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3. Refer to the graph as shown in Figure A3. (a) Determine the first moment of...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y +...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of...
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (1x); (4 marks) (b) the second moment of area about y axis (19); (4 marks) (c) the second moment of area of about z (I.), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x Figure A4
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of...
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (Ix): (4 marks) (b) the second moment of area about y axis (Iy); (4 marks) c) the second moment of area of about z (Iz), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x X 4 Figure A4 5. 1 Given the differential equation: dy +-y 3x2 dx х Find (a) the general...
Problem 3. (25 points total) Determine (a) The area A of the shaded region. (b) The...
Problem 3. (25 points total) Determine (a) The area A of the shaded region. (b) The x location of the centroid of the shaded area, which is called x. (Use an integral to confirm the value found by inspection from symmetry.) (C) The y location of the centroid of the shaded area, which is called y. (d) The moment of inertia, Ix, of the shaded area about the x axis. (e) The moment of inertia, ly, of the shaded area...
Consider the area shown in Figure 4. Determine; a) The 2nd Moment of Area (Ix and...
Consider the area shown in Figure 4. Determine; a) The 2nd Moment of Area (Ix and ly) about the axis system shown. b) The Polar Moment of Inertia (Jo) about point O. c) The 2nd Moment of Area (lx and ly) about an axis system that runs through the centroid of the area and the Polar Moment of Inertia (Jo) about the centroid of the area. [5+3+5 = 13 marks] 100 mm-100 mm 150 mm 150 mm 150 mm 75...
The next two problems refer to the figure 1 below. у 3 in.3 in.-- 6 in....
The next two problems refer to the figure 1 below. у 3 in.3 in.-- 6 in. 2 in. 4 in. х 1. Calculate the centroid of the shaded area from figure 1. 2. Determine the moment of inertia of the shaded area from figure 1 about the X axis.
In the figure shown, y' Determine by direct Vklx)1/2 integration the moment of inertia and the...
In the figure shown, y' Determine by direct Vklx)1/2 integration the moment of inertia and the radius of gyration of the shaded area (a) with respect to the x-axis, and (b) with respect to the y-axis. lo i k(x) ,LI
Q2 Figure Q2 illustrates a graph that contains two parallel straight lines, with a shaded region...
Q2 Figure Q2 illustrates a graph that contains two parallel straight lines, with a shaded region bounded by both lines and both axes. y Line A Line B Figure Q2 (a) Find the equation of Line A and Line B respectively. (2 marks) (b) (c) Compute the area of the shaded region. (3 marks) The shaded region is revolved around y - axis. (i) Compute the volume of solid generated by revolving the bounded region between Line A and both...
Determine the moment of inertia with respect to the x axis for the shaded area shown (Figure 2)...
Determine the moment of inertia with respect to the x axis for the shaded area shown (Figure 2) . The dimension is a = 2.00m .
Given: The shaded area as shown in the figure. Find: The moment of inertia for the...
Given: The shaded area as shown in the figure. Find: The moment of inertia for the area about the x-axis and radius of gyration, rx Plan: 100mm十100 mm -150mm the 150 mm 150 mm
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (1x); (4 marks) (b) the second moment of area about y axis (19); (4 marks) (c) the second moment of area of about z (I.), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x Figure A4
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (Ix): (4 marks) (b) the second moment of area about y axis (Iy); (4 marks) c) the second moment of area of about z (Iz), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x X 4 Figure A4 5. 1 Given the differential equation: dy +-y 3x2 dx х Find (a) the general...
Problem 3. (25 points total) Determine (a) The area A of the shaded region. (b) The x location of the centroid of the shaded area, which is called x. (Use an integral to confirm the value found by inspection from symmetry.) (C) The y location of the centroid of the shaded area, which is called y. (d) The moment of inertia, Ix, of the shaded area about the x axis. (e) The moment of inertia, ly, of the shaded area...
Consider the area shown in Figure 4. Determine; a) The 2nd Moment of Area (Ix and ly) about the axis system shown. b) The Polar Moment of Inertia (Jo) about point O. c) The 2nd Moment of Area (lx and ly) about an axis system that runs through the centroid of the area and the Polar Moment of Inertia (Jo) about the centroid of the area. [5+3+5 = 13 marks] 100 mm-100 mm 150 mm 150 mm 150 mm 75...
The next two problems refer to the figure 1 below. у 3 in.3 in.-- 6 in. 2 in. 4 in. х 1. Calculate the centroid of the shaded area from figure 1. 2. Determine the moment of inertia of the shaded area from figure 1 about the X axis.
In the figure shown, y' Determine by direct Vklx)1/2 integration the moment of inertia and the radius of gyration of the shaded area (a) with respect to the x-axis, and (b) with respect to the y-axis. lo i k(x) ,LI
Q2 Figure Q2 illustrates a graph that contains two parallel straight lines, with a shaded region bounded by both lines and both axes. y Line A Line B Figure Q2 (a) Find the equation of Line A and Line B respectively. (2 marks) (b) (c) Compute the area of the shaded region. (3 marks) The shaded region is revolved around y - axis. (i) Compute the volume of solid generated by revolving the bounded region between Line A and both...
Given: The shaded area as shown in the figure. Find: The moment of inertia for the area about the x-axis and radius of gyration, rx Plan: 100mm十100 mm -150mm the 150 mm 150 mm
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