The young boy discovered that m varied jointly as k and w2 , and inversely as the square root of x. The value of m was multiplied by what when x was multiplied by 8, w was multiplied by 3, and k was multiplied by 2?
You are describing: m ~ kw^2 / sqrtx
now add the changes you described: 2 (3)^2 / sqrt 8 the value of m will change by this amount.
simplifies to 18/sqrt8 = 18/2sqrt2 = 9 /sqrt2 or 9 (sqrt2/2)
m = [k w^2] / [√x ]
m = [ 2k (3w)^2 ] / √[8x]
m = [2k*9w^2] / (2 √[2x] )
m = [ 18kw^2 ] / (2 √[2x] )
m = [9kw^2]/ √[2x]
m = [9/√2] [ kw^2] / √x
So.....m is increased by a factor of 9/√2
+466 
