axis symmetry, graph max or min value, domain, range and all intervals where function increases or decreases. f(x)=5(x-3)^2+6 f(x)=-7(x-8)^2+1 f(x)=-6(x+4)^-8 f(x)=2(x+2)^2+9

Topic: Introduction to Convolution

Software used : Matlab

Course : Signal and Systems Lab

1.

a) Make the flowchart or pseudo code for convolution.

b) Implement convolution in MATLAB.

   Hint: Make a function using the format: function result = myconv (a,b)

            Where a and b are input matrix and result is convolution answer.

c) Compare it with conv command.

2. Let input signal x be [1, 3, –2, 4, -1] and the system h be [-2, 3, 4, –3, 6]. Find the output of the system y using the conv command.

3. Now suppose we add another system j = [3, –1, 2, 4, 1] in series with the above system. Now find the overall response and output y of the above system using the conv command. Hint: The systems h and j should be convolved first and then the resultant should be convolved with x to get the overall response.

4. Again suppose now j is attached in parallel to h. Now find the impulse response y for the system.

5. Now suppose the two systems h and j are again in series and a third system k = [2, 3, 4, 5, 6] has also been attached with them in parallel. Find the impulse response of the overall system and hence the output y. Hint: You will have to make sure that the size of the system k be made equal to the resultant of the size of the system obtained by convolving the systems h and k that are attached in series.

Up until now we have supposed that all signals starting point is same say 0. Now suppose the system h starting point is –2, that of system j is 0 and that of system k is 3. Now handle this situation carefully and get the overall impulse response of the system and hence the output y. Also please draw stem plot of each of system including the input x, systems, h, j, k, the overall response and finally the output y.

6. Write a program without using conv command and for loop to convolve two arbitrary length signals. (Hint: Use toeplitz command)  

Jeff is a sports fan. He has a wish list to see a 1. baseball, 2. basketball, and 3. football game this year. Two of his friends independently deicde to buy him tickets to one event. John has a probability of selecting tickets to 1,2, and 3 with a probability 1/5, 2/5, and 2/5. Jason has a probability of selecting tickets to 1, 2, and 3, respectively with probability 4/7, 1/7, 2/7, respectively. What is the probability John and Jason give Jeff a ticket to a different type of sporting event? Given the tickets are to different sporting events, what is the probability the event is baseball?

Write a C++ program where class 1 and class 2 (which is a base class) should have a derived class (class 4 and class 5). Each of the derived classes should include at least 1 variable, 2 functions (one will be showing the function overriding case, the second one will be showing the function overloading case), 2 constructors (with default values, with parameters).

Then class 3 (composition) (to relate class 1 and class 2) should include 3 variables (first variable is an object belongs to class 1, second variable is an object belongs to class 2,third variable is class 3 own variable), 3 functions.

1. A typical α-decay from a parent nucleus ^A_ZX may be indicated as :

Group of answer choices

^A_ZX → ^(A−4)_{(Z − 2)} Y + ⁴₂He

^A_ZX → ^(A+4)_(Z+2) Y + ²₂He

^A_ZX → ^(A−4)_Z Y + ⁴₂He

^A_ZX → ^(A−4)_(Z+2) Y + ⁴₂He

2. An element of atomic number 83 in a relatively higher energy state decays radioactively to an element of atomic number 84 with lower energy level. This must include

Group of answer choices

an α emission

a β emission

a γ emission

a β & γ emission

3. The half- life of radium-226 is 1.6 × 10³ . If a sample initially contains 3.0 × 10¹⁶ such nuclei, what is the number of radioactive radium-226 nuclei remaining after 4.8 × 10³ years?

Group of answer choices

2.25 × 10¹²

3.75 × 10¹⁶

2.2 × 10¹⁶

3.75 × 10¹⁵

Hi, I don't think my program is calcualting right at all. When I used a text editor to check the # of batches, for 20, it returned 0, but the program is calculated 543 and 1 batch. On 21, there are 29 batches, but the program calculates 28 batches for Chocolate Type #21. I'd like to make sure it calculates everything correctly before I turn it in on Monday.

