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.
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
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