Sharp EL-5230, Operation Manual

Page 1: ...PROGRAMMABLE SCIENTIFIC CALCULATOR OPERATION MANUAL EL 5230 EL 5250 ...

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Page 3: ...r 2 General Information Chapter 3 Scientific Calculations Chapter 4 Statistical Calculations Chapter 5 Equation Solvers Chapter 6 Complex Number Calculations Chapter 7 Programming Chapter 8 Application Examples SHARP EL 5230 5250 Programmable Scientific Calculator ...

Page 4: ...e calculator on and off 16 Entering and solving an expression 16 Editing an expression 17 Using variables 18 Using simulation calculations ALGB 19 Using the solver function 21 Other features 22 Chapter 2 General Information 23 Clearing the Entry and Memories 23 Memory clear key 23 Editing and Correcting an Equation 24 Cursor keys 24 Overwrite mode and insert mode 24 Delete key 25 Multi entry recal...

Page 5: ...ions 33 Constant calculations 34 Functions 34 Math menu Functions 36 Differential Integral Functions 38 Differential function 38 Integral function 39 When performing integral calculations 40 Random Function 41 Random numbers 41 Random dice 41 Random coin 41 Random integer 41 Angular Unit Conversions 42 Chain Calculations 42 Fraction Calculations 43 Binary Pental Octal Decimal and Hexadecimal Opera...

Page 6: ...er 4 Statistical Calculations 61 Single variable statistical calculation 62 Linear regression calculation 62 Exponential regression logarithmic regression power regression and inverse regression calculation 62 Quadratic regression calculation 63 Data Entry and Correction 63 Data entry 63 Data correction 63 Statistical Calculation Formulas 65 Normal Probability Calculations 66 Statistical Calculati...

Page 7: ... 86 Chapter 8 Application Examples 87 Programming Examples 87 Some like it hot Celsius Fahrenheit conversion 87 The Heron Formula 89 2B or not 2B N base conversion 91 T test 93 A circle that passes through 3 points 95 Radioactive decay 97 Delta Y impedance circuit transformation 99 Obtaining tensions of strings 102 Purchasing with payment in n month installments 104 Digital dice 106 How many digit...

Page 8: ...ion files and programs 119 If an Abnormal Condition Occurs 119 Error Messages 120 Using the Solver Function Effectively 121 Newton s method 121 Dead end approximations 121 Range of expected values 121 Calculation accuracy 122 Changing the range of expected values 122 Equations that are difficult to solve 123 Technical Data 124 Calculation ranges 124 Memory usage 126 Priority levels in calculations...

Page 9: ... this manual applies to both models EL 5230 and EL 5250 Either of the models described in this manual may not be available in some countries Screen examples shown in this manual may not look exactly the same as what is seen on the product For instance screen examples will show only the symbols necessary for explanation of each particular calculation All company and or product names are trademarks ...

Page 10: ...r dispose of batteries in a fire Keep batteries out of the reach of children This product including accessories may change due to upgrading without prior notice NOTICE SHARP strongly recommends that separate permanent written records be kept of all important data Data may be lost or altered in virtually any electronic memory product under certain circum stances Therefore SHARP assumes no responsib...

Page 11: ...in blue above the key press first Alpha numeric characters for input are not shown as keys but as regular alpha numeric characters 햴 Functions that are printed in grey gray adjacent to the keys are effective in specific modes Note To make the cursor easier to see in diagrams throughout the manual it is depicted as _ under the character though it may actually appear as a rectangular cursor on the d...

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Page 13: ...akable or sharp tip If you do not see the message on the right the battery may be installed incorrectly refer to Battery Replacement See page 115 and try installing it again 2 Press y The initial display of the NORMAL mode appears 3 Press o 0 and press or to adjust the display contrast until it is set correctly then press j o means you have to press followed by S key See The OPTION menu See page 1...

Page 14: ...and slide it onto the back as shown to avoid losing it When you are not using the calculator slide the hard case over the keyboard and display as shown Firmly slide the hard case all the way to the edge The quick reference card is located inside the hard case Remove the hard case while holding with fingers placed in the positions shown below Chapter 1 Before You Get Started ...

Page 15: ...r ON OFF and Clear key Turns calculator ON To turn off the calculator press then o This key can also be used to clear the display 3 Key operation keys Activates the second function printed in orange assigned to the next pressed key Activates the variable printed in blue assigned to the next pressed key 4 Cursor keys Enables you to move the cursor in four directions 1 Display screen 2 Power ON OFF ...

Page 16: ...n of a calculation 2ndF Appears when is pressed xy rθ Indicates the mode of expression of results in the complex calculation mode HYP Indicates that H has been pressed and the hyperbolic functions are enabled If are pressed the symbols 2ndF HYP appear indicating that inverse hyperbolic functions are enabled ALPHA Appears when a x or t is pressed FIX SCI ENG Indicates the notation used to display a...

Page 17: ...L mode Allow you to perform standard scientific calculations Differential Integral functions N base calculations Solver function Simulation calculation STAT statistics mode Allows you to perform statistical calculations PROG program mode Allows you to create and use programs to automate simple or complex calculations EQN equation mode Allows you to perform equation solvers such as quadratic equati...

Page 18: ...order as they would normally be written in To calculate the result of an expression press e at the bottom right of the keypad this has the same function as the equals key on some calculators Example Find the answer to the expression 82 았앙 3 7 10 5 1 8 A z 3 7 k S 10 5 This calculator has a minus key for subtraction and a negative key S for entering negative numbers To correct an error use the curs...

Page 19: ...ur times to move the cursor to the point where you wish to make a change The cursor has moved four places to the right and is now flashing over 3 3 Press O This changes the character entering mode from overwrite to insert When is pressed the 2ndF symbol should appear at the above of the display If it does not you have not pressed the key firmly enough The shape of the flashing cursor tells you whi...

Page 20: ...stored number is displayed on the next line ALPHA disappears from the display You can also store a number directly rather than storing the result of an expression Example 2 Find the area of a circle which has radius R Enter an expression containing variable R now equal to 8 from the last example 1 Press j s then Whenever you need to use a character written in blue on the keypad press beforehand AL...

Page 21: ...ss j 1 k 3 s R A H to enter the formula Note that 1 3 represents 1 over i e divided by 3 Variables can be represented only by capital letters 2 Press G I key to finish entering the equation The calculator automatically picks out the variables alphabetically contained in the equation in alphabetical order and asks you to input numbers for them at the bottom of the display reminds you that there is ...

