An enzyme is found that catalyzes the reaction x ⇌ y. researchers find that the km for the substrate x is 4 μm, and the kcat is 20 min−1.

(a) in an experiment, [x] = 6 mm, and v0 = 480 nm min−1. what was the [et] used in the experiment?

(b) in another experiment, [et] = 0.5 μm, and the measured v0 = 5 μm min−1. what was the [x] used in the experiment?

(c) the compound z is found to be a very strong competitive inhibitor of the enzyme, with an α of 10. in an experiment with the same [et] as in (a), but a different [x], an amount of z is added that reduces v0 to 240 nm min−1. what is the [x] in this experiment?

(d) based on the kinetic parameters given above, has this enzyme evolved to achieve catalytic perfection? explain your answer briefly, using the kinetic parameter(s) that define catalytic perfection.