Determine the quality (if saturated) or temperature (if superheated) of the following: (show details of your answer, not just write the final answer)

a) Water at p=50 kPa, v=1 m3/kg

b) Water at p=1.6 MPa, v=0.15 m3/kg

c) Water at p=7 MPa, h=3160 kJ/kg

d) Refrigerant R-134a at p=200 kPa, v=0.009 m3/kg

e) Refrigerant R-134a at p=0.2 MPa, v=0.12 m3/kg

Annotate these equations

v=d/t a=∆v/t average speed =total distance/total time v=v0+at d=v0t+1/2at² Fnet=ma w=mg ac=v²/r Fc=mv²/r W=Fd   P=W/t   

EK=1/2mv² W= ∆EK   Es=1/2kx² Eg=mgh TC=5/9(TF−32) TF=9/5TC+ 32 TK=TC+ 273 Q=mc∆t Q=±mL

Which of the following are true?

(1) The sum of two invertible matrices is invertible

(2) The determinant of the sum is the sum of the determinants

(3) The determinant of the inverse is the reciprocal of the determinant

(4) An nxn matrix is invertible if and only if its determinant is zero

(5) The product of two invertible matrices is invertible (so long as the product is defined)

(6) If A is a diagonal 3x3 matrix [a,0,0;0,b,0;0,0,c] then its determinant is the product of its diagonal entries

(7) The union of two subspaces is a subspace

(8) The intersection of two subspaces is a subspace

(9) The set of solutions [x,y,z,u,v] to the equations 3x + 4y + 5z + u + 3v = 12 and 4x + y + z + u - v = 13 form a vector space

(10) If V is a vector space of polynomials and p and q are in V then the product pq is also in V

(11) If V is a subspace of R^3 and w is a vector in v then whenever the dot product w dot u = 0, u must also be in the subspace V

(matrices are written as e.g. [a,b,c; d,e,f; g,h,i; j,k,l] to mean the matrix whose first row is [a,b,c], whose second row is [d,e,f] whose third row is [g,h,i] and whose fourth row is [j,k,l].)

MATLAB question!

4. (a) Modify the code, to compute and plot the quantity E = 1/2mv^2 + 1/2ky^2 as a function of time. What do you observe? Is the energy conserved in this case?

(b) Show analytically that dE/dt < 0 for c > 0 while dE/dt > 0 for c < 0.

(c) Modify the code to plot v vs y (phase plot). Comment on the behavior of the curve in the context of the motion of the spring. Does the graph ever get close to the origin? Why or why not?

given code
---------------------------------------------------------------

clear all;   
m = 4; % mass [kg]
k = 9; % spring constant [N/m]
c = 4; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 =-0.8; v0 = 0.3; % initial conditions
[t,Y] = ode45(@f,[0,15],[y0,v0],[],omega0, p); % solve for 0<t<15
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'ro-',t,v,'b+-');% time series for y and v
grid on; axis tight;
%---------------------------------------------------
function dYdt = f(t,Y,omega0,p); % function defining the DE
y = Y(1); v = Y(2);
dYdt=[ v ; -omega0^2*y-2*p*v]; % fill-in dv/dt
end

-----------------------------------------------------------------------------------------

In a survey of 100 NAU students, the following information was obtained:

               45 students had taken an accounting class

               40 students had taken an economics class

               29 students had taken a marketing class

               15 students had taken both accounting and economics classes

               14 students had taken both economics and marketing classes

               22 students had taken both accounting and marketing classes

               12 students had taken all three classes

1. How many students took accounting and marketing classes, but not an economics class?

2. How many students did not take any of the classes?

3. What is the probability that a randomly chosen student took all three classes?

1. Given a function φ(z) with z = x+iy let

   U(x, y) = ½ [φ(x+iy) + φ(x-iy)] and V(x, y) = i/2 [φ(x+iy) –φ(x-iy)]

