z varies inversely with the product of x and y. When x = 2 and y = 4, z = 0.5
What is the value of z when x = 4 and y = 9?
Since z varies inversely with the product of x and y, we can set up the equation z = k/(xy), where k is the constant of variation.
To find the value of k, we can substitute the given values of x, y, and z into the equation:
0.5 = k/(2*4)
0.5 = k/8
Next, we can solve for k by multiplying both sides of the equation by 8:
4 = k
Now that we have the value of k, we can substitute it into the equation and solve for z when x = 4 and y = 9:
z = 4/(4*9)
z = 4/36
z = 1/9
Therefore, when x = 4 and y = 9, z = 1/9.