Answer:
b = 81
Step-by-step explanation:
given a² and b are directly proportional then the equation relating them is
a² = kb ← k is the constant of proportionality
to find k use the condition a = 2 when b = 9 , then
2² = 9k
4 = 9k ( divide both sides by 9 )
[tex]\frac{4}{9}[/tex] = k
a² = [tex]\frac{4}{9}[/tex] b ← equation of proportion
when a = 6 , then
6² = [tex]\frac{4}{9}[/tex] b
36 = [tex]\frac{4}{9}[/tex] b ( multiply both sides by 9 to clear the fraction )
324 = 4b ( divide both sides by 4 )
81 = b