Here is my program:

#include <iostream>
#include <fstream>
#include <iomanip>

using namespace std;

ifstream infile;
ofstream outfile;

//Maximum number of Chocolate Types
const int ARRAY_SIZE = 25;

int printReport(int ChocTypeArray[], int ChocPiecesArray[])
{
//Opens output file
outfile.open("ChocolateCo_Production_Results.txt");

//Print Title
outfile << "======================================================================================================" << endl;
outfile << "================================ O-So-Good Chocolate Company Report ==================================" << endl;
outfile << "======================================================================================================" << endl;

//Print Header
outfile << "Chocolate Type" << setw(42) << " Pieces" << setw(20) << "Batches" << setw(20) << "Average/Batch" << endl;
outfile << "======================================================================================================" << endl;
for (int count = 0; count < ARRAY_SIZE; count++)
{
  float avg = 0;
  if (ChocTypeArray[count] > 0)
  {
   avg = (float)ChocTypeArray[count] / (float)ChocPiecesArray[count];
  }
  
  outfile << count + 1 << "\t\t\t\t" << right << setw(24) << ChocTypeArray[count] << right << setw(20) << ChocPiecesArray[count] << right << setw(20) << avg << endl;
}

// Closes outout file
outfile.close();

return 0;
}

int main()
{
int ChocTypeArray[ARRAY_SIZE];
int ChocPiecesArray[ARRAY_SIZE];

//Initialize arrays
for (int count = 0; count < ARRAY_SIZE; count++)
{
  ChocTypeArray[count] = 0;
  ChocPiecesArray[count] = 0;
}

//Try to find data file
infile.open("Chocolates.txt");
if (!infile)
{
  cout << "Failed to open Chocolates.txt. Make sure it is in the same directory as the program." << endl;
  return -1;
}

//Read data until the end of file
int _chocType, _chocPieces;
while (!infile.eof())
{
  infile >> _chocType >> _chocPieces;

  // Validates if chocType is between 1 and 25
  if (_chocType < 1 || _chocType > ARRAY_SIZE)
  {
   continue; //skip
  }
  else
  {
   //Adjust for array index
   _chocType--;
   //Add the pieces to their appropriate type
   ChocTypeArray[_chocType] = ChocTypeArray[_chocType] + _chocPieces;
   ChocPiecesArray[_chocType]++;
  }
}

//Print the report
printReport(ChocTypeArray, ChocPiecesArray);

return 0;
}

Here is the data from Chocolates.txt:

