5.1 Direct Variation (Sample Questions)

Posted on April 24, 2020 by user

Example:

Given that p varies directly as square root of q and p = 12 when q = 36, find

(a) The value of p when q = 16

(b) The value of q when p = 18

Solution:

$\begin{array}{l} p \propto \sqrt{q}, p = k \sqrt{q} \\ 12 = k \sqrt{36} \end{array}$
12 = k(6)

k = 2

$p = 2 \sqrt{q}$

(a)

$\begin{array}{l} p = 2 \sqrt{q} \\ p = 2 \sqrt{16} \end{array}$

p = 8

(b)

$\begin{array}{l} p = 2 \sqrt{q} \\ 18 = 2 \sqrt{q} \to 9 = \sqrt{q} \end{array}$

9² = q
q = 81