Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Expert Solution & Answer
Chapter 8.4, Problem 1P
Solution
To calculate : The estimated area of the given ellipse by using the rectangles of width 20 and explain that the estimate is better or worse than the given estimate.
The area of the ellipse using the rectangles of width 20 is 58,088 square meters and it is better than the estimated area of the elliptical region by using the rectangles of width 40 .
Given information :
The equation of the ellipse is x22002+y21002=1 and the estimated area of the elliptical region by using the rectangles of width 40 is 68800 square meters.
Formula used:
Area (A) of an ellipse is given by,
A=πab
Calculation :
If the width of the rectangles is 20 , then the number of rectangles will be,
=20020=10
The height of the first rectangle will be,
y1=100 .
Calculate the height of other nine rectangles using the formula y=√1002−x24 .
y2=√1002−2024=99.5y3=√1002−4024=98y4=√1002−6024=95.4y5=√1002−8024=91.6y6=√1002−10024=86.6y7=√1002−12024=80y8=√1002−14024=71.4y9=√1002−16024=60y10=√1002−18024=43.6
Calculate the total area (A) of the rectangles.
A=20(99.5+98+95.4+91.6+86.6+80+71.4+60+43.6)=14,522
So, the area of the portion of ellipse in first quadrant is 14,522 square meters.
The total area of the ellipse will be,
=4×14,522=58,088 square meters.
The area of the ellipse using formula is,
=3.14×200×100=62800 square meters
Therefore, the area of the ellipse using the rectangles of width 20 is 58,088 square meters and it is better than the estimated area of the elliptical region by using the rectangles of width 40 .
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
Ch. 8.1 - Prob. 1GPCh. 8.1 - Prob. 2GPCh. 8.1 - Prob. 3GPCh. 8.1 - Prob. 4GPCh. 8.1 - Prob. 5GPCh. 8.1 - Prob. 6GPCh. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4E
Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47PSCh. 8.1 - Prob. 48PSCh. 8.1 - Prob. 49PSCh. 8.1 - Prob. 50PSCh. 8.1 - Prob. 51PSCh. 8.1 - Prob. 52PSCh. 8.1 - Prob. 53PSCh. 8.1 - Prob. 54PSCh. 8.1 - Prob. 55PSCh. 8.1 - Prob. 56PSCh. 8.1 - Prob. 57PSCh. 8.2 - Prob. 1GPCh. 8.2 - Prob. 2GPCh. 8.2 - Prob. 3GPCh. 8.2 - Prob. 4GPCh. 8.2 - Prob. 5GPCh. 8.2 - Prob. 6GPCh. 8.2 - Prob. 7GPCh. 8.2 - Prob. 8GPCh. 8.2 - Prob. 9GPCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55PSCh. 8.2 - Prob. 56PSCh. 8.2 - Prob. 57PSCh. 8.2 - Prob. 58PSCh. 8.2 - Prob. 59PSCh. 8.2 - Prob. 60PSCh. 8.3 - Prob. 1GPCh. 8.3 - Prob. 2GPCh. 8.3 - Prob. 3GPCh. 8.3 - Prob. 4GPCh. 8.3 - Prob. 5GPCh. 8.3 - Prob. 6GPCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62PSCh. 8.3 - Prob. 63PSCh. 8.3 - Prob. 64PSCh. 8.3 - Prob. 65PSCh. 8.3 - Prob. 66PSCh. 8.3 - Prob. 67PSCh. 8.3 - Prob. 68PSCh. 8.3 - Prob. 69PSCh. 8.3 - Prob. 1QCh. 8.3 - Prob. 2QCh. 8.3 - Prob. 3QCh. 8.3 - Prob. 4QCh. 8.3 - Prob. 5QCh. 8.3 - Prob. 6QCh. 8.3 - Prob. 7QCh. 8.3 - Prob. 8QCh. 8.3 - Prob. 9QCh. 8.3 - Prob. 10QCh. 8.3 - Prob. 11QCh. 8.3 - Prob. 12QCh. 8.3 - Prob. 13QCh. 8.3 - Prob. 14QCh. 8.3 - Prob. 15QCh. 8.3 - Prob. 16QCh. 8.3 - Prob. 17QCh. 8.3 - Prob. 18QCh. 8.3 - Prob. 19QCh. 8.3 - Prob. 1PCh. 8.3 - Prob. 2PCh. 8.3 - Prob. 3PCh. 8.3 - Prob. 4PCh. 8.3 - Prob. 5PCh. 8.3 - Prob. 6PCh. 8.4 - Prob. 1GPCh. 8.4 - Prob. 2GPCh. 8.4 - Prob. 3GPCh. 8.4 - Prob. 4GPCh. 8.4 - Prob. 5GPCh. 8.4 - Prob. 6GPCh. 8.4 - Prob. 7GPCh. 8.4 - Prob. 8GPCh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48PSCh. 8.4 - Prob. 49PSCh. 8.4 - Prob. 50PSCh. 8.4 - Prob. 51PSCh. 8.4 - Prob. 52PSCh. 8.4 - Prob. 53PSCh. 8.4 - Prob. 1PCh. 8.4 - Prob. 2PCh. 8.4 - Prob. 3PCh. 8.4 - Prob. 1MRPSCh. 