Sketch the solid in the first octant bounded by: z= 6 - 3x and y=x, and...
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 25 − x2 and the plane y = 2.
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 - x2 and the plane y = 4.
Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 16 ? x2 and the plane y = 2.
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
1. Consider the solid in the first octant bounded by the coordinate planes, the plane x= 2,and the surface z= 9-y^2. The density is(x,y,z) = (x+ 1)(y+ 1)(z+ 1). Calculate the x,y, and z coordinates of the center of mass. Express your answer in decimal form. 2. Find Iz for the hollow cylinder (oriented along the z-axis) with inner radius R and thickness t. The base is the xy-plane, the height is h, and the density is(x,yz,) =kz^2.
of vector fields Determine the volume of the solid in the first octant bounded sbove by the p Sketch the graph. Hint: label the x-axis, y-axis and z-axis interceps Determine the limits of integration for the integral over the solid S given by the figure. You do not to solve the integral. 9. of vector fields Determine the volume of the solid in the first octant bounded sbove by the p Sketch the graph. Hint: label the x-axis, y-axis and...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x= a) and the curve (z=1-y). Find the volume of the solid by using : #-Double integration technique (Use order dy dx) a=51 b-Triple integration technique (Use order dz dy dx) ..
oi o 2. Find the area of the part of the paraboloidty that is cut off by the plane -4 3. Find volume of the solid in the first octant bounded by y 2r and the plane r-4 3. Find volume of the solid in the first octant bounded by y= 2x, and 4. Find the volume of the solid bounded above by the spherex2+y+ 4. Find the volume of the solid bounded above by the sphere+y?+ 2 9, below...
Find the volume of the solid in the first octant that is enclosed by the graphs z=1-y2 , x+y=1 and x+y=3. Sketch. -> USING Z-SIMPLE <- *** NOT using x-simple. ***
2x2, Problem #2: Find the mass of the solid bounded by the the graphs of y = y = 4, z = 0, and z = 5, in the first octant, if the density at a point P is equal to 8 times the distance to the yz-plane. Problem #2: Enter your answer symbolically, as in these examples