Question

The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 4x2 kg. (See this example.) (a) Find the linear density when x is 4 m. kg/m (b) Find the linear density when x is 6 m. kg/m (c) Find the linear density when x is 9 m. kg/m

Answer 1

Answer:

A) 32 kg/m

B) 48 kg/m

C) 72 kg/m

Step-by-step explanation:

We are given mass is; m = 4x²

Linear density is the derivative of mass with respect to the position x. So linear density is;

ρ = dm/dx

Differentiating 4x²,we have; ρ = 8x

A)at x = 4; ρ = 8(4) = 32 kg/m

B) at x = 6; ρ = 8(6) = 48 kg/m

C) at x = 9; ρ = 8(9) = 72 kg/m