Theory question 102
VariationThe quantity y is partly constant and partly varies inversely as the square of x. (a) Write down the relationship between x and y. (b) When x = 1, y = 11 and when x = 2, y = 5, find the value of y when x = 4.
Show the model answer
Model answer
(a) y = k + a/x2, where k and a are constants
(b) x = 1, y = 11: k + a = 11
x = 2, y = 5: k + a/4 = 5, i.e. 4k + a = 20
Subtract: 3k = 9, k = 3, a = 8, so y = 3 + 8/x2
When x = 4: y = 3 + 8/16 = 3½
Explanation
'Partly constant and partly varies' means a sum of a constant and a varying part.