calculater operations for discrete math

calculater operations for discrete math - PROCEDURES FOR...

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Unformatted text preview: PROCEDURES FOR THE TI-86 GRAPHICS CALCULATOR PROCEDURES (FINITE MATHEMATICS TOPICS) In what follows, we use the notations given in the TI-86 Graphics Calculator Guidebook. Consult your manual for full details to realize the full potential of your calculator. A.1 Graphing a Single Function 1. Enter the function into the function table as follows: a. Press GRAPH and select y(x) = . The function table Press GRAPH y(x) Plot 1 \y1 = will be displayed. (If a function has been entered previously, Plot 2 Plot 3 pressing CLEAR will clear the display.) CLEAR b. Enter the function. For example, to graph the function , b. we enter x^3(x - 3)^4 next to next \y1 = . 2. will be displayed. b. Enter the values for the viewing rectangle. For example, the viewing rectangle [-1,5] x [-40,40] has the following values: xmin = -1 xmax = xsc1 = ymin 5 1 Select the viewing rectangle as follows: a. Select WIND by pressing 2nd followed by F2. The range table = -40 ymax = 40 ysc1 ysc1 = 1 1 xres = 3. Press ENTER after entering each value. ENTER Select GRAPH to display the desired graph. A.2 Evaluating a Function Method A (Displaying the graph of the function) 1. Enter the function f using an appropriate viewing window as outlined in A.1. [See procedure for graphing a single function, Section A.1.] 2. Press MORE twice to display the function EVAL. Next select EVAL . MORE EVAL The display Eval x = will appear on the bottom of the screen. 3. Enter the value of x and press ENTER . The desired value of f (x) will be ENTER will displayed on the bottom of the screen. Method B (Without displaying the graph of the function.) Method 1. 1. 2. 2. Press 2nd CALC to select the CALC menu. 2nd CALC to Select evalF. The screen displays evalF The evalF( evalF( Enter the function, the variable, and the value of x at which the function is to Enter be evaluated. For example, to evalaute , where , we enter evalF (x^2 + 1, x, 2) [Don't forget to enter "x" after the function!] function and then press ENTER . The value of f at x = 2, which is 5, will be ENTER displayed displayed on the screen. A.3 Finding the Points of Intersection of Two Graphs 1. Plot the graphs of the two functions. To do this, follow Step 1 of the 1. Plot procedure procedure for graphing a single function (A.1) to enter the first function. Then press graphing ENTER to display ENTER \y2 = in the function table. Enter the second function. Then proceed to Step 2 of the of procedure for graphing a function (A.1). 2. Then b. b. 3. select MATH. Press MORE to obtain the ISECT function display. MATH Press MORE to Select ISECT to use this operation. ISECT Select the ISECT operation as follows: Select a. Press MORE once to display the function MATH in the menu. a. Press MORE To find the coordinates of a point of intersection, move the cursor close to the To point of intersection on one of the graphs and then press ENTER . The cursor point ENTER will automatically jump to a point on the other graph. Press ENTER twice ENTER and the display Intersection will appear at the bottom of the screen together with the coordinates of the point(s) of intersection of the two graphs. A.4 Using the ZOOM Function 1. Display the graph of the function. [See procedure for graphing a single Display function A.1.] function 2. Select ZOOM. To zoom-in select ZIN. ZOOM To ZIN 3. Use the left, right, up, or down arrow keys to move the cursor near the point of 4. interest. Press ENTER . ENTER To zoom-in again, move the cursor close to the desired point and press ENTER once more. ENTER once A.5 Using the TRACE Function 1. Display the graph of the function. [See procedure for graphing a single function (A.1).] function 2. Select TRACE. The cursor will appear on the graph. TRACE 3. By pressing , or , , the cursor can be made to move along the graph. The By the coordinates of the point indicated by the cursor appear on the bottom of the coordinates screen. screen. REMARK If more than one graph is displayed on the screen, then the cursor can be made to jump from one graph to the other by pressing , or . or A.6 Finding an Equation of a Least-Squares Line 1. to enter Enter the data as follows: a. Press 2nd STAT to call the statistics menu. Then select EDIT the data. The screen displays -------- -------- -------- Name = ( xStat appears in the first column. Next, move the cursor to the second column. Select NAMES, then select yStat. Press ENTER and the heading yStat appears in the second column. Repeat the process to enter fStat in the third column. The screen then displays. xStat yStat fStat 2 ) NAMES " OPS ► Select