*The information contained here is subject to change without notice. underproduction this manual either in part or its entirety is forbidden. e Note that the manufacturer assumes no responsibility for any injury or loss incurred while using this manual. *Noe that the manufacturer assumes no responsibility for any loss or claims by third parties which may arise through use of this unit.
Foreword Congratulations on you selection of a CASIO calculator. The latest in modern electronics and digital technology makes almost every calculating job quicker and easier.
[ Contents | Chapter 1 Getting Ready 1-1 Switching Power ON and OFF . ...l 12 1-2 Loading Batteries 1-3 Adjusting the Contrast. Chapter 2 Getting to Know Your Calculator 2-1 Using the Calculation Modes . Operation Calculation Modes: .. 2-2 Correcting Entries on the Display Changing a Character or Function, Deleting a Character or Function Inserting a Character or Function .. Chapter 3 Manual Calculations ' 3-1 Specifying the Format of Calculation Results... 22 Specifying the Number of Decimal Places .
Recalling Calculation Sequences Correcting Errors Indicated by Error Messages . .. 34 Chaining a Series of Calculations .35 3-4 Using Scientific Functions in Calculations .36 Specifying the Unit of Angular Measurement .36 Specifying the Unit of Angular Measurement for a Specific Value Using Trigonometric and inverse Trigonomatric. Functions Using Logarithmic and Exponential Functions . Hyperbolic and Inverse Hyperbolic Functions (f-5000F).
Power REGRESSION corridor oot s teabag e inputting data .. Deleting an put data pa Performing calculations 3.7 Using Scientific Constants in Calculations .. e, 59 Chapter 4 Built-in Formula Calculations 4-1 Using Built-in Formula Calculations. a4 Recalling Built-in Formulas . .64 Recalling a Built-in Formula Using lis Formula Number 64 Sequentially Searching Through Built-in Formulas: . B4 Canceling a Built-in Formula Recall Inputting Values for Built-in Formula Variables .
. Area of a Triangle . Sine Theorem (1) . Sine Theorem (2} . Rectangular— Polar Coordinate Converse . Coordinate Conversion. Logarithm with Random Base . Permutation.. . Combination , . Repeated Permutation) . Repeated Combination .-Sum of Arithmetic Progression . Sum of Geometric Progression. . Sum of Squares. . Sum of Cubes... . Inner Product .. .-Angle Formed by Vector . Distance Between Two Potts . Distance Between.Point and Straight Line . Angle of Intersect for Two Straight Lines.. .
. Cycle of Circular Motion .-Cycle of Circular Motion (3) . . Simple Harmonic Motion {1). .Simple Harmonic Motion (2). . Cycle of Spring Pendulum . Simple Pendulum (1} . Simple Pendulum (2) . Cycle of Simple Pendulum . Centrifugal Force . Centrifugal Fore (2} ;. Potential Energy. . . Kinetic Energy . Elastic Energy . Energy of Rotational Body . . Sound Intensity . Velocity of Wave Transmitted by a Chord . . Doppler Effect .ol . Relative Index of . Critical Angle of Incidence .
. Impedance in RC Series Circuit . Composite Reactance in LC Series Circuit . Impedance in LRC Series Circuit . . Impedance in LRC Parallel Circuit . Series Resonance Circuit. Parallel Resonance Circuit . Power Factor.. . Joule's Law . Joule's Law . Induced Electromotive Force . Voltage Gain . Current Gain . Power Gain . . A=Y Conversion . Y—A Conversion . Minimum Loss Malcolm . Change in Terminal Voltage Series Cancun . Probability Function of Binomial Distribution .
126. Module (4) 127. Reynolds Number ,128. Calculations Using a Appendices ‘Appendix A Keys and Indicators. General Guide . Upper dot display Indicators . Lower Power Switch Key Operations and Their Functions... Appendix B What to Do When an Error Q Occurs Error Message Table Appendix C Technical Reference. Order of Operations About.
HANDLING PRECAUTIONS *This unit is composed of precision electronic components, and should never be disassembled. Do not drop it or otherwise subject it to sudden impacts, or sudden temperature changes. Be especially careful to avoid storing the unit or leaving it in areas exposed to high temperature, humidity or large amounts of dust. When exposed to low temperatures, the unit will require more time 1o display answers and may even fail to operate. The display will return.
Chapter -1 Getting Ready This section describes everything you need to know to set up your Casio calculator for operation. It includes such: important information as how you change batteries and adjust the contrast of the display.
1-1/ Switching Power ON and OFF The power switch is located on the left edge of the calculator. You switch power ON by sliding the switch up, and OFF by sliding the switch down. Even if you leave the calculator ON, an Auto Power OFF function saves valuable battery power. This function automatically switches power OFF if you don't use the calculator for about six minuses. To switch power back on after operation of the Auto Power OFF function, simply press the IR key.
W Procedure (1 Switch the power of the calculator OFF Loosen the two screws on the back of the calculator and remove the back cover. a (3 Remove the screw fastening the battery holder in place and remove the holder. Remove the two batteries (if present) from the calculator, *You can remove the batteries by turning the calculator with its back downwards and tapping the corner of the calculator lightly on a desk or table.
13] Adjusting the Contrast The characters that are shown on the display of the calculator may sometimes appear dim because of your viewing angle or because the batters powering the calculator have become weak. You can adjust the contrast of the display-using a dial located on the right edge of the calculator. (f-1000F) (Ix-5000F) It you turn the dial in the direction shown by the arrow in the illustration, the characters on the display become darker.
Chapter. 2. Getting to Know Your Calculator This Chapter gives vou some basic information that is applicable to the general use of your calculator. It describes .the use of calculation modes; and. provides important information on how you can _change, delete, and insert characters on the display. You can find detailed descriptions of the keys and other controls in the general guide in ‘Appendix A-in the beck of this manual.
2 -1/ Using the Calculation Modes Your calculator can perform a large number of sophisticated calculations. In order to make operation as easy as possible, the calculator is programmed so that calculations are assigned to specific modes. You can select the mode you need using the key in the combinations noted below. Be sure that the calculator is set to the correct mode before you begin your calculation.
at olg This mode cannot be selected for calculations which contain scientific functions or when using the formula function. *SD mode: g} Standard deviation calculations (single-variable statistics). The symbol SD appears on the display when you select this mode, *LR mode Regression calculations {paired-variable statistics). The symbol LR appears on the display when you select this mode.
