Free Essay

Matrix Using Calculator

In: Other Topics

Submitted By kyhuan
Words 3638
Pages 15
Matrix Calculations Using Calculators
The calculators most commonly used by Foundation Studies students at UTAR are Casio fx-350MS, fx-570MS, and fx-570ES. Casio fx-350MS has no matrix function and cannot be used to perform matrix calculation. Both Casio fx-570MS and Casio fx-570ES have matrix mode. Casio fx-570ES can display fully a 3×3 matrix with all its 9 elements visible. Casio fx-570MS has only a 2-line display and can only show matrix elements one at a time. Hence the operations for matrix computation are different for these two series of calculators. The general procedures in matrix calculations are as follows: (1) Enter Matrix mode of the calculators. (2) Assign a variable to store the matrix. There are 3 variables available: MatA, MatB, and MatC. (3) Select the dimension or order (1×1 to 3×3) of the matrix. (4) Input the elements of the matrix; the data will be automatically saved in the matrix variable assigned. (5) Exit the matrix input or edit mode by pressing the coloured AC key. (6) Press SHIFT MATRIX or SHIFT MAT (Matrix function is at numeric key 4) to recall the stored matrix and perform matrix calculations as needed.

(a) Casio fx-570ES
(a) Entering a matrix. 1. 2. 3. 4. Press the MODE key. Select 6:Matrix mode. A display Matrix? will be shown to let us select one of the 3 possible matrix variables allowable. Let us choose 1:MatA by pressing 1. The next display permits us to select the order (m×n) of the matrix MatA. Let us choose 1: 3×3 by pressing 1. An input screen will be displayed for us to key in the elements of the matrix. Let us key in the following matrix as an exercise:
1 1 2    4 0 3  5 1 2  

Press 1=, 1=, 2=, 4=, 0=, 3=, 5=, 1=, and 2=. (The = key acts like the Enter key on a computer keyboard.) 5. Exit from the matrix input screen by pressing the AC key. (The AC acts like the ESC key on a computer keyboard.)

(b) Finding the inverse of a non-singular 3×3 matrix. 6. Next let us compute the inverse of MatA in memory that we have just keyed in. Press SHIFT MATRIX (Matrix function is at numeric key 4). Select option 3:MatA.

1/13

7. 8.

The word MatA will be displayed. To find out its inverse, press the x-1 key. The display becomes MatA-1. Press the = key. After a short delay, the inverse of the matrix will be displayed:
 1 − 4   7  12   1   3 0 − 2 3 1 3 1  4   5  12   1 −   3

(There will ne no inverse if the matrix is singular, i.e. its determinant is zero.) 9. The result of this matrix calculation, i.e. the inverse of the matrix, will be stored in the memory variable MatAns. We can do matrix calculation with MatAns. For example, we can multiply MatA with MatAns to get the identity matrix. Press SHIFT MATRIX. Select option 6:MatAns. MatAns will appear on the screen. Press the multiplication key ×. Press SHIFT MATRIX. Select 3: MatA. MatAns×MatA will appear on the screen. Press = to display the identity matrix:
1 0 0   0 1 0 0 0 1  

10. 11.

(c) Finding the determinant of a 3×3 matrix. 12. 13. 14. We can also compute the determinant of matrix MatA. Press SHIFT MATRIX. Select 7:det. The screen will display det(. Select the matrix whose determinant is to be determined. Press SHIFT MATRIX. Choose 3:MatA by pressing 3. The display becomes det(MatA. Close the bracket by pressing ). Press = to display the determinant. The determinant of value 12 will be displayed.

(d) Finding the transpose of a matrix. 15. 16. 17. We can also display the transpose of the matrix easily. Press SHIFT MATRIX. Choose 8: Trn. The screen will display Trn(. Tell the calculator the matrix we want to transpose. Press SHIFT MATRIX. Choose 3: MatA by pressing key 3. Close the bracket by pressing ), followed by =. The transpose of MatA will be displayed.

2/13

(e) Modifying the content of a matrix. 18. 19. To modify the matrix MatA already in memory, press SHIFT MATRIX. Choose 2:Data. The screen will display Matrix? 1: MatA 2: MatB 3: MatC. Since our matrix is stored in MatA, choose 1: MatA by pressing 1. The matrix A will be displayed. We can alter the values of the elements now. The changed values will be stored automatically when we exit from the edit display. Exit from the matrix edit screen by pressing the AC key.

20. 21.

(f) Multiplying one matrix by another matrix. 22. 23. 24. To multiply MatA already in memory by another memory, assign a variable to the second matrix first. Press SHIFT MATRIX. Select 2: Data. The screen will display Matrix? 2: MatB 3: MatC. 1: MatA Let us assign the second matrix to variable MatB. Select 2: MatB by pressing 2. The input screen for MatB will be displayed. As an exercise, enter the following matrix data:
2 3 1    5 7 3  4 0 6  

25.