Page 22: ...e is displayed on the third line 6 Press e and 8 to input the height for cone The display returns to a value entry screen with 8 substituted for 10 in variable H 7 Press e to confirm the change 8 Press 9 to enter the new radius then press e to solve the equation The volume of cone is now displayed In any step press h to obtain the solution using the values entered into the variables at that time C...

Page 23: ...luding in the NORMAL mode Press V then input the rest of the expression You must press m key not e to enter the sign 11 Press I 5 to move to the variable input display Note that the values assigned to the variables in the last example for the simulation calculations are retained and displayed 12 Press d to skip the height and then press 8 e to enter the radius R The cursor is now on V The value th...

Page 24: ...l calculations regression calculations and normal probability calculations Statistical results include mean sample standard deviation population standard deviation sum of data and sum of squares of data See Chapter 4 Equation solvers You can perform solvers of simultaneous linear equation with two three unknowns or quadratic cubic equation See Chapter 5 Complex number calculations You can perform ...

Page 25: ...nitialize the display mode press 0 The parameters set as follows Angular unit DEG See page 26 Display notation NORM1 See page 26 N base DEC See page 44 To clear all variables excluding local variables of saved equations statistical data and STAT variables press 1 y To clear statistical data and STAT variables press 2 y To RESET the calculator press 3 y The RESET operation will erase all data store...

Page 26: ...o jump the cursor to the beginning or the end of equation Overwrite mode and insert mode Pressing O switches between the two editing modes overwrite mode default and insert mode A rectangular cursor indicates preexisting data will be overwritten as you make entries while a triangular cursor indicates that an entry will be inserted at the cursor In the overwrite mode data under the cursor will be o...

Page 27: ...stored equations are deleted in the order of the oldest first Pressing g will display the previous equation Further pressing g will display preceding equations You can edit the equation after recalling it The multi entry memory is cleared by the following operations mode change memory clear P 1 y RESET N base conver sion Example Input three expressions and then recall them 1 3 5 2 2 3 5 2 3 3 5 3 ...

Page 28: ...ll be displayed and the number of decimal places TAB can be set to any value between 0 and 9 When J 1 1 SCI is pressed SIG 0 9 will be dis played and the number of significant digits SIG can be set to any value between 0 and 9 Entering 0 will set a 10 digit display When a floating point number does not fit in the specified range the calculator will display the result using the scientific notation ...

Page 29: ...es You can assign values numbers to global variables by pressing x then A Z and θ Example 1 Store 6 in global variable A 1 Press j 6 x A There is no need to press because ALPHA is selected automatically when you press x 100000 3 j J 1 3 Floating point NORM1 100000z 3e FIXed decimal point and TAB set to 2 SCIentific notation and SIG set to 3 ENGineering notation and TAB set to 2 J 1 2 2 Floating po...

Page 30: ... the local variable using two characters the first character must be a letter from A to Z or θ and the second must be a number from 0 to 9 Example Store 1 25 x 10 5 as local variable A1 in the NORMAL mode and recall the stored number 1 Press v The VAR menu appears If no local variables are stored yet ALPHA appears automatically and the calculator is ready to enter a name 2 Press A1 e shows that yo...

Page 31: ... and editing and running a program Using variables in an equation or a program Both global and local variables can be used directly in an equation or a program Local variables are useful when you need to use variables such as X1 and X2 at the same time in another equation The local variable names and their values can be saved in each equation See page 58 Example Using A 6 and A1 0 0000125 from the...

Page 32: ...433388 is held in ANS memory 2 Press j 5 e You now have the volume of the cylinder The last answer is cleared i e set to 0 if you press the RESET switch change the mode or memory clear operation P 1 y but not if you turn the calculator off Global variable M Using the M memory in addition to the features of global variables a value can be added to or subtracted from an existing memory value Example...

Page 33: ... cally stored in memories replacing any existing values rθ xy R memory r θ memory θ X memory x Y memory y Use of t or will recall the value stored in memory using up to 14 digits in accuracy Chapter 2 General Information Available Unavailable Mode ANS M A L N Z Local variables NORMAL STAT PROG EQN CPLX ...

Page 34: ... calculator with the tip of a ball point pen or similar object Do not use an object with a breakable or sharp tip A display appears asking you to confirm that you really want to reset the calculator 2 Press y All memories variables files and data are cleared The display goes back to the initial display in the NORMAL mode The calculator will revert to the very first settings that were made when you...

Page 35: ...ase functions Solver functions and Simulation Calculation ALGB in this chapter are all performed in the NORMAL mode In each example of this chapter press j to clear the display first If the FIX SCI or ENG indicator is displayed clear the indicator by selecting NORM1 from the SET UP menu Unless specified set the angular unit as DEG P 0 Arithmetic operations 3 428571429 90 140 1250000 45 285 3 j 45 ...

Page 36: ...t calculations constants will be displayed as Functions The range of the results of inverse trigonometric functions 34 57 34 57e 45 57 45 e 68 25 68k 25e 68 40 40e 91 102 1700 2720 Key operations Result Example 0 866025403 sin60 j v 60e cos rad J 0 1 s k 4e tan 1 1 g J 0 2 y 1 e P 0 π 4 0 707106781 50 Key operations Result Example θ sin 1 x θ tan 1 x θ cos 1 x DEG 90 θ 90 RAD GRAD 100 100 0 200 θ ...

Page 37: ...8 2 34 52 2024 984375 123 6 447419591 83 512 4 3 4 24 10P3 720 5C2 10 500 25 125 120 400 30 500 500 25 625 400 400 30 j H 1 5 H v 1 5 A e t 5 z 7 e i 20e l 50e 3e Y 1 7e 6 Z 7 Z e 4k 5A e 4 B e 5 c 2e 8m S 2 3m 81 e 12m 3m 4 Z e 49 4 D 81e q 27e 10 e 3e 500k 25 120z 400 500 25 400 30 280 5 7 1 6 1 7 1 4 Key operations Result 49 4 81 3 27 20 08553692 Example ...

Page 38: ...ulations 0 abs Displays the absolute value of a number 1 ipart Displays the integer part only of a number 2 int Displays the largest integer less than or equal to a number 3 fpart Displays the fractional part only of a number 4 RAND Before using the Random Numbers of Random functions designate 0 001 from 0 999 random number sequences available The calculator can regenerate the same random numbers ...

