23. A semicircle with radius 1 is partitioned into two adjacent sectors as shown below. a (a) Find formulas for the areas of the two sectors in terms of 0. (b) If f(0) is the product of these two areas, find the exact value of that maximizes f(0).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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23. A semicircle with radius 1 is partitioned into two adjacent sectors as shown below.
a
Ө
(a) Find formulas for the areas of the two sectors in terms of 0.
(b) If f(0) is the product of these two areas, find the exact value of that maximizes
ƒ(0).
Transcribed Image Text:23. A semicircle with radius 1 is partitioned into two adjacent sectors as shown below. a Ө (a) Find formulas for the areas of the two sectors in terms of 0. (b) If f(0) is the product of these two areas, find the exact value of that maximizes ƒ(0).
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