26. 27. 28.

Exit from the matrix edit screen by pressing the AC key. Now we can call MatA and MatB and multiply them together. Press SHIFT MATRIX. Select 3: MatA. MatA will appear on the screen. Press the multiplication key ×. Press SHIFT MATRIX. Select 4: MatB. MatA×MatB will appear on the screen. Press = to display the result:
 15 10 16     20 12 22   23 22 20   

(g) Solving system of linear equations in three variables. 29. Suppose we are required to solve the following system of linear equations: 2 x + 3 y + 3z = 0 4x − y − 6z = 1 − 4x + 3y + 6z = 3 3/13

The equations can be expressed in matrix form as:  2 3 3  x   0        4 −1 −6   y  =−1   4 3 6  z   3       The values of x, y, z are given by −1  x 2 3 3   0         y =  4 −1 −6   −1  z  4 3 6   3        30. We now enter the values of the matrices. Press SHIFT MATRIX. Select 2: Data. Assign the first matrix to variable MatA and select the order of the matrix MatA as 3×3. Note: If MatA is already in memory, selecting 2: Data would bring up the already defined MatA and we can edit the matrix elements. If MatA is not yet in memory, then we need to assign MatA to the new matrix by selecting the order of the matrix. If MatA is already in memory and its order is not what we wanted, then we need to start from scratch - press the MODE key, select 6:Matrix mode, choose 1:MatA, and define the order. 31. An input screen will be displayed for us to key in the elements of the MatA:
2 3 3     4 −1 −6  4 3 6   

32. 33. 34.

Exit from the matrix input screen by pressing the AC key. Next we create a second matrix. Press SHIFT MATRIX. Select 2: Data. Assign the second matrix to variable MatB and select the order of MatB as 3×1. The input screen for MatB will be displayed. Enter the following matrix data:
0    −1 3  

35. 36.

Exit from the matrix edit screen by pressing the AC key. Now we are ready to find the solutions to the system of linear equations. Compute the inverse of MatA in memory that we have keyed in. Press SHIFT MATRIX. Select option 3:MatA. The word MatA will be displayed. To determine its inverse, press the x-1 key. The display becomes MatA-1. Press the = key. After a short delay, the inverse of MatA will be displayed: 4/13

37. 38.

1 5   1 − 6 8 24    1  2 0 −  3 3   7  − 2 − 1   12 36   9 The inverse matrix will be stored in memory as MatAns.

39. 40. 41.

Exit from the matrix edit screen by pressing the AC key. Recall from memory the inverse matrix we have just computed. Press SHIFT MATRIX. Select 6: MatAns. MatAns will appear on the screen. Press the multiplication key ×. Press SHIFT MATRIX. Select 4: MatB. MatAns×MatB will appear on the screen. Press = to display the result: 1 2    −1 2   3  x    y = z   1 2    −1 2   3

42.

Hence,

Note: (i)

The defined matrix in memory can be cleared by changing the entry mode from matrix back to general computation: Press the MODE key. Select 1:COMP. Please note that using SHIFT CLR (key 9) does not clear the memory of the matrix entered.

(ii)

If seeing the data on the display is a problem, change the contrast in display using the following steps: Press Shift Setup, followed by the navigation key  to display the second screen. Choose 6: Cont. Press the keys [Light] and [Dark] to change the display contrast as desired. Press AC to exit contrast adjustment.

5/13

(b) Casio fx-570MS
(a) Entering a matrix. 1. Press the MODE key three times. The displays are as follows: First time : COMP CMPLX Second time : SD REG BASE Third time : EQN MAT VCT 1 2 3 2. Press 2 to select Matrix mode. A tiny MAT indicator will be visible at the central topmost row of the display. 3. Press SHIFT MAT (Matrix function is at numeric key 4). The screen will display : Dim Edit Mat 1 2 3 Press 1 to select the order (or dimension) of the matrix. Always define the dimension of the matrix first when creating a new matrix. 4. The next display will show A B C 1 2 3 A, B, C stands for three possible matrix variables: MatA, MatB, MatC. Choose MatA by pressing 1. 5. The next display will be MatA (m×n) m? Press 3 followed by = to define the row number of a 3×3 matrix. (The = key functions like the Enter key on a computer keyboard.) 6. The next display will be MatA (m×n) n? Press 3 followed by = to define the column number of a 3×3 matrix As an exercise, key in the matrix below.
1 1 2    4 0 3  5 1 2  

7. The next display is MatA11. Key in 1 followed by = to define the element for row 1 and column 1. 8. The next display is MatA12. Key in 1 followed by = to define the element for row 1 and column 2. 9. The next display is MatA13. Key in 2 followed by = to define the element for row 1 and column 3. 10. The next display is MatA21. Key in 4 followed by = to define the element for row 2 and column 1.

