# 5.3 Joint Variation

5.3 Joint Variation

5.3a Representing a Joint Variation using the symbol ‘α’.
1. If one quantity is proportional to two or more other quantities, this relationship is known as joint variation.
2.y varies directly as x and z’ is written as y α xz.
3. y varies directly as x and inversely z’ is written as
4. y varies inversely as x and z’ is written as

Example 1:
State the relationship of each of the following variations using the symbol ‘α’.
(a) varies jointly as y and z.
(b)varies inversely as y and $\sqrt{z}.$
(c) varies directly as r3 and inversely as y.

Solution:

5.3b Solving Problems involving Joint Variation
1. If  , where k is a constant and n = 2, 3 and ½.

2. If , where k is a constant and n = 2, 3 and ½.

3. If , where k is a constant and n = 2, 3 and ½.

Example 2:
Given that $p\text{}\alpha \text{}\frac{1}{{q}^{2}\sqrt{r}}$ when = 4, q = 2 and r = 16, calculate the value of when p = 9 and q = 4.

Solution: