The shaded area represents the planted seeds. SMte Por a Find the area, A, planted with seeds, in terms of a. b. If the length of the garden plot was 13.5 metres, what was the area that Napier planted with seeds?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
icon
Related questions
Question
As cach year passed Napier became more eccentric and in his third year he designed a garden
bordered by a parabolic curve y = x and the x - axis. Again he did not plant anything in the
first metre.
PaT
e. Find the area, A, that Napier planted with seeds, in terms of a.
I. Find the exact area he planted with seeds if his garden plot was
metres in length.
In his final and most bizarre year he decided to build a garden designed with hyperbolae. The
garden was bordered by the curve y = the x - axis and again nothing was planted in the first
metre. This time he struggled to find a formula, even in his historical mathematics books, that
would allow him to cakulate the exact area. So he decided to find the approximate area by breaking
the planted section up into 4 strips of equal width.
GMN
Pet
2 For part g only, we are given the length, , of the garden plot is 5 metres.
Use the left endpoint approximation, with rectangles of width 1 metre, to find the
approximate area that Napier planted with seeds. (Use the diagram on the right hand side
to find area required)
i.
ii. Use the right endpoint approximation, with rectangles of width I metre, to find the
approximate area that Napier planted with seeds.
Transcribed Image Text:As cach year passed Napier became more eccentric and in his third year he designed a garden bordered by a parabolic curve y = x and the x - axis. Again he did not plant anything in the first metre. PaT e. Find the area, A, that Napier planted with seeds, in terms of a. I. Find the exact area he planted with seeds if his garden plot was metres in length. In his final and most bizarre year he decided to build a garden designed with hyperbolae. The garden was bordered by the curve y = the x - axis and again nothing was planted in the first metre. This time he struggled to find a formula, even in his historical mathematics books, that would allow him to cakulate the exact area. So he decided to find the approximate area by breaking the planted section up into 4 strips of equal width. GMN Pet 2 For part g only, we are given the length, , of the garden plot is 5 metres. Use the left endpoint approximation, with rectangles of width 1 metre, to find the approximate area that Napier planted with seeds. (Use the diagram on the right hand side to find area required) i. ii. Use the right endpoint approximation, with rectangles of width I metre, to find the approximate area that Napier planted with seeds.
Оuestion Twe
Early in the 1900s Mount Lilydale Mercy College employed a Scottish gardener by the name of Lord
Napier. He was rather eccentric and loved mathematics, especially geometry. He loved to plant his
gardens in interesting shapes. He was particularly frugal and insisted on knowing the exact arca of
each plot so that he woukd not waste a single seed. His first plot was a rectangular plot of fixed width
I metre and variable length a metres; however for beauty, he decided not to plant anything in the first
metre.
The shaded area represents the planted seeds.
SMe Por
a Find the area, A, planted with seeds, in terms of a
b. If the length of the garden plot was 13.5 metres, what was the area that Napier planted with seeds?
The next year Napier became more adventurous. He designed a triangular garden bordered by the
line y = x and the x - axis. He still insisted on not planting anything in the first metre of length.
Put
c. Show the area, A, that Napier planted with seeds, in terms of a is ta -
d. If he insisted on planting exactly 100 m² of seed, what was the length of his garden plot?
Transcribed Image Text:Оuestion Twe Early in the 1900s Mount Lilydale Mercy College employed a Scottish gardener by the name of Lord Napier. He was rather eccentric and loved mathematics, especially geometry. He loved to plant his gardens in interesting shapes. He was particularly frugal and insisted on knowing the exact arca of each plot so that he woukd not waste a single seed. His first plot was a rectangular plot of fixed width I metre and variable length a metres; however for beauty, he decided not to plant anything in the first metre. The shaded area represents the planted seeds. SMe Por a Find the area, A, planted with seeds, in terms of a b. If the length of the garden plot was 13.5 metres, what was the area that Napier planted with seeds? The next year Napier became more adventurous. He designed a triangular garden bordered by the line y = x and the x - axis. He still insisted on not planting anything in the first metre of length. Put c. Show the area, A, that Napier planted with seeds, in terms of a is ta - d. If he insisted on planting exactly 100 m² of seed, what was the length of his garden plot?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Area
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
PREALGEBRA
PREALGEBRA
Algebra
ISBN:
9781938168994
Author:
OpenStax
Publisher:
OpenStax