A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100 inches. Choose the radius of the semicircular part so that the mirror has maximum area. [Note: The perimeter consists of three sides of the rectangle and the semicircle.] 25 (a) Find an equation for the A, the area of the mirror, in terms of the variables r and y shown in the diagram below. (b) Write an equation for the constraint (s) in this problem. (c) Write A as a function of only the variable r. You can use your equality constraint from part (b) to substitute for y in your equation for A. (You do not need to simplify your answer.)
A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100 inches. Choose the radius of the semicircular part so that the mirror has maximum area. [Note: The perimeter consists of three sides of the rectangle and the semicircle.] 25 (a) Find an equation for the A, the area of the mirror, in terms of the variables r and y shown in the diagram below. (b) Write an equation for the constraint (s) in this problem. (c) Write A as a function of only the variable r. You can use your equality constraint from part (b) to substitute for y in your equation for A. (You do not need to simplify your answer.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. On our optimization handout, we listed steps in solving optimization problems. Step
1 is to draw a picture, which is done for you. Complete STEPS 2, 3, and 4 (in parts
(a), (b), (c) below) for this optimization problem.
A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100
inches. Choose the radius of the semicircular part so that the mirror has maximum
area. [Note: The perimeter consists of three sides of the rectangle and the semicircle.]
21
(a) Find an equation for the A, the area of the mirror, in terms of the variables r and
y shown in the diagram below.
(b) Write an equation for the constraint (s) in this problem.
(c) Write A as a function of only the variable r. You can use your equality constraint
from part (b) to substitute for y in your equation for A. (You do not need to
simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c8b7ba2-2f5c-4af4-9d55-526a1df4f821%2Fb82be279-4c11-4cd3-99ea-1d68a7aa64a5%2Fuvmxddm_processed.png&w=3840&q=75)
Transcribed Image Text:1. On our optimization handout, we listed steps in solving optimization problems. Step
1 is to draw a picture, which is done for you. Complete STEPS 2, 3, and 4 (in parts
(a), (b), (c) below) for this optimization problem.
A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100
inches. Choose the radius of the semicircular part so that the mirror has maximum
area. [Note: The perimeter consists of three sides of the rectangle and the semicircle.]
21
(a) Find an equation for the A, the area of the mirror, in terms of the variables r and
y shown in the diagram below.
(b) Write an equation for the constraint (s) in this problem.
(c) Write A as a function of only the variable r. You can use your equality constraint
from part (b) to substitute for y in your equation for A. (You do not need to
simplify your answer.)
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