A very long straight current-carrying wire produces a magnetic field of 20 mT at

A. 4d

Explanation:

Magnetic field strength is inversely proportional to distance. So in order to have a smaller magnetic field, we need to move further out from the wire. How far we go exactly can be determined from the formula: B=(μ₀I)/(2πr)

(That is derived from Ampere's Law, which states ∫B•dl=μ₀I)

With that you can set up a ratio between the magnetic fields in both cases. Because the current is the same for both instances, everything reduces out on one side of the equation and leaves you with something that relates the two distances by a ratio of each magnetic field value.

My work is in the attachment, comment for questions.

Given is:

The initial height of the candle is 9 inches.

And rate of burning is 0.5 inches per hour.

Part A:

The ordered pairs are: {(0,9),(1,8.5),(2,8),(3,7.5),(4,7),(5,6.5)}

Here we will subtract 0.5 each time, with increasing the time per hour as the rate of burning is 0.5 inches per hour.

Part B:

Yes, it is a function because each x value has its own y value.

Part C:

Yes, the relation would still be a function. The only difference is the time, the candle reduces its height 0.45 inches per each hour so ordered pairs will be :  (0,9)  (1,8.55) (2,8.1)  (3,7.65)