2-2 Correcting Entries on the Display After you have input a calculation formula, you can make any changes you need without having 1o restart input from the beginning: B Changing a ar Function You can make changes in a display at any time by moving 1o the character or function to be changed and then pressing the key for ihe correct entry. (i) Use the cursor keys to move the cursor to the ligation of the correction.
W Deleting a Character or Function You can delete characters or functions from a display by moving the cursor to the delete position and then pressing the & key. (1) Use the cursor keys. to move the cursor to-the location of the deletion. (2 Press the B key to delete the character or function, (3 Press B8 to perform the calculation or use the cursor keys to move the cursor to another position. Example Change 369x x2 to 369x2.
Chandler 3 Manual Calculations Tnr this ‘manta, the' term ) manual telecommunications to mean calculations that-you enter by hand, using the keys. These calculations are different from formula calculate and formula memory calculations . which are explained in: another . part .of this manual. This-Chapter describes. the manual calculations: which . you can perform, as well as certain functions which make handling such calculations quicker and cagier.
3 -1/ Specifying the Format of Calculation Results You can change the precision of calculation results by specifying the number of decimal places or the number of significant digits. You can also shift the decimal place of a displayed value three places to the left or right for one-touch conversions of metric weights and measures. *You cannot specify the display format (FIX, SC1) while the calculator is in the Base-n mode. Such specifications can only be made if you first exit the Base-a mode. .
Example Operation Display 1008 16. EDGE (4 decimal places) 16. 6667 SERRIED (Cancel specification) 16. 2007 X 14=400 20007 R4 400. {rounded te 3 decimal pieces, & without rounding of Ihs stored BT (2 decimal places) 400. 000 intermediate resistivity 200@87 E2 28,571 The stored 10-digit resit (28.57142867) is used when you continue the calculation by simply pressing £3 or any other arithmetic/function key. (The intermediate result is -automatically rounded to the specified threat decimal places.
¥ Rounding the Intermediate Result Compare the final result you obtained in the previous example with the final result of the following example. Example Operation Display 20057 X 14=400 20004763 1468 400, {rounded ta 3 decimal places, with R (3 decimal places} 400, 000 of the stored intermediate 2008876 28 571 {The intermediate. resit is automatically rounded to the specified three decimal places ) REDDER 28.571 {This rounds the stored intermediate result to the specified three decimal places.) < 28.
=2 *This cancels any specification and returns the number of significant digits to the original value. If you do not perform step the number of significant digits you specified in step (@ will remain in effect, even if you switch the power of the calculator OFF. Example Operation Display 100M8668 16. FEASIBLE (6 significant digits) 1.88687% (EEE (Cancel pacification} 16, W Shifting the Decimal Place You can use the @ key to shift the decimal point of the displayed value three places 1o the left or right.
3 2| Basic Calculations Basic calculations are those which include such arithmetic operations as addition, subtraction, multiplication, and division, as well.as terms contained within parentheses. To input basic calculations press keys for numbers, operators, and parentheses in left to-right sequence, just as the calculation would be written on paper. M Performing Arithmetic Calculations {1 Enter the calculation. *Press the proper keys in the left-to-right Sequence of the calculation as it is written.
M Using Parentheses in Calculations Riser open parentheses by pressing the (0 key, and closed parentheses by pressing the 0J key. Example Operation " Display X4=80 100G I 0R4E 80 243X (4+8) “You may omit closed parentheses which come immediately before the [ key (no matins how Mary are required). 7@ sE 65. *You may also omit 3 for the multiplication operation immediately before an open parentheses.
3-3, Making Calculations Quicker and Easier M Using Resells in Other Calculations Once you obtain the result for a calculation by pressing the @ key you can use that result in further calculations if it is still displayed. 3% 4=12, continuing with /3,14 Rl < Alas) [ 12 {followed by} (Ext] Compare: 1 /3x3 173, followed by. X3 1E3E® = 12438 allowed Recalling Results from the Answer Memory The-answer memory automatically stores the result of the last calculation that you have performed.
*Using the Answer Memory in a Calculation You can recall “Ans” at any time, and even use it within a formula or calculation. Remember, when you press the &8 key at the end of the calculation, the answer memory contents change ta the result of the Calculation you have just performed. = Perform the calculation 123 + 456 = 579, followed by 789 — 578 (which is the result of the previous calculation).
® Using Constant Memories Your calculator is equipped with. ten independent constant memories which let you individually store values and use them i calculations. You specify these memories by pressing the ® key followed by any umber key from through (3. *Storing a Value to a Constant Memory (D) Enter the value to be stored. @ Press the (3 key. @) Specify a constant memory number. @ Press [e.
*Recalling from a Constant. Memory (D Specify a constant memory number. Press E9. *This step is necessary to change the displayed constant memory number to the actual value stored in the constant memory. ‘ Recall the value stored in constant memory *Using Constant Memories in Calculations R You can use values stored in constant memories by simply specifying the memory number where the value would informally dapper in‘a calculation.
Note that you do not need to press the €3 key when a variable memory is used in a multiplication operation. Operation 'Input! 2x 1Ko DENBE® K1 x (K0 +IK2) 'Clearing a Specific Constant Memory D Press the (6 key. Press the = key. 3) Specificity the beriberi of the constant memory to be cleared. Press the §9 key. Clear constant memory KO. RERECORDED +Clearing All Constant Memories (@ Press the & key. (@ Press the [ key. @) Press the @ key. Example ] Clear ali constant memories.
M Recalling Calculation Sequences After you obtain the result of a calculation by pressing the @ key'you notice a mistake: Or maybe you have to do a long series of calculations which are only sightly different from each other. With your Casio calculator, you don’t need to input the entire calculation sequence from beginning to end. Just do the following. (@ Press either the @& or @ key. *Which key you should press depends on Where in the sequence the mistake is located.
W Correcting Errors Indicated by Error Messages Certain errors are pointed.out by the appearance of the error messages described in-Appendix. B when the & key is pressed. Your Casio calculator lets you recall the calculation sequence and instantly locate the error. When an error is displayed: (33 Press either, the (& or & key (it doesn’t matter which). *The calculation sequence appears on the display with the cursor postponed . automatically at the location of the error, (Haymaker. the required corrections.
M Chaining a Series of Calculations Your Casio calculator lets you chain multiple calculations into a series that is treated as a single calculation sequence. You can use one of three different symbols to connect each calculation in the chain, Chained calculations are performed one by-one, in the same left-to-right sequence as they would appear when written down. “1” — This connector tells the calculator to pause.until the. E8 key is pressed, and retains the values which. have been assigned to variables.
3-4 Using Scientific Functions in Calculations n Speedy the Unit of Angular. Measurement You will often find it necessary to work with various units of angular measurement when performing calculations that include scientific functions.
