Question

If p varies directly as the cube of q, and p = 26 when q = 2, find p when q = 5

Answer 1

Answer:

The value of p at q = 5 is 406.25

Step-by-step explanation:

∵ p varies directly as the cube of q

→ That means p ∝ q³

∴ The equation of variation is p = kq³, where k is the constant of variation

∵ p = 26 when q = 2

→ Use them to find the value of k

∵ 26 = k(2)³

∴ 26 = k(8)

∴ 26 = 8k

→ Divide both sides by 8

∴ $\frac{26}{8}=\frac{k}{8}$

∴ 3.25 = k

→ Substitute it in the equation of variation

∴ p = 3.25 q³ ⇒ equation of variation

∵ q = 5

→ Substitute it in the equation of variation to find p

∴ p = 3.25 (5)³

∴ p = 406.25

∴ The value of p at q = 5 is 406.25