6/13

11. The next display is MatA22. Key in 0 followed by = to define the element for row 2 and column 2. 12. The next display is MatA23. Key in 3 followed by = to define the element for row 2 and column 3. 13. The next display is MatA31. Key in 5 followed by = to define the element for row 3 and column 1. 14. The next display is MatA32. Key in 1 followed by = to define the element for row 3 and column 2. 15. The next display is MatA33. Key in 2 followed by = to define the element for row 3 and column 3. 16. This will bring us back to the beginning of the matrix MatA11. We may use the navigation key to scroll through all the elements for checking purpose. Press AC to exit matrix input mode. (The AC key functions like the ESC key on a computer keyboard – it clears the display screen.) (b) Finding the inverse of a non-singular 3×3 matrix. 17. Press SHIFT MAT (Matrix function is at numeric key 4). The screen will display : Dim Edit Mat 1 2 3 Press 3 to select the 3×3 matrix just entered that is stored in memory. 18. The next display will be A B C 1 2 3 A, B, C stands for three matrices: MatA, MatB, MatC. Choose MatA by pressing 1. 19. The word MatA will be displayed. To find out its inverse, press the x-1 key. The display becomes MatA-1. Press = to find the inverse of the matrix, which is stored in variable MatAns. 20. The display becomes MatAns11, the row 1, column 1 of the inverse matrix element, the value of which is displayed at the second row of the screen. By default, the values b/c are in decimal form. Press the a key to change it into a fraction, if necessary. 21. Use the navigation key  to move to the next column. The display is MatAns12 with the value at the second row of the screen. 22. Repeat pressing the navigation keys   to display all the elements of the inverse matrix, an element at a time.
 1 − 4   7  12   1   3 0 − 2 3 1 3 1  4   5  12   1 −  3

7/13

(There will ne no inverse if the matrix is singular, i.e. its determinant is zero.) 23. Press AC to exit from the matrix display mode. 24. The result of this matrix calculation, i.e. the inverse of the matrix, will be stored in the memory variable MatAns. We can do matrix calculation with MatAns. For example, we can multiply MatA with MatAns to get the identity matrix. 25. Press SHIFT MAT. Press 3 to select a matrix in memory. 26. The next display will be A B C Ans 1 2 3 4 The symbols stands for the four possible matrices: MatA, MatB, MatC, and MatAns. Choose MatAns by pressing 4. MatAns will appear on the screen. 27. Press the multiplication key ×. Press SHIFT MAT. Press 3 to select a matrix. 28. Press 1 to select MatA. MatAns×MatA will appear on the screen. Press = to display the identity matrix, again one element at a time.
1 0 0   0 1 0 0 0 1  

(c) Finding the determinant of a 3×3 matrix. 29. Press SHIFT MAT (Matrix function is at numeric key 4). The screen will display : Dim Edit Mat 1 2 3 30. Use the navigation key  to scroll to the right: Det Trn 1 2 Press 1 to select Det. 31. The display will next show Det _ . Load the stored MatA by pressing SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 Press 3 to call the 3×3 matrix just entered. 32. The next display will show A B C Ans 1 2 3 4 A, B, C stands for three possible matrices: MatA, MatB, and MatC. Choose MatA by pressing 1. 33. The display will become Det MatA. Press =. The value of the determinant will be displayed at the second screen row.

8/13

(d) Finding the transpose of a matrix. 34. Press SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 35. Use the navigation key  to scroll to the next screen: Det Trn 1 2 Press 2 to select Trn. 36. The screen will display Trn _. Press SHIFT MAT. 37. The screen will display : Dim Edit 1 2 Press 3 to select a matrix. Mat 3

38. The next display will show A B C Ans 1 2 3 4 A, B, C stands for three possible matrices: MatA, MatB, and MatC. Choose MatA by pressing 1. The screen will display Trn MatA. Press = key. 39. The first element of the transpose of MatA MatAns11 will be displayed. Use the navigation keys  or the = key to show the required element of the transposed matrix. (e) Modifying the content of a matrix. 40. Press SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 Select Edit by pressing 2. 41. The next display will show A B C Ans 1 2 3 4 A, B, C stands for three possible matrices: MatA, MatB, and MatC. Choose MatA by pressing 1. 42. The first element of MatA MatA11will be displayed. Change the value of the element as required. We may use the navigation keys  to move to the required element. (f) Multiplying one matrix by another matrix. 43. To multiply MatA already in memory by another memory, assign a variable to the second matrix by first defining its dimension.

