The sea ice around the south pole fluctuates between 18 million square kilometers in September to 3 million square kilometers in March. During how many months are there more than 15 million square kilometers of sea ice?

Well, it seems like the sea ice around the south pole has a flair for dramatics! Let's do some math. If the sea ice fluctuates between 18 million square kilometers in September to 3 million square kilometers in March, we need to count how many months have more than 15 million square kilometers.

So, let's start from September. In September, we have 18 million square kilometers, which is more than 15 million. That's one month down! Moving on to October... Oh, wait, I'm just clowning around! You get the picture. From September to March, that's a total of 7 months, my friend! So, for seven months, there are more than 15 million square kilometers of sea ice around the south pole. Ice, ice, baby!

To find out during how many months there are more than 15 million square kilometers of sea ice, we need to determine the months when the sea ice extent is greater than 15 million square kilometers using the given information.

The sea ice extent around the South Pole is 18 million square kilometers in September and 3 million square kilometers in March.

Let's break it down:

September:
Sea ice extent > 15 million square kilometers (18 million square kilometers > 15 million square kilometers)

October, November, December, January, February:
Sea ice extent > 15 million square kilometers (entirely between September and March)

March:
Sea ice extent > 15 million square kilometers (3 million square kilometers > 15 million square kilometers)

From the given data, we can see that there are a total of 7 months (September, October, November, December, January, February, March) during which the sea ice extent around the South Pole is more than 15 million square kilometers.

To determine the number of months with more than 15 million square kilometers of sea ice, we need to analyze the data on sea ice fluctuations given in the question.

The sea ice around the south pole fluctuates between 18 million square kilometers in September and 3 million square kilometers in March.

To solve this, we need to determine the specific months when the sea ice extent exceeds 15 million square kilometers.

Here's how we can do that:

1. Start by identifying the months when the sea ice extent is above 15 million square kilometers.

- In September, the sea ice extent is 18 million square kilometers, which is above 15 million.

- In March, the sea ice extent is 3 million square kilometers, which is below 15 million.

2. We know that the sea ice extent decreases from September to March, so we need to determine the months in between when the sea ice extent is above 15 million.

- Let's assume that the sea ice extent linearly decreases on a monthly basis. This means the decrease from 18 million square kilometers to 3 million square kilometers occurs over a span of 6 months (September to March).

- The average decrease in sea ice extent per month would then be (18 million - 3 million) / 6 months = 15 million / 6 months = 2.5 million square kilometers per month.

3. Now, we can determine the specific months when the sea ice extent is above 15 million square kilometers.

- Starting from September, we have 18 million square kilometers of sea ice.

- We need to determine how many months it takes for the sea ice extent to fall below 15 million square kilometers.

- We can calculate this by dividing the difference between 18 million square kilometers and 15 million square kilometers by the decrease per month: (18 million - 15 million) / 2.5 million = 3 million / 2.5 million = 1.2 months.

- Since we cannot have fractions of a month, we round up to the next whole month. Therefore, it takes 2 months for the sea ice extent to fall below 15 million square kilometers.

4. Now, we add the months from September (1) to the months it takes for the sea ice extent to fall below 15 million square kilometers (2): 1 + 2 = 3 months.

Therefore, there are three months in which the sea ice extent around the South Pole is more than 15 million square kilometers.

Assuming a sinusoidal function, we have the area is (letting x=0 in September)

a(x) = 7.5 cos(pi/6 x) + 10.5
we want a(x) > 15. In other words,

cos(pi/6 x) > 0.6

-1.77 < x < 1.77 so, using symmetry, in one complete period (a year), there are 3.54 months with more than 15 Mmi^2 of ice