Example Q Operation Display Result in radians 243 +85, Brad 8576077464 Result in grads 36.9'+ 41, I 24EI6E (2RSS . 3438 36 REFEREE 76077464 2663, 873462 B Using Trigonometric and Inverse Trigonometric Functions You can include trigonometric and inverse trigonometric functions in calculations. You should also check that the unit of angular measurement Is set to the unit you want the final resit to be. Example Operation 297859012 Colorado) =05 2:5ind5” % Cosby’ = 0.597672477 (Find the value of x.when sinning.
Example Operation Display sinning X cosmos. 25rad= :239410404 *The above is calculated in radians, 0.25 ). 2 SERRIED. BELIED) 0. 3 Coffey (6 18EI B0 . 26EFIEE(S) | and is identical io 687 13°13. 53 0.298410404 ® Using Logarithmic and Exponential Functions You can include logarithmic and exponential functions in calculations. Example Q Operation Display. log!. 23 (logy! . 28) = @1.2368 0. 089905111 . n90{log. 90) =4.49980367 9068 4, 49980967 logo In456=0. 434284481 (53 456 AR 45660 0.
N Hyperbolic and Inverse Hyperbolic Functions (f-5000F) You can include hyperbolic and inverse:hyperbolic functions-in calculations. -Example Operation Display . 658 ) 18. 28545536 856761057 e 2368 1.856761057 BE2. 58 0. 986614298 §= &1 . T 58 0.22313016 0.22313016 | (Continuing) (e EFREN] 1.8 et (Provo of coshxtsinhy=e* ) RS0 B oohs 793865461 Value of x when tang ; o=t 0.8 sonatas sing 2% cosh *f 5= 1.389288923 23 i 4 1.723757406 sing-!| A CB EH) @108 ARG 2 B ED @.58 CAREER 2 H $ BARRERA) BROMIDE 0.
W Using Other Scientific Functions :: Example Operation Display V2 +/5 =3.65028154 ©2 @5 3. 65028154 2+ 5404 50= 54 FER 380 408 12, see 40320. 40320 | “With the P-5000F, press SEEDED. VREX4TKAG =42 EDEITI36E42E3490)E8 4z, Random number generation {escudo-random amber from | B &) 0.792. 0.000 to 0.989) SERIES T =7 fakirs ez m) ital B ’ 08D 4BE 7. EEE 8" i | CosmosDB 0 @ Ore 0. (Pratt of cos =1 8i') {Continuing) +err g = 2EETE4FIDE6 543080357 0.
| 3-5) Working: with Number Systems The Base-» mode lets you perform a variety of operations with values of different number systems. These include actual calculations, conversions from one number system to another; analogical operations. The Base-» mode is very useful because it lets you move'among binary, octal, decimal and hexadecimal umber systems. Due to the complexity of some conversions, however, you must observe the following precautions” when using this mode.
The fallowing shows the number systems that you can specify, as well as the Indicator which appears on the display and the maximum size of values that you can use in each number system. Maximum Size -~ Key Nuremberg System Display =B Binary T b 10 digits | EE o Octal o 10-digits Decimal d 10 digits Hexadecimal h 8 digits cSpec:fymg the Number, System for a Specific Value. No matter what standard number system is.now specified, you can still input a value from another number system.
M Converting Number Systems You can convert a value from one number system to another using one of two different methods by specifying the applicable number system. «Converting to the Standard Number System (73 Specify the standard number system. Enter the number system for a value and input the value. 3 Press the ¥4 key. Example Operation Display Decimal equivalent of 2Aw and B 27t EE2AE : 42,4 AIMEE ' 188.d Hexadecimal equivalent of 123w | @~ h" and 10162 EDE123E8 7.
*Converting from the Standard Number System (D Specify the standard number system @ Enter a value (of the standard number system). @ Press the B8 key. @ Specify a different standard burner system. ® Press the & key. *The displayed value changes to the number system specked in this step Example Operation Display BE— ' 22068 22, d Binary equivalence of 22+ &6 10110, b Octal equivalent Hexadecimal equivalent of 2210 ) 16.
™ Using Basic Arithmetic Operations You can.add, subtract, multiply and divide-using values of different number systems. Remember, that decimals are cut off in the Base-n mode. Example Operation | Display 101115+ 11010.= 110001 : 101 1ERNI0106D 110001, b B47 s~ DF s =AbB1 ) B47ERDFEE ABB. h 123X ABC 1, 37AF 41z EE123E@ ACE 37AF4. h = 228084 EE 228084, 4 1FZD 16— 10088 7881..d =1ECS,s &I 1EC9.h 76545+ 12,5= B d" =516s . ERE765420 2@ 334. d ) & 516. ¢ 123400+ @) 1234 REREAD =1258.0 Grue 2352.
M Using Logical Operations Logical operations are performed-using the & key for logical product, the key for logical sum, the &l key for negation, and the @ key for exclusive logical sum, Example Operation Display INDIANIAN =T8¢ 1110:AND36,= 1110, 23, 1206 OR1101:= 120 1010: AND (A, OR7.5) = 10105 55 Xor 6.0 Negation of 1234, Negation of offends B~ b 19681 @& b" 1110 PEEWIT 136 E) D o” 226861 B Fem 120 LITER) 10160 EEK 10106 @A @EDE 10088 308 il 128458 B h" REFFED 1110, 83, t2d. 1010, 6.
36| Performing Statistical Calculations The statistical functions of your Casio calculator simplify a wide variety of commonly used statistical operations. The actual formulas used by the-calculator for internal statistical calculations can be found in ‘Appendix C. Statistical calculations are divided into two types: standard deviation which is performed in the SD mode, and regression calculation which is performed in the LR mode.
Example 2| Data: Input;; 1015720 66730 The value which you input after the semicolon. (here, 6) tells the calculator how many times to repeat the previously input data item. there, 20). Deleting an input data item The method you used to delete in data depends upon. when and how the data were input. 40-pt clear 5O, press the (&0 Key. Exam 200 clear 20, press 20 [, Example 3 30E0 506 120 EA D) To clear 120TH (3, press &8. Example 5067 120 B 131 o T To clear 12088031, press 3.
Performing calculations Perform.the following operations.in any sequence.to display the results noted. Key Operation Result IRE :Standard deviation ‘g FREER Standard deviation a4 & ) Mean HORDE Sum of squares 9 (K) (2168 Sum G () (3189 Number of data Example Operation Display Data: FEd WEED (Ornery clear) 556754 @5 15755 5153 BEET 54E705257 52, (Standard d0d2ton oy e 1. 316956719 deviation N 1:407885953 (Mean) EERIE £3.3758 (Number of data ) EEIE)3 E ) 8. {Sum) BEEBE 427.
