There are 10 vehicles in a queue when an attendant opens a toll booth. Vehicles arrive at the booth at a rate of 4 per minute. The attendant opens the booth and improves the service rate over time following the function u(t) = 1.1 + .30t, where u(t) is in vehicles per minute and t is in minutes. I need to find the maximum queue length. I included my solution below for the total delay.

u(t) = 4 when t = (4-1.1)/0.3 = 9.67mins
(9.67 to t) ? (1.1+0.3t)dt = 10
? 1.1t + 0.15t2 ](9.67 to t)= 10
? t = 11.97mins
So, delay = 11.97 – 9.67 = 2.30mins

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

The higher the astm grain-size number, the coarser the grain is. a)-true b)-false

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk