A (12+2*y)-tooth 20 pressure angle spur pinion rotates at (2000-10*z) rev/min and transmits 6 hp to a 60-tooth disk gear. The diametral pitch is 16 teeth/in, the face width is 3 in, and the quality standard is No. (3 + x). The gears are straddle-mounted with bearings immediately adjacent. The pinion is a grade 1 steel with a hardness of (200 + z) Brinell tooth surface and through-hardened core. The gear is steel, through-hardened also, grade 1 material, with a Brinell hardness of 200, tooth surface and core. The loading is smooth because of motor and load. Assume a pinion life of 108 cycles and a reliability of 0.999. The tooth profile is uncrowned. This is a commercial enclosed gear unit. (a) Find the factor of safety of the pinion against failure due to bending. (b) Find the factor of safety of the pinion against failure due to wear (contact) (c) By examining the factors of safety, determine the critical failure mode for the pinion. In your spreadsheet/program, do not use x, y and z as the input parameters. Instead use the actual term as the input parameter. For example, the spreadsheet/program should require the user to input N as the number of teeth for the pinion, instead of y in (12 + 2*y).