P3=(X,y) P1 Area=8.1 P4=(r,0) -4 -3 -2 -1 3 -1 -O Tt (a) The area of trapezoid is the height times the average of the two bases with this parameterization: Tt 2r + 2x • y. What equation describes the constraint between x and y? 2² +y? =r 2²+y? = r2 2²+y? = r/2 Oy? – x2 = r2 %3D 2. 2.
P3=(X,y) P1 Area=8.1 P4=(r,0) -4 -3 -2 -1 3 -1 -O Tt (a) The area of trapezoid is the height times the average of the two bases with this parameterization: Tt 2r + 2x • y. What equation describes the constraint between x and y? 2² +y? =r 2²+y? = r2 2²+y? = r/2 Oy? – x2 = r2 %3D 2. 2.
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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Question
![P3=(x,y)
Area=8.1
P1
P4-(r,0)
-4
-1
O TE
(a) The area of trapezoid is the height times the average of the two bases
with this parameterization:
Tt
2r + 2x
y.
What equation describes the constraint between x and y?
2² +y? = r
+ y? = r2
2+y? = r/2
Oy? – a2 = r2
(b) If area is expressed as a function of x, what is the range of possible
values for x, assuming x 0?
[0, 00)
[0, r/2]
00, r]
(0, 72)
(c) What is the maximum area of an inscribed trapezoid when r = 5, as
described above?
8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccf3d201-cfb7-4547-b61b-2795570fad1a%2F9514611d-5652-43f5-9a1d-a9f0ae15ecbf%2Frfcqpgp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:P3=(x,y)
Area=8.1
P1
P4-(r,0)
-4
-1
O TE
(a) The area of trapezoid is the height times the average of the two bases
with this parameterization:
Tt
2r + 2x
y.
What equation describes the constraint between x and y?
2² +y? = r
+ y? = r2
2+y? = r/2
Oy? – a2 = r2
(b) If area is expressed as a function of x, what is the range of possible
values for x, assuming x 0?
[0, 00)
[0, r/2]
00, r]
(0, 72)
(c) What is the maximum area of an inscribed trapezoid when r = 5, as
described above?
8.
Transcribed Image Text:A trapezoid is inscribed in a semicircle of radius r so that one side is along
the diameter (the x-axis in the figure).
We will find the maximum possible area for the trapezoid.
In the figure, the value of r can be adjusted by moving point P4. The point
P3 can be moved along the semicirce of radius r to change the inscribed
trapezoid. When adjusted the inscribed area changes. This area can be
used to roughly identify the values for a and y that maximize the area for a
given r, but in the problem you will identify this value exactly.
JSXGraph v1.2.2 Copyright (C) see https:sxgraph.org
P3=(x,y)
1
Area=8.1
P4-(r,0)
-4
-3
2
3
4
- O + +
(a) The area of trapezoid is the height times the average of the two bases or
with this parameterization:
2r +2x
y.
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