please show all work 10) Use a change of variables to find the volume of the...
please show all work 245 1) Sketch the region represented by 55 dydis on the attached grid. DA 2) SET UP the integral for both orders of integration of R: region bounded by y = x, y = 2x, x = 2 SS Vx++y* dxdy 3) Evaluate the following integral by converting to polar. 4) Use a double integral in polar to find the volume of the solid bounded by the equations z = x + y +1,2-0, x +...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2) Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
Please solve all of these questions and do not skip any one of them. Also label them by 2, 3, 4a and 4b in this order. Sketch the region and find the area of the triangle with the given vertices. . (0,0), (1,8), (4,3) Let R be the region in the first quadrant bounded by the graphs of x=y and x = 4y. Which is greater, the volume of the solid generated when Ris revolved about the x-axis or the...
Please help with 1-10 and please show all work thanks. Show all of your work neatly, and express solutions as exact answers unless otherwise requested. No credit will be given to solutions that have no work shown! BOX or CIRCLE your final answer. 1. Sketch a graph and shade the area of the region bounded by the following equations. Set up an integral that would give this area. 2x + y2 = 6 and y=x+1 2. Sketch a graph and...
(a) Find the volume of the solid under the paraboloid z x +3y2 and above the triangle with vertices (0,0), (4, 8), (8, 0). (b) Find the average value of (.y)-yover the rectangle with vertices (4,0), (-4,3), (4,3) (4, 0) (a) Find the volume of the solid under the paraboloid z x +3y2 and above the triangle with vertices (0,0), (4, 8), (8, 0). (b) Find the average value of (.y)-yover the rectangle with vertices (4,0), (-4,3), (4,3) (4, 0)
please show all the work #11.) Using "shells" find the volume obtained by rotating the region in the first quadrant that is bounded by y=x and y=x?about the y- axis.
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1 point) Find the mass of the triangular region with vertices (0,0), (1, 0), and (0, 5), with density function ρ (x,y) = x2 +y. plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1...
Do both questions and show all steps for good rating. Thanks. 7. Set up an iterated double integral to compute the volume of the solid bounded above by r2 y and below by the region R that is a triangle in the ry-plane with vertices (0,0), (0,3) and (5,3). z = (8) Do not evaluate. Exam 2-u ath 260-01 8. Set up a double integral in polar coordinates to find the volume of the solid bounded by zry 2 =...
please show all steps. Problem 23. Let the random variables X and Y have a joint PDF which is uniform over the triangle with vertices at (0,0), (0,1), and (1.0). (a) Find the joint PDF of X and Y. (b) Find the marginal PDF of Y. (c) Find the conditional PDF of X given Y. (d) Find E[X|Y = y), and use the total expectation theorem to find E[X] in terms of E(Y). (e) Use the symmetry of the problem...
Show All Work: 4. Use the shell method to find the volume of the solid generated by rotating y = x2 – 3 and y = 15 – x2 about the line x = 7. (Set up only). You must graph the functions and draw the appropriate rectangle for full credit.