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 exampl
e.) (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
1 answer:
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
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