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mw 6 [Maximum A semicircle has diameter AB with length 2. The centre of AB is labelled O. The point P is on the curved edge of the semicircle and POA is the acute angle 0. A rectangle is drawn with one edge on part of the line segment AB, one corner at P and another corner also on the curved part of the semicircle. a Prove that the area of the rectangle is given by k sin 20 where k is a constant to be determined. b Hence find the largest area of such a rectangle.

mw 6 [Maximum A semicircle has diameter AB with length 2. The centre of AB is labelled O. The point P is on the curved edge of the semicircle and POA is the acute angle 0. A rectangle is drawn with one edge on part of the line segment AB, one corner at P and another corner also on the curved part of the semicircle. a Prove that the area of the rectangle is given by k sin 20 where k is a constant to be determined. b Hence find the largest area of such a rectangle.

Advanced Engineering Mathematics
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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mw 6 [Maximum A semicircle has diameter AB with length 2. The centre of AB is labelled O. The point P is on the curved edge of the semicircle and POA is the acute angle 8. A rectangle is drawn with one edge on part of the line segment AB, one corner at P and another corner also on the curved part of the semicircle. a Prove that the area of the rectangle is given by k sin 20 where k is a constant to be determined. b Hence find the largest area of such a rectangle.
Transcribed Image Text:mw 6 [Maximum A semicircle has diameter AB with length 2. The centre of AB is labelled O. The point P is on the curved edge of the semicircle and POA is the acute angle 8. A rectangle is drawn with one edge on part of the line segment AB, one corner at P and another corner also on the curved part of the semicircle. a Prove that the area of the rectangle is given by k sin 20 where k is a constant to be determined. b Hence find the largest area of such a rectangle.
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