A bulldozer acquired at a cost of $$487,000$ has an estimated residual value of $$38,000,$ has an estimated useful life of $359,200$ hours and was operated for $57,500$ hours during the year. Determine $($a$)$ the depreciation cost, $($b$)$ the depreciation rate, and $($c$)$ the units$-$of$-$activity balance depreciation of the year