Page 39: ...ns Result 5 SOLVE Enter the Solver function mode See page 52 6 Ωsec Sexagesimal numbers are converted to seconds notation See page 46 7 Ωmin Sexagesimal numbers are converted to minutes notation See page 46 I 5 24 I 6 0 0 1500I 7 24 Ωsec 86400 0 0 1500Ωmin 25 ...

Page 40: ... recalculate after changing the minute interval dx or subinterval n Since differential and integral calculations are performed based on the following equations in certain rare cases correct results may not be obtained such as when performing special calculations that contain discontinuous points Integral calculation Simpson s rule S h f a 4 f a h f a 3h f a N 1 h 2 f a 2h f a 4h f a N 2 h f b N 2n...

Page 41: ...t the starting value a of a range of integral and press e 5 Input the finishing value b of a range of integral and press e 6 Input the subinterval n 7 Press e to calculate To exit the integral function press j After getting the answer press e to return to the display for inputting a range of integral and subinterval and press h to recalculate at any point Chapter 3 Scientific Calculations Example ...

Page 42: ...range and for periodic functions etc where positive and negative integral values exist depending on the interval For the former case make the integral interval as small as possible For the latter case separate the positive and negative values Following these tips will provide calculations results with greater accuracy and will also shorten the calculation time Chapter 3 Scientific Calculations y x...

Page 43: ...die rolling a random integer between 1 and 6 can be gener ated by pressing w 1 e To generate further random numbers in succession press e Press j to exit Random coin To simulate a coin flip 0 head or 1 tail can be randomly generated by pressing w 2 e To generate further random numbers in succession press e Press j to exit Random integer An integer between 0 and 99 can be generated randomly by pres...

Page 44: ...tructions When using postfix functions sin etc a chain calculation is possible even if the previous calculation result is cleared by the use of the j key Chapter 3 Scientific Calculations 90 rad j 90 1 570796327 g 100 90 sin 1 0 8 w 0 8e 53 13010235 rad 0 927295218 g 59 03344706 53 13010235 Example Key operations Result 6 4 ANS j 6 4 e 10 ANS 5 5 e 15 8 2 ANS 8 k 2 e 16 ANS2 A e 256 44 37 ANS 44 3...

Page 45: ...s a decimal number Chapter 3 Scientific Calculations 3 a j 3 k 1 k 2 4 k 3 e 4ı5ı6 a xxx k 4 833333333 d c F 29ı6 10 Y 2 k 3 e 4 641588834 5 16807ı3125 1 k 8 m 1 k 3 e 7 k 5 m 5 e 1ı2 64k 225e 8ı15 23 2 m 3 k 34 3 m 4 e 8ı81 1 2 1 2k 2 3e 12ı23 2 3 1 2 3 1 2 3 k 2 e 0 31 1 5 2 1 103 1 3 k 2 3 e 1ı2 2 103 A 7 j 7 x A 7 4 k A e 4ı7 1 25 a xxx 1 25 2 k 5 e 1 65 a k 1ı13ı20 4ı5ı6 4 1 2 4 3 b c 2 3 7 5...

Page 46: ... Converts to the octal system f appears h Converts to the hexadecimal system 6 appears Converts to the decimal system q f and 6 disappear from the display Conversion is performed on the displayed value when these keys are pressed Note Hexadecimal numbers A F are entered into the calculator by pressing m A 1 l and i key respectively In the binary pental octal and hexadecimal systems fractional part...

Page 47: ...0 b BIN 111 NEG d 111e 1111111001 b HEX 1FF a 1FF g OCT 512 512e 1511 0 HEX a 349 H 2FEC j x M a 2FEC 2C9E A 2C9Em 34E H 2000 2000 1901 B 1901m 6FF H C t M A4D H 1011 AND j z 10114 101 BIN 101e 1 b 5A OR C3 HEX a 5Ap C3e DB H NOT 10110 z n 10110e 1111101001 b BIN 24 XOR 4 OCT g 24x 4e 20 0 B3 XNOR a B3C 2D HEX 2De FFFFFFFF61 H DEC 159 Example Key operations Result ...

Page 48: ...be performed using the sexagesimal system Notation for sexagesimal is as follows 12 39 18 05 j 12 39 18 05 10 12 65501389 123 678 60 123 678 123 40 40 8 3h30m45s 3 30 45 6 6h45m36s 60 45 36e 10 16 21 1234 56 12 1234 56 12 0 0 34 567 60 0 0 34 567e 1234 56 47 3h45m 3 45 1 69e 1 69h 60 2 3 36 sin62 12 24 10 v 62 12 24 e 0 884635235 24 24 I 6 86400 1500 0 0 1500I 7 25 Example Key operations Result 12...

Page 49: ...a calculation select the angular unit The calculation result is automatically stored in memories Value of r R memory Value of θ θ memory Value of x X memory Value of y Y memory r and x values are stored in the last answer memory j 6 4 x 6 r u r 7 211102551 y 4 θ 33 69006753 14 36 r 14 x E x 11 32623792 θ 36 y y 8 228993532 Example Key operations Result Chapter 3 Scientific Calculations ...

Page 50: ...and Technology or on ISO specifications 01 Speed of light in vacuum 02 Newtonian constant of gravitation 03 Standard acceleration of gravity 04 Electron mass 05 Proton mass 06 Neutron mass 07 Muon mass 08 Atomic mass unit kilogram relationship 09 Elementary charge 10 Planck constant 11 Boltzmann constant 12 Magnetic constant 13 Electric constant 14 Classical electron radius 15 Fine structure const...

Page 51: ... 2 pi 43 Hartree energy 44 Conductance quantum 45 Inverse fine structure constant 46 Proton electron mass ratio 47 Molar mass constant 48 Neutron Compton wavelength 49 First radiation constant 50 Second radiation constant 51 Characteristic impedance of vacuum 52 Standard atmosphere No Constant Symbol Unit eV J t K AU m pc m M 12 C kg mol 1 µµ J T 1 h J s λc m Eh J λc p m 0 G s σ W m 2 K 4 α 1 NΑ L...

Page 52: ...following 12 types of prefixes Prefix Operation Unit E P T G M k m µ n p f a Exa Peta Tera Giga Mega kilo milli micro nano pico femto atto j 0 j 1 j 2 j 3 j 4 j 5 j 6 j 7 j 8 j 9 j A j B 1018 1015 1012 109 106 103 10 3 10 6 10 9 10 12 10 15 10 18 100m 10k 100 j 6 k 10 j 5 e 1000 Example Key operations Result Chapter 3 Scientific Calculations ...

