use Laplace transforms to solve the following system:- y'- Z=o Y-Z' =o Y(0)=1, Z(0)=1 Find the general solution of the system:- x=x+2y y = 4x + ³y
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- Evaluate the triple integral. 3xyz dV, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0, 1)In isosceles triangle XYZ, XY = YZ = 10, and XZ = 16. Where C is the centroid of triangle XYZ, find the distance from C to side XZ of the triangle.Find the image of the annulus 1 < |z| < 2 under the transformation w = z/z −1 Please dont provide hand written solution
- Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,7,0),(0,0,7).The solid generated by revolving the regionbounded by the graphs of x = , y = 0, andx = 2 about the y-axis isDetermine a region of the xy-plane for which the given differentail equation would have a unique solution whos graph passes through point (x,y) in the region. (y-x)y' = y +x
- Evaluate the triple integral. (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2) and base vertices at (0, 0, 0), (2, 0, 0), (0, 2, 0), and (2, 2, 0)A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that has its vertex at one corner of ℛ and passes through the opposite corner. Find the centroids of both ℛ1 and ℛ2.Find the center of mass of the given system of point masses lying on thexaxis. m1 = 0.1, m2 = 0.2, m3 = 0.2, m4 = 0.5 x1 = 1, x2 = 2, x3 = 3, x4 = 4
- Let n ≥ 1 be constant, and consider the region bounded by f(x) = xn, the x-axis, and x = 1. Find the centroid of this region. As n→∞, what does the region look like, and where is its centroid?Consider the system x' - x = u(t). Can one steer 1 to 0 by a differentiable contro function u(t)?Consider a block sliding over a horizontal surface with friction. Ignore any sound the sliding might make. If the system is the surface, this system is (a) isolated (b) nonisolated (c) impossible to determine