F. if a 2 x 6 (which means the actual dimensions of the board are 1.5 in. x 5.5 in.) milled from the same wood (and therefore has the same density) weighs 3.2 lb, how long is the board?

By definition, we have to

 W = V * Dw

 W: weight

 V: Volume

 D: Density

 Clearing and Substituting we have:

 V = W / Dw = (3.2 lb) / (0.021 (lb / in ^ 3)) = 152.38 in ^ 3

 Then, on the other hand, the volume is

 V = l * w * d

 l: long

 w: width

 d: depth

 Clearing and substituting

 l = V / (w * d) = (152.38 in ^ 3) / ((1.5 in) * (5.5 in)) = 18.5 in

 The answer is 18.5 in

where's the diagrams?

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.