Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.6, Problem 7PS
To determine
To find: the centroid for the regions
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Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
Ch. 12.1 - Prob. 11PSCh. 12.1 - Prob. 12PSCh. 12.1 - Prob. 13PSCh. 12.1 - Prob. 14PSCh. 12.1 - Prob. 15PSCh. 12.1 - Prob. 16PSCh. 12.1 - Prob. 17PSCh. 12.1 - Prob. 18PSCh. 12.1 - Prob. 19PSCh. 12.1 - Prob. 20PSCh. 12.1 - Prob. 21PSCh. 12.1 - Prob. 22PSCh. 12.1 - Prob. 23PSCh. 12.1 - Prob. 24PSCh. 12.1 - Prob. 25PSCh. 12.1 - Prob. 26PSCh. 12.1 - Prob. 27PSCh. 12.1 - Prob. 28PSCh. 12.1 - Prob. 29PSCh. 12.1 - Prob. 30PSCh. 12.1 - Prob. 31PSCh. 12.1 - Prob. 32PSCh. 12.1 - Prob. 33PSCh. 12.1 - Prob. 34PSCh. 12.1 - Prob. 35PSCh. 12.1 - Prob. 36PSCh. 12.1 - Prob. 37PSCh. 12.1 - Prob. 38PSCh. 12.1 - Prob. 39PSCh. 12.1 - Prob. 40PSCh. 12.1 - Prob. 41PSCh. 12.1 - Prob. 42PSCh. 12.1 - Prob. 43PSCh. 12.1 - Prob. 44PSCh. 12.1 - Prob. 45PSCh. 12.1 - Prob. 46PSCh. 12.1 - Prob. 47PSCh. 12.1 - Prob. 48PSCh. 12.1 - Prob. 49PSCh. 12.1 - Prob. 50PSCh. 12.1 - Prob. 51PSCh. 12.1 - Prob. 52PSCh. 12.1 - Prob. 53PSCh. 12.1 - Prob. 54PSCh. 12.1 - Prob. 55PSCh. 12.1 - Prob. 56PSCh. 12.1 - Prob. 57PSCh. 12.1 - Prob. 58PSCh. 12.1 - Prob. 59PSCh. 12.1 - Prob. 60PSCh. 12.2 - Prob. 1PSCh. 12.2 - Prob. 2PSCh. 12.2 - Prob. 3PSCh. 12.2 - Prob. 4PSCh. 12.2 - Prob. 5PSCh. 12.2 - Prob. 6PSCh. 12.2 - Prob. 7PSCh. 12.2 - Prob. 8PSCh. 12.2 - Prob. 9PSCh. 12.2 - Prob. 10PSCh. 12.2 - Prob. 11PSCh. 12.2 - Prob. 12PSCh. 12.2 - Prob. 13PSCh. 12.2 - Prob. 14PSCh. 12.2 - Prob. 15PSCh. 12.2 - Prob. 16PSCh. 12.2 - Prob. 17PSCh. 12.2 - Prob. 18PSCh. 12.2 - Prob. 19PSCh. 12.2 - Prob. 20PSCh. 12.2 - Prob. 21PSCh. 12.2 - Prob. 22PSCh. 12.2 - Prob. 23PSCh. 12.2 - Prob. 24PSCh. 12.2 - Prob. 25PSCh. 12.2 - Prob. 26PSCh. 12.2 - Prob. 27PSCh. 12.2 - Prob. 28PSCh. 12.2 - Prob. 29PSCh. 12.2 - Prob. 30PSCh. 12.2 - Prob. 31PSCh. 12.2 - Prob. 32PSCh. 12.2 - Prob. 33PSCh. 12.2 - Prob. 34PSCh. 12.2 - Prob. 35PSCh. 12.2 - Prob. 36PSCh. 12.2 - Prob. 37PSCh. 12.2 - Prob. 38PSCh. 12.2 - Prob. 39PSCh. 12.2 - Prob. 40PSCh. 12.2 - Prob. 41PSCh. 12.2 - Prob. 42PSCh. 12.2 - Prob. 43PSCh. 12.2 - Prob. 44PSCh. 12.2 - Prob. 45PSCh. 12.2 - Prob. 46PSCh. 12.2 - Prob. 47PSCh. 12.2 - Prob. 48PSCh. 12.2 - Prob. 