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
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
To find the law connecting x and y, we can start by using the inverse square relationship. The general formula for an inverse square relationship is:
y = k/x^2
where k is a constant. Given that the difference between y when x=6 and x=10 is 16, we can use this information to solve for k.
Let's first substitute the values of x=6 and x=10 into the equation:
y(6) = k/6^2
y(10) = k/10^2
Now we can use the given difference to set up an equation:
y(6) - y(10) = 16
(k/6^2) - (k/10^2) = 16
(k/36) - (k/100) = 16
To solve for k, we can find a common denominator:
[(k * 100) - (k * 36)] / (36 * 100) = 16
(100k - 36k) / 3600 = 16
64k / 3600 = 16
Now we can solve for k:
64k = 16 * 3600
64k = 57600
k = 900
Therefore, the law connecting x and y is:
y = 900/x^2