A rectangle is to be inscribed in a semicircle of radius 6 cm as shown in the following figure. 6 cm (a) Find the function that models the area of the rectangle. A(8) = (b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u = n/2.] cm? (c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.) smaller dimension cm larger dimension cm

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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A rectangle is to be inscribed in a semicircle of radius 6 cm as shown in the following figure.
-6 cm
(a) Find the function that models the area of the rectangle.
A(8) =
(b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u = n/2.]
cm?
(c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.)
smaller dimension
cm
larger dimension
cm
Transcribed Image Text:A rectangle is to be inscribed in a semicircle of radius 6 cm as shown in the following figure. -6 cm (a) Find the function that models the area of the rectangle. A(8) = (b) Find the largest possible area for such an inscribed rectangle. [Hint: Use the fact that sin(u) achieves its maximum value at u = n/2.] cm? (c) Find the dimensions of the inscribed rectangle with the largest possible area. (Round your answers to two decimal places.) smaller dimension cm larger dimension cm
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