A grain silo is supported on a $20\mathrm{.}0$ by $50\mathrm{.}0$ m mat foundation. The total weight of the silo and the mat is $180,000$ kN$.$ Using Boussinesq$$s method, compute the induced vertical stress, $\backslash$Delta $\backslash$sigma z$,$ in the soil at a point $15\mathrm{.}0$ m below the center of the mat. First use the full analytical solution given by Equations $9\mathrm{.}34$ and $9\mathrm{.}35.$ Repeat the computation using the approximate method given by Equation $9\mathrm{.}41.$ Finally, repeat the computation using the figure below. Compare the results from these three methods and comment on whether the differences are significant.

Please verify if my numbers are correct $116$ kPa, $109\mathrm{.}8$kPa, and $117\mathrm{.}36$ kPa