Question

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

connecting x and y, ii) Find the value of x when y=6, iii) Calculate the value
of y when x=108. *

Answer 1

(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) } \\ (32)/(8) = (x)/(216) \\ x = 864`

(iii)

`(32)/(8) = \frac{108}{y {}^(3) } \\ {y}^(3 ) = 27 \\ y = \sqrt[3]{27 } \\ y = 3`