Answer:
g = 14
Step-by-step explanation:
Given that f varies directly as g and inversely as h then the equation relating them is
f = [tex]\frac{kg}{h}[/tex] ← k is the constant of variation
To find k use the condition f = - 12 when h = 4 and g = - 3, that is
- 12 = [tex]\frac{-3k}{4}[/tex] ( multiply both sides by 4 )
- 48 = - 3k ( divide both sides by - 3 )
16 = k
f = [tex]\frac{16g}{h}[/tex] ← equation of variation
When f = 28 and h = 8 , then
28 = [tex]\frac{16g}{8}[/tex] = 2g ( divide both sides by 2 )
g = 14