9/13

44. Press SHIFT MAT (Matrix function is at numeric key 4). The screen will display : Dim Edit Mat 1 2 3 Select Dim by pressing 1 to define the order of the second matrix. 45. The next display will show A B C Ans 1 2 3 4 Select B to assign the second matrix to MatB. Press 2. 46. The next display will be MatB (m×n) m? Press 3 followed by = to define the row number of a 3×3 matrix. The key = functions like the Enter key on a computer keyboard. 47. The next display will be MatB (m×n) n? Press 3 followed by = to define the column number of a 3×3 matrix. As an exercise, key in the following second matrix:
2 3 1    5 7 3  4 0 6  

48. The next display is MatB11. Key in 2 followed by = to define the element for row 1 and column 1 of MatB. 49. The next display is MatB12. Key in 3 followed by = to define the element for row 1 and column 2. 50. Similarly key in all the remaining elements of MatB : MatB13, MatB21, MatB22, MatB23, MatB31, MatB32, and MatB33. 51. This will bring us back to the beginning of the matrix MatB11. Exit from the matrix input mode by pressing AC. 52. Now we can call MatA and MatB and multiply them together. Press SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 Select Mat by pressing 3. 53. The next display will show A B C 1 2 3 Select A to load in the matrix MatA. Press 1. Ans 4

54. MatA will appear on the screen. Press the multiplication key ×.

10/13

55. Press SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 Select Mat by pressing 3. 56. The next display will show A B C 1 2 3 Select B to load in the matrix MatB. Press 2. 57. MatA×MatB will appear on the screen. Press =. 58. The first element of the matrix product MatAns11 will be displayed. Use the navigation keys  to display the rest of the elements: MatAns12, MatAns13, MatAns21 MatAns22, MatAns23, MatAns31, MatAns32, and MatAns33. The resulting matrix should be:
 15 10 16     20 12 22   23 22 20   

Ans 4

(g) Solving system of linear equations in three variables. 59. Suppose we are required to solve the following system of linear equations: 2 x + 3 y + 3z = 0 4x − y − 6z = 1 − 4x + 3y + 6z = 3 The equations can be expressed in matrix form as:  2 3 3  x   0        4 −1 −6   y  =−1   4 3 6  z   3       The values of x, y, z are given by

 x    y = z  

2 3 3   0       4 −1 −6   −1 4 3 6   3     

−1

60. We now enter the values of the matrices. Press SHIFT MATRIX. The screen will display : Dim Edit Mat 1 2 3 Select Edit by pressing 2. 61. The next display will show A B 1 2 Choose MatA by pressing 1. C 3 Ans 4

11/13

62. Since we have previously defined MatA, the first element of MatA MatA11 will be displayed. Replace MatA11 with 2. Press the navigation keys  to move to MatA12 and replace it with 3. Continue using navigation keys to modify the matrix MatA as
2 3 3     4 −1 −6  4 3 6   

63. Exit from the matrix input screen by pressing the AC key. 64. Next we create a second matrix. Press SHIFT MAT. The screen will display : Dim Edit Mat 1 2 3 Select Dim by pressing 1 to define the order of the new matrix. 65. The next display will show A B C Ans 1 2 3 4 Select B to assign the second matrix to MatB. Press 2. 66. The next display will be MatB (m×n) m? Press 3 followed by = to define the row number of a 3×1 matrix. 67. The next display will be MatB (m×n) n? Press 1 followed by = to define the column number of a 3×1 matrix. 68. The next display is MatB11. Enter 0 for MatB11, −1 for MatB21, 3 for MatB31 as in
0    −1 3  

69. Exit from the matrix edit screen by pressing the AC key. 70. Now we are ready to find the solutions to the system of linear equations. Compute the inverse of MatA that we have keyed in. Press SHIFT MATRIX. Select option 3:Mat., and then 1: A. 71. The word MatA will be displayed. To determine its inverse, press the x-1 key. The display becomes MatA-1. 72. Press the multiplication key ×. Press SHIFT MATRIX. Select 3: Mat. , then select matrix 2: B. The first element of MatA-1×MatB, MatAns11, will appear on the screen. Use the navigation keys  to display the other elements. The resulting matrix b/c MatAns should be (the results may be in decimal values; press the a key to change it into a fraction, if necessary):

12/13

1 2    −1 2   3  x    y = z   1 2    −1 2   3

73. Hence,

Note: The defined matrix in memory will be cleared by pressing the Shift CLR key.

Leong Sow Chew Lecturer Centre of Foundation Studies, Universiti Tunku Abdul Rahman (Kampar Campus)

13/13…...