Page 53: ... places indicated the internal calculation result may differ from that shown in the display By using the modify function the internal value is converted to match that of the display so that the displayed value can be used without change in subsequent operations 5 9 ANS j J 1 0 1 ANS 9 5 z 9 e 0 6 FIX TAB 1 k 9 e 1 5 0 5 z 9 e n 0 6 k 9 e 2 5 4 P 0 1 5 5555555555555 10 1 9 2 0 6 9 Example Key opera...

Page 54: ...ear several times in an equation You can use both global and local variables in your equation See page 58 Using the solver function will cause variables memory to be overwritten with new values To exit the solver function press j Changing the value of variables and editing an equation When you are in the solution display press e to return to the display for entering values of variables then return...

Page 55: ...cally 4 Press 10 e Enters a value for known variable A The cursor moves onto the next variable 5 Press 5 e Enters a value for known variable B 6 Press 2 5 e Enters a value for known variable C The cursor moves onto the next variable indicates that this is the last variable 7 Press h After showing the calculating display the calculator finds the value for the unknown variable that was indicated by ...

Page 56: ...on To cancel calculation press j when calculating is displayed Before entering the equation the appropriate angular unit must be selected The calculator uses Newton s method to solve equations Due to this there may be some equations that it fails to solve even though they are in fact solvable See page 123 The calculator stops calculating when the values it has obtained for the left and right sides...

Page 57: ...ation but only local variables will be stored if you save the equation See page 58 You need enter only the side of the equation that contains the variables Performing simulation calculation will cause the variables memories to be overwritten with new values The answer calculated will be stored in last answer memory To exit simulation calculation press j Changing a value of variables and editing an...

Page 58: ... automatically calls the display for entering variables and picks out the variables in alphabetical order If a variable already has a value the calculator displays that value automati cally indicates that there are more variables 5 Press 90 e The calculator picks out the next variable 6 Press 3 e 5 indicates that this is the last variable 7 Press e NORMAL MODE 0 BCsinA 2_ BCsinA 2 A z 0 BCsinA 2 B...

Page 59: ... 9 Press h Sides b and c are both the same length in triangle 2 as in triangle 1 so you do not have to re enter these values 10 Press e and then d 4 e h Area of triangle 3 is displayed BCsinA 2 7 071067812 BCsinA 2 5 303300859 Chapter 3 Scientific Calculations 2BCsinA 2 B z 3 Area of triangle 2 is displayed ...

Page 60: ... EQUATION FILE menu The file name display appears asking you to enter a title The calculator automatically locks ALPHA on to enable you to enter alphabetic characters easily To cancel the ALPHA setting press 2 Enter the title of the file up to seven characters If you change your mind and no longer want to save the equation press j 3 Press e to save the equation The display returns to the display b...

Page 61: ...sh to retrieve or delete and press e The display asks for confirmation if you are deleting an equation Press y to proceed with deletion or e to cancel the operation Note If the equation being retrieved contains local variables the local variable names and their values will be retrieved along with the equation Any other equation on the display and local variables before the equation was retrieved a...

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Page 63: ... the desired sub mode by pressing the number key that corresponds to your choice To change statistical sub mode reselect statistics mode press b 1 then select the required sub mode 0 SD Single variable statistics 1 LINE Linear regression calculation 2 QUAD Quadratic regression calculation 3 EXP Exponential regression calculation 4 LOG Logarithmic regression calculation 5 POWER Power regression cal...

Page 64: ...imate x Since the calculator converts each formula into a linear regression formula before actual calculation takes place it obtains all statistics except coefficients a and b from converted data rather than entered data I 0 0 I 0 1 I 0 2 I 0 3 I 0 4 I 0 5 I 0 6 I 0 7 I 0 8 I 0 9 I 0 A I 0 B I 2 0 I 2 1 I 2 2 I 2 3 Q n Number of samples y Mean of samples y data sy Sample standard deviation y data ...

Page 65: ... frequency _ To enter multiples of the same data Two variable data Data x Data y _ Data x Data y frequency _ To enter multiples of the same data x and y Up to 100 data items can be entered With single variable data a data item without frequency assignment is counted as one data item while an item assigned with frequency is stored as a set of two data items With two variable data a set of data item...

Page 66: ...the correct value then press _ or e To delete a data set display and move the cursor to an item of the data set to delete by using u d then press The data set will be deleted To add a new data set press j to exit the display of previously entered data and input the values then press _ Chapter 4 Statistical Calculations DATA 30 b 1 0 40 30 _ 40 40 2 _ 50 50 _ DATA 30 d d d 45 45 _ X 45 45 3 _ 3 45 ...

Page 67: ... made to take the square root of a negative number No solution exists for a quadratic regression calculation Chapter 4 Statistical Calculations Type Regression formula Linear y a bx Exponential y a ebx Logarithmic y a b ln x Power y a xb Inverse y a b Quadratic y a bx cx2 1 x xy x1y1 x2y2 xnyn y y1 y2 yn x x1 x2 xn x2 x1 2 x2 2 xn 2 y2 y1 2 y2 2 yn 2 sx x2 nx2 n 1 sy y2 ny2 n 1 y y n x x n x x2 nx...

Page 68: ...lways take positive values even when t 0 because these functions follow the same principle used when solving for an area Values for P t Q t and R t are given to six decimal places x x x σ t Standardization conversion formula Chapter 4 Statistical Calculations ...

Page 69: ... e sx I 0 2 e sx2 A e 95 x 10 50 95 I01 sx zI02k10 50 e x 60 I1160 I10 e t 0 5 I13S0 5 e Σ x2 Σ 75 71428571 σ 12 37179148 n 7 Í 530 Í Œ 41200 13 3630621 sx 178 5714286 64 43210706 0 102012 0 691463 Stat 0 SD 0 x σ x R t DATA SET 1 DATA SET 2 DATA SET 3 DATA SET 4 DATA SET 5 P t Example Result Key operations Statistical Calculations Examples ...

