As dry air moves upward, it expands and in so doing cools at a rate of about 10C for 100m rise, up to about 12 km.

a) If the ground temperature is 220, write a formula for the temperature at height x km.

b) What range of temperature can be expected if a plane takes off and reaches a maximum height of 9 km.Write answer in interval notation.

220-x/100

a) To calculate the temperature at a certain height x km, we can use the rate of cooling of 10°C per 100m rise. We know that at ground level (0 km), the temperature is 220°C.

Let's assume that the temperature at height x km is T(x). Since there are 1000 meters in a km, we can use the rate of cooling to calculate the change in temperature as we rise by x km.

We can write the formula as:
T(x) = 220°C - (10°C/100m) * (1000m/km) * x

Simplifying this equation, we get:
T(x) = 220°C - 10°C * x

b) If the plane reaches a maximum height of 9 km, we can determine the temperature range by substituting the height values into the formula we derived in part a.

Using the formula T(x) = 220°C - 10°C * x, we can substitute x = 0 km and x = 9 km to calculate the temperature range.

At x = 0 km (ground level):
T(0) = 220°C - 10°C * 0
T(0) = 220°C

At x = 9 km (maximum height):
T(9) = 220°C - 10°C * 9
T(9) = 220°C - 90°C
T(9) = 130°C

Therefore, the range of temperature can be expected between 220°C and 130°C. In interval notation, we can represent this range as [130°C, 220°C].