(1 point) Find the volume of the region enclosed by z = 1 – y2 and...
Find the volume of the solid enclosed by the paraboloid z = 5x2 + 5y 2 and the planes x = 0, y = 3, y = x, z = 1225 3 Evaluate the double integral. SS 9. y2 - xdA, D = {lar,y) |0<y< 4,0 <r<y} 24 Evaluate the double integral. I, 4xy dA, D is the triangular region with vertices (0,0), (1, 2), and (0,
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
Find: 1. Find (2x2 + y2) DV where Q = { (x,y,z) 0 < x <3, -2 <y <1, 152<2} ЛАЛ
Given z = 2 y2 – 3xy , find the slope of the surface at (1,1,-1) in the direction of ū =< 2,3>
(1 point) Find the volume of the region enclosed by the cone z-V2 + y? and the sphere2y222 1. Volume- (1 point) Find the volume of the region enclosed by the cone z-V2 + y? and the sphere2y222 1. Volume-
i will rate. thanks. [20 pts) Let Q be the solid region Q={ (1,Y,Z): 2Vx2 + y2 < < <2} The density at each point (1,y,z) of Q is given as o(x, y, z) = x2 + y2 + z2. Calculate the moment of inertia about the z-axis, 1,, by hand, showing all work.
solve both please Sketch the region enclosed by y = 3x and y 6.0². Find the area of the region. Find the average value of the function f(x) 3x4 on the interval 0 < x < 2
1. Consider the surface of revolution that is given by the equation Z-R= -(x2 + y2)/R where [x],[y] < R/V2 . (a) Find the volume enclosed between the surface and the x-y plane. (b) Find the normal vector în and an equation for the tangent plane to the surface at i = ? (î+ ſ + Â). (Hint: Choose appropriate coordinate systems in each part).
The solid S sits below the plane z = 2x + 5 and above the region in the xy-plane where 1 < x2 + y2 = 4 and x + y < 0. The volume of S is:
1. Find the volume of the solid described by the inequality Vz? + y2 <2< 2.