Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2 5. 7. 8 -1 -2

Q: What is the x centroid position for the shape below? Center:D, 2m 10m 3.4m 3.9m 4.4m 4.9m

A: Formula for centroid, C C=∑Ax∑A

Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: Determine the distance y measured from the x axis to the centroid of the area of the triangle shown…

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Q: H = (x – y)a, + (x² + zy)a, + 5yza, uate ſ, H · dl along the contour of Figure 3.28. 0.

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Q: Determine the x-component (m) of the centroid of the given figure if the cut portion is a semicircle…

A: Given, a=39 m, b=16 m and c=2 m To find the x-component of the centroid of the given figure.

Q: y=x¯, y= 2x

A: We can find the centroid using the required formula as below

Q: Find the equation of the tangent plane to +y? at the point (2,-2,5) the surface z= 4 O r + 4y - % =…

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Q: find the area of rotation of the following curve.(y axis)

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Q: Find the coordinates of the centroid of the curvex = et cos t, y = et sin t, 0 ≤ t ≤ p.

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Q: Find the centroid of the shape with endpoints (0,0),(0,4),(-2,4).(-2,6),(2,6),(2,3),(4,3) and (4,0)…

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Q: Find the coordinates (in inches) of the centroid of the uniform flat-plate machine part shown to the…

A: Solution:-

Q: Find the equation of the tangent plane to the surface z = at the point (2,-3, 10) O r- 6y – z = 10…

A: We have to find the equation of tangent plane.

Q: Calculate the y-coordinate of the centroid of the shaded area. 66 mm Answer: y = y i | 27 27 → mm mm…

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Q: Find the equation of the tangent plane to the surface =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: Find a parametrization a = #(t), y = y(t), t E [0, 1] for the line segment from (-2, –5) to (-3,…

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Q: 3

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Q: Find the centroid of the region in the polar coordinate plane defined by the inequalities 0<=…

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Q: y? = 3x 2 in. 3 in.

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Q: Find the Centroid of the shaded area y -30– 30 15

A: Lets draw co-ordinates in the figure as such: Also lets guess mass-density per unit area is unit.

Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: 1 2.5" y 3" 6 -Х

A: Given data:-

Q: In ANPQ, U is the centroid. If NS=15 find US. R S U

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Q: ). Find the centroid of the first quadrant area bounded by the parabola y = x2 and the line y = x.…

A: According to the guidelines answer of first question can be given, for other please ask in a…

Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,

Q: Determine the y-coordinate of the centroid of the shaded area. bl x=y²/b 0.62b b Answer: y = i b

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Q: Identify a generating curve on the xz-plane for the surface of revolution with equation a² + y? + 2?…

A: Consider the surface of revolution with equation, x2+y2+z2=e2x it is required to find the generating…

Q: Most centroid calculations for curves are done with a calculator or computer that has an integral…

A: Given: The coordinate of the centroid of the curve

Q: Find the centroid of the surface cut from the cylinder y2 + z2 = 9, z>= 0, by the planes x = 0…

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Q: R mm 150 mm Y-

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Q: Determine the y-coordinate of the centroid of the shaded area. bl. | x=y²/b b Answer: y = i 0.48b MI…

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Q: y 1 X 1 2.

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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.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: Locate the centroid of the plane area shown. 20 in. Ans: 9.00 20 in- Fig. P5.12

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Q: Find the Centroid tor the Shaded area. [Q2] 120 r=5 150 6 30 90 130

A: Solution to Question (1) Given a shaded area with dimensions,we have to find the centroid of that…

Q: Find the centroid of the third quadrant area bounded by the following curves y2+ 2y + 8x = −1 and y…

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Q: Use the polar coordinates to evaluate volumes : 1) Below z = x2 + y² above z=0 , inside x² + y² = 9

A: As you not mentioned the question number and both question has independent solution  so according…

Q: Find the centroid of the third quadrant area bounded by the following curves y? + 2y + 8x =-1 and y…

A: According to question given:y2+2y+8x=-1y=-5We have to calculate the centroid of the third quadrant…

Q: Locate the centroid of the shaded area shown. y%3D 4 3 -3 -4T-

A: The centroid represents the centre point of the curve . For example if we have a point in…

Q: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: Find the centroid of the lamina cut by the parabolas y2=x and y=x2.

A: For the clear understanding of curve we have the following graph which is shown below as:

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: Calculate the points of intersection of the curves x² = 4y and bre yavas r3 099wied biloa 9d1 to 9…

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Q: Calculate the Y-coordinate of the centroid of the rectangle shown in .Figure

A: In this question, the coordinate of the centroid of the rectangle is applied.

Q: find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle…

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Q: Find the equation of the tangent plane to the given surface at the point (0,-1,-2). y = L - O + 2z =…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the x-axis, the lines x = 2…

A: Given information:

Q: Determine the coordinates of the centroid of the shaded area. y 25 E 50 60 25 60 70 50

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Q: find the centroid of the thin plate bounded by thegraphs of the given functions. Use Equations (6)…

A: First, we need to find a mass of the plate.

Q: Find the centroid of the fourth quadrant area bounded by the following curves y? + 2y + 8x =-1 and y…

A: We will use double integration to solve this

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.