The World Runs On Pipes

The builders of the Trans-Alaska pipeline used insulated pads to keep the heat from the pipeline from melting the permanently frozen soil beneath. To design the pad, it was necessary to take into account the variation in air temperature through the year. The function fit into data was

$f(x) = 37 \sin \left( \dfrac{2\pi}{365}(x-101) \right) + 25,$

where $f(x)$ measures the temperature in Fahrenheit scale and $x$ is the number of days counting from the beginning of the year. The maximum temperature will thus be in the $k^\text{th}$ month of the year where $k$ is $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Image courtesy: Wikipedia.