Similar Documents

Premium Essay

Analyse B & Q’s Proposed Move Into the Bike Market Using Ansoff’s Matrix (12 Marks)

...Analyse B & Q’s proposed move into the bike market using Ansoff’s matrix (12 marks) The Ansoff Matrix is a marketing plan that helps a business to decide market and product growth strategy; it looks at the degree of risk and potential for reward from the different strategic options. Using the Ansoff Matrix, the proposal to sell bikes in the existing shops is an example of Product Development, A benefit of this would be that it would help them reach there corporative objective which is Growth, in order to do this they are planning to start by converting 50 BnQs stores in the midlands, this will mean they can test out the bike with their existing market, as about 20% of bikes are brought from online and 38% are brought from their biggest competitors Halfords as shown in Appendix A, and only about 28% of that market are willing to definitely go back and buy it from the same outlet which mean there is about 72% of 16-35 year olds who are willing to shop from someone else. Using the Ansoff Matrix, the proposal to sell bikes in a new chain of high streets is an example of Diversification, A benefit of this would be that they will be able to spread the risk so if demand falls in one market the business will not suffer too much because it can still archive profits in its other market with its other products, this will mean they can spend £60millon on this project as the other market is slowly decreasing, but the main problem in this is Halfords plc who has 33% of the share in......

Words: 321 - Pages: 2

Free Essay

Dissertation for Desk Calculator

... Desk Calculator BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI WORK INTEGRATED LEARNING PROGRAMMES DIVISION BITS-WIPRO Collaborative Programme: MS in Information Technology, YEAR-2012. Abstract: The project is to solve an infix expression using a desk calculator. Input is given as an infix expression and output is obtained in a text file. Method followed to solve the expression is, the input is fetched from the input text document and converted to postfix notation using expression tree data structure, the resulted RPN expression is evaluated and the result is shown in output text file. Infix is converted to postfix because, it is easy for the compiler to execute the expression in postfix format. Commonly used data structures for evaluating expressions are stacks and expression trees, both of the above data structures are analyzed and concluded that expression trees are the best suited data structure for solving infix expression. 1.Introduction: Consider a situation where you are writing a programmable calculator. If the user types in 10 + 10, how would you compute a result of the expression? You might have a solution for this simple expression. But what if he types in 3 * 2 / (5 + 45) % 10 ? What would you do then? The expression that you see above is known as Infix Notation. It is a convention which humans are familiar with...

Words: 1838 - Pages: 8

Premium Essay

Ovulation Calculator

...Ovulation calculator Are you trying to get pregnant? Or are you trying to find out the days which you ovulate and planning for a baby. Use an ovulation calculator. Ovulation calculator is a tool which helps to predict the days in a month in which you are likely to ovulate. The chances of getting pregnant are more if you have intercourse on the ovulating days. For a woman who has a regular menstrual cycle of 28 -32 days, ovulation is likely to happen between 11 – 21 days. It is calculated from the day one of your last periods. For eg, if you had your last periods on 12 of the previous month, your ovulating period is likely to be between 22nd – 2nd of the next month. The calculation needs to be done taking the number of days in a month. The given one is just an example. If you are trying to get pregnant, this ovulating period is considered as the best time for intercourse and gets a positive result. Though not very accurate, it can be used as a safe period for avoiding sex and to avoid getting pregnant. But its not 100% fool proof. Many websites offer online ovulation calculators. Enter the details asked by them, it will be your first day of last menstrual period and normal menstrual cycle , whether it is 28 days or 30 days. Ovulation depends on that as well. Some websites where you can check this are http://www.webmd.com/baby/healthtool-ovulation-calculator,......

Words: 345 - Pages: 2

Free Essay

Whiz Calculator

...Whiz Calculator Company Case 4-4 Whiz Calculator Company adalah sebuah perusahaan yang memproduksi penuh lini kalkulator elektronik, yang dijual ke seluruh cabang kepada pedagang perantara dan ritel, secara langsung baik kepada pemerintah dan pengguna industri. Perusahaan ini merupakan salah satu perusahaan yang terbesar dalam industri. Whiz Calculator Company dipimpin oleh Bernard Riesman. Riesman sudah bekerja di perusahaan selama 5 tahun dan untuk 2 tahun sebelumnya menjabat sebagai wakil presiden manufaktur. Setelah menjabat sebagai presiden, Riesman mengadakan konferensi dengan pengendali untuk mendiskusikan tentang pengendalian anggaran. Ia berpikir metode lama dalam perencanaan dan pengendalian biaya penjualan tidak memuaskan. Oleh karena itu, ia meminta pengendali untuk membuat sistem baru yang memiliki pengendalian yang lebih baik atas biaya. Metode lama penganggaran biaya penjualan menerapkan basis “tetap” atau “yang ditetapkan”. Setiap bulan Oktober, departemen akuntansi mengirim catatan biaya aktual departemen atau cabang-cabang tahun sebelumnya dan tahun ini sampai bulan Oktober, ke masing-masing manajer cabang dan manajer lainnya yang berada di bawah departemen penjualan. Kemudian dengan berpandu pada catatan ini dan perkiraan penjualan tahun depan serta penilaian manajer, pemimpin cabang akan membuat dan menyerahkan perkiraan biaya untuk tahun berikutnya. Perkiraan ini diberikan pada manajer penjualan yang memimpin semua penjualan cabang. Ia......

