A lamina has the shape of a triangle with vertices at (-2, 0), (2,0), and (0, 9). Its density isp=2. A. What is the total mass? B. What is the moment about the x-axis? C. What is the moment about the y-axis? D. Where is the center of mass? (

Q: (b) A cubc has sidcs length of a cm and it is made of a matcrial of variable density. If one corner…

A: Given: Cube of side length a cm, and density function of cube  is δx,y,z=b+xyz gm/cm3 where one…

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A:

Q: Referring to the Figure 1, determine the center of the mass for area given. y 4 х Figure 1

A: We will use area of lamina and its moment about axis to find its center of mass

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Q: Find the center of mass of a cylinder of radius 2 and height 4 and mass density e^(−z), where z is…

A: Given that,  δ(x,y,z) = e-z,  r = 2  and z=4 By using of formula, M = ∫∫∫W δx,y,z dvMxy = ∫∫∫W z…

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A:

Q: Find the center of mass of the lamina that has the given shape and density. y = sqrt3(x) x, y = 0 ,…

A: We have to find the center of mass of the lamina that has shape y=3x,y=0,x=4 and ρr,θ=r2 Now…

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A:

Q: 2. Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides…

A:

Q: Find the total mass of the given rod and the center of mass The length of a rod is 6m and the…

A: Given that, the length of the rod is 6 m and linear density of the rod is 2x+3kgm. Find the total…

Q: Find the mass of a 3 meter bar with a density of p(x)= 150e^-x/3 for 0

A: See the details solution in below

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A:

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A:

Q: p= 2 yA quarter-circle

A: Given a quarter circle of radius r with density ρ=2. To find the center of mass and moments Mx and…

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A: Mass of a lamina is given by M=∫∫A δ dAhere δ is the density function.

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Q: Find the total mass M of a 2-m rod of linear density ρ(x) = 1 + x(2 − x) kg/m, where x is the…

A: Consider the given given information. ρx=1+x2-x kg/m   The mass of the rod is given by the formula.…

Q: f(x) = ax+b, if one

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve c, where c is the top…

A: Given a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top half…

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Q: A large metal disk with radius of 2 m has been made. The density of the metal disk is given by p(r,…

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Q: Find the center of mass of a lamina as pictured below, with inner radius 3 and outer radius 5, with…

A: Given problem:-

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A: Given density at each point r units from the center of the ball is 11+r2.

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Q: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid r = 2 +…

A: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid…

Q: Q5: A- Find the mass of the region cut from the sphere++d by the cone z= density &?? +y² if the

A: Mass is given by M=∬∫V δ dv

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A:

Q: ゴー aab

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Q: A lamina occupies the part of the disk æ? + y < 16 in the first quadrant and the density at each…

A:

Q: Suppose a solid mass is in the shape of the unit ball in R³, that is, the region with ² +y? + 2? <…

A: We are given the region is x2+y2+z2≤1. And the mass density of the solid mass is fx, y,…

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A: Mass and Center of Mass of a Wire:- Mass and center of mass of a wire: - The following formulas are…

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A:

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A: We have to find center of maas of the lamina.

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A:

Q: (3) Find the mass of the lamina described by the inequalities, given that its density p(x, y) = xy.

A: Given,             ρ(x, y)=xy and  x≥0, 3≤y≤3+9-x2

Q: e mass of the solid bounded below by the c phere z = 6.52 – a? – y² if the density

A: The given equation of the circular cone z=x2+y2 and the hemisphere z=6.52-x2-y2 and the density…

Q: Find the mass of the lamina described by the inequalities 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, given that its…

A: We know that if ρ is a continuous density function on the lamina corresponding to a plane region R,…

Q: Consider an elliptic piece of wire, represented by the curve E : + y? = 1 4 in R?. Assume that this…

A:

Q: (3) Consider a wire in the shape of a semi circle of radius 2, given by x² + y² = 4 and y ≥ 0.…

A: Formula: The mass of the region R with density function ρx, y is: m=∫∫Rρx, y dA The center of mass…

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.