49PSCh. 12.2 - Prob. 50PSCh. 12.2 - Prob. 51PSCh. 12.2 - Prob. 52PSCh. 12.2 - Prob. 53PSCh. 12.2 - Prob. 54PSCh. 12.2 - Prob. 55PSCh. 12.2 - Prob. 56PSCh. 12.2 - Prob. 57PSCh. 12.2 - Prob. 58PSCh. 12.2 - Prob. 59PSCh. 12.2 - Prob. 60PSCh. 12.3 - Prob. 1PSCh. 12.3 - Prob. 2PSCh. 12.3 - Prob. 3PSCh. 12.3 - Prob. 4PSCh. 12.3 - Prob. 5PSCh. 12.3 - Prob. 6PSCh. 12.3 - Prob. 7PSCh. 12.3 - Prob. 8PSCh. 12.3 - Prob. 9PSCh. 12.3 - Prob. 10PSCh. 12.3 - Prob. 11PSCh. 12.3 - Prob. 12PSCh. 12.3 - Prob. 13PSCh. 12.3 - Prob. 14PSCh. 12.3 - Prob. 15PSCh. 12.3 - Prob. 16PSCh. 12.3 - Prob. 17PSCh. 12.3 - Prob. 18PSCh. 12.3 - Prob. 19PSCh. 12.3 - Prob. 20PSCh. 12.3 - Prob. 21PSCh. 12.3 - Prob. 22PSCh. 12.3 - Prob. 23PSCh. 12.3 - Prob. 24PSCh. 12.3 - Prob. 25PSCh. 12.3 - Prob. 26PSCh. 12.3 - Prob. 27PSCh. 12.3 - Prob. 28PSCh. 12.3 - Prob. 29PSCh. 12.3 - Prob. 30PSCh. 12.3 - Prob. 31PSCh. 12.3 - Prob. 32PSCh. 12.3 - Prob. 33PSCh. 12.3 - Prob. 34PSCh. 12.3 - Prob. 35PSCh. 12.3 - Prob. 36PSCh. 12.3 - 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Prob. 15PSCh. 12.5 - Prob. 16PSCh. 12.5 - Prob. 17PSCh. 12.5 - Prob. 18PSCh. 12.5 - Prob. 19PSCh. 12.5 - Prob. 20PSCh. 12.5 - Prob. 21PSCh. 12.5 - Prob. 22PSCh. 12.5 - Prob. 23PSCh. 12.5 - Prob. 24PSCh. 12.5 - Prob. 25PSCh. 12.5 - Prob. 26PSCh. 12.5 - Prob. 27PSCh. 12.5 - Prob. 28PSCh. 12.5 - Prob. 29PSCh. 12.5 - Prob. 30PSCh. 12.5 - Prob. 31PSCh. 12.5 - Prob. 32PSCh. 12.5 - Prob. 33PSCh. 12.5 - Prob. 34PSCh. 12.5 - Prob. 35PSCh. 12.5 - Prob. 36PSCh. 12.5 - Prob. 37PSCh. 12.5 - Prob. 38PSCh. 12.5 - Prob. 39PSCh. 12.5 - Prob. 40PSCh. 12.5 - Prob. 41PSCh. 12.5 - Prob. 42PSCh. 12.5 - Prob. 43PSCh. 12.5 - Prob. 44PSCh. 12.5 - Prob. 45PSCh. 12.5 - Prob. 46PSCh. 12.5 - Prob. 47PSCh. 12.5 - Prob. 48PSCh. 12.5 - Prob. 49PSCh. 12.5 - Prob. 50PSCh. 12.5 - Prob. 51PSCh. 12.5 - Prob. 52PSCh. 12.5 - Prob. 53PSCh. 12.5 - Prob. 54PSCh. 12.5 - Prob. 55PSCh. 12.5 - Prob. 56PSCh. 12.5 - Prob. 57PSCh. 12.5 - Prob. 58PSCh. 12.5 - Prob. 59PSCh. 12.5 - Prob. 60PSCh. 12.6 - Prob. 1PSCh. 12.6 - Prob. 2PSCh. 12.6 - Prob. 3PSCh. 12.6 - Prob. 4PSCh. 12.6 - Prob. 5PSCh. 12.6 - Prob. 6PSCh. 12.6 - Prob. 7PSCh. 12.6 - Prob. 8PSCh. 12.6 - Prob. 9PSCh. 12.6 - Prob. 10PSCh. 12.6 - Prob. 11PSCh. 12.6 - Prob. 12PSCh. 12.6 - Prob. 13PSCh. 12.6 - Prob. 14PSCh. 12.6 - Prob. 15PSCh. 12.6 - Prob. 16PSCh. 12.6 - Prob. 17PSCh. 12.6 - Prob. 18PSCh. 12.6 - Prob. 19PSCh. 12.6 - Prob. 20PSCh. 12.6 - Prob. 21PSCh. 12.6 - Prob. 22PSCh. 12.6 - Prob. 23PSCh. 12.6 - Prob. 24PSCh. 12.6 - Prob. 25PSCh. 12.6 - Prob. 26PSCh. 12.6 - Prob. 27PSCh. 12.6 - Prob. 28PSCh. 12.6 - Prob. 29PSCh. 12.6 - Prob. 30PSCh. 12.6 - Prob. 31PSCh. 12.6 - Prob. 32PSCh. 12.6 - Prob. 33PSCh. 12.6 - Prob. 34PSCh. 12.6 - Prob. 35PSCh. 12.6 - Prob. 36PSCh. 12.6 - Prob. 37PSCh. 12.6 - Prob. 38PSCh. 12.6 - Prob. 39PSCh. 12.6 - Prob. 40PSCh. 12.6 - Prob. 41PSCh. 12.6 - Prob. 42PSCh. 12.6 - Prob. 43PSCh. 12.6 - Prob. 44PSCh. 12.6 - Prob. 45PSCh. 12.6 - Prob. 46PSCh. 12.6 - Prob. 47PSCh. 12.6 - Prob. 48PSCh. 12.6 - Prob. 49PSCh. 12.6 - Prob. 50PSCh. 12.6 - Prob. 51PSCh. 12.6 - Prob. 52PSCh. 12.6 - Prob. 53PSCh. 12.6 - Prob. 54PSCh. 12.6 - Prob. 55PSCh. 12.6 - Prob. 56PSCh. 12.6 - Prob. 57PSCh. 12.6 - Prob. 58PSCh. 12.6 - Prob. 59PSCh. 12.6 - Prob. 60PSCh. 12.7 - Prob. 1PSCh. 12.7 - Prob. 2PSCh. 12.7 - Prob. 3PSCh. 12.7 - Prob. 4PSCh. 12.7 - Prob. 5PSCh. 12.7 - Prob. 6PSCh. 12.7 - Prob. 7PSCh. 12.7 - Prob. 8PSCh. 12.7 - Prob. 9PSCh. 12.7 - Prob. 10PSCh. 12.7 - Prob. 11PSCh. 12.7 - Prob. 12PSCh. 12.7 - Prob. 13PSCh. 12.7 - Prob. 14PSCh. 12.7 - Prob. 15PSCh. 12.7 - Prob. 16PSCh. 12.7 - Prob. 17PSCh. 12.7 - Prob. 18PSCh. 12.7 - Prob. 19PSCh. 12.7 - Prob. 20PSCh. 12.7 - Prob. 21PSCh. 12.7 - Prob. 22PSCh. 12.7 - Prob. 23PSCh. 12.7 - Prob. 24PSCh. 12.7 - Prob. 25PSCh. 12.7 - Prob. 26PSCh. 12.7 - Prob. 27PSCh. 12.7 - Prob. 28PSCh. 12.7 - Prob. 29PSCh. 12.7 - Prob. 30PSCh. 12.7 - Prob. 31PSCh. 12.7 - Prob. 32PSCh. 12.7 - Prob. 33PSCh. 12.7 - Prob. 34PSCh. 12.7 - Prob. 35PSCh. 12.7 - Prob. 36PSCh. 12.7 - Prob. 37PSCh. 12.7 - Prob. 38PSCh. 12.7 - Prob. 39PSCh. 12.7 - Prob. 40PSCh. 12.7 - Prob. 41PSCh. 12.7 - Prob. 42PSCh. 12.7 - Prob. 43PSCh. 12.7 - Prob. 44PSCh. 12.7 - Prob. 45PSCh. 12.7 - Prob. 46PSCh. 12.7 - Prob. 47PSCh. 12.7 - Prob. 48PSCh. 12.7 - Prob. 49PSCh. 12.7 - Prob. 50PSCh. 12.7 - Prob. 51PSCh. 12.7 - Prob. 52PSCh. 12.7 - Prob. 53PSCh. 12.7 - Prob. 54PSCh. 12.7 - Prob. 55PSCh. 12.7 - Prob. 56PSCh. 12.7 - Prob. 57PSCh. 12.7 - Prob. 58PSCh. 12.7 - Prob. 59PSCh. 12.7 - Prob. 60PSCh. 12.8 - Prob. 1PSCh. 12.8 - Prob. 2PSCh. 12.8 - Prob. 3PSCh. 12.8 - Prob. 4PSCh. 12.8 - Prob. 5PSCh. 12.8 - Prob. 6PSCh. 12.8 - Prob. 7PSCh. 12.8 - Prob. 8PSCh. 12.8 - Prob. 9PSCh. 12.8 - Prob. 10PSCh. 12.8 - Prob. 11PSCh. 12.8 - Prob. 12PSCh. 12.8 - Prob. 13PSCh. 12.8 - Prob. 14PSCh. 12.8 - Prob. 15PSCh. 12.8 - Prob. 16PSCh. 12.8 - Prob. 17PSCh. 12.8 - Prob. 18PSCh. 12.8 - Prob. 19PSCh. 12.8 - Prob. 20PSCh. 12.8 - Prob. 21PSCh. 12.8 - Prob. 22PSCh. 12.8 - Prob. 23PSCh. 12.8 - Prob. 24PSCh. 12.8 - Prob. 25PSCh. 12.8 - Prob. 26PSCh. 12.8 - Prob. 27PSCh. 12.8 - Prob. 28PSCh. 12.8 - Prob. 29PSCh. 12.8 - Prob. 30PSCh. 12.8 - Prob. 31PSCh. 12.8 - Prob. 32PSCh. 12.8 - Prob. 33PSCh. 12.8 - Prob. 34PSCh. 12.8 - Prob. 35PSCh. 12.8 - Prob. 36PSCh. 12.8 - Prob. 37PSCh. 12.8 - Prob. 38PSCh. 12.8 - Prob. 39PSCh. 12.8 - Prob. 40PSCh. 12.8 - Prob. 41PSCh. 12.8 - Prob. 42PSCh. 12.8 - Prob. 43PSCh. 12.8 - Prob. 44PSCh. 12.8 - Prob. 45PSCh. 12.8 - Prob. 46PSCh. 12.8 - Prob. 47PSCh. 12.8 - Prob. 48PSCh. 12.8 - Prob. 49PSCh. 12.8 - Prob. 50PSCh. 12.8 - Prob. 51PSCh. 12.8 - Prob. 52PSCh. 12.8 - Prob. 53PSCh. 12.8 - Prob. 54PSCh. 12.8 - Prob. 55PSCh. 12.8 - Prob. 56PSCh. 12.8 - Prob. 57PSCh. 12.8 - Prob. 58PSCh. 12.8 - Prob. 59PSCh. 12.8 - Prob. 60PSCh. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Prob. 4PECh. 12 - Prob. 5PECh. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Prob. 8PECh. 12 - Prob. 9PECh. 12 - Prob. 10PECh. 12 - Prob. 11PECh. 12 - Prob. 12PECh. 12 - Prob. 13PECh. 12 - Prob. 14PECh. 12 - Prob. 15PECh. 12 - Prob. 16PECh. 12 - Prob. 17PECh. 12 - Prob. 18PECh. 12 - Prob. 19PECh. 12 - Prob. 20PECh. 12 - Prob. 21PECh. 12 - Prob. 22PECh. 12 - Prob. 23PECh. 12 - Prob. 24PECh. 12 - Prob. 25PECh. 12 - Prob. 26PECh. 12 - Prob. 27PECh. 12 - Prob. 28PECh. 12 - Prob. 29PECh. 12 - Prob. 30PECh. 12 - Prob. 1SPCh. 12 - Prob. 2SPCh. 12 - Prob. 3SPCh. 12 - Prob. 4SPCh. 12 - Prob. 5SPCh. 12 - Prob. 6SPCh. 12 - Prob. 7SPCh. 12 - Prob. 8SPCh. 12 - Prob. 9SPCh. 12 - Prob. 10SPCh. 12 - Prob. 11SPCh. 12 - Prob. 12SPCh. 12 - Prob. 13SPCh. 12 - Prob. 14SPCh. 12 - Prob. 15SPCh. 12 - Prob. 16SPCh. 12 - Prob. 17SPCh. 12 - Prob. 18SPCh. 12 - Prob. 19SPCh. 12 - Prob. 20SPCh. 12 - Prob. 21SPCh. 12 - Prob. 22SPCh. 12 - Prob. 23SPCh. 12 - Prob. 24SPCh. 12 - Prob. 25SPCh. 12 - Prob. 26SPCh. 12 - Prob. 27SPCh. 12 - Prob. 28SPCh. 12 - Prob. 29SPCh. 12 - Prob. 30SPCh. 12 - Prob. 31SPCh. 12 - Prob. 32SPCh. 12 - Prob. 33SPCh. 12 - Prob. 34SPCh. 12 - Prob. 35SPCh. 12 - Prob. 36SPCh. 12 - Prob. 37SPCh. 12 - Prob. 38SPCh. 12 - Prob. 39SPCh. 12 - Prob. 40SPCh. 12 - Prob. 41SPCh. 12 - Prob. 42SPCh. 12 - 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Prob. 97SPCh. 12 - Prob. 98SPCh. 12 - Prob. 99SP