® Performing Regression Calculations Once'you input a set of data in the LR mode, you can perform linear, logarithmic, exponential and power regression. It should be noted that some calculation results are automatically stored in certain constant memories as noted below. This means-that any values previously stored in these memories are lost. Memory Calculation Result K1 Sum of squares of x-data K2 Sum of x-data K3 Number of data items K4 Sum of squares of y-data Ks Sum of y.
e (Example 2 Data: 10/20, 20/30, 20/30, 20/30, 20/30, 20/30, 40/50 Input: 10 & [3]20 60 2013056 40315069 The value which you input after the semicolon (here, 5) tells the calculator. how many times to repeat-the previously input data pair (here, 20/30). Deleting an input data pair The method you used to delete in data depends upon when and how the data were input. : Example 1| 10ER 406D 20 ER{7) 2 30ER 306D clear 408 (7] 50, press. the @3 key. Example 2 106 (1)40ED .
Performing calculations Perform the following operations in any sequence to display the results noted. Key Operation Result (4 Constant term A ®=0 & Regression coefficient B E=E EEO Carr elation coefficient o= Estimated value Estimated value of y 3= Example Operation Display Temperature and length of LR steel bar Temp. Length EARPIECE (Memory clear) 1we 1003mm 10 15°C 1005mm 15EED) 1005 15, 20°C 101 0mm 20610101 20 o] 1011 nm CONDITIONED 25, 80'c 1014mm 3071101460 30.
logarithmic Regression The regression formula used for logarithmic regression is inputting data O Press for the LR mode. Press EIEIED 1o clear the statistical memories. (3 Input data pairs using the following operation: i) ¢x-data) @MY {y-satay If you have a number of data pairs which afe identical, you can input them as a group using the two procedures described for linear regression. Don't forget to' press the (i) key before inputting x-data. Deleting an input data pair .
Example Operation Display i i EEE— 23.5 28GR .66 3.36729583 74 28.0 EISENSTEIN. 55 3. 912023005 103 16.4 TI74EA)38. 067 4.304085093 118 8.9 103146, 46T 4. 634728988 ()t 18E148. 96T (Constant term A} (Regression coefficient B) EEE (Correlation coefficient r} G (9 when xi=80) [DDED =78) DR 4.770684624 —~111, 12833876 34, 02014749 0.994013248 37.
e *Exponential Regression The regression formula-used for exponential regression is nA+Bx). Outlining data (1 Press @€ for the LR mode. Press BAEDEKER to clear the statistical memories. @) Input data pairs using the following operation: { x-data ) { y-data)y B0 If you have a number of data pairs-which are identical, you can input them as a-group using the two procedures described for linear regression.
Example Operation Display 9@ILIE21 4B 6 9 12,3 15.7 12. 9GS5 7D 12.9 19.8 12.1 169 19.8 26.7 8.5 26. 7G2S, 567 26..7 35.1 5.2 85. 1715 . 268 351 (Constant term A} Renee «{Regression coefficient B) Eel E (Correlation coefficient r) (5 when 8 16 E PRI E X when y ) Commerce 30, 49758742 ~0. 049203708 ' =0. 997247351 13..
*Power Regression . The regression formula-used-for power regression is Nina + Blown. Inputting data (O Press for the LR mode: @ Press @IS to clear the statistical memories. 3 Input data pairs using the following. operation: (i) {x-data) @)l {y-data) BT If you have & number of data pairs which are identical, you cap input them as a group using the two procedures described for linear regression. Don't forget to press the [ key before inputting ¥-data and y-data.
Example Operation Display 2410 [28Em 241080 3.33220451 30 3033 )30@HE 303380 3.401197382 33 3895 (RI33ER]In3895E) 3. 496507561 35 4191 3@ w4491 3 555348061 38 5717 (DI )MS 75 3, 63758616 {Constant term A} FEED (Regression coefficient B).. @O (Correlation coefficient 7) feet )] (7 when xi=40) TEPEE ST (£ when' yi=1000) 238801082 2,771866148 0, 998906256 6587.674743 20.
3-7| Using Scientific Constants in Calculations You can.use any of the 13 scientific constants programmed in the memory of the ‘ calculator. Constants are selected by using the. following operations. i Operation Item Symbol Value Unit R i Speed of light in vacuum ¢ 200792458 ms™! o ED Planck’s constant A 6.828176 | Gravitational constant G 6.672x 10" NM? @mes E) | Elementary charge e 1.6021892x10°" Electron rest mass e 9.109534 x 10-31 Atomic mass unit " 1,6605655 % 10-7 kg | Avogadro constant Na 6.
Example Operation Display Gravitational constant (G) What is the force of alteration of two people weighing 60 kg and 80 kg separated by'a distance Formula: £ G227 2 Elementary charge Electron rest mass (17e) Obtain the Sustained force and acceleration -of electrons between two parallel electrodes 3 cm apart. when a voltage of 200 V is applied. Formula: ‘Atomic mass unit (i) The mass. of a hydrogen atom is 1.00783amu and ‘the electron mass is 1/1800 of this.
3-15 2418 84, 25 Example Operation Display Molar gas constant (R) An inflated rubber balloon is 2.5 atm. in pressure, 2.8 liters in velum, and 37°C in inside temperature. What is the total number of gas molecules in ine conical? PV Formula: maul; = Permittivity of vacuum (o) Hera is 3 condenser formed by two 700 cm® copper plates held parallel and 2 mim apart.
4-1 Using Built-in Formula Calculations Your Casio calculator is programmed with 128 built-in formulas that you can easily recall by entering the correct formula numbers. H Recalling Built-in Formulas You can recall butt-in formulas either by entering the correct formula number or by sequentially searching through the built-in formulas untie you find the one you need. *Recalling a Built-in Formula Using Its Formula Number You can recall any specific built-in formula by inputting its formula number.
precanceling a Built-in Formula Recall After you have recalled a bully-in formula, you can cancel it at any time by pressing (3. This switches to manual calculations, and the computer stars by waiting for truther input. R inputting Values for Built-in Formula Variables Once & boot-in formula is recalled, the next step is to input values for variables. The variables appear on the display with a question mark to request that you input a numeric value.
