Question

The average monthly temperature T(m), in degrees Celsius, of a particular city varies according to the model T of m equals 10 times cosine of the quantity pi over 6 times m end quantity plus 5 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?

Answer 1

The temperature will be below 0°C when the cosine of π/6 * m is negative. This occurs when m is between 2π/3 and 4π/3. In other words, the temperature will be below 0°C between March and September.

Answer 2

Explanation:

To determine the months when the temperature will be below 0°C, we need to find the values of m for which T(m) is less than 0.

Given the model T(m) = 10 * cos((π/6) * m) + 5, we can set up the inequality:

10 * cos((π/6) * m) + 5 < 0

Subtracting 5 from both sides:

10 * cos((π/6) * m) < -5

Dividing both sides by 10:

cos((π/6) * m) < -0.5

To find the values of m that satisfy this inequality, we need to find the angles (π/6) * m where the cosine function is less than -0.5.

Using the unit circle, we know that the cosine function is negative in the second and third quadrants. In the second quadrant, the cosine is less than -0.5, so we can set up the inequality:

(π/6) * m > π

Simplifying:

m > 6

Therefore, the temperature will be below 0°C for the months greater than 6. Since January is represented by m = 0, the months when the temperature will be below 0°C are July, August, September, October, November, and December.