Atmospheric pressure V decreases as altitude h increases. At a temperature of the pressure is 101.1kilopascals kPa at sea level, 86.4 kPa at h = 1 km, and 77.1 kPa at h = 2 km. Use a linear approximation to estimate the atmospheric pressure at an altitude of 3 km. Please round your answer to the nearest tenth.
________ kPa
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To estimate the atmospheric pressure at an altitude of 3 km, we can use a linear approximation.
Given the points (h, V) where h represents the altitude in kilometers and V represents the atmospheric pressure in kilopascals (kPa), we can create a linear equation to approximate the values.
Using the two given points (1, 86.4) and (2, 77.1), we can find the equation of the line that passes through them.
First, we calculate the slope of the line using the formula:
slope (m) = (V2 - V1) / (h2 - h1)
= (77.1 - 86.4) / (2 - 1)
= -9.3
Next, we use the point-slope form of a linear equation to find the equation of the line:
V - V1 = m(h - h1)
Substituting the values of (h1, V1) = (1, 86.4) and m = -9.3, we get:
V - 86.4 = -9.3(h - 1)
Simplifying the equation, we get:
V = -9.3h + 95.7
Now, we can substitute h = 3 into the equation to estimate the atmospheric pressure at an altitude of 3 km:
V = -9.3(3) + 95.7
V = -27.9 + 95.7
V ≈ 67.8 kPa
Therefore, the estimated atmospheric pressure at an altitude of 3 km is approximately 67.8 kPa.