A quantity y varies inversely as the square of X.The difference between the value of y when x=6 and when x=10 is 16.Find the law connecting x and y

Answer 1

Let y represent the quantity and x represent the variable. Since y varies inversely with the square of x, we can express this relationship as:

y = k/x^2

where k is a constant.

To find the value of k, we can use the given information that the difference between the value of y when x=6 and when x=10 is 16:

y(6) - y(10) = 16

Substituting the expression for y, we have:

k/6^2 - k/10^2 = 16
k/36 - k/100 = 16

Multiplying through by the common denominator of 3600:

100k - 36k = 16 * 3600
64k = 16 * 3600
k = (16 * 3600) / 64
k = 900

Therefore, the law connecting x and y is:

y = 900/x^2