Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y + 3z = 6, then when caleulating .Gx +y+z+ 1)dS is obtained as an approximate result:

Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

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Q: et a =i- 2j + k and b= 2i+j +k. Show that la + b| s lal + b|

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: 5. Use Cartesian coordinates to evaluate If ₁² dv D where D is the tetrahedron in the first octant…

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Q: wnich of the followi ng functrons is homogeneous? 5x - 12メy ty? Po.) sm xy Ci) eln xy 2

A: To find which of the following function is a homogeneous function. A)fx, y=5x3-12xy+y3B)fx,…

Q: Find the Uolume of the Solid under de the 2:1+ xy2 & the a Gove te region Sorface en cased by y= x²…

A: Consider the given surface z=1+x2 y2 Since, y=1 and y=x2 Then, x=±1 That is, -1≤x≤1  and    x2≤y≤1

Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² | 3x +…

A: We have to draw the solid Q in first octant and is generated by the surfaces  y- 1=( x- 2)2 3x+2z=11…

Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: Sketch the solid described by the given inequalities. 2 sps 3, 0s p s a/3, 0s0sa 1.5 1.0 0.5 0.0

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Q: Use Cartesian coordinates to evaluate [[[ ²² y² dv D where D is the tetrahedron in the first octant…

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Q: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: Consider the solid Q that is generated in the first octant by the surfaces S1 : y+z = 4, S2 : y - 1…

A: Solution is below.

Q: Find the difference c-d for the following cubic spline S(x) with natural boundary conditions: S(2) =…

A: To find - Find the difference c - d for the following cubic spline S(x) with natural boundary…

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1,…

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Q: 10. Let D be the solid inside the cylinder r= cos , above the xy-plane and under the paraboloid…

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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Q: please explain it step by step

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Q: Consider the solid Q that is generated in the first octant by the surfaces S1: X + y = 4, S2: y +z =…

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Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

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Q: Evaluate the triple Integral. 3xyz dV, where T

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Q: 5. Use Cartesian coordinates to evaluate ƒƒƒ v³² av where D is the tetrahedron in the first octant…

A: Given problem:-

Q: Evaluate the triple integral. 4xyz dv, where Tis the solid tetrahedron with vertices (0, 0, 0), (1,…

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Q: Solve the DE, dy =y²-a? E, = , using the homogeneous method. ry (a) Hint: Rewrite the RHS as 2 -…

A: dydx=y2-x2xy⇒dydx=y2xy-x2xy⇒dydx=yx-xy⇒dydx=yx-yx-1 Now put, y=vx⇒dydx=v+x·dvdx

Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² 3x + 2z…

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Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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Q: Consider the solid Q that is generated in the first octant by the surfaces S, : 2x + 3y + 3z = 6 S,:…

A: The region S2 is clearly a parabola y2 = 2-x and it is symmetrical in the x-axis.

Q: The solid S is obtained by rotating the region enclosed by y = f(x) 2 0, a = 5+ 5e6 1- e6 5+ 5e16 1-…

A: The given question is solved below.

Q: Use Cartesian coordinates to evaluate SSS y² dv av where D is the tetrahedron in the first octant…

A: Given D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x +…

Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: 1 Evaluate dV, where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y? + z2 x2 + y? + z2 36 in…

A: we want to find the triple integral ∫∫∫E1x2+y2+z2  dVwhere E lies between the sphere x2+y2+z2=9  and…

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: 1.Let 3 le the solid obtained by rotating by region shown in the fiqure about the Assume as3 and b=…

A: Given: y=ax(x-b)2 and y=0 and  0≤x≤b The rotation about the y-axis. Assume a=3 and b=1

Q: 5 Use Cartesian coordinates to evaluate [[[ v² av dV D where D is the tetrahedron in the first…

A: Please follow the next step.

Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: ) Use the eisenfunctan expausian melbud Solve the vibrating strng Problem = 4 uxx + Sin zx…

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Q: 5. Use Cartesian coordinates to evaluate [[["² y² dV where D is the tetrahedron in the first octant…

A: Coordinates are distances or angles, represented by numbers, that uniquely identify points on…

Q: Given: ARST = AXYZ; SK bisects ZRST; K YL bisects 2XYZ. Prove: SK = YL S

A: Prove SK≅YL.

Q: Consider the solid Q, in the first octant, which is generated by the surfaces: S1 : x2 = −(z − 3),…

A: Given:  S1 : x2 = −(z − 3), S2 : y + z = 3, S3 : z = 2, S4 : z = 0, S5 : y = 0 and S6 : x = 0  The…

Q: find the valume 9tntrat ed by y= X? on [0,31 rotating abaut thlina X-5.(shell melthod) rated

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Q: 1 SI. Evaluate dV, where E lies between the spheres x2 + y? + z? a2 + y? + z2 = 1 and æ? + y? + z²…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Use Cartesian coordinates to evaluate JJJ² dV D where D is the tetrahedron in the first octant…

A: Given ∭y2 dVD

Q: Solve the BVP for the disk (exterior Dirchlet problem) v'u = 0, 1< r <o∞ u (1,0) = sin 0 + cos 20

A: The given function is ∇2u=0 The given condition is u(1,θ)=sinθ+cos 2θ We have to find the general…

Q: 3. Set up the integral to find fffr x dV where T is the tetrahedron in the first octant under the…

A: To set up the integral to find ∭TxdV