Find the mass of the one-dimensional object. A pencil that is 10 in long (starting at x= 2) and has a density function of ρ(x)= 5/x oz/in

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: Consider a thin wire of mass m and length L going from x = a to x = b. Let the density of the wire…

A: Given that a thin wire of mass m and length L going from x=a to x=b. The density of the wire is…

Q: The linear density of a rod of length 4 m is given by p(x) = 9 + 2V measured in kilograms per meter,…

A:

Q: A square plate with sides a is submerged vertically in water as shown. Express the hydrostatic force…

A:

Q: Find the center of mass of  Y = x2/3    and. y = 4.

A:

Q: The radius of a sphere increases at a rate of 6m/sec, then the rate at which the volume increases…

A: Let's find.

Q: 3. The mass of part ofa wire is x(5+Sx )kilograms, w here x is measured in meters from one end of…

A: The linear density is given as λ=dMdx So, differentiate the given function with respect to x we get…

Q: Find the mass of the two-dimensional object. An oversized hockey puck of radius 4 in with a density…

A:

Q: A certain gas expands to fill a 3 L container. Its mass is measured to be 0.6 kg. What is its…

A:

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.