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- 3. Show that S, has the presentation (x, ylx* = y2 = (xy) 1). %3D %3D %3Darrow_forward30. Evaluate (3x+ 4y) dx + (2x – 3y) dy where 'C' is the circle x +y = 4. [A %3D Carrow_forward11. Let E be the region between the ellipses 9x² +4y² = 1 and 9x² +4y² 16 and to the right of the Y-axis. Find the average X-coordinate and the average Y-coordinate of a point in this region.arrow_forward
- 21. Let D denote the region between the parabola y = 8 - x² and the line y = x + 2. Compute ff 2x + y dA.arrow_forward4. Consider a square service region of unit area in which travel is right angle and directions of travel are parallel to the sides of the square. Let (X, Y₁) be the location of a mobile unit and (X₂, Y₂) the location of a demand for service. The travel distance is D =Dx + Dy where Dx = |X₁ - X₂ and Dy = |Y₁ — Y2\. Assume that the two locations are independent and uniformly distributed over the square. a. Show that the joint pdf for Dx and Dy is (4(1-x)(1-y), fpx.D¸y (x, y) = {4(1 – b. Define Ryx = D/Dr. Show that the pdf of Ryx is 2 3 fryx (r) = . 2 3r² 1 r, 3 1 3r3' 0, 0≤x≤ 1,0 ≤ y ≤ 1 otherwise 0 ≤r≤1 1 ≤r <∞0arrow_forwardPlease explain clearly.arrow_forward
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- 6 In Fig.11.23, the curve (y - 1)² = x + 4 meets the y-axis at A and B. (a) Find the coordinates of A and B and (b) calculate the areas of (i) the shaded region P, (ii) the shaded region Q. Fig.11.23 A 0 (y-1)=x+4arrow_forward1. 2(2ay+ 4y – 3)dx + (x +2)²dy = 0 -arrow_forwardFind the centroid of the region above the curve (shaded in green) in Figure 4. This region is ranges in x from 0 to 600, in y from 0 to 430, and above y = kx0.7. 500 y y =kx 0.7 430 (600, 430) 400 Find centroid 300 of this region 200 100 0. 500 600 700 300 400 100 200 Figure 4: Find the centroid of the green shaded region for Problem 2arrow_forward
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