Find an equation of variation where y varies directly as x and inversely as the square of w, and y=24 when x=8 and w=3.
To find an equation of variation where y varies directly as x and inversely as the square of w, we can express it in the form:
y = kx / w^2
Here, k is the constant of variation that we need to determine. We can find the value of k using the given information.
Given that y = 24 when x = 8 and w = 3, we can substitute these values into the equation and solve for k:
24 = k*8 / 3^2
To simplify the equation, square 3:
24 = k*8 / 9
Multiply both sides of the equation by 9:
216 = 8k
Divide both sides of the equation by 8:
k = 27
Now that we have determined the value of k, we can substitute it back into the equation:
y = 27x / w^2
Therefore, the equation of variation, where y varies directly as x and inversely as the square of w, is y = 27x / w^2.