The factorial of an integer ? is defined using the following equation: ?! = ? ∗ (? − 1) ∗ (? − 2) ∗ … ∗ 2 ∗ 1 In combinatorics, permutations is the number of ways of selecting a subset of some elements such that the order matters. For example, there are 6 permutations of letters A, B, and C. A B C ,A C B, B A C, B C A, C A B, C B A, The permutation of selecting ? elements from a set of ? elements can be calculated using the following equation: ?(?, ?) = ?! (? − ?)! On the other hand, combinations is the number of ways of selecting a subset of some elements such that the order does not matter. The combination of selecting elements from a set of m elements can be calculated using the following equation: ?(?, ?) = ( ? ? ) = ?! ?! (? − ?)! Instructions Add a section / cell in your MATLAB m-file script for problem 3 that: • Prompts the user to enter integer ? between 2 and 12 (inclusive) o If the input is invalid, displays an error message and prompt the user to try again, as many times as necessary (use a loop to accomplish this instead of terminating the program) • Prompts the user to enter integer ? between 2 and ? (inclusive) o If the input is invalid, displays an error message and prompt the user to try again, as many times as necessary (use a loop to accomplish this instead of terminating the program) • Determines and displays the following: o ?! o ?(?, ?) o ?(?, ?) This program must use loops to calculate the results – DO NOT use any pre-defined MATLAB functions related to factorials, permutations, and/or combinations.

In: Mechanical Engineering

Five common welding methods are: oxy-acetylene gas welding; tungsten-inert-gas (“TIG”) welding; metal-inert-gas (“MIG”) welding; resistance spot welding; and laser welding. Of these five methods, which are applicable to carbon steels and which to wrought aluminum alloys? Discuss.

In: Mechanical Engineering

At steady state, air at 200 kPa, 330 K, and mass flow rate of
0.5 kg/s enters an insulated duct having differing inlet and exit
cross-sectional areas. The inlet cross-sectional area is 6
cm^{2}. At the duct exit, the pressure of the air is 100
kPa and the velocity is 250 m/s.

Neglecting potential energy effects and modeling air as an ideal
gas with constant *c*_{p} = 1.008 kJ/kg · K,
determine:

(a) the velocity of the air at the inlet, in m/s.

(b) the temperature of the air at the exit, in K.

(c) the exit cross-sectional area, in cm^{2}.

In: Mechanical Engineering

If you are operating at 1000 knots and altitudes of 60,000 feet, what type of propulsion system should you use?

In: Mechanical Engineering

The velocity profile for a steady laminar flow in a circular
pipe of radius *R* is given by
*u*=*u*0(1−*r*2*R*2) . If the fluid
density varies with radial distance *r* from the centerline
as *ρ*=*ρ*0(1+*r**R*)14 , where
*ρ*_{0} is the fluid density at the pipe center,
obtain and choose the correct relation for the bulk fluid density
in the tube.

In: Mechanical Engineering

A) What is the specific internal energy of water at 50 kPa and 190°C? Use data from the steam tables. The specific internal energy of water is ___ kJ/kg.

B) What is the specific volume of R-134a at 20°C and 730 kPa? What is the internal energy at that state? Use data from the steam tables.

The specific volume is ___m3/kg.

The internal energy is ___kJ/kg.

In: Mechanical Engineering

for loop practice – Taylor Series!The moment you finish implementing the trigonometric functions, you realize that you have forgotten your favorite function: the exponential! The Taylor Series for the exponential function is 푒푥=1+푥1!+푥22!+푥33!+...,‒∞<푥<∞a) Using a for loop, compute and display the error of the Taylor series when using 12 and 15 terms, each as compared to the exponential function when evaluated at x = 2. b) Can you figure out how to compute and display the number of terms necessary for this function to have an error within your allowed range of 0.001 when evaluated at x = 3. Display this error. For MATLAB

In: Mechanical Engineering

A 9-cm-diameter vertical water jet is injected upward by a nozzle at a speed of 15 m/s. Determine the maximum weight of a flat plate that can be supported by this water jet at a height of 2 m from the nozzle. Take the density of water to be 1000 kg/m3. The maximum weight of a flat plate that can be supported by the water jet is ____ N

In: Mechanical Engineering

(a) Briefly describe the usefulness of the knowledge of Mechanical Vibration in the industries by discussing at least two examples with regards to effects of machinery vibrations and reduction/control.

(b) Briefly explain the following terms: i. Modal analysis ii. Modal parameters

(c) Briefly explain resonance.

(d) Briefly explain how measurement and monitoring of machine vibration can be used for preventive maintenance.

in short pls

In: Mechanical Engineering

What is the minimum distance between two trains? like
regulations on Federal railroad association..

For example if 1 train left the station, when can the next train
depart? like is there regulation for the distance?

If you find it.. can u cite it too?

In: Mechanical Engineering

Determine which of the following polymers are the result of
*polymerization*, and which are the result of
*post-polymerization processing*. Explain!

1. low density polyethylene

2. high density polyethylene

3. phenol-formaldehyde

4. heavily cross-linked polyisoprene (glass trans. temp: 50C)

5. lightly cross-linked polyisoprene (glass trans. temp: -60C)

In: Mechanical Engineering

when it is 2 pm. Mountain standard time on februvary 3 in north platte (longitude=101,latitude=41) what is solar time

In: Mechanical Engineering

An air-standard dual cycle has a compression ratio of 8.6 and displacement of Vd = 2.2 L. At the beginning of compression, p1 = 95 kPa, and T1 = 290 K. The heat addition is 4.5 kJ, with one quarter added at constant volume and the rest added at constant pressure. Determine: a) each of the unknown temperatures at the various states, in K. b) the net work of the cycle, in kJ. c) the power developed at 3000 cycles per minute, in kW. d) the thermal efficiency. e) the mean effective pressure, in kPa.

In: Mechanical Engineering

The displacement volume of an internal combustion engine is 2.22 liters. The processes within each cylinder of the engine are modeled as an air-standard Diesel cycle with a cutoff ratio of 2.5. The state of the air at the beginning of compression is fixed by p1 = 1.6 bar, T1 = 325 K and V1 = 2.36 liters. If the cycle is executed 2100 times per min, determine: a) the compression ratio, b) the net work per cycle, in kJ, c) the maximum temperature, in K, d) the power developed by the engine, in kW, e) and the thermal efficiency.

In: Mechanical Engineering

Derive the reduced stiffness matrix Qxy relating stress_xy to strain_xy

Derive the reduced compliance matrix relating strain_xy to stress_xy

Determine the Ex, Ey, nu_xy, Gxy, in the reference frame (x and y) as a function of angle 0 and 45 degrees for a unidirectional lamina having the properties

What are your observations of the values increasing or decreasing with respect to the 0 degree lamina when the lamina is rotated to 45 degrees.

E_{1}=181 GPa; E_{2}=10.3 GPa;
u_{12}=0.28; G_{12}=7.17 GPa

please explain in detail. thanks!

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