Final answer:
To find y when y varies jointly with x and z, first solve for the constant of variation using the given values. The constant k is determined to be 3, and then it's used to calculate y when x = 10 and z = 9, which is found to be 270.
Step-by-step explanation:
If y varies jointly with the product of x and z, we can express this relationship with the equation y = kxz, where k is the constant of variation. Given that y = 105 when x = 7 and z = 5, we can first solve for k:
105 = k × 7 × 5k = 105 / (7 × 5)k = 3
Now that we have the value of k, we can find y when x = 10 and z = 9:
y = 3 × 10 × 9y = 270
Therefore, when x = 10 and z = 9, the value of y is 270.