84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up a flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open. 20 a. Write an expression for the cross-sectional area in terms of x, the length of metal which is bent upwards. b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the maximum cross-sectional area?
84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up a flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open. 20 a. Write an expression for the cross-sectional area in terms of x, the length of metal which is bent upwards. b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the maximum cross-sectional area?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
84 please
![XRevathi Narasimhan, College Alge X X Revathi Narasimhan, College Alge X
← → C ✰ xyztextbooks.com/ebook/title/reva_ca
E CONTENTS
72°F
Clear
CATALOG
+
SECTION: 3.1
a. Sketch a graph of h.
b. When will the ball reach its maximum height, and what is the maximum height?
20-2x
PAGE 240
84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up a
flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open.
a. Write an expression for the cross-sectional area in terms of x, the length of metal which is
bent upwards.
b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the
maximum cross-sectional area?
Use the information below to work Exercises 85 and 86.
The quadratic function p(x) = -0.387(x-45)² +2.73(x45) - 3.89 gives the percentage (in
decimal form) of puffin eggs that hatch during a breeding season in terms of x, the mean sea surface
temperature of the surrounding area, in degrees Fahrenheit.
(Source: Gjerdum et al., "Tufted puffin reproduction reveals ocean climate variability,"
Proceedings of the National Academy of Sciences, August 2003.)
85. Ecology What is the percent e of puffin eggs that will hatch at 49°F? At 47°F?
86. Ecology For what mean temperature is the percentage of hatched puffin eggs a maximum? Find
the percentage of hatched eggs at this temperature.
a
CC
VIDEOS
Mr. Hampton
▶ Play
BOOKSHELF
SUPPLEMENTS
m(x) = -0.0108X² +0.981 X + 8.05
30-
b) mileage 35mph
m(35) =
-0.0108(35)² +15-
0.98 (39)+8.05 19.
29.2 mpg
20.
CC
maximum, using a graphing utility.
Shelby
▶ Play
5
hat speed is mileage at a maximum
V=(45.5, 30.4)
PROGRESS
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
CC
Breylor
▶ Play
ES
m(x)
-0:00
Math
1x
TOOLS III
сс
CC
Julieta
▶ Play
[]
español
X
8:53 PM
10/20/2022
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa32b080e-315a-4cdc-b676-262d2151a2fd%2F27d73a84-5d3c-414b-b562-be061052f4e1%2Fdrt8gar_processed.png&w=3840&q=75)
Transcribed Image Text:XRevathi Narasimhan, College Alge X X Revathi Narasimhan, College Alge X
← → C ✰ xyztextbooks.com/ebook/title/reva_ca
E CONTENTS
72°F
Clear
CATALOG
+
SECTION: 3.1
a. Sketch a graph of h.
b. When will the ball reach its maximum height, and what is the maximum height?
20-2x
PAGE 240
84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up a
flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open.
a. Write an expression for the cross-sectional area in terms of x, the length of metal which is
bent upwards.
b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the
maximum cross-sectional area?
Use the information below to work Exercises 85 and 86.
The quadratic function p(x) = -0.387(x-45)² +2.73(x45) - 3.89 gives the percentage (in
decimal form) of puffin eggs that hatch during a breeding season in terms of x, the mean sea surface
temperature of the surrounding area, in degrees Fahrenheit.
(Source: Gjerdum et al., "Tufted puffin reproduction reveals ocean climate variability,"
Proceedings of the National Academy of Sciences, August 2003.)
85. Ecology What is the percent e of puffin eggs that will hatch at 49°F? At 47°F?
86. Ecology For what mean temperature is the percentage of hatched puffin eggs a maximum? Find
the percentage of hatched eggs at this temperature.
a
CC
VIDEOS
Mr. Hampton
▶ Play
BOOKSHELF
SUPPLEMENTS
m(x) = -0.0108X² +0.981 X + 8.05
30-
b) mileage 35mph
m(35) =
-0.0108(35)² +15-
0.98 (39)+8.05 19.
29.2 mpg
20.
CC
maximum, using a graphing utility.
Shelby
▶ Play
5
hat speed is mileage at a maximum
V=(45.5, 30.4)
PROGRESS
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
CC
Breylor
▶ Play
ES
m(x)
-0:00
Math
1x
TOOLS III
сс
CC
Julieta
▶ Play
[]
español
X
8:53 PM
10/20/2022
20
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