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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
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