NAMES, then select xStat. Press ENTER. The heading -------- -------- -------- yStat = ( ) NAMES " OPS ► b. Enter the data for in the first column using the left, right, up or down arrow keys and pressing ENTER after each entry. In a similar manner, enter the data for in the second column. Enter 1's for the entries in the third column. [ Previous data can be cleared using the DEL key.] Return to the calculator mode by pressing 2nd QUIT. 2. Find the least-squares equation as follows: Select the statistics menu by pressing 2nd STAT. Then select CALC. Next, select LinR, the linear regression operation. The operation LinR appears on the screen. Press ENTER and the screen will display the values of a, b, corr, and n. A desired equation of the least-squares line is A.7 1. Entering a Matrix Press 2nd MATRX to call the matrix menu. Then select EDIT . Press 2nd MATRX EDIT 2. Enter the name of the matrix. For example, pressing ALPHA A will give the Enter ALPHA matrix matrix the label “A.” If the name already appears on the screen, then just select it by pressing pressing the appropriate key. Press ENTER . the ENTER 3. Enter the size of the matrix. For example, if A has order 3 x 4, press 3 , Enter ENTER , 4 , ENTER . ENTER ENTER 4. Enter the elements of the matrix row by row, starting with the first row. Enter 5. Return to calculator mode by pressing 2nd QUIT . To enter more than one 5. Return 2nd QUIT matrix, repeat the above procedure as necessary. matrix, REMARK To view a matrix, press 2nd MATRX . Then select the name of the matrix to REMARK 2nd MATRX be viewed. Press ENTER . If necessary, use the right or left cursor keys to ENTER move any hidden part of the matrix into view. A.8 1. 1. Using Row Operations on Matrices, rref, and SIMULT Using Row Operations Using Enter the matrix A. Press 2nd MATRX and then select OPS . Press MORE Press 2nd MATRX OPS MORE to display the menu for the row operations on the screen. The calculator is now ready to perform the following operations. a. Operation 1 (): Select rSwap to use rSwap, the row swap operation. Operation rSwap The command is rSwap(A , i, j). Press ENTER . ENTER b. b. Operation 2 (): Select multR to use multR, the row multiplication Operation multR operation. The command is multR(c, A, i). Press ENTER . ENTER Operation 3 (): Select mRAdd to use mRAdd, the multiply and mRAdd add row operation. The command is mRAdd(a, A, j, i). Press ENTER . ENTER c. c. 2. 2. Using rref Enter the matrix A. Press 2nd MATRX and then select OPS to display the Enter Press 2nd MATRX OPS menu. Select rref to use rref , the reduced row echelon form operation. Enter A rref and then and press ENTER . The row-reduced (equivalent) matrix is displayed. press ENTER 3. Using SIMULT Press 2nd SIMULT . Enter the number of variables (and equations) in the Press 2nd SIMULT system. Press ENTER . Then enter the coefficients of the system ENTER (written in standard form), row by row, starting with the first. Select SOLVE to solve SOLVE the system. A.9 A.9 a Operations on Matrices: Addition, Subtraction, Multiplication by Operations Scalar, and Matrix Multiplication To perform any of the above operations on matrices, first enter the matrices A, B, To C, and so on, and go back to the calculator mode. Then press 2nd MATRX . The 2nd MATRX calculator calculator is now ready to perform the following operations: 1. Addition of two matrices: To find the sum A + B of two matrices A and B Addition press, in succession, A, + , B, and ENTER . and ENTER 2. Subtraction of two matrices: To find the difference A - B of two matrices A and B press, in succession, A , - , B, ENTER . ENTER 3. Multiplication of a matrix by a scalar: To find the matrix cA enter the scalar Multiplication cA c . Then press A and ENTER . ENTER 4. Multiplication of two matrices: To find the product AB of two matrices A Multiplication AB and B, press in succession, A, x , B, ENTER . press ENTER REMARK More then two of the above operations may be combined into a single REMARK statement. For example, we can compute (cA + dB)C by entering (cA + dB) × C dB cA dB and pressing ENTER . ENTER A.10 Finding the Transpose of a Matrix and Finding the Inverse of an n x n Matrix. 1. Finding the transpose of a matrix: Enter the matrix as the matrix A and go Finding and back to the back calculator mode by pressing 2nd QUIT. Press 2nd MATRX and select calculator 2nd QUIT Press 2nd MATRX MATH. MATH Press ALPHA A followed by T and press ENTER . ALPHA ENTER Finding the inverse of a matrix: Enter the matrix as the matrix A and go back Finding and to the to calculator mode by pressing 2nd QUIT. Press ALPHA A followed by 2nd calculator 2nd QUIT Press ALPHA 2nd x-1 , and then press ENTER . ENTER 2. 