Question

Y varies directly as x and inversely as the square of z. y equals 16 when x equals 18 and z equals 3 . Find y when x equals 2 and z equals 8 .

Answer 1

In this problem, we are given a direct and inverse variation relationship between y, x, and z. We can solve for the constant of variation using the given values, and then use it to find the value of y for different x and z values.

Step-by-step explanation:

In this problem, we are given that y varies directly as x and inversely as the square of z. This means that the relationship between y, x, and z can be represented by the equation: y = k * (x/z^2), where k is a constant of variation.

We are also given that when x = 18 and z = 3, y = 16. Using this information, we can substitute the values into the equation and solve for the constant k:

16 = k * (18/3^2)

Now, we can solve for k: k = 16 * (3^2/18) = 8.

Finally, we can use the value of k to find y when x = 2 and z = 8:

y = 8 * (2/8^2) = 8 * (2/64) = 1/4 = 0.25.

Learn more about Direct and Inverse Variation