The expression 0.01E+0.003E^2 gives the thickness in millimeters (mm) of the insulation needed for a high voltage cable. E is the number of kilovolts carried by the cable. What thickness of insulation material is needed for 7 kilovolt cable?

To determine the thickness of the insulation, we need a function that would relate the thickness of the insulation to the kilovolt carried by the cable since it is the only value that is given here. From the problem statement, we are given the function which is T = 0.01E + 0.003E^2. To determine the thickness, we simply substitute the value of the kilovolt to the function and solve for the value of T. We do as follows:

T = 0.01E + 0.003E^2

T = 0.01 (7) + 0.003 (7) ^2

T = 0.217 mm

Therefore, the thickness of the insulation needed would be 0.217 mm.