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Mathematics
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Algebra and Trigonometry Study Set 1
Quiz 3: Polynomial and Rational Functions
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Question 81
Multiple Choice
Solve the problem. -You have 184 feet of fencing to enclose a rectangular region. What is the maximum area?
Question 82
Multiple Choice
Solve the problem. -The owner of a video store has determined that the profits
P
\mathrm { P }
P
of the store are approximately given by
P
(
x
)
=
ā
x
2
+
150
x
+
71
P ( x ) = - x ^ { 2 } + 150 x + 71
P
(
x
)
=
ā
x
2
+
150
x
+
71
, where
x
x
x
is the number of videos rented daily. Find the maximum profit to the nearest dollar.
Question 83
Multiple Choice
Solve the problem. -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 624 feet of fencing is used. Find the maximum area of the playground.
Question 84
Multiple Choice
Solve the problem. -The owner of a video store has determined that the cost
C
C
C
, in dollars, of operating the store is approximately given by
C
(
x
)
=
2
x
2
ā
26
x
+
640
C ( x ) = 2 x ^ { 2 } - 26 x + 640
C
(
x
)
=
2
x
2
ā
26
x
+
640
, where
x
x
x
is the number of videos rented daily. Find the lowest cost to the nearest dollar.
Question 85
Multiple Choice
Solve the problem. -The profit that the vendor makes per day by selling
x
x
x
pretzels is given by the function
P
(
x
)
=
ā
0.002
x
2
+
1.6
x
ā
300
P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300
P
(
x
)
=
ā
0.002
x
2
+
1.6
x
ā
300
. Find the number of pretzels that must be sold to maximize profit.
Question 86
Multiple Choice
Solve the problem. -The cost in millions of dollars for a company to manufacture
x
x
x
thousand automobiles is given by the function
C
(
x
)
=
3
x
2
ā
30
x
+
200
C ( x ) = 3 x ^ { 2 } - 30 x + 200
C
(
x
)
=
3
x
2
ā
30
x
+
200
. Find the number of automobiles that must be produced to minimize the cost.
Question 87
Multiple Choice
Solve the problem. -You have 136 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.
Question 88
Multiple Choice
Solve the problem. -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 528 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area.
Question 89
Multiple Choice
Solve the problem. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 244 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
Question 90
Multiple Choice
Solve the problem. -A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.
Question 91
Multiple Choice
Solve the problem. -Among all pairs of numbers whose sum is 88 , find a pair whose product is as large as possible.
Question 92
Multiple Choice
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. -
f
(
x
)
=
ā
3
x
2
+
9
x
f ( x ) = - 3 x ^ { 2 } + 9 x
f
(
x
)
=
ā
3
x
2
+
9
x
Question 93
Multiple Choice
Solve the problem. -An arrow is fired into the air with an initial velocity of 128 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = -16t2 + 128t. Find the maximum height of the arrow.
Question 94
Multiple Choice
Solve the problem. -Among all pairs of numbers whose difference is 48, find a pair whose product is as small as possible.
Question 95
Multiple Choice
Solve the problem. -You have 84 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.