If m<DBC=(12x-3)°, m<DBE=(5x+12)°, and m<EBC=(3x+13)°, find m<EBC.

It is stated that a straight rod has one endpoint at the origin (0,0) and the opposite endpoint at (L,0), with a linear density defined by , where a is a constant and x is the x coordinate.

Thus, the infinitesimal mass is expressed as:

The total mass can be calculated by integrating the above expression as follows:

Consequently,

Now, we can calculate the center of mass, of the rod as:

Now, it follows that

x_{cm}=\frac{1}{\frac{aL^3}{3}}\int_{0}^{L}ax^3dx=\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}

Therefore, the center of mass, is located at:

Answer:

(1, 3)

Step-by-step explanation:

Provided:

A circle containing these specified points-

(4, 2), (-2, 2), (-1, 4), (1, 1), (1, 3), (2, -3).

A function resembles a mechanism that produces an output for each unique input. Each input must yield a distinct output.

The function's input is characterized as the domain, and the output corresponds to its range.

The domain is indicated by the 'x' coordinate while the range is represented by the 'y' coordinate.

This means the domain serves as the independent variable, and the range is contingent upon the domain’s values.

In this case, a relation or set of points constitutes a function only if every 'x' in the ordered pairs is unique.

Within the described relation, the pairs (1, 1) and (1, 3) share the same input. Thus, removing either one will convert the relation into a function.

Therefore, choosing (1, 3) is the right answer.