Question

2. If x is directly proportional to y^3 and x=32 when y=2, i) Find an equation

Answer 1

Answer:

(i)

$x \alpha y {3} \\ \frac{x}{y {3} } = k$

(ii)

$\frac{x}{y {3}^{} } = \frac{x}{y {3}^{} } \\ \frac{32}{ {2}^{3} } = \frac{x}{6 {}^{3} } \\ \frac{32}{8} = \frac{x}{216} \\ x = 864$

(iii)

$\frac{32}{8} = \frac{108}{y {}^{3} } \\ {y}^{3 } = 27 \\ y = \sqrt[3]{27 } \\ y = 3$