2. A.11 Evaluating n!, P(n,r), and C(n,r) To use any of the operations n!, P(n,r), or C(n,r), press 2nd MATH to !, ), ,r), 2nd MATH display the Math menu. Then select PROB to use the PROB functions. PROB 1. To evaluate n! : Enter the number n, then select ! to use the factorial then function. Press ENTER and the answer will appear on the right-hand side of ENTER the screen. the 2. To evaluate P(n, r) : Call for the PROB functions as before. Then enter the To number n. Select nPr to use the P(n,r) function. Next, enter the number r. Finally, press nPr function. ENTER ENTER to obtain the answer which will be displayed on the right-hand side of the to screen. screen. 3. To evaluate C(n, r): Proceed as in part 2, but select nCr instead of nPr . 3. ): nCr A.12 Generating a Random Number Press 2nd MATH to call the Math menu. Then select PROB to use the PROB 2nd MATH PROB menu. menu. Observe that the rand function is displayed on the bottom of the screen. To generate a random number between a and c, enter a + b where b = c - a. Select rand to enter Select rand obtain obtain the display a + b rand. Then press ENTER to obtain the random number. For the ENTER example, to generate a random number between 2 and 6, enter 2 + 4, followed by rand. rand Then press ENTER. Then A.13 1. 2. 3. Graphing a Histogram Enter the data as follows: a. Press 2nd STAT to call the statistics menu. Then select EDIT from the menu. Enter the data x1 , x2 , ..., x , into the first column under xStat. Previous Enter ..., n data can be deleted by using DEL. data DEL Plot the histogram as follows: a. Select the appropriate viewing rectangle by pressing GRAPH and GRAPH selecting WIND. WIND b. Go back the statistics menu by pressing 2nd STAT . Select PLOT 2nd STAT PLOT and then select PLOT1. The screen displays PLOT1 The On On Off Type = Xlist Name = xStat Freq=1 Plot1 Plot2 Plot3 PLon Ploff Then turn on Plot 1 by moving the cursor to ON and pressing ENTER . Next use the cursor to move to ENTER Type= . Select HIST from the menu and press ENTER . Exit by pressing HIST ENTER 2nd Quit. 2nd Quit c. Return to the statistics menu by pressing 2nd STAT. Select 2nd STAT DRAW. DRAW The histogram now appears on the screen. A.14 A.14 Finding the Mean and Standard Deviation 1. Enter the data as per Step 1 in A.6. The fStat-values can be 1. Enter left as 1's. 2. To find the mean and standard deviation of X go to the statistic menu by To pressing 2nd STAT. Then select CALC. From the menu displayed, select pressing 2nd Then CALC OneVa . Press ENTER . The values of the mean and the standard OneVa ENTER deviation X are displayed along with other quantities. A.15 Programming the TI-86 1. To enter a new program: a. Press PRGM and select EDIT from the menu. The a. PRGM EDIT display display PROGRAM Name = will appear on the screen. will b. Enter the name of the program—up to 8 characters— and then press Enter ENTER . [In what follows, we will write and then execute the ENTER program COMPINT appearing in the Using Technology Section 5.1, Applied COMPINT Finite Mathematics] We enter the name COMPINT using ALPHA and the ALPHA key corresponding to the alphabet required. After the name has been corresponding typed in, typed press ENTER. The following display now appears in the window. ENTER PROGRAM: COMPINT . . I/O I/O Page Page Page CTL INSc ► c. Enter the program (see the textbook referred to earlier). To enter the first line first : DISP "P" select I/O . Next, press 2nd STRING . From the menu now on select I/O 2nd STRING display, select Disp followed by " . Then type in the letter P followed by " . Disp Press ENTER. The calculator is ready for the next line of the ENTER program. program. [Note: Use 2nd Alpha to enter lower-case letters.] 2nd Alpha d. After the complete program has been entered into the calculator, d. After press 2nd QUIT to exit the programming mode. 2nd QUIT 2. To execute a program: a. Press PRGM and select NAMES from the menu. Then select a PRGM NAMES program from the menu. The name of that program will appear on the top of the screen. Press ENTER . ENTER b. Enter the numerical values of the quantities asked for, pressing b. ENTER after each entry. For the example in the textbook, we enter ENTER 500 for the value of P, 0.1 for the value of r, 10 for the value of t, and 0.1 10 and 12 for the value of m. The answer is $1,353.52. 3. 3. To erase a program: a. Press 2nd MEM and select DELET from the menu. The word 2nd MEM DELET DELETE will appear on the screen. b. Press MORE and then select PRGM . The screen will display all MORE PRGM the programs entered into the calculator. c. Move the cursor to the program to be deleted and press ENTER . ENTER d. To exit the delete menu, press 2nd QUIT . 2nd QUIT ...
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