During a rainfall, the depth of water in a rain gauge increases at a rate modeled by R (t) = 0.5 + t cos(pi*t^3/ 80) where t is the time in hours since the start of the rainfall and R (t) is measured in centimeters per hour. How much did the depth of water in the rain gauge increase from t = 0 to t = 3 hours?
A student writes four different expression for the displacement y in a period motion y = a sin”(2 pi r)/(T)y = a sin vty = (a)/(t) sin”(t)/(a)y = (a )/(sqrt(2))[sin'(2 pi r)/(T)+ cos ‘(2 pi r)/(T)]where a is maximum displacement , x is the speed and T is the time period then dimensionally.