Answer:
y = 1.5
Step-by-step explanation:
Given y is inversely proportional to [tex]\sqrt{1+x}[/tex] , then the equation relating them is
y = [tex]\frac{k}{\sqrt{1+x} }[/tex] ← k is the constant of variation
To find k use the condition when x = 8, y = 2 , then
2 = [tex]\frac{k}{\sqrt{1+8} }[/tex] = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )
6 = k
y = [tex]\frac{6}{\sqrt{1+x} }[/tex] ← equation of variation
When x = 15, then
y = [tex]\frac{6}{\sqrt{1+15} }[/tex] = [tex]\frac{6}{\sqrt{16} }[/tex] = [tex]\frac{6}{4}[/tex] = 1.5