      12     1026
      15      248
       7      402
      10     1076
      16      948
      14     1174
       6     1137
       8      719
       9      952
      14     1516
       9      830
      14      296
      19      596
      15      874
      23      100
      15     1063
      16      867
       6       87
      11     1330
       1      217
      18      802
      15      943
      15      165
      23      100
       2      866
      21      656
      18      885
       7     1221
       9     1032
      22      490
       9     1328
      12      584
      11      561
      14     1355
      22      750
      12      800
       9      686
      19      401
      11     1121
      16      389
       3      664
       8      676
      12      692
       1      844
       1      994
       1      847
      24     1173
       7      792
       8     1076
      19      613
      14     1085
       3     1107
      12      891
       3     1121
       6      870
      16      300
      16     1092
      24      969
      12      515
       6      403
      11      885
       7      839
      14      328
       1     1023
       7      653
       6      276
      11      217
       3     1288
       6     1109
      23      643
      23      384
       7     1213
       6      556
       4     1224
       9     1271
      15     1167
       8      595
       6      746
       1     1284
      18     1300
      14      747
       5      650
       4      934
       9      952
      16     1408
      24     1012
      12      696
      14      333
      14      478
       5      434
       1      548
       6      285
       9      341
      23      925
       3      150
      11     1166
       5      963
       8     1010
      11     1272
       1      587
      21      866
      12      152
      11     1280
       2      821
       4      778
      19     1087
      15      690
      11     1239
       6     1267
       4      361
      12      704
       3      560
      16     1231
      21     1198
       6      697
       3      696
       6      632
      16     1543
      10      211
       2      285
      10      845
      24      554
      16     1105
       6     1048
       4     1050
      16      552
       3     1077
      19     1333
      19      669
       8     1172
      21     1217
       2      826
      18      995
       7     1140
       5     1084
       7     1016
      21      624
       3      654
       5      990
       9     1115
      23      991
       3      324
       8      959
      16     1483
      16     1036
       9      694
       4      817
      24      247
       6      477
      12     1307
      10      596
      19     1008
       1      843
      12     1166
      24      693
       3      397
      16     1000
      19      368
       9     1101
      11     1270
      15      172
       8      839
      12      760
       6     1099
      16     1119
       1      673
      10      742
       2      858
      11     1015
       8      771
      10      537
      11      475
       6      857
       1      932
      14      728
      11      914
      10      652
      19      436
       2      415
      23      724
      10      974
       2      874
      18      365
      14     1158
       1      986
       7      283
      21      870
      10      708
       2      546
       7      919
      15      429
       9      607
      19      591
      16      938
       2      662
       6     1044
       3      549
       5     1012
      19     1003
       3      654
      18     1436
       1      738
      14      695
      14      655
      10      266
      11      510
       6     1265
       7      603
      24      687
      23     1014
       9      557
       1      677
      16     1177
      24      712
       9     1275
      14     1188
      16      311
      19      581
      23      237
      21     1228
      23      717
      24      729
      10      511
       7      584
      23     1043
      21      941
      23      100
       2      966
      23      492
       5     1312
       1      968
      18      699
       2      249
      24     1062
      18     1015
       2      924
      16      952
      14      591
       4      899
       5      692
      11     1435
       7      760
       2      852
      15      964
      21      921
       7     1131
       4      919
       6      870
       4      778
       2     1507
      14      213
      23      713
      23      861
       1      595
       4      623
       7      794
       7      880
      23     1371
       9      455
      19     1217
      16      187
       6     1219
      10     1135
      24      365
      18      906
      14      576
      23      700
      19      444
      10       11
       3      817
      19     1394
      10      948
       7      666
      24      883
       6     1447
       7      385
       1      976
       9     1037
      14      373
       2      526
      19     1148
      16     1185
      24     1338
      11      854
       5     1004
      15     1212
       8      281
      24     1316
       6       15
      18     1224
      19      654
      14      483
       4     1428
       8      769
      19      473
      14     1185
      12      691
       5     1252
       1      425
       6      459
      18     1036
      15      713
       6      840
       9      545
      12      515
       4      599
       1      619
       6     1162
       9      561
       5     1105
      24      453
      15      456
      24      644
      15      324
      18      808
      12      860
      23      307
      18      552
      18      568
       8      256
      16     1458
      23      562
      19      660
      19      983
       9      970
       7     1154
      21      594
       9      590
      15      174
       3     1048
       9     1079
       3      536
      11     1301
      16      508
       1      810
      21      647
      10      802
      11       50
      24      921
      18      195
       4      273
       5      564
      11      314
      21      710
       7      267
      15      224
      18      215
       9      975
       9      328
       9      475
      23      470
      12      649
       7      782
      16      765
      16     1019
       9      537
       4     1089
      21      221
      15      372
       7      706
      19      379
      10     1015
       8     1244
      23      443
       1      121
       6      732
      10      718
      23     1084
      12      424
      23      536
      11      308
       7      637
      18      611
      19      870
      24      310
      15     1145
       9     1005
      10      672
      10       59
      16     1235
      19      764
      18      430
      12     1122
       8      956
      23      704
       1      507
       8      822
       3      761
       2     1084
      11     1066
      19      439
      15      859
       5      494
      15      498
       5     1092
      15     1457
      15      458
      18     1133
      23       44
      10     1215
      16      856
       8      942
       1      321
      16      663
       1      463
       5     1324
       6      676
       7      858
      23      536
       2      476
      24      358
      21      481
       5      917
      10     1293
       4     1176
       9      768
      10      742
      10     1294
       6      608
      11      237
      15     1038
      11      330
       2     1117
       4       82
      21      516
      16     1222
       8     1347
      11      922
      23     1126
       4      868
      18      296
      24      412
      18      407
      23     1421
       4      930
      23      981
       2      146
       3      348
      16      361
      18      553
      24     1046
       2      557
       6      396
      23      104
       3     1197
       1      892
       6      218
       1      865
      11      644
       6      471
      12      938
      14      759
       2      180
      19      739
       5     1276
      19     1067
       7      299
      10      715
      19      514
       7      225
       5      574
      14      797
      18      556
      23      531
      21      516
      15     1463
       4     1264
      11     1006
      12      605
       6      592
       4      759
       6      628
      16     1469
       8      843
      16      638
      23      614
      24      439
      19      775
       9      711
       8     1304
      24      749
      16     1143
      12      829
      16     1063
       9      581
       8     1113
      10      851
      14      853
      19      781
   10       49
      16     1035
      19      264
      18      490
      12      922
       8      956
      23      704
       1      507
       8      822
       3      761
       2     1084
      14     1221
       6      772
       7      911
       7      545
       8      724
      10     1005
       7     1133
       2      189
      24     1212
      18     1118
      21      241
      15     1178
       3      659
      24      867
       4      497
       8      708
      18     1308
      11      411
       7      500
      15      538
       8      366
       1     1185
      19      989
       9      759
      10      144
       8     1210
      15     1284
       5      361
      23      962
       5      517
       8      637
      15     1239
      11      992
       7      394
       2      725
      24      114
      19     1518
       8     1127
      12      415
       1     1014
      15      637
       9      860
       3      986
      21      799
      24      211
       4     1212
       5     1348
       8      530
       5     1362
       9     1114
      10      294
       8     1414
      15     1010
       7      987
       7      608
      10      923
      21      837
      15      325
      16     1127
      10     1037
      12      980
      10     1160
       6      331
       1      840
      18      673
       3      561
       9      921
      24      752
      23     1123
      21      757
       3      722
       4      996
      19      415
      10      650
      11      239
       5      813
       2      349
       3      484
      16       70
       4      596
       7      753
       9      716
       6     1022
       4      351
      11      185
       2      403
      12      570
      24      905
       4       50
       9      211
      14      737
       8      587
       5      532
       1      544
      19       21
       5     1096
      11      232
       1      185
      24      507
       3      345
      16      340
       3      755
      15      487
       7      971
       2     1309
      11      500
      15      968
      10      739
       8      755
      12       60
       3      770
      18      601
       9      284
      21       55
      15     1144
      19     1524
       6     1214
       7      221
      19      391
      23      422
       9      476
       1     1054
       1      967
       5     1149
       1      794
      23     1014
       4      605
      23      860
       4      311
      14      443
       6      659
      19       85
       1      501
      23      346
       1      268
       8      941
      12      918
      23      779
      18      791
       8      561
       7     1051
      24      554
       8      444
      14      502
      12     1043
       9     1080
       6      771
       1     1274
       8      737
      19      197
       3      703
       6      748
      10     1029
      14     1095
      10     1141
       9      924
       5      962
       3      192
      10      963
      12      521
       1     1195
       4      529
       3     1330
       7      900
      21     1118
      18     1118
       5     1060
      15      459
      18     1107
      24      788
      16      689
       5      392
      18     1106
      15      848
      18      531
      12      242
      12      669
      18      962
      14      658
       9      799
       8      712
      21      873
      10     1191
      11      577
       5      499
      24      817
      23      569
       1      529
       1     1152
       3      813
      10      901
      21      739
       3      641
      23      581
      10      768
       6      810
       2     1457
       8      698
      14     1351
      11     1081
      21      589
       9      848
      16     1043
       8      710
      15      904
      11     1171
      10       62
      16     1097
      14      691
       3     1183
      11     1286
       7      606
      23       89
       7      859
      14      481
      12      839
       2      550
       3     1457
       3      512
      12      465
      14      657
      21     1149
      10     1340
       3      765
       2      948
       9      395
      16      662
       5      961
      23     1389
      23     1214
       5      890
       8      134
      22      666
      22      777
      23      100
      22      555
       3     1295
      11      307
      11      605
      15     1064
       6     1214
       1       64
       8      907
      18     1133
       9      636
       3     1134
      16     1101
       6      313
       7      791
       7     1130
       1     1221
      21      332
      24      697
       6      807
       2       36
       2      747
      16     1219
       3      859
      18      639
      18      312
       7     1079
      10     1074
       5      678
      18       59
       1      325
      21     543

