Below is my question and a solution to this question with k = 8c. I need to find

Question

Below is my question and a solution to this question with k = 8c. I need to find the solution with k = 2c. I have tried using this example solution to answer the problem with k = 2c, but nothing I put is accepted. Please help me figure this out with k = 2c, not k = 8c.

A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacksdmiles apart, the concentration of the combined deposits on the line joining them, at a distancexfrom one stack, is given by

xmin= mi

Explanation / Answer

S(x)=c/x2 +k/(d-x)2

k=2c

S(x)=c/x2 +2c/(d-x)2

S'(x)=-2cx-3 + 4c(d-x)-3

now equate S'(x)=0 to get that point where concentration is minimum

-2/x3 + 4/(d-x)3 =0

(d-x)=(2)1/3(x)

d=(2)1/3(x) +x

x=d/((2)1/3 +1)

x=d/(1.26+1)=d/(2.26)

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