Question

Given that r varies directly as t^3, and r=54 when t=3. Find t when r=250

Answer 1

t = 5

Explanation:

Given r varies directly as t³ then the equation relating them is

r = kt³ ← k is the constant of variation

To find k use the condition r = 54 when t = 3 , then

54 = k × 3³ = 27k ( divide both sides by 27 )

2 = k

r = 2t³ ← equation of variation

When r = 250 , then

250 = 2t³ ( divide both sides by 2 )

125 = t³ ( take cube root of both sides )

`\sqrt[3]{125}` = t , that is

t = 5