(10 pts) Follow the steps to solve the IVP: x ′′ − x ′ − 6x = (t − 3) cos(πt) , x(0) = 1, x ′ (0) = 3. a. Find the Laplace transform, ℒ{x(t)}, of the solution. Do not perform partial fraction decomposition yet. b. Solve for the solution, x(t), using the inverse Laplace transform. Use h(t − c) for the Heaviside function.

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.

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

Agas mixture consists of 8 kmol of h2 and 2 kmol of n2. determine the mass of each gas and the apparent gas constant of the mixture.