What are the perpendicular generators on (P) to 4 %3D of the surface

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: O Calcalate the integea/ over the giren region by dhangng to polar cocalinater fcx,y) = 14xy/;

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Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

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Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: y? dV, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)

A: Given function f(x,y,z)=y2 Tetrahedron T is region with vertices (0,0,0), (2,0,0), (0,2,0) and…

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: What is the area of the conic (x + 3) + y 25

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Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

Q: Classify the surface: 1 – x = 3y + 4z?

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

Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: Sketch the surface r = 2y? + 32².

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Q: xy = 4

A: Solution

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: Find the average height of the paraboloid z = x2 + y2 over the square 0<= x <= 2, 0…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: In ABCD, H is the centroid. If HE=11 find DE. E F B D

A: We can use the theorem that centroid of a triangle divides the median in 2:1.

Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Sketch the surface = 2y + 32².

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Q: 3. Use traces to sketch and identify the following surface 25x2 + 4y² + z2 = 100.

A: Consider the given: Given:25x2+4y2+z2=100Let x=k∴25x2+4y2+z2=100             4y2+z2=100−25x2Hence,…

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: in R°sketch the graph of the cylinder x = (y – 2)?

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Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: What is the surface of the box formed by the net above

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Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…