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 y α x z .
4. y varies inversely as x and z’ is written as y α 1 x z .

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 z .  
(c) varies directly as r3 and inversely as y.

Solution:
( a ) x α y z ( b ) x α 1 y z ( c ) x α r 3 y


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

2. If y α 1 x n z n , then y = 1 k x n z n , where k is a constant and n = 2, 3 and ½.

3. If y α x n z n , then y = k x n z n , where k is a constant and n = 2, 3 and ½.

Example 2:
Given that p α 1 q 2 r when = 4, q = 2 and r = 16, calculate the value of when p = 9 and q = 4.

Solution:
Given that p α 1 q 2 r , p = k q 2 r When p = 4 , q = 2 and r = 16 , 4 = k 2 2 16 4 = k 16 k = 64 p = 64 q 2 r When p = 9 and q = 4 , 9 = 64 4 2 r 9 = 4 r r = 4 9 r = ( 4 9 ) 2 = 16 81

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