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

1 answer

Let y and x be the variables representing the quantity and the independent variable, respectively. According to the given information, we can write the equation as:

y = k/x^2,

where k is a constant.

To find the value of k, we can use the given difference in values between y when x=6 and when x=10.

When x = 6, y = k/6^2 = k/36.

When x = 10, y = k/10^2 = k/100.

The difference between these two values is given as 16:

k/36 - k/100 = 16.

To solve this equation for k, we can find a common denominator:

(100k - 36k)/(36*100) = 16,

64k = 16 * 36 * 100,

k = (16 * 36 * 100)/64,

k = 9 * 9 * 100,

k = 8100.

Therefore, the law connecting x and y is:

y = 8100/x^2.