The Lucas Numbers are a sequence very similar to the Fibonacci Sequence discussed in class, the only difference being that the Lucas Numbers start with L0=2L0=2 and L1=1L1=1 as opposed to Fibonacci’s F0=0F0=0 and F1=1F1=1. Concretely, they are defined byL0=2,L1=1 and Ln:=Ln−1+Ln−2 for n>1L0=2,L1=1 and Ln:=Ln−1+Ln−2 for n>1Write a Python function called first_D_digit_Lucas that takes an integer argument D less than 30 and returns the first D-digit Lucas number.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Manometers are good examples of measuring instruments, nowadays they are not as common as before. a)-capacitive probe gauges b)-gravitational gauges deformation ) gauges d)-digital gauges

A)-in the process of engineering design, explain the contribution of material selection. b)- explain the procedure of synthesis as is employed in engineering design. c)- is there any relationship between ergonomics and engineering design? explain. d)- safety consideration in engineering design includes human, product and the enviroment . explain how safety will be incorporated into the design?