Partial Variation

Partial Variation is expressed as the sum of two or more parts. In partial variation, the number of constants depends on the variables involved. 

The values of these constants can be obtained separately by solving simultaneous equations. Here are some examples of partial variation.  

(a) If x is partly constant and partly varies inversely as the square of y, then we can write:

x = a =  \( \frac{b}{y^2} \)

Where a and b are constants of proportionality 

(b) If y varies directly as x and partly directly as the square of x, then we can write:

y = ax + bx². 

Where a and b are constants of proportionality. 

Example 9.2.1:

If y varies partly directly as x and partly inversely as the square of x when x = 2, y = 10 and when x = 1, y = 5 

(a) find y in terms of x
(b) find y when x = 8 
(c) find x when y = 15 

Solution

(a)

If y varies partly directly as x and partly inversely as x², then