Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write M le, y. 2) aV in the form pe(z) po(0,z) f(x, y, 2) dy da dz u(2) = v(z, 2) =

Q: Find the equations r = g (0, z) (cylindrical) and p = f (0, 4) (spherical) for the hyperboloid x² =2…

A: To find-  Find the equation r = gθ, z (cylindrical) and ρ = fθ, ϕ (spherical) for the hyperboloid…

Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: et D be the triangle with vertices (0,0), (1,0) and (0, 2). Compute ffp (e2y + 1) dA.

A: Given is the triangle D with vertices 0,0,1,0,0,2 The objective is to evaluate the integral ∫∫D…

Q: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that C is the positively oriented square with vertices (-3,-1), (1, −1 ), (1, 71), and (-).…

A: If F=Px,yi+Qx,yj is a vector-valued function, then according to Green's theorem…

Q: 7. Suppose that C is the positively oriented square with vertices (-1, 1), (1, 1), (1, 1), and (-).…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: 3) Evaluate elz+y)/(z-y) dA where Ris the quadrilateral with vertices (0,1), (0,-2), (1,0), and…

A:

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: Calculate / Ss (4xy + e- )dS, where S is the triangle in Figure 1 with vertices (0, 0, 3), (1,0, 2)…

A:

Q: Consider the parallelogram with vertices O, A, B, C, with vertex B opposite O, where O = (0, 0, 0),…

A: