Consider a flat ceiling that is built around $38-mm90-mm$ wood studs with a center$-$to$-$center distance of $400mm.$ The lower part of the ceiling is finished with $13-$mm gypsum wallboard, while the upper part consists of a wood subfloor $)=(0\mathrm{.}166m^2*\frac{C}{W},$ a $13-$mm plywood, a layer of felt $)=(0\mathrm{.}011m^2*\frac{C}{W},$ and linoleum W$).$ Both sides of the ceiling are exposed to still air. The air space constitutes $82$ percent of the heat transmission area, while the studs and headers constitute $18$ percent. Determine the winter R$-$value and the U$-$factor of the ceiling assuming the $90-$mm$-$wide air space between the studs. Extra needed information can be found in Table $3-8$ below.

TABLE $3-8$

$($below i provided R values$)$

outside surface still air: R$=0\mathrm{.}030$ m$2\backslash$deg C$/$W

linoleum: R$=0\mathrm{.}009$ m$2\backslash$deg C$/$W

plywood: R$=0\mathrm{.}11$ m$2\backslash$deg C$/$W

wood subfloor: R$=0\mathrm{.}166$ m$2\backslash$deg C$/$W

plane air space: R$=0\mathrm{.}16$ m$2\backslash$deg C$/$W

gypsum: R$=0\mathrm{.}079$ m$2\backslash$deg C$/$W

inside surface still air: R$=0\mathrm{.}12$ m$2\backslash$deg C$/$W