PA11-3 Comparing, Prioritizing Multiple Projects [LO 11-1, 11-2, 11-3, 11-6]

Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume straight line depreciation method is used.   

Project 1: Retooling Manufacturing Facility

This project would require an initial investment of $5,500,000. It would generate $982,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,156,000.

Project 2: Purchase Patent for New Product

The patent would cost $3,855,000, which would be fully amortized over five years. Production of this product would generate $732,450 additional annual net income for Hearne.

Project 3: Purchase a New Fleet of Delivery Trucks

Hearne could purchase 25 new delivery trucks at a cost of $180,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $6,300. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $855,000 of additional net income per year.


Required:
1. Determine each project's accounting rate of return. (Round your answers to 2 decimal places.)

Accountng Rate of Return:

Project 1 percentage =

Project 2 percentage =

Project 3 percentage =

2. Determine each project's payback period. (Round your answers to 2 decimal places.)
Payback Period

Project 1 years =

Project 2 years =

Project 3 years =

3. Using a discount rate of 10 percent, calculate the net present value of each project. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Use appropriate factor(s) from the tables provided. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Net Present Value

Project 1 =

Project 2 =

Project 3 =

4. Determine the profitability index of each project and prioritize the projects for Hearne. (Round your intermediate calculations to 2 decimal places. Round your final answers to 4 decimal places.)

Profibility Index

Project 1 =

Project 2 =

Project 3 =

Equilibria with Weak Acids & Weak Bases - Results

Solution 1. Use the concentration of NH₃ and the measured pH above to determine the Kb of NH₃. (show the ICE table and calculations)

          Use the equation (Ka*Kb = 1*10^-14) to calculate the Ka for NH₄⁺ ?

Solution 2 Use the equation M₁V₁ = M₂V₂ to calculate new conc. of NH₃.

Conc. of NH₃ ____         pH measured:    10.82

Compare solutions 1 & 2. What effect did diluting the base have on the pH?

• Decreased the pH of the solution.

Use the new concentration and pH to measure the Kb of NH₃ again. Did it change?

Solution 3    Conc. of NH₄⁺                                pH of solution 3: 6.01

Use the diluted concentration of NH₄⁺ and measured pH to determine the Ka of NH₄⁺

How does this Ka value compare to the value on pg. 1? (within a power of 10 is good)

Calculate the concentrations for solution 4 and solution 5

Compare pH of solutions 2&4. What effect did adding NH₄⁺ have on the equilibrium/pH?

Compare the pH from dilution in solutions 1&2 to the pH change in solutions 4 & 5. Why is the pH change smaller for solutions 4&5 than in solutions 1&2? Think above the ratio of base and conjugate acid. You can also show this mathematically by using the Kb from part 1 with NH₃/NH₄⁺ conjugates to determine what the OH- concentration should be.

Note: Solution 4 (page 2) should already be made.                                                                                                                                           (total volume)

Calculate the dilution concentrations of solution 6.

Compare solutions 4 & 6. What effect did NaOH have on the pH of the solution?

If the NaOH concentration from solution 6 was in water by itself (without the buffer), what would the pH be?

Did NH₃ & NH₄⁺ buffer against NaOH? How can you tell?

Calculate the concentrations of solution 7 & 8

Compare solutions 4, 7 & 8. The ingredients are essentially the same, but the solutions of 7 & 8 should have a dramatically different pH.   Why did 7 work as a buffer, but 8 did not? Compare the concentration of NH₃ vs the concentration of HCl.  

Calculate the concentrations of solution 9

a) This solution has equal amounts of acid and base. Why is the pH acidic? Explain.

Please show work.

1. Find the derivatives dy/dx and d2y/dx and evaluate them at t = 2.

x = t², y = tln t

2. Find the arc length of the curve on the given interval

x = ln t, y = t + 1, 1 ≤ t ≤ 2

3. Find the area of region bounded by the polar curve on the given interval.

r = tan θ, π/6 ≤ θ ≤ π/3

4. Find the length of the polar curve on the given interval. (12 points)

r = θ, 0 ≤ θ ≤ π/2

Problem 9-2A In recent years, Avery Transportation purchased three used buses. Because of frequent turnover in the accounting department, a different accountant selected the depreciation method for each bus, and various methods were selected. Information concerning the buses is summarized as follows.

Bus Acquired Cost Salvage Value Useful Life in Years Depreciation Method

1 1/1/15 $ 98,300 $ 7,000 5 Straight-line

2 1/1/15 118,000 10,000 4 Declining-balance

3 1/1/16 88,640 8,000 4 Units-of-activity

For the declining-balance method, the company uses the double-declining rate. For the units-of-activity method, total miles are expected to be 126,000. Actual miles of use in the first 3 years were 2016, 24,000; 2017, 31,500; and 2018, 30,000.

For Bus #3, calculate depreciation expense per mile under units-of-activity method. (Round answer to 2 decimal places, e.g. 0.50.)

Depreciation expense $________ per mile

Compute the amount of accumulated depreciation on each bus at December 31, 2017. (Round depreciation cost per unit to 2 decimal places, e.g. 0.50 and depreciation rate to 0 decimal places, e.g. 15%. Round final answers to 0 decimal places, e.g. 2,125.)

Accumulated depreciation

BUS 1 $ ________

BUS 2 $ ________

BUS 3 $ ________

If Bus 2 was purchased on April 1 instead of January 1, what is the depreciation expense for this bus in (1) 2015 and (2) 2016? (Round answers to 0 decimal places, e.g. 2,125.)

(1) 2015 (2) 2016

Depreciation expense $_____ $_____