Cost of Natural Gas In March 2018 , Spire, Inc. had the following rate schedule for natural gas usage in single-family residences. Monthly service charge $ 23.44 Delivery charge First 30 therms $ 0.91686 / t h e r m Over 30 therms $ 0 Natural gas cost First 30 therms $ 0.26486 / t h e r m Over 30 therms $ 0.50897 / t h e r m What is the charge for using 20 therms in a month? What is the charge for using 150 therms in a month? Develop a function that models the monthly charge C for x therms of gas. Graph the function found in part (c).
Cost of Natural Gas In March 2018 , Spire, Inc. had the following rate schedule for natural gas usage in single-family residences. Monthly service charge $ 23.44 Delivery charge First 30 therms $ 0.91686 / t h e r m Over 30 therms $ 0 Natural gas cost First 30 therms $ 0.26486 / t h e r m Over 30 therms $ 0.50897 / t h e r m What is the charge for using 20 therms in a month? What is the charge for using 150 therms in a month? Develop a function that models the monthly charge C for x therms of gas. Graph the function found in part (c).
Solution Summary: The author explains that the rate schedule for natural gas usage in single-family residences is given by the table 47.0744.
(2) (12 points) Let f(x,y) = x²e¯.
(a) (4 points) Calculate Vf.
(b) (4 points) Given x
directional derivative
0, find the line of vectors u =
D₁f(x, y) = 0.
(u1, 2) such that the
-
(c) (4 points) Let u= (1+3√3). Show that
Duƒ(1, 0) = ¦|▼ƒ(1,0)| .
What is the angle between Vf(1,0) and the vector u? Explain.
Find the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)
a
b
29
39
66.50
C
17.40
d
0
54.0
126°
a
Ꮎ
b
d
(5) (10 points) Let D be the parallelogram in the xy-plane with vertices
(0, 0), (1, 1), (1, 1), (0, -2).
Let f(x,y) = xy/2. Use the linear change of variables
T(u, v)=(u,u2v) = (x, y)
1
to calculate the integral
f(x,y) dA=
0
↓
The domain of T is a rectangle R. What is R?
|ǝ(x, y)
du dv.
|ð(u, v)|
Chapter 2 Solutions
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