The mass of the first x meters of a thin rod is given by the function grams for Find the linear mass density function for the rod and determine whether the composition of the rod is homogeneous or nonhomogeneous.
A) nonhomogeneous
B) homogeneous
C) nonhomogeneous
D) homogeneous

Question

The mass of the first x meters of a thin rod is given by the function  grams for  Find the linear mass density function for the rod and determine whether the composition of the rod is homogeneous or nonhomogeneous.
A) nonhomogeneous 
B) homogeneous 
C) nonhomogeneous 
D) homogeneous

Quizplus · Accepted Answer

The linear mass density function for a thin rod is given by the mass per unit length. In this case, we can find the mass per unit length by dividing the mass function by the length of the rod.

Let's assume that the length of the rod is L meters. Then, the mass per unit length (linear mass density) is given by:

ρ(x) = (11e^(2x/L)) / L

This function is of the form ρ(x) = ae^(bx), which is an exponential function. This indicates that the density of the rod is not constant and varies exponentially with distance x from one end of the rod. However, the exponential function is of a single form, which means that the composition of the rod is homogeneous.

Therefore, the correct answer is B) 11eaa88b_923f_64a9_a696_9b1e2dec5e73_TB5869_11 homogeneous.

The Mass of the First X Meters of a Thin