Heat index The highest recorded temperature in the state of Alaska was 100°F , occurring on June 27,1915, at Fort Yukon. The heat index is the apparent temperature of the air at a given temperature and humidity level. If x denotes the relative humidity (in percent), then the heat index (in degrees Fahrenheit) for an air temperature of 100°F can be approximated by the function f ( x ) = 0.009 x 2 + 0.139 x + 91.875 (a) At what rate is the heat index changing when the humidity is 50 % ? (b) Write a sentence that explains the meaning of your answer in part (a).
Heat index The highest recorded temperature in the state of Alaska was 100°F , occurring on June 27,1915, at Fort Yukon. The heat index is the apparent temperature of the air at a given temperature and humidity level. If x denotes the relative humidity (in percent), then the heat index (in degrees Fahrenheit) for an air temperature of 100°F can be approximated by the function f ( x ) = 0.009 x 2 + 0.139 x + 91.875 (a) At what rate is the heat index changing when the humidity is 50 % ? (b) Write a sentence that explains the meaning of your answer in part (a).
Solution Summary: The author calculates the instantaneous rate of change of heat index when humidity is 50%.
Heat index The highest recorded temperature in the state of Alaska was
100°F
, occurring on June 27,1915, at Fort Yukon. The heat index is the apparent temperature of the air at a given temperature and humidity level. If x denotes the relative humidity (in percent), then the heat index (in degrees Fahrenheit) for an air temperature of
100°F
can be approximated by the function
f
(
x
)
=
0.009
x
2
+
0.139
x
+
91.875
(a) At what rate is the heat index changing when the humidity is
50
%
?
(b) Write a sentence that explains the meaning of your answer in part (a).
The saturation concentration of oxygen dissolved in water is a function of temperature and chlorine
concentration as given in the table. For T=18°C and chlorine concentration =10,000mgL/, calculate
the dissolved oxygen level by sequential interpolation.
Temperature°C
Chlorine= 0 mg/L
Chlorine= 10,000 mg/L
Chlorine 20,000 mg/L
12.8
11.6
10.5
10
11.3
10.3
9.2
15
10.0
9.1
8.2
20
9.0
8.2
7.4
25
8.2
7.4
6.7
30
7.4
6.8
6.1
Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formulat gives one way of estimating body surface area B in square meters. The formula uses the weight w in kilograms and the
height h in centimeters. The relation is
hw
B =
60
In this exercise we consider people who are 170 centimeters tall.
(a) Write a formula for B as a function of w.
B =
(b) Make a graph of B versus w. Include weights up to 100 kilograms.
B
B
3.0
3.0r
2.5
2.5
2.0
2.0-
1.5
1.5
1.0
1.0
0.5
0.5-
0.0
0.0
20
40
60
80
100
20
40
60
80
100
B
3.0
3.0
2,5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
20
40
60
80
100
20
40
60
80
100
a cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. The oil begins draining at a constant rate of 2 cubic feet per second. write the volume of the oil remaining in the tank t seconds later as a function of t
Chapter 9 Solutions
WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term
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