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
.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
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