Answer:
b = 125
Step-by-step explanation:
Given a varies directly as [tex]\sqrt[3]{b}[/tex] then the equation relating them is
a = k[tex]\sqrt[3]{b}[/tex] ← k is the constant of variation
To find k use the condition a = 3 , b = 64 , then
3 = k[tex]\sqrt[3]{64}[/tex] = 4k ( divide both sides by 4 )
[tex]\frac{3}{4}[/tex] = k
a = [tex]\frac{3}{4}[/tex] [tex]\sqrt[3]{b}[/tex] ← equation of variation
When a = [tex]\frac{15}{4}[/tex] , then
[tex]\frac{15}{4}[/tex] = [tex]\frac{3}{4}[/tex] [tex]\sqrt[3]{b}[/tex] ( multiply both sides by 4 to clear the fractions )
15 = 3[tex]\sqrt[3]{b}[/tex] ( divide both sides by 3 )
5 = [tex]\sqrt[3]{b}[/tex] , then
b = 5³ = 125