Page 70: ...0 e I 2 1 e I 2 2 e x 10 y 10 I 2 5 y 22 x 22 I 2 4 x y 12 41 8 13 5 2 23 200 15 71 x y DATA Stat 1 LINE 0 Stat 2 QUAD 0 DATA SET 1 DATA SET 2 DATA SET 3 DATA SET 4 DATA SET 5 DATA SET 1 DATA SET 2 DATA SET 3 DATA SET 4 DATA SET 5 5 357506761 3 120289663 0 503334057 y 24 4880159 9 63201409 3 432772026 1 050261097 1 826044386 0 995176343 8 541216597 15 67223812 6 528394256 24 61590706 Example Resul...

Page 71: ...100 an error occurs The results obtained by this function may include a margin of error Example 1 2x 3y 4 x 5x 6y 7 Ò y det D 1 Press b 3 0 to select 2 VLE of the EQN mode 2 Enter the value of each coefficient a1 etc 2 e 3 e 4 e 5 e 6 e 7 Coefficients can be entered using ordinary arithmetic operations To clear the entered coefficients press j Press d or u to move line by line Press d or u to jump...

Page 72: ...ch coefficient a1 etc 1 e 1 e S 1 e 9 e 6 e 6 e S 1 e 17 e 14 e S 7 e 2 e 42 Coefficients can be entered using ordinary arithmetic operations To clear the entered coefficients press j Press d or u to move line by line Press d or u to jump to the last or top line 3 After inputting the last coefficient press e to solve the 3 VLE Press d to display the det D After solving press e or j to return to th...

Page 73: ...e a margin of error Example 1 3x2 4x 95 0 x 1 Press b 3 2 to select QUAD of the EQN mode 2 Enter the value of each coefficient a etc 3 e 4 e S 95 Coefficients can be entered using ordinary arithmetic operations To clear the entered coefficients press j Press d or u to move line by line 3 After inputting the last coefficient press e to solve the quadratic equation After solving press e or j to retu...

Page 74: ...entered coefficients press j Press d or u to move line by line Press d or u to jump to the last or top line 3 After inputting the last coefficient press e to solve the cubic equation After solving press e or j to return to the coefficient entering display You can use h to solve the cubic equation regardless of the cursor position Chapter 5 Equation Solvers a z 0 b 0 c 0 X 1 233600307 X 0 216800153...

Page 75: ...try 1 Rectangular coordinates are entered as follows x coordinate y coordinate Q or x coordinate Q y coordinate 2 Polar coordinates are entered as follows r R θ r absolute value θ argument On selecting another mode the imaginary part of any complex number stored in the M memory will be cleared A complex number expressed in rectangular coordinates with the y value equal to zero or expressed in pola...

Page 76: ... 16 sin30 16 k v 30 icos30 sin60 icos60 13 85640646 8 i u 8 R 70 12 R 25 e 18 5408873 42 76427608 r1 8 θ1 70 r2 12 θ2 25 r θ 1 i E 1 Q e 1 1 i u 1 414213562 r θ 45 E 2 3 Q 2 3i 2 A e 5 12 i 1 1 Q Z e 0 5 1 i 0 5i conj 5 2i I 0 5 2 Q e 5 2 i 12 6 Q 7 15 Q Q 30 z Q 60 e v 60 Example Key operations Result e 0 COMPLEX MODE ...

Page 77: ...ations In the NBASE program mode you can perform logical operations and calculations using N base numbers Programming concept It is not within the scope of this manual to describe how to write programs for the calculator in detail Previous programming experience is required to read this section The programming language for this calculator is similar to those in general use today All conventional c...

Page 78: ...am under this name as you create it You do not have to save the program manually Creating a NEW program 1 Press b 2 to enter the PROG mode and then press 1 to create a NEW program The display prompts you to select the NORMAL program mode or the NBASE program mode 2 For this example press 0 to select the NORMAL program mode The display prompts you to enter a program name 3 Type the name of the prog...

Page 79: ... Y equal to M1 X 5 On encountering this equation while running the program if the value of the local variable M1 has not been defined earlier in the program the calculator prompts you with the display M1 to enter a value for M1 The global variable X will already be set to the value last stored in that memory With just a little practice you will soon become proficient at typing programs into your c...

Page 80: ...command will wrap to the next line if the text length exceeds the display width You can only enter one command per line except for special cases such as the If Goto structure For more programming examples see Chapter 8 Application Examples Chapter 7 Programming Print B BASE i 1 v B1 e e Print H HEIGHT a BASE e i 1 v d H1 e e a HEIGHT e A 1 k 2 v e v d e e A 1ı2B H Print AREA i 1 a AREA e i 0 A e P...

Page 81: ...t A Input B Wait 5 hexadecimal mode binary mode Print B Print SHARP Print variable Displays the value of the specified variable The display format is determined by the SET UP menu Displays the text entered after the quotation mark If the text exceeds three lines only the last three lines will be displayed Temporarily stops the program and prompts you to enter a value for the variable with the disp...

Page 82: ...nning a program Excessive use of this command will use up a considerable amount of memory Terminates the program If the program finishes at the last command an End command is not required If there is no End command in the program the last calculated answer will be displayed when the program finishes You can use more than one End command in the same program to terminate after different branches sub...

Page 83: ...nt line that indicates where to go Defines the end of a subroutine Operation returns to the command following the corresponding Gosub statement The If clause must be followed by a conditional statement and then a Goto command Goto is the only command allowed to be used after the If clause You can enter s before the Goto command to make the line easier to read Runs the subroutine beginning at the s...

Page 84: ...ables You can also enter by simply pressing Symbols i C If B 0 Goto ZERO Equals This function is also used to form a substitution command that assigns a new value to a variable including incrementing or decrementing If B 0 Goto NGTV i D Less than If B 0 Goto RECALC i F Greater than or equal to If B 0 Goto PSTV i G Greater than If A B Goto DIF i H Not equal to If B 0 Goto CALC i E Less than or equa...

Page 85: ...hapter 7 Programming Command Description Key operations Examples i I STATx Selects single variable statistics mode SD STATx i J STATxy Selects linear regression calculation mode LINE STATxy i K Data 5 Data 25 2 Data 72 175 Data 9 96 3 Enters new statistical data The data format must be consistent with the statistics mode selected single variable or linear regression A statistical data set entered ...

Page 86: ... to enter two or more commands on a single line The line you modify is saved after you press u d or e If you do not wish to change the line press j twice The line will disap pear at this point however the contents of the line are not deleted To clear an entire line of a program press j then u d or e To delete a blank line move the cursor to the blank line and press y Any blank lines will be ignore...

