Let D be a region in the (a, y)-plane. If a, b, e>0, let Sa be the part of the hyperbolic parabol...
Let D be a region in the (x, y)-plane. If a, b,c >0, let Sa be the part of the hyperbolic paraboloid z = axy in R3 with (x,y) E D, and let Tổ.c be the part of the elliptic paraboloid·bz2 + суг in R3 with (x,y) D. For a given a > 0, find b,c >0 such that Tb,e has the same area as Sa Let D be a region in the (x, y)-plane. If a, b,c >0, let...
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
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 〈...
(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...
13. Let D be a region in the xy plane. Let A-dx dy JJ D Let aD be the region in which every point (x, y) in D is replaced by (az, ay) for α 0. Interpret the double integral as a Riemann sum and find the area of aD in terms of A and a.
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 S={(u, ujo < u < 1, 0<u<1) 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 r-y plane for the case ad - be>0. (a) Sketch D in the r-y plane for the case ad - be < 0. (c) Calculate the area of D. Show all working.
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...