine function is symmetrical about π/2, so this also means solutions will be of the form ...
πt/6 ≤ π -0.574575
t ≤ 6 -1.097 ≈ 4.903
Months
The month numbers that will have rainfall at least 10.5 cm will fall in the range ...
1.097 ≤ t ≤ 4.903
t ∈ {2, 3, 4}
If July is month 0, then these months are September, October, November.
Jacy's hometown will get at least 10.5 cm of rain in September, October, and November.
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Additional comment
The attachment confirms this result. We have shifted the rainfall function so it can use conventional month numbers. It shows months 9, 10, 11 have rainfall above 10.5 cm.
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