### Heat Index Calculation and Partial Derivatives#### Heat Index FormulaThe **heat index** $ I $ is a measure of how hot it feels when the relative humidity is $ H $ (as a percentage) and the actual air temperature is $ T $ (in degrees Fahrenheit). The approximate formula for the heat index that is valid for $ (T, H) $ near (90, 40) is:\[ I(T, H) = 45.33 + 0.6845T + 5.758H - 0.00365T^2 - 0.1565HT + 0.001HT^2 \]#### Calculating the Heat IndexCalculate $ I $ at $ (T, H) = (97, 43) $.(Use decimal notation. Give your answer to three decimal places.)\[ I(97, 43) = \]#### Determining the Partial DerivativeDetermine the partial derivative.(Use symbolic notation and fractions where needed.)\[ \frac{\partial I}{\partial T} = \]#### Calculating the Partial DerivativeCalculate this partial derivative when $ (T, H) = (97, 43) $.(Use decimal notation. Give your answer to three decimal places.)\[ \frac{\partial I}{\partial T}(97, 43) = \]

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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