Page 87: ...lem while running your program For example if you have more than one label with the same name in your program you will see the message on the right To display the faulty line in the EDIT mode press r or l To return to the program menu press j You can press j to stop your program at any time while it is running This will be necessary if your program enters an endless loop After BREAK is temporarily...

Page 88: ...or s memory To free up space for new programs you must delete old ones 1 Press b 2 to enter the PROG mode 2 Press 3 The delete window appears All the stored programs are listed 3 Move the cursor to the program you wish to delete and press e The calculator asks you if you are sure you want to delete the program Press y to delete the program or e to cancel this operation Chapter 7 Programming ...

Page 89: ...ahrenheit and vice versa 1 Press b 2 1 0 to open a window for creating a NEW program 2 Type TEMP for the program title then press e A NEW program called TEMP will be created 3 Enter the program as follows See below for further explanation Program code Key operations Label START i 6 a START e Print 1 C TO F i 1 1 a s C s TO s F e Print 2 F TO C i 1 2 a s F s TO s C e Input T i 2 T e TEMP NORMAL PRO...

Page 90: ...e Print C i 0 C e End i 5 e Running the program 4 Press j to return to the PROG mode menu 5 Press 0 select the program TEMP and press e The program prompts you to choose which conversion you wish to perform Then it asks you to enter the tempera ture value PROGRAM MODE ƒRUN NEW EDIT DEL Chapter 8 Application Examples The program automatically prompts you to enter a value for the local variable C0 T...

Page 91: ...A NEW program called HERON will be created 3 Enter the program as follows Program code Key operations Label START i 6 a START e Print SIDE LENGTHS i 1 a SIDE s LENGTHS e Input A i 2 A e Input B i 2 B e Input C i 2 C e If A B C Goto ERROR i 8 A B i E C s i 9 a ERROR e If B C A Goto ERROR i 8 B C i E A s i 9 a ERROR e If C A B Goto ERROR i 8 C A i E B s i 9 a ERROR e T A B C 2 T A B C z 2 e S T T A ...

Page 92: ...35 cm B and 40 cm C 4 Press j to return to the PROG mode menu 5 Press 0 select the program HERON and press e If the values you enter do not satisfy the conditions to make a triangle e g A B C where A B C are the side lengths the program prompts you to re enter the values from the beginning If you wish to stop the program press j 6 Enter 20 for A 35 for B and 40 for C Result The area of the triangl...

Page 93: ... creating a NEW program in the NBASE program mode 2 Type NBASE for the title then press e A NEW program called NBASE will be created 3 Enter the program as follows Program code Key operations Print ENTER A i 1 a ENTER s A e Print DECIMAL NUMBER i 1 a DECIMAL s NUMBER e Input Y i 2 Y e Y BIN Y z e Print BINARY i 1 a BINARY e Print Y i 0 Y e Wait i 3 e Y PEN Y r e Print PENTAL i 1 a PENTAL e Print Y...

Page 94: ...isplays it in binary format Press any key to display the number in pental format then press any key to see it in octal format and again press any key to see it in hexadecimal format Be careful when using the Wait command in NBASE program mode Numbers followed by Wait are processed according to the current number base binary pental octal decimal or hexadecimal To specify the wait time in decimal fo...

Page 95: ...mean value as 100 m 100 g a t test value is obtained If it is larger than the expected t value obtained from a t distribution table at 5 of risk rate the estimation is wrong In this case A s SHOP does not sell honestly Sample 1 2 3 4 5 6 grams 102 95 107 93 110 98 1 Press b 2 1 0 to open a window for creating a NEW program 2 Type TTEST for the title then press e A NEW program called TTEST will be ...

Page 96: ... i 2 M e T M sxΠT I 5 1 M z I 5 2 A z I 5 0 e Print T i 0 T e End i 5 e Running the program 4 Press j to return to the PROG mode menu 5 Press 0 select the program TTEST and press e 6 Enter the expected mean value 100 and press e Result The t test value of 0 303 is smaller than the 2 571 expected mean value obtained from a t test distribution table at 5 of risk rate showing that they sell honestly...

Page 97: ...ese points To satisfy the above conditions the distances between P Q S and O should be equal as they are the radius of the same circle Therefore PO QO SO R Using the Pythagorean theorem PO2 X1 X 2 Y1 Y 2 R2 QO2 X2 X 2 Y2 Y 2 R2 SO2 X3 X 2 Y3 Y 2 R2 then To enhance both readability and writability of the program intermediate variables G H I J K and M are used The above equations reduce to 1 Press b...

Page 98: ... I e Print Y i 0 Y e Wait i 3 e R X X ΠY Y ΠR X v 0 A Y v 1 A e Print R i 0 R e Example Obtain the center coordinates X Y and radius R of the circle that passes through points P 1 9 Q 7 1 and S 0 2 4 Press j to return to the PROG mode menu 5 Press 0 select the program CIRCLE and press e 6 Enter the coordinates X1 to X3 Y1 to Y3 for the three points Result The center is 4 5 and radius is 5 Chapte...

Page 99: ... C 1 Press b 2 1 0 to open a window for creating a NEW program 2 Type DECAY for the title then press e A NEW program called DECAY will be created 3 Enter the program as follows Program code Key operations Print ORIGINAL MASS i 1 a ORIGINAL s MASS e Input M i 2 v M0 e e e Print CURRENT MASS i 1 a CURRENT s MASS e Input M i 2 v d M1 e e e Chapter 8 Application Examples The mass of 14C contained in a...

Page 100: ...Print YEARS i 1 a YEARS e End i 5 e The half life of a radioactive isotope is the time required for half of its mass to decay Running the program 4 Press j to return to the PROG mode menu 5 Press 0 select the program DECAY and press e 6 Enter 100 for M0 and 50 for M1 Result The half life of 14 C is 5719 980034 years Chapter 8 Application Examples ...

Page 101: ...eated 3 Enter the program as follows Program code Key operations Print 1 DELTA TO Y i 1 1 a DELTA s TO s Y e Print 2 Y TO DELTA i 1 2 a Y s TO s DELTA e Input X i 2 X e If X 1 Goto DTOY i 8 X 1 s i 9 a DTOY e If X 2 Goto YTOD i 8 X 2 s i 9 a YTOD e Label DTOY i 6 a DTOY e R1 Z1 R2 Z2 R3 Z3 The Delta Y transformation is defined by the following formula R1 R2 R3 where Z Z1 Z2 Z3 Z1 Z2 Z Z2 Z3 Z Z3 Z...

