Code key: 1=a, 2=b, 3=c, 4=d, 5=e, 6=f, 7=g, 8=h,
9=1, 10=), 11=k, 12=l, 13=m, 14=n, 15=0, 16=p, 17=q,
18=r, 19=s, 20=t, 21=u, 22=v, 23=w, 24=x, 25=y, 26=z
use the code key to break the code of this nine-letter
word: 5 19 16 9 15 14 175
abc

Step-by-step explanation:

5 = E

19 = S

16 = P

9 = I

15 = O

14 = N

1 = A

7 = G

5 = E

ur word is espionage

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.