W Obtaining the Result of a Built-in Formula After.you enter values for all of the variables which appear on the display, you can execute the formula by pressing the &g key. Continuing from the previous example. (1) Press the &8 key. . axé+br+c=0 Notice that the symbol appears, along with an arrow.on the left side of the display. This indicates that there are other values in the solution set. Press the B3 key.
0 *Shifting the Built-in Formula on the Display Some of the built-in formulas contained in the memory.of the calculator are longer than the 14.columns on the display. In this case, you can shift the formula to the left and right on the display to read-it. Example | (@ Recall built-in formula number 41. D Press the & key 1o shift to the right. =28 va? o ve? 0 B indicators on the display below the formula show you the direction that 1he currently displayed formula continues.
® What to Do When an Error Is Generated The action you should take when an error is generated depends upon whether you are still inputting values or whether you are executing the formula. When an Ma error or Syn error appears while you are inputting values: () Press either the @& or & key (it doesn’t matter which). *Use the (@ and [ keys when you only want to make changes. If you want to clear afl of the values which you have input up to that point and start over again, press the &8 key and continue.
5-1| About User Formulas Of course, it is very possible.that you might need to use a formula which is not in the memory of the calculator. In this case, you can input a formula and either executes it once or store it in memory until you need it. You can also recall one of the built-in formulas, make any changes in it you want and then use it as a new user formula.
@ Display of C (30) and stop. @ Press E8. & Input of value for A {ex. 30). ® Input of value for B (ex. 40). (@ Display of D (70). * ' —This connector tells the calculator to clear the values which have been assigned to variables, without displaying any intermediate results. Example| . C=A+B ] D=A+B (1) Input of value for A (ex. 10), (@ Input of value for B (ex. 20). Input of value for A {ex. 30} @) Input of value for B (ex. 40). (® Display of D {70).
5.2 Using Manually Entered User Formulas You can input user formulas for one-me execution without storing them in memory. These are called manually emerged user formulas. Such formulas are mpu[ in the following format: Variable == Formula {Example | Manually input the user formula: /2 BEECHER R REINDEER 2 & M= (A+B) 65.. e @@ M= 605 5-3| Understanding User Formula Memories Your Casio calculator comes equipped with a total of 12 independent memories for storage of user formulas.
e a1 T The top line shows the formula memories which are empty and ready for storage. We refer to these memories using such names as memory P1, memory P2, memory PA, etc. Each time you store a formula in one of the memories, the name oi the memory you use is replaced on this display with a dash The number on the bottom line of the display shows the number of formula steps remaining in the entire user formula memory. This is a very important point.
The following lists the key operation and restrictions for each calculation mode. Comp & E) Base-n EDE Scientific function calculations cannot be performed *Unit of angular measurement cannot be specified. *Built-in formulas cannot be recalled. SD Eng *Abs and ¥ cannot be used. *E1 cannot be entered consecutively. LR *Abs and-¥ cannot be used. 7 cannot be entered consecutively. Press the B8 key. .*The display should appear as shown here. The.
m Modifying a Built-in Formula and Storing It as a User Formula You can recall any of the-128 built-in formulas programmed in the memory of the calculator, modify it, and then store it in one of the user formula memories. (D Enter the built-in formula name and press the @@ key. Note that you select the built-in formula before you enter the WRT made. @ Press 1o switch to the WRT mode.
W Executing a Formula Stored in a User Formula Memory Once a formula is stored, it'can be-executed at any time by specify the user formula memory name. (D Press @[T to enter thunder mode. @) Press @ followed by the formula memory name. @ Press the B key to execute the selected formula. Once you execute a formula, subsequent operation.depends on the type of formula that you recalled. For example, prompts may appear to tell you to input values for variables, etc.
Exam) Delete the formula #1..4.6789AB 5= 523 == P Oi_fif_6789@fi 5= 523 P Sz 589 *Deleting All User Formulas (T Press B33 to enter the PCL mode. (& Press @R 6. This deletes all user formulas, and causes all of the user formula memory names to appear on the display. Example | Delete all formulas.
Chapter 6 Formula Library This chapter lists all of the built-in formulas which are programmed in your calculator. A short explanation of the formula is followed by a brief operational example.
l *The quadratic equation can be solved when constants a, & and ¢ are known. Solve: Operation (a=0 8 1. Quadratic Equation Solution 4acz0) {Recall quadratic equation solution.} 209 {Enter value for .} 168 . {Enter value for @10 {Enter value for dummy.} B —80 — Display ara+bx+c=0 a? Q. axi+bx+c=0 b? 0. ax2+hx+c=0 c? 0.
2_ Simultaneous Linear Equation with Two Unknowns . @ b latex bey=c, by~ Cruz 0 [ax+hy=c a b e ::newsmen) +The simultaneous linear equation with two unknowns can be solved when and ¢z are known, Solve: S5x+4y Operation Display azz (Recall simultaneous linear equation with two a1° 0. unknowns.) 26 a2x 7 (Enter value for a1.) bi? Q. 268 a2% 6 (Enter value for azx {Enter value for ¢, az”? 0. 56 gax € {Enter value for a3:x (Enter value for 42.
Jr _JL.Z 1 (@1x+ byt cited, ax b by tez=dp ( a3x + sy + csz=ch 3. Simultaneous Linear Equation * with Three Unknowns @byt bicameralism cinchonas —biascs—aibacy w0 *The simultaneous linear equation with three unknowns can be solved when w30 by, €3 and dy are known. le Solve: [ X+6y+3z=1 ~Sx+d4y+z= -7 Q Operation Display i 1X+b1Y+C1Z 3 2 gL {Recall simultaneous linear equation with three a1’ 0. unknowns.) 268 (Enter value for a,.) bi1? 0. 16 ® (Ernie value for b,.) ci? 0. . 2 s (Enter value for c,.) od1? 0.
4_ Cosine Theorem @bt = becomes 2be cos 6 {0,074 T 1807 a, b and c are:sides of a triangle. ¢ is adjoining angle. *The cosine theorem is used when the lengths of two sides of a triangle and their adjoining angle are known to determine the length of the remaining side Two sides of a triangle are b= 15¢m and The angle formed by these two sides is §=62.3 degrees. Determine the length of the remaining side a. Operation Display @8] (Degree) ; Ea v (Recall-cosine thereon) b? Q.
5. Heron’s Formula And ¢ are sides of a triangle. ( *Heron’s formula is used to calculate the area of a triangle for which the lengths of its three sides ‘are-known. Example Determine the area of a triangle with the three sides a=12cm, b=8cm, c=17cm. Operation Display s (Recall Heron’s formula.} ar Q. (s~b 12/ . @ (Triter value for (5-b 8 5w (Enter value for b.) c? Q. 185 {Enter value for-c.