Page 102: ...1 z Z e Print R i 0 v 3 e Wait i 3 e R Z Z Z v d d d d R2 e e v 1 v 2 z Z e Print R i 0 v 4 e Wait i 3 e R Z Z Z v d d d d d R3 e e v 2 v 0 z Z e Print R i 0 v 5 e End i 5 e Label YTOD i 6 a YTOD e R R R R R R R R v 3 v 4 v 4 v 5 v 5 v 3 e Z R R v 0 R z v 4 e Print Z i 0 v 0 e Chapter 8 Application Examples ...

Page 103: ...ly obtain the impedances R1 R2 R3 of a Y circuit 4 Press j to return to the PROG mode menu 5 Press 0 select the program DELTAY and press e The direction of transformation will be asked 6 Press 1 e to select DELTA TO Y transformation 7 Enter 70 for Z1 35 for Z2 and 140 for Z3 Result The impedances R1 R2 R3 of the targeted Y impedance circuit are 10 20 and 40 respectively Chapter 8 Application Examp...

Page 104: ...ype TENSION for the title then press e A NEW program called TENSION will be created 3 Enter the program as follows Program code Key operations Print ANGLES i 1 a ANGLES e Input A i 2 A e Input B i 2 B e Print WEIGHT i 1 a WEIGHT e Input W i 2 W e C AΩDEG C A e D BΩDEG D B e W T S B A Perpendicular line W T S B A T W S W where W weight T S tension in strings A B angles that strings make from perpen...

Page 105: ... 0 to set the angular unit to DEG then J 1 0 3 to set display to fixed mode with the decimal point of 3 In this program input angles by degree minute second format They will be automatically converted to decimal degrees 5 Press b 2 0 select the program TENSION and press e 6 Enter 30 15 20 for angle A and press e 7 Enter 27 45 40 for angle B and press e 8 Enter 40 for weight W and press e for S 9 P...

Page 106: ...N will be created 3 Enter the program as follows Program code Key operations Print PRICE i 1 a PRICE e Input P i 2 P e Print DOWN PAYMENT i 1 a DOWN s PAYMENT e Input D i 2 D e Print MONTHS i 1 a MONTHS e Input N i 2 N e Print RATE i 1 a RATE e Input I i 2 I e I I 100 I I z 100 e S P D I 1 1 I N S P D k I z 1 1 I m S N e Chapter 8 Application Examples S P D where S payment due every month n n mont...

Page 107: ...r in 11 month s installments with a monthly interest rate of 1 how much is the monthly payment 4 Press j to return to the PROG mode menu 5 Press 0 select the program PAYBYMN and press e 6 Enter 3000 for P 500 for D 11 for N and 1 for I Result Your monthly payment is approx 241 Chapter 8 Application Examples PAYBYMN NORMAL PRICE P 1 S 241 1351893 ...

Page 108: ...ogram called DICE will be created 3 Enter the program as follows Program code Key operations Print NO OF DICE i 1 a NO s OF s DICE e Input N i 2 N e Label PLAY i 6 a PLAY e M 1 M 1 e X 0 X 0 e Label ROLL i 6 a ROLL e X X r dice X X w 1 e M M 1 M M 1 e If M N Goto ROLL i 8 M i E N s i 9 a ROLL e Print X i 0 X e Wait i 3 e Goto PLAY i 9 a PLAY e Running the program 4 Press j to return to the PROG mo...

Page 109: ... window for creating a NEW program 2 Type NUMBER for the title then press e A NEW program called NUMBER will be created 3 Enter the program as follows Program code Key operations M 1 M 1 e A 0 A 0 e Print HOW MANY DIGITS i 1 a HOW s MANY s DIGITS e Label NINE i 6 a NINE e Print LESS THAN 9 DIGITS i 1 a LESS s THAN s 9 a s DIGITS e Input N i 2 N e If N 9 Goto NINE i 8 N i G 9 s i 9 a NINE e Print H...

Page 110: ...REE e Q ipart Sx10 N Q I 1 S k Y N e Goto DISPLAY i 9 a DISPLAY e Label SIX i 6 a SIX e Q I 1 S k Y N 6 k Y 6 w 0 k Y 6 w 0 k Y 3 e Goto DISPLAY i 9 a DISPLAY e Label THREE i 6 a THREE e Q I 1 S k Y N 3 k Y 3 w 0 k Y 3 e Label DISPLAY i 6 a DISPLAY e Clrt i 7 e Print Q i 0 Q e Chapter 8 Application Examples Q ipart S 10 N 6 10 6 random 10 6 random 10 3 Q ipart S 10 N 3 10 3 random 10 3 ...

Page 111: ...ORE s IS e Print A i 0 A e End i 5 e Running the program 4 Press j to return to the PROG mode menu 5 Press 0 select the program NUMBER and press e 6 Enter the number of digits you wish to play with N 7 Enter the number of seconds to display the numbers 8 Immediately after you press e the game will start 9 After ANSWER X is displayed enter the number you remembered and press e After 10 tries the sc...

Page 112: ...etermining the value of T 2 Press x T to store the result as global variable T 3 Press J 1 1 4 Select the scientific display format with four significant digits Use the solver function to solve the equation for r 4 Press j T A 4 s A z G M k R 1 5 Check the equation on the display and press I 5 to enter the solver function Chapter 8 Application Examples 23 56 4 09 Ωse c 86164 09 86164 09 AnsÒT 8 61...

Page 113: ...he star is and the luminosity of the star Since stars are seen from different distances their luminosities must be standardized before they can be compared This is done using a quantity called the absolute magnitude which is a measure of how bright that star would appear if it was viewed from a distance of 10 parsecs about 32 6 light years If the absolute magnitude of two stars is known the ratio ...

Page 114: ...he star is nearly six times as luminous as the sun Example 2 A second star has only 0 0003 times the luminosity of the sun What is its absolute magnitude The previous equation is equivalent to 1 Press 4 8 l 0 0003 z 0 4 e Result The absolute magnitude of the second star is approximately 13 6 Chapter 8 Application Examples M2 M1 where 0 0003 L2 L1 L2 L1 log 0 4 4 8 log0 0003 0 4 13 60719686 10 0 4 ...

