3.1 Quadratic Functions Examples And Worksheet - Chapter 3: Polynomial And Rational Functions Page 10
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1:20 PM
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Section 3.1
Quadratic Functions
(d) Write the area function in standard form to find
58. Automobile Aerodynamics The number of horsepower
H
algebraically the dimensions that will produce the
required to overcome wind drag on a certain automobile is
maximum area.
approximated by
(e) Compare your results from parts (b), (c), and (d).
2
H s
0.002s
0.05s
0.029,
0 ≤ s ≤ 100
55. Height of a Ball The height
y
(in feet) of a punted
where is the speed of the car (in miles per hour).
s
football is approximated by
(a) Use a graphing utility to graph the function.
16
9
3
2
y
x
x
2025
5
2
(b) Graphically estimate the maximum speed of the car if
where is the horizontal distance (in feet) from where the
x
the power required to overcome wind drag is not to
football is punted.
exceed 10 horsepower. Verify your result algebraically.
59. Revenue The total revenue R (in thousands of dollars)
earned from manufacturing and selling hand-held video
games is given by
2
R p
25p
1200p
where p is the price per unit (in dollars).
(a) Find the revenue when the price per unit is $20, $25,
y
and $30.
(b) Find the unit price that will yield a maximum revenue.
x
Not drawn to scale
(c) What is the maximum revenue?
(a) Use a graphing utility to graph the path of the football.
(d) Explain your results.
(b) How high is the football when it is punted? (Hint: Find
60. Revenue The total revenue R (in dollars) earned by a dog
y
when
x
0.
)
walking service is given by
(c) What is the maximum height of the football?
2
R p
12p
150p
(d) How far from the punter does the football strike the
where p is the price charged per dog (in dollars).
ground?
(a) Find the revenue when the price per dog is $4, $6, and
56. Path of a Diver The path of a diver is approximated by
$8.
4
24
2
y
x
x
12
9
9
(b) Find the price that will yield a maximum revenue.
where
y
is the height (in feet) and
x
is the horizontal
(c) What is the maximum revenue?
distance (in feet) from the end of the diving board (see
(d) Explain your results.
figure). What is the maximum height of the diver? Verify
61. Graphical Analysis From 1960 to 2004, the annual per
your answer using a graphing utility.
capita consumption
C
of cigarettes by Americans (age 18
and older) can be modeled by
2
C t
4306
3.4t
1.32t
,
0 ≤ t ≤ 44
where
t
is the year, with
t
0
corresponding to 1960.
(Source: U.S. Department of Agriculture)
(a) Use a graphing utility to graph the model.
(b) Use the graph of the model to approximate the year
when the maximum annual consumption of cigarettes
occurred. Approximate the maximum average annual
57. Cost A manufacturer of lighting fixtures has daily
consumption. Beginning in 1966, all cigarette
production costs of
packages were required by law to carry a health warn-
2
C x
800
10x
0.25x
ing. Do you think the warning had any effect? Explain.
(c) In 2000, the U.S. population (age 18 and older) was
where
C
is the total cost (in dollars) and is the number of
x
209,117,000. Of those, about 48,306,000 were
units produced. Use the table feature of a graphing utility
smokers. What was the average annual cigarette
to determine how many fixtures should be produced each
consumption per smoker in 2000? What was the
day to yield a minimum cost.
average daily cigarette consumption per smoker?
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