Q$4)(30$ pts$.)$ The results of a standard compaction test are given in the table below:

$\backslash$table$[[$Test$,1,2,3,4,5,6,7],[$w$(\%),3,4\mathrm{.}45,5\mathrm{.}85,6\mathrm{.}95,8\mathrm{.}05,9\mathrm{.}46,9\mathrm{.}9],[(\backslash$gamma $\_($d$))/(\backslash$gamma $\_($w$)),1\mathrm{.}94,2\mathrm{.}01,2\mathrm{.}06,2\mathrm{.}09,2\mathrm{.}08,2\mathrm{.}06,2\mathrm{.}05]]$

Use ${}_w=10k\frac{N}{m^3}$

a$)$ Plot the compaction curve.

b$)$ Determine the maximum dry unit weight and the optimum moisture content

c$)$ Find the degree of saturation at the maximum dry density if $G_s=2\mathrm{.}70$