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Use double integrals to calculate the volume of the tetrahedron bounded by the coordinate planes (x= 0, y = 0, z = 0) and the plane 7x + 5y +z-35 0. Find the double integral needed to determine the volume of the region. Set up the inner integral with respect to y, and the outer integral with respect to x. Use double integrals to calculate the volume of the tetrahedron bounded by the coordinate planes (x= 0, y = 0,...
10. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y = 0, and 2 = 0. Express the following integral as an iterated double integral. Do not evaluate. SIS 6.ry dy
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the region R (label lines, intercepts, axes and shade region) (b) SET UP the integral over this region (c) Assuming f(x.y)- xa is the density function for the lamina R given above, determine the mass for R 5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the...
Set up the integral to find the volume of the tetrahedron bounded by the planes x + 2y + z = 8, x = 2y, x = 0, and z = 0, using a: a) double integral with order dydx. b) double integral with order dxdy. c) triple integral with any order of integration. YOUR WORK SHOULD INCLUDE A SKETCH OF THE REGION YOU ARE INTEGRATING OVER AND A CLEAR DESCRIPTION (CAN USE THE PICTURE HERE) OF HOW YOU ARE...
Find the volume of the tetrahedron bounded by the planes x + 2y + z = 2, x = 2y, x = 0 and z = 0 . Sketch the diagram of the tetrahedron with labeled points with coordinate axes and the boundary equations.
Please do #2 40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
can you please answer all of them please need it for a review F(x y, z) = 6x over the rectangular solid in the first octant bounded by the coordinate planes and the planes X-9, y-3, 2-S 27 1458 162 243 Find the center of mass of a thin triangular plate bounded by the coordinate axes and the line x + y = 4 if o(x, y) = x + y. 5 5 -3.73 . Oz Find the center of...
4. Let E be a solid bounded by the following planes: r = 0, y=0,2 = 0, z = 6-y, z = 8-T; see Fig.1. This solid is a region in the space of I, II and III type. Express SSS f(, y, z)dV by means of a triple iterated integral, which corresponds to the fact that E is of type II and next by means of a triple iterated integral, which corresponds to the fact that E is of...
7. Let R be the quadrilateral bounded by the lines: y-2x = 0, y --23 = -9, 2y - x = 0, and 2y - = 4. Set up, but do not compute, the following integral with the given change of variables | || (34 – 30) da, u= »–20, y = 2y
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...