The area, A of 2 semi-circles separated by a fixed length can be expressed as a quadratic equation provided the perimeter of the shape, P is known: A = -xr² + Pr (1) Consider an application of this equation where a pool is to be constructed as shown below with the following dimensions: 1 Figure 1: Top view of a pool design. a) Derive an equation for the perimeter of the pool, P in terms of 1 and r. b) Express the area of the pool, A in terms of 1 and r.
The area, A of 2 semi-circles separated by a fixed length can be expressed as a quadratic equation provided the perimeter of the shape, P is known: A = -xr² + Pr (1) Consider an application of this equation where a pool is to be constructed as shown below with the following dimensions: 1 Figure 1: Top view of a pool design. a) Derive an equation for the perimeter of the pool, P in terms of 1 and r. b) Express the area of the pool, A in terms of 1 and r.
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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Transcribed Image Text:The area, A of 2 semi-circles separated by a fixed length can be expressed
as a quadratic equation provided the perimeter of the shape, P is known:
A = -лr² + Pr
(1)
Consider an application of this equation where a pool is to be constructed
as shown below with the following dimensions:
Figure 1: Top view of a pool design.
a) Derive an equation for the perimeter of the pool, P in terms of 1
and r.
b) Express the area of the pool, A in terms of 1 and r.
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Follow-up Question
Transcribed Image Text:e) If the pool shape is restricted such that the dimension, 1 is 1.5 m,
what will be the radius, r if the pool is to maintain its perimeter,
P of 8 m?
Solution
by Bartleby ExpertFollow-up Question
Transcribed Image Text:d) Find the radius, r and the dimension, I that maximises the pool
area for a pool perimeter, P of 8 m.
Solution
by Bartleby ExpertFollow-up Question
Transcribed Image Text:c) Hence, or otherwise show that A = -² + Pr.
Solution
by Bartleby ExpertFollow-up Question
Transcribed Image Text:b) Express the area of the pool, A in terms of 1 and r.
Solution
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