Question

If a^2 and b are directly proportional, and a=2 when b=9, then what is b when a=6?

Answer 1

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 )

$\frac{4}{9}$ = k

a² = $\frac{4}{9}$ b ← equation of proportion

when a = 6 , then

6² = $\frac{4}{9}$ b

36 = $\frac{4}{9}$ b ( multiply both sides by 9 to clear the fraction )

324 = 4b ( divide both sides by 4 )

81 = b