Se differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and 8 cm in diameter if the metal in the top and the bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.)

the amount of metal is approximately 19.47 cm³

Step-by-step explanation:

the volume enclosed by the cylinder is

V= π*R²*L

then using differentials

dV = ∂V/∂L *dL + ∂V/∂R *dR

dV = π*R²*dL +  2*π*R*L *dR

ΔV ≈ π*R²*ΔL +  2*π*R*L *ΔR

replacing values

ΔV ≈ π* (4 cm)²* (0.1 cm*2) +  2*π*R*30 cm *0.05 cm = 19.47 cm³

then the amount of metal ( in volume ) Vmetal is

V metal = V(R+dR, L+dL) - V(R, L) = ΔV ≈ 19.47 cm³

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: