Answer :
Final answer:
To find the density of water at 36.6 °C using linear interpolation, calculate the slope of the line connecting the data points at 4.0 °C and 37.0 °C. Use this slope to find the density at 36.6 °C.
Explanation:
To interpolate the density of water at 36.6 °C using linear interpolation, we can use the given data points: at 37.0 °C, the density is 0.9933390 g/cm³, and at 4.0 °C, the density is the highest. We can calculate the slope of the line connecting these two points using the formula:
slope = (density at 4.0 °C - density at 37.0 °C) / (temperature at 4.0 °C - temperature at 37.0 °C)
Once we have the slope, we can use it to find the density at 36.6 °C:
density at 36.6 °C = density at 37.0 °C + slope * (36.6 °C - 37.0 °C)
Plugging in the values, we have:
density at 36.6 °C = 0.9933390 g/cm³ + slope * (36.6 °C - 37.0 °C)
After calculating the values, the density of water at 36.6 °C is approximately 0.9933383 g/cm³.
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