Explanation:
Based on the given information, we know that T varies directly as the square of U, which can be expressed as:
T ∝ U^2
We can also use the given values to form a proportionality constant k:
T = kU^2
To find the value of k, we can use the given values for T and U:
6 = k(3)^2
Simplifying this equation, we get:
6 = 9k
Dividing both sides by 9, we get:
k = 6/9 = 2/3
Now we can use this value of k to find T when U = 3:
T = (2/3)(3)^2 = 6
Therefore, the value of T when U = 3 is 6.