Page 115: ...ow at the prices and in the quantities shown What was the total sales figure Item Price Quantity TV set 599 95 10 Phone 159 95 27 Clock 39 95 52 Calculator 7 95 108 1 Press b 1 0 to select the single variable statistics mode 2 Press 599 95 10 _ 159 95 27 _ 39 95 52 _ and 7 95 108 _ All the data is entered 3 Press I 0 4 e The calculator displays Σx that is the total sales value Result Total sales w...

Page 116: ...35 but you must pick them in the correct order Which lottery gives you the better chance of winning In the first lottery your chances of winning with one ticket are one in 50C6 1 Press b 0 50 N 6 e Your chances of winning the second lottery with one ticket are one in 35P5 2 Press 35 e 5 e Result Your chances are better in the first lottery Chapter 8 Application Examples 0 50Ç6 15890700 15890700 35...

Page 117: ...atteries are factory installed before shipment so may become exhausted before reaching the service life stated in the specifications When to replace the batteries Replace the batteries immediately when any of the following situations occur The calculator does not turn on when j is pressed The message Change Batteries appears Continued use of the calculator when in low battery status may result in ...

Page 118: ...partially used batteries and be sure not to mix batteries of different types Keep batteries out of the reach of the children Exhausted batteries left in the calculator may leak and damage the calculator Explosion risk may be caused by incorrect handling Do not throw batteries into a fire as they may explode Replacement procedure All memory contents will be cleared if you remove both batteries at t...

Page 119: ...ce the cover and screws 8 Press the RESET switch using the tip of a ball point pen or similar object If you cannot see the message on the right repeat steps 1 7 9 Press e Do not press y If y is pressed the memory contents will be cleared 10 Adjust the LCD contrast See page 118 Automatic power off function The calculator will turn itself off to save battery power if no key is pressed for approximat...

Page 120: ... press X press o 0 and then press repeatedly to darken the display Memory check Press 1 in the OPTION menu to show the MEMORY CHECK display The amount of free memory in bytes is shown on the first line When the calculator is used for the first time the following amount of memory is available EL 5250 4 096 bytes EL 5230 1 280 bytes The figures after EQTN are the numbers of equations Filing equation...

Page 121: ...s y to delete data Press e to cancel the operation Once a file has been deleted there is no way to recover it To delete individual files enter the mode that contains the data you want to delete and use the specific delete function from the menu See pages 59 and 86 If an Abnormal Condition Occurs Should an abnormal condition occur such as none of the keys including j functioning press the RESET swi...

Page 122: ...hat are not pointed to by Goto or Gosub commands without affecting program operation Make sure your program does not have more than 20 labels Make sure your program does not have more than 10 levels of nested subroutines Make sure your program does not have a Return command with no corresponding Gosub command Not enough free memory remains for what you are trying to do Delete unneeded files and tr...

Page 123: ...ero if no value is stored to be the initial expected value for the unknown variable and tries to solve the equation If it fails to find an acceptable solution using this expected value it tries again using up to nine more initial expected values until a solution is found If none of the values lead by successive approximation toward an acceptable solution but rather to a dead end the calculator wil...

Page 124: ...ected values After entering your equation by pressing I 5 press J to adjust the range of expected values The calculator will then prompt you for a range of expected values between 1 1099 and 1 1099 to be used in the calculation The range of expected values returns to its default setting 1 1010 to 1 1010 when the current equation is cleared or the mode is changed After entering the lower and upper ...

Page 125: ... x the gradient near peaks or troughs is very shallow If the initial expected value falls too close to a peak or trough the calculator may iterate to a totally different cycle of the function and will not obtain an accurate solution Make sure the initial expected value is an appropriate distance between a peak and a trough Where appropriate you can try rearranging the equation so that the unknown ...

Page 126: ...and singular points of functions and in programmed repetitive calculations Calculation ranges 10 99 to 9 999999999 1099 and 0 If the absolute value of an entry or a final or intermediate result of a calculation is less than 10 99 the value is considered to be 0 in calculations and on the display Function Dynamic range DEG x 1010 tan x x 90 2n 1 sin x cos x RAD x 1010 tan x tan x x 2n 1 GRAD x 1010...

Page 127: ... GRAD DEG x 10100 DRG RAD GRAD x 1098 n n r n n r 180 10 9 π ex 10100 x 230 2585092 10x 10100 x 100 sinh x cosh x x 230 2585092 tanh x sinh 1 x x 1050 cosh 1 x 1 x 1050 tanh 1 x x 1 x2 x 1050 x3 x 2 15443469 1033 x 0 x 10100 x 1 x 10100 x 0 n 0 n 69 __ θ 2 π A Bi C Di A C 10100 B D 10100 A Bi C Di A C 10100 B D 10100 A Bi C Di AC BD 10100 AD BC 10100 AC BD 10100 C2 D2 A Bi C Di BC AD 10100 C2 D2 C...

Page 128: ...0 x 111111111 OCT PEN 2222222223 x 4444444444 HEX 0 x 2222222222 AND OCT 4000000000 x 7777777777 OR 0 x 3777777777 XOR HEX FDABF41C01 x FFFFFFFFFF XNOR 0 x 2540BE3FF Memory usage The amounts of memory the calculator uses for variables programs and equations are shown below Variables Each variable uses 1 byte and each local variable uses 9 bytes to store its value Programs Creating a new program us...

Page 129: ...rs or commands Priority levels in calculations Operations are performed according to the following priority Fractions 1ı4 etc engineering prefixes Functions preceded by their argument x 1 x2 n etc Yx x Implied multiplication of a memory value 2Y etc Functions followed by their argument sin cos etc Implied multiplication of a function 2sin30 etc nCr nPr AND OR XOR XNOR M M M 왘DEG 왘RAD 왘GRAD DATA CD...

Page 130: ...ations solver functions simulation calculations complex number calculations etc Statistical calculations One variable statistics two variable statistics normal probability calculations etc Equation solvers Simultaneous linear equations and quadratic cubic equation solvers Programming function New programming running a program and editing a program and deleting a program Option menu LCD contrast me...

Page 131: ... door 93 68 EEG Dette udstyr overholder kravene i direktiv nr 89 336 EEC med tillæg nr 93 68 EEC Quest apparecchio è conforme ai requisiti della direttiva 89 336 EEC come emendata dalla direttiva 93 68 EEC 89 336 93 68 Este equipamento obedece às exigências da directiva 89 336 CEE na sua versão corrigida pela directiva 93 68 CEE Este aparato satisface las exigencias de la Directiva 89 336 CEE modi...

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