Final answer:
The value of Z when W is 40 and Y is 9 is 1800, calculated by first finding the constant of proportionality from the given values and then using it to find the new value of Z.
Step-by-step explanation:
The student's question involves finding the value of a variable that varies jointly with two other variables. Joint variation means that when one variable (in this case, Z) is directly proportional to the product of the other two variables (in this case, W and Y).
We are given that Z = 450 when W = 6 and Y = 15. We can express this relationship algebraically as:
Z = k · W · Y
Where k is the constant of proportionality. To find k, we substitute the known values:
450 = k · 6 · 15
Next, we solve for k:
k = 450 / (6 · 15)
k = 5
Now that we have the constant of proportionality, we can find Z when W = 40 and Y = 9:
Z = 5 · 40 · 9
Z = 1800
Therefore, Z is 1800 when W is 40 and Y is 9.