1 6. Area of a Triangle S= %hn sin b and ¢ are sides of a triangle. A is adjoining angle. +This equation is used o calculate the area of a triangle when the lengths of two sides and their adjoining angle are known. Example' ‘ Determine the area of a. triangle when twa sides measure b = 15cm and with the adjoining angle to the two sides being A =62.3 degrees. Operation Display #658 (2)B8 (Degree) : : ; Tocsin /s meme ‘ Parmesan Asz (Retail area of a triangle.) b? 0.
7. Sine Theorem (1) =k (U5 sin A a is one side of a-triangle, A is its-opposite angle, R is a radius of circumscribed circle *This-calculator is programmed with the following three formulas. (@ This formula uses the sine theorem to calculate the length-of the side opposite a known angle. @) This formula calculates the radius of a circle that circumscribes a triangle for which the length of one side and the angle opposite the side are known.
Sine Theorem (2) a_ b sin | sin B sin (0‘
. Rectangular = Polar Coordinate * Conversion (x>0, ~90° % 4 =90%) *Rectangular to polar coordinate conversion is Used when the lactation of the rectangular coordinates is known. important A Quadrant 11 Quadrant Be sure to perform cne of the following correction procedures on the calculated value of ¢ when x<0: olf =0 (Quadrant II), 6+ 180° olf y< 0 (Quadrant HI) 4-180° Also note that x=0 is undefined, and 0 such a result produces an error (Ma ERROR). Quadrant.
Polar = Rectangular Coordinate Conversion narcosis nursing@ 0sr) «Polar to rectangular coordinate conversion is used when the location of the polar coordinates is known. . Example Convert the distance from the origin and the angle from:the x-axis 18 degrees) to rectangular coordinates for point A. Operation Display (Degrees) . velours {Recall polar to rectangular coordinate r 0. conversion.) narcosis {Enter value for Marcos g ] . (Enter value for 8.) .
11. Logarithm with Random Base bl bxl O
Permutation ! al bars ) (n‘ are integers / Permutation is used to determine the total number of arrangements possible when number of items are taken from a total of items. With this calculator, the maximum value Exemplar Determine the number of permutations possible when three stems (= 3) are taken from a total of 10 #rems Operation s Display m'u {Recall permutation.) L e 0. 106 {Enter value for x.) r?* 0.
13. Combination *Combination i used to determine the total number of combinations possible when r number of items are taken from a total of 2 items. With this calculator, the maximum value ’Example Determent the number of combinations of three items (7 = 3) are possible from a total of 10 items Operation Display . %gafi combination) n? 0. eigenvalue for n) re 0. é%r value for r.
14. Repeated Permutation ally are positive integers) +Repeated permutation is used to-determine the total number of arrangements possible when 7 number of items. are taken from a total of » items, and-when repeated use of the mass item. is allowed. Example Determine the number of permutations possible when three terns 3) are taken from a total of 10 stems Repeated use of the samey item is allowed. Operation Display . T=nx>r @146 A . {Recall repeated permutation.) nt 0.
15. Repeated Combination are integers *Repeated combination is used to determine the total number of combination ‘ possible when 7 number of steins are taken from a total of n Stems; and when repeat use of the same item is allowed. With this calculator, the maximum vagus of iris 70. Example Determine the number: of combinations of threesomes (r=3) are possible from a total of 10 items (= 10). Repeat use of the same item is allowed. Operational Display . @S5 (Recall repeated combination.) n? 0.
46. Sum of Arithmetic Progression 2 *This equation is used to determine the sum from the initial term to ths nih term when the initial term and common difference are known. . | Example | Determine the sum for an arithmetic progression with an meal term of a==1 and a common difference of g=2. Operation v Display : {Recall sum of arithmetic progression.) n? 0.. 1060 Y (Enter value for 169 e (Enter value for a.) d? 0.
17. Sum of Geometric Progression This equation'is used to deferring the sum from the initial term to the'nth term when the initial term @nd’ common ratio are known.’ : Determine the sim up to 7=10for a geometric progression with an meal term of g=1 and @ common ratio of r=2." Q Operation . Display @vfl (Reciprocal of geometric’ progression.} (Enter values for a.) ‘ re Boas (Enter value for 1006 ‘o {Enter ‘value for n.
sum of Squares (s a positive integer) *This equation is used to determine the sum of the squares of fumblers from 1'to . Example Determine the sum of squares from 116 10. Operation + Display (2nd) 318 () . g {Recall sum of squares.) (2nd? 1088 8 {Enter value for 7.
19. Sum of Cubes =13 34, positive integer) *This equation is used to determine the sum of the cubes of numbers from 1 to . ample | Determine the sum of cubes from 1 to 10, Operation Display /232 @ Y Cos (Recall sum of cubes.) n? , 0. 1068 EXE] a8 (Enter value for n) S3025.
20, Inner Product Qb= b baas (a1, @) (b1, b2} are elements of vectors 7 and b. *This equation is used to determine the scale produce (inner product) when the elements of two vectors are known. Example Find the inner product for.the following wo vectors: 7 Operation Display ‘ , 5= aib1+aa 820 fiy ; bz (Recall inner product.) ayr? a1b1+a2ba Y (Enter value for.a..) bi1? Lo 0. P (Enter-value for S=aibitazb? 1469 o (Enter value for ¢z.) bha? 0.
*This equation is used when the elements of twe vectors are known to modeler the angle formed by the two vectors. 21. Angle Formed by Vector 7,5 a b+ ashy all Vald+a® VhE+b? {ar, @) (b1, bo) are elements of vectors & and 2%0) Determine the angle formed by the following two vector‘ 7 {~25 b Operation Display @ B=cos-l ((alibi (Recall angle formed by vector.) © 2 6 {Enter value for a1} @3 {Enter value for 5.} 5 B (Enter value for a;.) 29 {Enter value for by.} B=cos((aibi+ Lbt? : f=cos( ae? 0.
22, Distance Between Two Points ¢ == 27+ (32— 3 7 (x1, ¥1) (x2, y2) are coordinates of a point. *This equation is'used to determine the distance between two poms when the x, y“coordinates of the points are known, Predeterminer the distance between. 6) and 12). Operation . B . Display 226 A {Recall distance between two points.} x2? 0. : 2 7 1 Xe-x1l2+( {Enter value for x;.) (Enliven value for ({xe~ g 1088 1 ex-x1d e+l {Enter value for y2.) (txz—x1)e 6@ 1 X132+ () (Eigenvalue for y..