Words: 1092 - Pages: 5

Free Essay

Scientific Calculator

... SCIENTIFIC CALCULATOR [pic] SUBMITED TO: SUBMITED BY: Ms. Sukhdilpreet Kaur Name: Anuj Sharma &Naman Roll NO.:R246A16 & R246A11 Regn.No.: 10802451 &10800991 AKNOWLEDGMENT First and the foremost I would like to thank to my almighty for giving me courage to bring up this term assignment. At the outset, I would like to propose a word of thanks to my teacher, friends and other sources that gave an unending support and helped me in numerous ways from the first stage of my term assignment conceived. I would also like to thank my family members for their whole hearted support and cooperation. I duly acknowledge the contribution of ms.Sukhdilpreet Kaur for invaluable help. Coding scientific calculator is an uphill task and would have not been possible without proper and timely assistance of ms.Sukhdilpreet Kaur. I would also thanks to all my friends for forwarding their suggestions to make necessary modifications. Special thanks to Ms.Sukhdilpreet Kaur for her able guidance in my term assignment. INTRODUCTION Scientific Calculator | | |Top of Form | |[pic] | |Bottom of Form | |[pic] | The calculator was written by Rolf Howarth in early 1996. A fully featured scientific calculator with proper operator......

Words: 3778 - Pages: 16

Free Essay

Rechargeable Calculator with Mp3

...Datamex Institute of Computer Technology RECHARGEABLE CALCULATOR W/ MP3 Submitted by: Albento Maricel Submitted to: Mr. Aris D. Artates Instructor Table of Contents Title Page I. Introduction………. 1 II. Overview……………2 III. How to Use Rechargeable Calculator w/ MP3… 4 IV. Handling Precaution.. 7 V. Trouble Shooting……..8 i And do not try to fix the damage because this may cause permanent damage and void the warranty of your rechargeable calculator w/ mp3. 9 cause interference with TV or Radio reception. * Avoid dropping your rechargeable calculator w/ mp3 and subjecting it to strong impact. * Do keep your rechargeable calculator away from moisture. Contact with water or any liquid may cause to malfunction and overheat. Troubleshooting When you encounter malfunction in your rechargeable calculator w/ mp3, just go to the nearest service center. 8 Introduction Calculator is made for calculating numbers such as: Addition, Subtraction, Multiplication and Division. But in our product you can enjoy listening music while you’re calculating because our calculator has a built-in mp3 that you can choose whatever music you want to play in the music playlist. This Rechargeable Calculator w/ MP3 is a pocket size and hand carry so you can enjoy of bringing it anytime, anywhere. And when the battery is empty you can charge your calculator w/ mp3 for 3-4 hours and when it’s already full you can use it up......

Words: 553 - Pages: 3

Premium Essay

Using Financial Calculators

...Using Financial and Business Calculators Daniel J. Borgia Table of Contents Texas Instruments (TI) BA-35 SOLAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Texas Instruments (TI) BA II PLUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Hewlett Packard (HP) 12C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Hewlett Packard (HP) 17BII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 Hewlett Packard (HP) 19BII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 Using Financial and Business Calculators Most business and financial calculators offer a multitude of powerful functions. The purpose of this guide is to provide students with an easy and quick reference for some of the most commonly used financial functions. More detailed operational descriptions can be obtained from the owner’s manuals that accompany the calculators. This calculator guide discusses the basic functions of five business and financial calculators: the Texas Instruments (TI) BA-35 SOLAR, the Texas Instruments (TI) BA II PLUS, the Hewlett-Packard (HP) 12C, the Hewlett-Packard (HP) 17BII, and the HewlettPackard (HP) 19BII. The sections for each calculator present step-by-step instructions for using general and financial functions offered by each calculator. The calculations for each type......

Words: 12987 - Pages: 52

Premium Essay

Matrix

...University of Phoenix Material Health Insurance Matrix As you learn about health care delivery in the United States, it is important to understand the various models of health insurance to develop a working knowledge as you progress through the course. The following matrix is designed to help you develop that knowledge and assist you in understanding how health care is financed and how health insurance influences patients and providers as important foundational information for your role as a future health care worker. Fill in the following matrix. Each box must contain responses between 50 and 100 words using complete sentences. Include APA citations for the content you provide. | Origin: When was the model first used? | What kind of payment system is used, such as prospective, retrospective, or concurrent? | Who pays for care? | What is the access structure, such as gatekeeper, open-access, and so forth? | How does the model affect patients? Include pros and cons. | How does the model affect providers? Include pros and cons. | Health maintenance organization (HMO) | Example: HMOs first emerged in the 1940s with Kaiser Permanente in California and the Health Insurance Plan in New York. However, they were not adopted widely until the 1970s, when health care costs increased and the federal government passed the HMO Act of 1973, which required that companies that offered health insurance and employed more than 25 employees include an HMO option. The law......

