Question

If a varies directly as the cube root of b and if a=3 and b=64.find the formula connecting the variables hence find b when a=15/4

Answer 1

Answer:

b = 125

Step-by-step explanation:

Given a varies directly as $\sqrt[3]{b}$ then the equation relating them is

a = k$\sqrt[3]{b}$ ← k is the constant of variation

To find k use the condition a = 3 , b = 64 , then

3 = k$\sqrt[3]{64}$ = 4k ( divide both sides by 4 )

$\frac{3}{4}$ = k

a = $\frac{3}{4}$ $\sqrt[3]{b}$ ← equation of variation

When a = $\frac{15}{4}$ , then

$\frac{15}{4}$ = $\frac{3}{4}$ $\sqrt[3]{b}$ ( multiply both sides by 4 to clear the fractions )

15 = 3$\sqrt[3]{b}$ ( divide both sides by 3 )

5 = $\sqrt[3]{b}$ , then

b = 5³ = 125