8.4 - Prob. 2MRPSCh. 8.4 - Prob. 3MRPSCh. 8.4 - Prob. 4MRPSCh. 8.4 - Prob. 5MRPSCh. 8.4 - Prob. 6MRPSCh. 8.4 - Prob. 7MRPSCh. 8.4 - Prob. 8MRPSCh. 8.4 - Prob. 9MRPSCh. 8.5 - Prob. 1GPCh. 8.5 - Prob. 2GPCh. 8.5 - Prob. 3GPCh. 8.5 - Prob. 4GPCh. 8.5 - Prob. 5GPCh. 8.5 - Prob. 6GPCh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Prob. 21ECh. 8.5 - Prob. 22ECh. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - Prob. 25ECh. 8.5 - Prob. 26ECh. 8.5 - Prob. 27ECh. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - Prob. 35ECh. 8.5 - Prob. 36ECh. 8.5 - Prob. 37ECh. 8.5 - Prob. 38PSCh. 8.5 - Prob. 39PSCh. 8.5 - Prob. 40PSCh. 8.5 - Prob. 41PSCh. 8.5 - Prob. 42PSCh. 8.5 - Prob. 43PSCh. 8.5 - Prob. 44PSCh. 8.5 - Prob. 1QCh. 8.5 - Prob. 2QCh. 8.5 - Prob. 3QCh. 8.5 - Prob. 4QCh. 8.5 - Prob. 5QCh. 8.5 - Prob. 6QCh. 8.5 - Prob. 7QCh. 8.5 - Prob. 8QCh. 8.5 - Prob. 9QCh. 8.5 - Prob. 10QCh. 8.5 - Prob. 11QCh. 8.5 - Prob. 12QCh. 8.5 - Prob. 13QCh. 8.6 - Prob. 1GPCh. 8.6 - Prob. 2GPCh. 8.6 - Prob. 3GPCh. 8.6 - Prob. 4GPCh. 8.6 - Prob. 5GPCh. 8.6 - Prob. 6GPCh. 8.6 - Prob. 7GPCh. 8.6 - Prob. 8GPCh. 8.6 - Prob. 9GPCh. 8.6 - Prob. 10GPCh. 8.6 - Prob. 11GPCh. 8.6 - Prob. 12GPCh. 8.6 - Prob. 13GPCh. 8.6 - Prob. 14GPCh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - Prob. 12ECh. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - Prob. 16ECh. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Prob. 39ECh. 8.6 - Prob. 40ECh. 8.6 - Prob. 41ECh. 8.6 - Prob. 42ECh. 8.6 - Prob. 43ECh. 8.6 - Prob. 44ECh. 8.6 - Prob. 45ECh. 8.6 - Prob. 46ECh. 8.6 - Prob. 47ECh. 8.6 - Prob. 48PSCh. 8.6 - Prob. 49PSCh. 8.6 - Prob. 50PSCh. 8.6 - Prob. 51PSCh. 8.6 - Prob. 52PSCh. 8.6 - Prob. 53PSCh. 8.7 - Prob. 1GPCh. 8.7 - Prob. 2GPCh. 8.7 - Prob. 3GPCh. 8.7 - Prob. 4GPCh. 8.7 - Prob. 5GPCh. 8.7 - Prob. 6GPCh. 8.7 - Prob. 7GPCh. 8.7 - Prob. 8GPCh. 8.7 - Prob. 9GPCh. 8.7 - Prob. 10GPCh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - Prob. 30ECh. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - Prob. 35ECh. 8.7 - Prob. 36ECh. 8.7 - Prob. 37ECh. 8.7 - Prob. 38ECh. 8.7 - Prob. 39PSCh. 8.7 - Prob. 40PSCh. 8.7 - Prob. 41PSCh. 8.7 - Prob. 42PSCh. 8.7 - Prob. 43PSCh. 8.7 - Prob. 44PSCh. 8.7 - Prob. 45PSCh. 8.7 - Prob. 1QCh. 8.7 - Prob. 2QCh. 8.7 - Prob. 3QCh. 8.7 - Prob. 4QCh. 8.7 - Prob. 5QCh. 8.7 - Prob. 6QCh. 8.7 - Prob. 7QCh. 8.7 - Prob. 8QCh. 8.7 - Prob. 9QCh. 8.7 - Prob. 10QCh. 8.7 - Prob. 11QCh. 8.7 - Prob. 12QCh. 8.7 - Prob. 13QCh. 8.7 - Prob. 14QCh. 8.7 - Prob. 1PCh. 8.7 - Prob. 2PCh. 8.7 - Prob. 3PCh. 8.7 - Prob. 4PCh. 8.7 - Prob. 5PCh. 8.7 - Prob. 6PCh. 8.7 - Prob. 7PCh. 8.7 - Prob. 8PCh. 8.7 - Prob. 9PCh. 8.7 - Prob. 10PCh. 8.7 - Prob. 11PCh. 8.7 - Prob. 12PCh. 8.7 - Prob. 13PCh. 8.7 - Prob. 14PCh. 8.7 - Prob. 15PCh. 8.7 - Prob. 1MRPSCh. 8.7 - Prob. 2MRPSCh. 8.7 - Prob. 3MRPSCh. 8.7 - Prob. 4MRPSCh. 8.7 - Prob. 5MRPSCh. 8.7 - Prob. 6MRPSCh. 8 - Prob. 1VECh. 8 - Prob. 2VECh. 8 - Prob. 3VECh. 8 - Prob. 4VECh. 8 - Prob. 5REAECh. 8 - Prob. 6REAECh. 8 - Prob. 7REAECh. 8 - Prob. 8REAECh. 8 - Prob. 9REAECh. 8 - Prob. 10REAECh. 8 - Prob. 11REAECh. 8 - Prob. 12REAECh. 8 - Prob. 13REAECh. 8 - Prob. 14REAECh. 8 - Prob. 15REAECh. 8 - 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