Words: 717 - Pages: 3

Premium Essay

Carbon Calculator

...Writing #4: Carbon Calculator Many of our daily activities trigger emissions of greenhouse gases. We produce greenhouse gas emissions by burning gasoline on our daily commutes, burning gas for home heating, or using electricity. Greenhouse gas emissions vary among individuals depending on a person's location, habits, and personal choices. It is good to know how much green house gasses an individual produces in their daily habits to be aware of their carbon footprint. From there a person can change their habits in an effort to reduce their footprint for a better life style and for the general health of the world. For this assignment I went through and checked all of my homes shared bills for accurate dollar amounts and measurements. For the questions about my car and my grandparent’s car, those were estimated through various websites including fuleeconomy.com. The lowest reliable value that I entered was my cars MPG. I found it easier to determine the average MPG from the reports on fuleeconomy.com rather than determining it myself. By the end of the carbon calculator, my estimated household carbon usage was 37,393 pounds of CO2 per year. Per individual this amount translates to roughly 12,464 pounds of CO2 per year. In comparison to the class average as seen below in figure 1.1, my house hold emissions were definitely on the lower end of the spectrum. To find the class average I took the higher number in the ranges offered, multiples each of those numbers by the responses......

Words: 1118 - Pages: 5

Premium Essay

Financial Calculator Exercises

...FINANCIAL ANALYST Texas BA II Calculator Workshop CHARTERED FINANCIAL ANALYST Setting up your BAII Calculator Workshop Setting up your calculator (BAII Plus)  Decimal places &|F!  Set to mathematical precedence &|"&!  No. of payments per year &-K  Clear time value calculations &0 Calculator Workshop Memory function  The calculator can store numbers for you Example:  You calculate the answer to 2 + 3.5 = 5.5 and then wish to store it  Press D then K (5.5 has now been stored and assigned to button K  Having cleared the screen (P), it is now possible to recall the number by pressing J then K It is always possible to recall the last answer from the calculator by pressing & and then x CHARTERED FINANCIAL ANALYST Nominal vs. Effective Interest Rates Calculator Workshop Calculating nominal and effective rates Periodic rate (r) Nominal/stated rate r x Annual no. of periods Effective Annual Rate (EAR) EAR = (1 + r)12/n – 1 Where n = number of months Example: Calculating nominal and effective rates  Calculate the nominal rate from a 4% six-monthly periodic rate  Calculate the EAR from a 4% six-monthly rate  Calculate the EAR from a nominal rate of 8% paid quarterly Calculator Workshop Example:  8% paid 6-monthly is, in effect, 8.16%  8% paid quarterly is, in effect, 8.243%  0.08  FV = $100 1 +  = $108.243 4   r  Effective rate =  1 +  − 1  n where r is the nominal rate n 4 Calculator Workshop  You......

Words: 2388 - Pages: 10

Free Essay

Calculation of Household’s Ecological Footprint Using the Calculator Developed by Wackernagel

...and government and public services operate. In order to allow citizens to achieve a lifestyle that fits within one planet, governments need to dramatically improve the efficiency of the built environment and invest in renewable energy and smart land-use planning. (Network, 2014) In 2000, Wackemagel et al developed an Ecological Footprint Calculator that allows individuals assess their personal and societal impacts on the environment. It is critical for people involved in built environment and construction industry to have a broad understanding of sustainability and elements that have to be carefully considered to minimise the negative impacts on the surroundings we live in. In this report, I am going to use above calculator to evaluate my household ecological footprint located at 14 Waiben Crescent, Point Cook Vic 3030 and assess alternatives that can reduce the household Ecological Footprint. Below table is illustrates the findings of this calculation in 6 different categories based on the current lifestyle in September 2014. The Ecological Footprint per household member (presented as a land-use consumption matrix) FOSSIL ARABLE PASTURE FOREST CATEGORIES ENERGY LD. LAND 1.-FOOD 38131 126969 5960 0 2.-HOUSING 3747 0 0 3.-TRANSPORTATION 16657 0 4.-GOODS 1456 5.-SERVICES BUILT-UP expressed in average land with world average productivity......