23. Distance Between Point and Straight Line by +¢f {2, b%0) (x1, ») are coordinates of a point; a, & and ¢ are constants. i -+This equation.is used to determine the distance between a-point and.a straight 3 line when the x, coordinates of the point and the: equation for the straight line | are known, Example i Determine the distance between point P (3, 5) and ‘straight line Operation’ Display , dabs (aXti+bYyt | mas Em A 2"~ (Recall distance between point and straight line.} ar . 0.
Angle of Intersect for Two Straight Lines tan are slopes of fines. »This equation is. used:ta determent ths angle of intersect for two straight lines when their stops are known. Example Determinism the angle of intersect ¢ for the:following two straight lines: ¥ =0:5x+2 Operation Display (2] E (Degree) g=tan-! E24 . o {Recall angle of intersect for two straight lines.) maQ. B=tan-t 2 . i (Enter value for m;.) mic 0. B=tan-l 05 {Enter value for m,.) B =36.
25, Area of a Triangle hz0) « is base of triangle, & is height of triangle »This-equation-is used to determine the area of a triangle when the length of the base and the height of the triangle are known. Example | Determine the area of a triangle with a base of «=9cm and a height of 2 = 6.5cm. Operation Display S=ah/2 05 2560) ; : {Recall area of a triangle.) a’ Q. S=ah/s oF hs2 {Enter value for a.) h? 0. S=ah/2 6.5 . @ (Enter value for 4.
S=ab (e, b20) 2. Area of a Rectangle « and b are sides of a rectangle, «This equation is used to:determine the area of a rectangle when the lengths of its sides are known. : mole Determine the area.of a rectangle that is 2= 8cm by b= 17cm. Operation @26 f : {Recall area of a rectangle.) 8 [ (Enter value for a.
27. Area of a Parallelogram (1) Sakai the base, /4 is the height *This equation is used to determine the area of & parallelogram when the length of the base and the height are known. o i ’?maple Determine the area of a parallelogram with a base'of and a height of Operation Display S=ah (Recall.area. of parallelogram (1)) a? 9.2 “{Enter value for o) 4.
28. Area of a Parallelogram bzl Signorina (0, ~a<180°> = and b are sides, « is adjoining angle *This equation is used to determine the area of a parallelogram when the length of two sides and their adjoining Angie are known. . Two sides of a parallelogram are g=7cm and b= 12om. The angle formed by these wo sides is o =36 degrees. Determine the area of the parallelogram: ! . Operation . . Display Rung) (2] (Degree) _ Absinthe (Recall area of a parallelogram @) a? 0.
i 29, Area of a Trapezoid 8221 (a+b)h (2. 6. hing) @ is upper side, »'is base, 7 js height *This equation is-use d to determine the ar ©a.of a trapezoid when the upper side, base, and height are known. Co [Example | Determine the:area of trapezoid with an upper SIDS of g = 7cm, abase of = 13em and a height of /=3, 6cm. . o i Operation Display : [ {Recall area of a trapezoid} (Enter value for @) . 1389 ! (Enter value for 5, ' S= 3.
Area of a Circle G = gry? (rz0) r is radius *This equation is.used to.determine the area of a circle when the.radius is known. Determine the area of a circle with a radius of Operation Display Snare foam ) {Recall area of a circle.) re Q0. Snare . 11.560 5 (Enter value for r.
31. Area of a Sector (1) S=ér€ (r £20) ris radius, ¢is length of arc *Whig-equation is.used to determine the area of a sector when its radius and arc are known, ’ Determine the area of a sector with a radius of r=5cm and an arc of i= 7em. Operation Display S=rls2 @31 \ » (Recall area of a sector I 0. . S=r1s2 5 , ” {Enter value for r.) 17 0.
32. Area of a Sector (2) «_art [ r20 5 360 ( 075 &5 360" ) ris radius, ¢ is central angle +This to determine the area of a sector when-its radius and central angle are known. Example | Determine the area of a sector with.a radius of r=6cm and entanglement of #= 42 degrees. LY S Operation oo it
33. Area of an Ellipse S=gab (. b20) *This equation is used to determine the area of an ellipse when its major and minor radii are known. Example Determine the area of an ellipse with a major radius of ¢ = a miner radius of b=17cm. :b\ &i/ Operation Display S=nah mas Em ) (Recall area.of an ellipse) a 0. Schnabel e for a.) b? 0.
34. volume of a Sphere ris radius s This equation is used to determine the volume of 4 sphere when its radius is known. Example Determine the volume of a sphere with a radius of r=8cm. Operation Display 34 4 2 (Recall volume of a sphere.) r? 0. =4nras 86 Sunrise . (Enter value for 1.
35. surface Area of a Sphere S=dxr? 7 is radius *This equation is used to determine the surface area of-a sphere when its radius is known, . Example | Determine the surface area of a.sphere with a radius of r=5cm. " 'Operation Display S=4mnre B35 . @ {Recall surface area of a sphere.
36. Volume of a Circular Cylinder V=gt (r iz0) 7 is radius of beds, & is height *»This equation is used to determine the volume of a circular cylinder when the radius of its base and its height are known. Determine the volume of a circular cylinder with-a-height of 4= 14cm and @ base of radius r=6cm. : Operation . Display (Recall volume of a circular cylinder.) Uznr2h . {Enter value for r.) h? Q. Rehung 1469 . @ (Enter vale for 4.
37. Lateral Area of a Circular Cylinder Se=2nrk (r.hz0) 7 is radius of base, # is height *This equation is used to determine the lateral area of'a circular cylinder when the radius of its base and its height.are known. . Example Determine the lateral area of a circular cylinder-with a height of h=14cm and a base of radius r=6cm. Operation Display | w37 S0 fz nri Y (Recall lateral area of a circular cylinder.} So=2nrh ] g&%r value for Seagram .
38. volume of a Pyramid (& hz0) A is area of bass, #.is height »This equation is used to determine the volume of a pyramid when Its height and the area of its base are known. Determine the volume of pyramid-with a height of /=7cm and a base of area A=56cm’. Operation Display U=Ah/3 mas Em s . (Recall volume of a pyramid.) A? 0. U=Ah/3 56 ® (Enter value for A} h? 0.
39. volume of a Circular Cone (r. hz0) r is radius of base, #.is height *This equation‘is used to determine the volume of a circular cone when the radius of its base and its height are known. T Example | Determine the volume of & circular-cone with a height of % =9cm and a base uf radius r=2cm. Operation Display U=nreh/3 {939 {Recall volume of a circular mne) U=nreh/3 . (Enter value for .} h ?_ w200 Lo Uznreh/3 9@ {Enter value for.
