The wind-chill index is modeled by the function W = 13.12 + 0.6215 T − 11.37 v 0.16 + 0.3965 T v 0.16 where T is the actual temperature (in ° C ) and v is the wind speed (in km / h ). The wind speed is measured as 26 km / h , with a possible error of ± 2 km / h , and the actual temperature is measured as − 11 ° C , with a possible error of ± 1 ° C . Use differentials to estimate the maximum error in the calculated value of W due to the measurement errors in T and v .
The wind-chill index is modeled by the function W = 13.12 + 0.6215 T − 11.37 v 0.16 + 0.3965 T v 0.16 where T is the actual temperature (in ° C ) and v is the wind speed (in km / h ). The wind speed is measured as 26 km / h , with a possible error of ± 2 km / h , and the actual temperature is measured as − 11 ° C , with a possible error of ± 1 ° C . Use differentials to estimate the maximum error in the calculated value of W due to the measurement errors in T and v .
Solution Summary: The author explains the maximum error in the calculated value of wind chill index.
The wind-chill index is modeled by the function
W
=
13.12
+
0.6215
T
−
11.37
v
0.16
+
0.3965
T
v
0.16
where
T
is the actual temperature (in
°
C
) and
v
is the wind speed (in
km
/
h
). The wind speed is measured as
26
km
/
h
, with a possible error of
±
2
km
/
h
, and the actual temperature is measured as
−
11
°
C
, with a possible error of
±
1
°
C
. Use differentials to estimate the maximum error in the calculated value of
W
due to the measurement errors in
T
and
v
.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY