arab O =2 Unid Coanward onentuhun) F-<パッザンで) Evaluale sSS div F dv V. Show the LHS #, E-dS] Pls include dia gram and how ho the 2 for each surfaces when doing , Fds. Thank you! get ナ

Q: * :classify the surface. 1 – y = 5x² + 6z? Cone O Plane O Ellipsoid O

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Q: (a) Cavalieri’s Principle states that if a family of parallelplanes gives equal cross-sectional…

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Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: Describe the surface whose equation is 2x2 + 2y? + 2z² – 9x – 7y + z – 2= 0. NOTE: Enter the exact…

A: Given the equation of the surface 2x2+2y2+2z2-9x-7y+z-2=0.

Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Find the surface area of the portion of the sphere x^2 + y^2 + z ^2 = 1 that lies abovethe cone z…

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Q: e surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show…

A: Solution:- y=x3       0,1 y'=3x2 y'2=3x22y'2=9x4 Now find surface area S= ∫012πy1+y'2dx…

Q: lume of a tetrahedron with adjac 1 w is Ju· (v x w)| to determine 6. tices P(-3,2,0), Q(2, 1, –3), R…

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Q: 4. Let S be the surface of the solid region in the first octant bounded be- tween the spheres a2 +…

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Q: Let S be the surface with defining equation x + 12y + 12z + 8yz = 16. Find all points P = (a, b, c)…

A: The function of the surface is given by:  fx,y,z=x2+12y2+12z2+8yz-16=0

Q: ns are pre uestionnaire). Box Luck!!! Question 46 Which of the following best describes the surface…

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Q: 6l@) n spnenical oordinates (p,O,Ø), the equation Ô = C where C s a constert repretents in eg. á…

A: (a) In spherical coordinates, ρ,θ,φ, θ is the angle made by the position vector with the z-axis,…

Q: 3 Describe in words the region in R° represented by the equation x2 + y² – 10y + z? + 2z = 0 A A…

A: Consider the equation

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

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Q: Describe in words the region in R' represented by the equation x² + y² – 10y + z² + 2z = 0 O A…

A: we have to check the region of the given equation in R^3 is

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: Plot the surface z = x+y with a finer mesh (of 0.25 units in each direction),using [x,y] = meshgrid…

A: MATLAB is a computer language that engineers and scientists use to study and build systems and…

Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: Consider the portion of the plane x + 2y + 3z = 12 that sits above the circle (x − 2)^2 + (y − 2)^2…

A: The solution are next step

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 137 u = 8i + 7j + k v = i + j…

A: Directly use the formula for the volume of parallelepiped.

Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: 13. classify the surface: * 1 – y = 5x² + 6z² Elliptic paraboloid Cone O Sphere Plane O Ellipsoid

A: The given equation of the surface is: 1-y2=5x2+6z2

Q: Consider a unit disc of radius 1 centred at the origin. The straight lines y = x and y= -x break…

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Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: 8. Identify each of the following surfaces (i.e. what type of surface is it), and if it "opens",…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: The base of a solid is bounded by y= x² and y= 4. All parallel cross – sections are squares…

A: Please rate

Q: he cone z^2= x^2+ y^2, for z ≥0, cuts the sphere x^2+ y^2+ z^2= 16 along a curve C. That is, C is…

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Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 102 u = 8i + 7j + k v = i + j…

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Q: 2 What Is the equatlon of the clrcle with a radius of 5 and center at (2, 3)? F (x + 2)2 + (y + 3)2…

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Q: Maximize the lateral surface area of an inverted cone, if V = 100 cm³. S trvr² + h? V = 1h = 100 t…

A: According to company rule we can answer only first question and rest can be reposted.

Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

Q: 1. Let S be the part of the plane 2.x – 2y + z = 1 inside the “cylinder" whose walls are given by…

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Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: Find the points on the surface y = 9 + xz that are closest to the origin. (x, y, z) = (smaller…

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Q: (7] identify the following surfaces from the list NO justification needed for this problem Simply…

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

Q: Consider the parallelepiped with adjacent edges u = 9i + 8j + k v =i+j+9k w =i+5j + 2k Find the…

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Q: A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of…

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Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

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Q: 1. Find the surface area of the part of the sphere x+ y +z = 4 that lies above the plane z =1.

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Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: Given the surface r(u,v) =  (0 ≤ u ≤ 5, 0 ≤ v ≤ 4pi) Explain clearly what gridlines are found when…

A: Given surface is ru,v=ucosv,usinv,v To find the equation of tangent plane for u=3, v=8π3…

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: Find the surface area of that part of the plane

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