A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from
Posted: Tue May 10, 2022 4:45 pm
A smokestack deposits soot on the ground with a
concentration inversely proportional to the square of the distance
from the stack. With two smokestacks d miles apart, the
concentration of the combined deposits on the line joining them, at
a distance x from one stack, is given by
S=c/x^2 + k/(d−x)^2
where c and k are positive constants which depend
on the quantity of smoke each stack is emitting. If k=5c, find
the point on the line joining the stacks where the concentration of
the deposit is a minimum.
xmin =
mi
concentration inversely proportional to the square of the distance
from the stack. With two smokestacks d miles apart, the
concentration of the combined deposits on the line joining them, at
a distance x from one stack, is given by
S=c/x^2 + k/(d−x)^2
where c and k are positive constants which depend
on the quantity of smoke each stack is emitting. If k=5c, find
the point on the line joining the stacks where the concentration of
the deposit is a minimum.
xmin =
mi