Find i Partial derivat ive level Surface i) Gradien of F

Q: A ring is formed by rotating the shaded area 360° about y-y axes. Determine (1) its surface area and…

A: We find the surface area and volume

Q: Find the surface area of the part of the spherex +y² +z = 16 that lies above the plane z = 2.

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Q: find a parametrization of the surface Parabolic cylinder between planes The surface cut from…

A: To find a parametrization of the surface: Given that, Between the planes z=0 & z=3 Thus, 0≤z≤3…

Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Find the area of the surface generated by revolving the region bounded by, y6 1 x = + 16y4 i 1<ys 5…

A: In this question, we find the surface area generated by rotating the region bound by the given curve…

Q: Find the area of the elliptical region cut from the plane x + y + z = 1 by the cylinder x 2 + y 2 =…

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Q: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

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Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 16 – x – y.…

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Q: Find the centroid of the region that is enclosed between: y = x and y = 2 – 2?.

A: Let fx=2-x2, gx=x. Find the intersections. fx=gx2-x2 =x2-x2…

Q: integrate ƒ over the given region. ƒ(u, y) = y - √u over the triangular region cut from the first…

A: Given  The function is ƒ(u, y) = y - √u . The triangular region cut from the first quadrant of the…

Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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Q: How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(x)…

A: Given:How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y =…

Q: Find the area of the surface. The part of the surface y = 4x + z2 that lies between the planes x =…

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Q: Find the area of the surface generated by revolving the region bounded by, 1 1syss 16y4 y6 1<y< 5 6.…

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Q: Calculate the surface area x2+y2+z2=25, between the z=1 and z=4 planes

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Q: Surface at 0 = 30° and r = 10 is a.. Cylinder Cone Circle Plane

A: Solve

Q: Surface at θ = 40⁰ and r = 20 is a     plane    cirlce   cone

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

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Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: Find Surface area after revolving about х-ахis y = Vx, 1 < y < 2

A: Use the formula of surface area of revolution along x-axis.

Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Find the center of gravity of the homogeneous plate placed in this region by showing the region…

A: Given that  The equation of two circles x2+y2=4xx2+y2=13x and the lines on the coordinate axis…

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: Find the coordinates of the center of gravity of the homogeneous wire showen below. The portion on…

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Q: Find the centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Consider the diagram of the lamina as per given information, The centriod of the lamina is defined…

Q: A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half…

A: Draw the region R as follows.

Q: Find the area of the section of the surface x = u2, y = uv, z = v2/2 bounded by the curves u = 0, u…

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Q: Surface at 0 = 40° and r = 20 is a.. Cylinder Plane Circle Cone

A: Given:  r=20, θ=40°

Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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Q: find the areas of the surfaces generated by revolving the curves about the given axes. 27. x = 24y -…

A: To determine the surface area of solid of revolution about the y-axis.

Q: Classify the surface: 1– x = 3y² + 4z² O Elliptic paraboloid O sphere O Ellipsoid O Plane O cone

A: In this question we have to classify the surface.

Q: Calculate

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Q: Find the area of the surface obtained by rotating the curve x = Va – y², 0 < y s about the y-аxis

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Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

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Q: Find the centroid by revolving the given plane area about the indicated axis y^2=5-x, x=0 ; about…

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Q: Find the centroid of the semicircular area inside x2+ y2 = a2 with y ≥ 0. Show the graph for it.

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Q: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…

A: This is parameterisation of curve problem

Q: Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2x and y =…

A: Solution of question is written in step2 and step3.

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. x = √y, 2 ≤ y…

A: We first find dx/dy

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: Find the surface area of the surface generated by revolving a portion of the curve y = x", from x =…

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Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…

A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…

Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.