Words: 1607 - Pages: 7

Premium Essay

Swap Calculator

...swap can be calculated using standards methods of determining the present value of fixed leg and the floating leg. PV of fixed leg is computing as follows: , where C – fixed interest rate M – number of fixed payments P – notional ti – number of days in the period Ti – basis period dfi – discount factor Similarly, PV of floating leg: , where fi – floating rate And resulting swap present value: Excel work Vanilla interest rate swap calculator, developed and designed in Excel with some use of VBA, is completely based on swap theory described above. All the requirements imposed for the calculator are met. Before we value the plain vanilla swap, we need to input the following parameters: • Notional • Contract period (Since the majority of interest rate swaps have a contract period between 1 year and 5 years, I decided to specify it within this interval.) • Fixed interest rate • Frequency of payments (1, 2 or 4 times a year) After all the values of the required variables are entered, the button “Calculate” should be clicked to obtain the swap present value and such intermediate values like PV of fixed CF and PV of floating CF, the difference of which is actually the swap present value. The table below represents the logic of the swap calculator. Explanation of columns: • Column (1) represents maturity in parts of the year. The scale interval is set as 0.25, since maximum possible payment frequency (for this calculator) is 4 times......

Words: 892 - Pages: 4

Free Essay

Mortgage Calculator

...Mortgage calculator One of my favorite tools and that I have used on many occasions is the mortgage amortization calculator from the internet. Using some basic information and a calculator it will help you have an elementary idea of monthly payments. Also, it can give you average information about the period of time needed for the full payment of the loan. Furthermore, an amortization schedule will show the payment, the interests, the distribution of capital, and the unpaid balance of the loan for each month until the full balance is paid off. The online mortgage calculator can be use easily without the need to understand complicated formulas. Simply enter the amount of the mortgage, interest rates and desire period of years, in order to be given immediately the amount of monthly payment plus a division of interest and the principal amount to be paid. With some calculator’s mortgage amortization, you can choose to check the consequences of the monthly over or lack of payments in efforts for the buyer to be mindful of the penalties if there are any in regards to their mortgage. Moreover, the debtor will determine how much they might save on interest payments if they were to pay the prematurely the loan. Prepared with awareness and understanding of your own financial abilities is key to make a tangible and wise decision on purchasing a home. Consequently you will be armed with the knowledge in efforts to negotiate terms and conditions that will be beneficial to your......

Words: 255 - Pages: 2

Free Essay

Matrix

...multiply the matrix by the position vector of the point. Example: A transformation is represented by the 2 by 2 matrix M = . To find the image of the point (3, 2) under this transformation, you need to find the result of the following matrix multiplication So the coordinates of the image are (8, -1). Example 2: A rectangle has coordinates (1, 1), (4, 1), (4, 3) and (1, 3). Find the coordinates of the image of the rectangle under the transformation represented by the matrix . Solution: You could find the image of each vertex in turn by finding , etc. However, it is more efficient to multiply the transformation matrix by a rectangular matrix containing the coordinates of each vertex: . So the image has coordinates (2, 0), (11, -3), (9, -1) and (0, 2). The diagram below shows the object and the image: Any transformation that can be represented by a 2 by 2 matrix, , is called a linear transformation. 1.1 Transforming the unit square The square with coordinates O(0, 0), I(1, 0), J(0, 1) and K(1, 1) is called the unit square. Suppose we consider the image of this square under a general linear transformation as represented by the matrix : . We therefore can notice the following things: * The origin O(0, 0) is mapped to itself; * The image of the point I(1, 0) is (a, c), i.e. the first column of the transformation matrix; * The image of the point J(0, 1) is (b, d), i.e. the second column of the transformation matrix; ......

Words: 2245 - Pages: 9

Free Essay

Calculators

...Calculators, lemmings or frame-makers? The intermediary role of securities analysts Daniel Beunza and Raghu Garud Introduction As Wall Street specialists in valuation, sell-side securities analysts constitute a particularly important class of market actor.1 Analysts produce the reports, recommendations and price targets that professional investors utilize to inform their buy and sell decisions, which means that understanding analysts’ work can provide crucial insights on the determinants of value in the capital markets. Yet our knowledge of analysts is limited by insufficient attention to Knightian uncertainty. Analysts estimate the value of stocks by calculating their net present value or by folding the future back into the present. In so doing, they are faced with the fundamental challenge identified by Frank Knight, that is, with the difficulty of making decisions that entail a future that is unknown. These decisions, as Knight wrote, are characterized by ‘neither entire ignorance nor complete . . . information, but partial knowledge’ of the world (Knight, [1921] 1971: 199). The finance literature has not examined the Knightian challenge faced by analysts. Indeed, existing treatments circumvent the problem by adopting one of two extreme positions. In the first, put forward by orthodox economists, it is assumed that Knightian uncertainty is non-existent and that calculative decision-making is straightforward. Analysts are presented as mere calculators in a probabilistic......

Words: 12718 - Pages: 51