e heat index I is a measure of how hot it feels when the relative humidity is H (as a perce mperature is T (in degrees Fahrenheit). An approximate formula for the heat index that is va I(T, H) = 45.33 + 0.6845T +5.758H -0.00365T2 -0.1565 HT+0.001HT2 lculate I at (T, H) = (97, 43). se decimal notation. Give your answer to three decimal places.)
e heat index I is a measure of how hot it feels when the relative humidity is H (as a perce mperature is T (in degrees Fahrenheit). An approximate formula for the heat index that is va I(T, H) = 45.33 + 0.6845T +5.758H -0.00365T2 -0.1565 HT+0.001HT2 lculate I at (T, H) = (97, 43). se decimal notation. Give your answer to three decimal places.)
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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![### Heat Index Calculation and Partial Derivatives
#### Heat Index Formula
The **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 Index
Calculate \( I \) at \( (T, H) = (97, 43) \).
(Use decimal notation. Give your answer to three decimal places.)
\[ I(97, 43) = \]
#### Determining the Partial Derivative
Determine the partial derivative.
(Use symbolic notation and fractions where needed.)
\[ \frac{\partial I}{\partial T} = \]
#### Calculating the Partial Derivative
Calculate this partial derivative when \( (T, H) = (97, 43) \).
(Use decimal notation. Give your answer to three decimal places.)
\[ \frac{\partial I}{\partial T}(97, 43) = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F721da9e6-56ca-4fff-bad1-06b01dcc2531%2F07b6d33e-cedb-40a8-84b8-c0fc2b98c7ea%2Fu520uej_processed.png&w=3840&q=75)
Transcribed Image Text:### Heat Index Calculation and Partial Derivatives
#### Heat Index Formula
The **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 Index
Calculate \( I \) at \( (T, H) = (97, 43) \).
(Use decimal notation. Give your answer to three decimal places.)
\[ I(97, 43) = \]
#### Determining the Partial Derivative
Determine the partial derivative.
(Use symbolic notation and fractions where needed.)
\[ \frac{\partial I}{\partial T} = \]
#### Calculating the Partial Derivative
Calculate 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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