A) For φ(z) = z² find U and V and their induced vector fields E =▼U and

F =▼V also show that ▼²U = ▼²V = 0

B) Repeat for f(z) = z³

C) For f(z) = ln z we get U(x, y) = ½ ln (x²+y²) and V(x, y) = arctan (y/x) Find ▼U (electrostatic field) and ▼V (magnetic field) . Also, show that ▼²U = ▼²V = 0 for x²+y² ǂ 0.

a 2d collision

Perform a linear fit, of the form x = A*t + B, to each graph and determine the initial velocity v1 and the final velocities v′1x, v′1y, v′2x, and v′2y. How do I find the v′1y

if: time (sec)= 0.400, 0.460, 0.500, 0.530, 0.560, 0.600, 0.630, 0.670, 0.700, 0.730, 0.700,0.800, 0.830, 0.867, 0.900

position (m) in y dxn= 85, 100, 120, 140, 160, 180, 190, 210, 230, 240, 260, 270, 290, 300, 320

position (m) in x dxn= 800, 850, 920, 980, 1000, 1080, 1140, 1190, 1230, 1280, 1300, 1400, 1440, 1490, 1500

a) Calculate the cell potential at 25°C for the cell

Fe(s) I (Fe²⁺ (0.100 M) II Pd²⁺ (1.0 × 10^-5 M) I Pd(s)

given that the standard reduction potential for Fe²⁺/Fe is -0.45 V and for Pd²⁺/Pd is +0.95 V. - Please show the steps

QUESTION 11

1. A sample of 5000 college students were asked if they support the legalization of marijuana and if they support the legalization of abortion (results are presented below). Using StatCrunch (you don't need to open a dataset from the textbook), calculate the confidence interval for percentage of people more likely to support legalizing marijuana than legalizing abortion. List the lower confidence interval below ____________- round to 2 decimal places.

   	Support the Legalization of Abortion
   Support the Legalization of Marijuana	Yes	No	Totals
   Yes	2000	2000	4000
   No	200	800	1000
   Totals	2200	2800	5000

1. List the upper confidence interval from question _______ - round to 2 decimal places.

2. Now perform a hypothesis test on the data presented in question 11. You are testing the null hypothesis that there is no difference in the proportion of those that believe in legalizing marijuana and the proportion of those that believe in legalizing abortion. Your alpha or p-level is set at .05. List the z statistic below - round to 2 decimal places.____________

What is the p-value in the test you just ran? _________ Round to 2 decimal places.

Assuming that the p-level or alpha level was set at .05, based on the p-value you calculated, would you reject or fail to reject the null hypothesis that there is no difference in the proportion of people who support the legalization of marijuana and the proportion that support the legalization of abortion?

QUESTION 13

1. Implement in Python and test the classes shown in the UML below. The LibraryItem class shown in the UML, represents an item that the library issues to students. The partial Python code is provided and It has the following attributes. Test the program by creating a list of books and a list of DVDs and printing the details of each element in the list.

   Attribute	Description
   ID	The ID of the item.
   createdate	The date the item was created as dd/mm/yyyy
   title	The title of the item.

   class LibraryItem:
       def __init__(self,ID="",year=0,title=""):
           self.ID=ID
           self.year=year
           self.title=title
   
       def getLoanPeriod(self):
           return 0
   

   A) Implement the Book class. It inherits from LibraryItem. Furthermore, it has this additional attribute

   Attribute	Description
   author	The author of the book
   Electronic	This tells whether the book is available as an electronic book (e book)

   Implement the getLoanPeriod function in this way:

   - If the book was written before the year 2000, the loan period will be 14 days.

   - If the book was written after or in 2000, the loan period will be 7 days.

   B) Implement the DVD class. It inherits from LibraryItem. Furthermore, it has this additional attribute

   Attribute	Description
   length	The length of the DVD. Example: “2 hours: 30 minutes”
   HD	Whether the DVD is available in HD (High Definition) or not

   Implement the getLoanPeriod function in this way:

   - If the DVD is available in HD format, the loan period will be 3 days. Otherwise, the loan period will be 7 days.