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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Question

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 Questions

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Follow-up Question

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

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Follow-up Question

d) Find the radius, r and the dimension, I that maximises the pool
area for a pool perimeter, P of 8 m.

Solution

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Follow-up Question

c) Hence, or otherwise show that A = -² + Pr.

Solution

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Follow-up Question

b) Express the area of the pool, A in terms of 1 and r.

Solution

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