Answer:
y = 140
Step-by-step explanation:
Given y varies directly with [tex]\sqrt{x}[/tex] then the equation relating them is
y = k[tex]\sqrt{x}[/tex] ← k is the constant of variation
To find k use the condition y = 42 when x = 9 , then
42 = k [tex]\sqrt{9}[/tex] = 3k ( divide both sides by 3 )
14 = k
y = 14[tex]\sqrt{x}[/tex] ← equation of variation
When x = 100 , then
y = 14 × [tex]\sqrt{100}[/tex] = 14 × 10 = 140
