Let D be a region in the (x, y)-plane. If a, b,c >0, let Sa be the part of the hyperbolic parabol...
Let D be a region in the (a, y)-plane. If a, b, e>0, let Sa be the part of the hyperbolic paraboloid zary in R3 with (x,y) E D, and let Tb,e be the part of the elliptic paraboloid bz2 + суг in R3 with (z.J) D. For a given a > 0, find b, c > 0 such that Tb.c has the same area as Sa Let D be a region in the (a, y)-plane. If a, b, e>0,...
4. Let D be a region in the (ar,y)-plane. If a, b,c > 0, let S be the part of the hyperbolic paraboloid ary in R3 with (r, y) E D, and let Thc be the part of the elliptic paraboloid :-bz2 + суг in R3 with (z, y) E D. For a given a >0, find b,>0 such that The has the same area as S
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working. (7) Let 0くa 〈 b 〈 c 〈...
Please try helping with all three questions.......please 1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
Let 0< a<b<e<d for a, b, c, d E R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation x=au + bu, y=cu + dv. (a) Sketch D in the r-y plane for the case ad -bc > 0. (a) Sketch D in the r-y plane for the case ad bc < 0. (c) Calculate the area of D. Show all working. Let 0
(7) Let 0 < a < b < c 〈 d for a,b,c,de R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation ( d -bc > 0. a) Sketch D in the x-y plane for the case a -bc< (a) Sketch D in the r-y plane for the case ad 0. (c) Calculate the area of D. Show all working. (7) Let 0
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠ 0. (b) Find the marginal probability density functions ??(?) and ??(?) of ? and ? respectively. (c) Are X and Y independent? (d) Find P(Y>X). (e) Let y be some real number in the range 0 ≤ y ≤ 1. Find the conditional probability density function ??|?(?|?). (f) Find ?[?|? = ?] (where ? is some real number in the range 0 ≤ ? ≤ 1). The joint...
8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12 8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2v3 d) 8 e) 12
please help with Q1 and 3 1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...