f is inversely proportional to √g
.When f=12, g=64
Work out g when f=16


Sagot :

Answer:

36

Step-by-step explanation:

f * √g = k

12 * √64 = k

k = ± 96

g = k² / f² = (± 96)² / 16² = 36

Answer:

g = 36

Step-by-step explanation:

Given f is inversely proportional to [tex]\sqrt{g}[/tex] then the equation relating them is

f = [tex]\frac{k}{\sqrt{g} }[/tex] ← k is the constant of proportion

To find k use the condition when f = 12 , g = 64 , then

12 = [tex]\frac{k}{\sqrt{64} }[/tex] = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 )

96 = k

f = [tex]\frac{96}{\sqrt{g} }[/tex] ← equation of proportion

When f = 16 , then

16 = [tex]\frac{96}{\sqrt{g} }[/tex] ( multiply both sides by [tex]\sqrt{g}[/tex]

16 × [tex]\sqrt{g}[/tex] = 96 ( divide both sides by 16 )

[tex]\sqrt{g}[/tex] = 6 ( square both sides )

g = 6² = 36