To model the relationship where y varies jointly with w and x and inversely with z, we can start with the concept of joint and inverse variation.
Since y varies jointly with w and x, we can express this part of the relationship as:
y = k * w * x
where k is the constant of proportionality.
Next, since y also varies inversely with z, we modify the equation to include this inverse relationship:
y = k * (w * x) / z
Now, we can use the given values to find the constant k. We know that when w = 8, x = 25, z = 5, and y = 360:
360 = k * (8 * 25) / 5
This simplifies to:
360 = k * (200) / 5
Further simplifying:
360 = k * 40
Now, solving for k:
k = 360 / 40 = 9
With k found, we can now write the complete equation:
y = 9 * (w * x) / z
This equation accurately models the relationship between y, w, x, and z based on the variations described.