$3\mathrm{.}1$ For a given soil, show that,

a$.{}_{\text{s}\text{a}\text{t}}={}_d+(\frac{e}{1+e}){}_w$

b$.{}_d=\frac{eS{}_w}{(1+e)w}$

c$.e=\frac{{}_{\text{s}\text{a}\text{t}}-{}_d}{{}_d-{}_{\text{s}\text{a}\text{t}}+{}_w}$

d$.w_{\text{s}\text{a}\text{t}}=\frac{n{}_w}{{}_{\text{s}\text{a}\text{t}}-n{}_w}$