Soar (o020 +This equation is.usedto determine the lateral area of a circular cone when the radius of its:base and.its generate are known. Example Determine the lateral area of & circular cone with.a refrigerate of (=6cm and a base of radius r=3cm. ' Operation 40, Lateral Area of a Circular Cone 7 is radius of base, ¢ is generate Display Se=nrl o ) = (Recall lateral area of a circular cone.) So=nrl Y (Enter value for ) 1? Q. S0=7nrl 660 {Enter value for £) —~21R2L = $0.
4. Acceleration vy g=27 velocity for time 75, v, is velocity for time ¢ (>4 z0) +This:equation is used to determine the average acceleration between two points in time when the velocities are known for the two different points -in time. Example Determine the average acceleration whey the speed is v =64 km/h and v, =72 km/h at 12 =2:15. Operation . Display 41 @ (g~ Gz [FLa (Recall acceleration.) 7269 = (Enter value for v,.) vi? Q. 84E] (Enter value for t2? 2,25 » e {Enter value for ;.
42 Distance of Advance (rz0) vg is initial velocity, 4 is acceleration and ¢ is time «This equation is used-to determine-the distance advanced in ¢.seconds when the initial velocity and acceleration are known. [Example Determine the distance advanced by a mass in =5 seconds when the initial velocity is ve=12 mics and the acceleration is a= demise. Operation Display : ) @42 {Recall distance of advance.} vo?, o0 ) 12/ . {Enter value for vo.} t? 0: 59 £} a? 0. 2 3@ 5 (Enter value for a.
4.3, Distance of Drop 120y vo is initial velocity, g is gravitational acceleration *This equation is used to determine the distance of drop'in'f seconds when the initial velocity is known. | Example Determine the' distance of drop in 1--4 seconds ‘when-the initial velocity i$ 'Operation .. Display mas Em ML {Recall distance of drip) vo? .0, {Enter-value for vo.
44, Law of Universal Gravitation M and i are mass, r is distance between two objects, G is universal gravitation constant *This equation is used to determine the universal gravitation acting between two objects when the mass of each object and the distance between the two objects are known. Determine the universal gravitation acting between two objects of masses M —12kg and m =8kg, when the distance between the masses is r=6m. Operation _ ' Display maa N {Recall law-of universal gravitation.
45, Cycle of Circular Motion (1) T= 2z {w=0) @ «@ Is angular velocity *This regulation is used to determine the cycle of circular motion when the angular velocity is known. Example Determine the cycle of circular motion for movement at an angular velocity of w =2 radians, Operation Display T=2n/u 45 s o {Recall cycle of circular motion (1)) w? . T=2n/0 2B ® (Enter value for w.
)~ A6, Cycle of Circular Motion (2) T 2ny v (pa0) r is radius of circular motion, v is velocity of motion hen the angles equation is used to determine the cycles of circular motion when the radius id velocity of the mason are known. ; «ample ] ferocity of o st ermine the cycle of circular motion for movement around a radius of 7= 12em a velocity of Operation Display o T2 =2Znrsv * miasma s 5 Recall cycle of circus son (2). call cycle of circular motion u T=21rsv 54\ (Enter value for T=2nrsv .
47. cycle of Circular Motion frequency *This equation is used to determine the cycle of circular motion when the frequency of the motion is known. Example Determine the cycle of circular motion when:its frequency is /=13 Operation Display : : nave . ° | (Recall cycle of circular motion T=1/f ., . {Enter value for .
48, simple Harmonic Motion (1) x =7 fins (r>0) r s ‘amplitude, 4 is phase *This equation is used to determine the displacement when the oscillation amplitude and pass are known. Determine. the displacement for an amplitude of and.a phase of =30 degrees. . Operation Display ecru) , nursing 8 samosa , . {Recall simple harmonic motion nursing 8 420 w {Enter values for r.) g°? 0 Nursing (Enter value for 6.
49, simple Harmonic Motion (2) x =¥ sin wt (r>0) + is amplitude, « is angular velocity, ¢ is time «This equation is used to determine the displacement wham the amplitude of simple harmonic motion, time and angular velocity are known. Example | Determine the displacement for a simple harmonic motion with an amplitude of . r=5cm, time -3s and an angular velocity of =30 radians/s. Operation Display ) (5)E) (Rain) v nursing ot E4a9fm (Recall simple harmonic motion r 0.
50. cycle of Spring Pendulum T calm mass, & is spring constant *This equation is used-to determine the simple oscillation cycle when the mass of the weight and the spring constant are known. [Example Determine the. simple oscillation cycle for:a spring with & constant of £=3.6 N/m with a weight of mass. m = 12kg attached fo its end. Q Operation Display T=2nd (m/k) @ 50Em ‘ 2 z (Recall cycle of spring pendulum) m’ _ 0. 1268 T=2mi m/Ky {Enter value for T=2md (msk) | : (Enter value for \
51. Simple Pendulum (1) (m>0) m is mass of weight, ¢ is the angle of deflection from perpendicular, g is gravitational acceleration +This equation is used ta determine the movement force of a weight when its mass and the angle of deflection ¢ are known. [Example Determine the movement force of a weight with a mass of in = 34kg forming a simple pendulum with an angle of deflection of §=48 agrees. Operation Display [omd ()0 (Degree) (Recall simple pendulum 8 (Enter value for m.) B? 0.
52, simple Pendulum 0) m is mass of weight, ¢is length of string, x is location of weight, g is‘Gravitational acceleration *This equation is used to determine the movement force of a weight when its mass, the length of the string, and the position of the mass are. known. Determine the movement force of a weight with a-mass of m = 28kg forming a simple pendulum with a string of length when the weight is at position Operation Display 0526 FIZmBX/I o +{Recall simple pendulum m~ 0.
B53. cycle of Simple Pendulum (>0 2is length of string, g is gravitational acceleration *This equation js used to determine the cycle of a simple pendulum when the length of the string is known. Example | Determine the cycle of a simple pendulum with a string /=1.8 meters long. Operation Display . . T=2n{ (1,3) =536 : Y {Recall cycle of simple pendulum.) 1° 0.
54, centrifugal Force (1) F = mre® mass, r is radius, o js angular velocity #This equation is'used to determine the centrifugal force for-an object-moving in a circular pattern when the mass, radius and angular velocity are known. Example Determine the centrifugal force for abjection with a mass of i =4.2kg, moving at an angular velocity of w= 0.8 radians/s, in a circular pattern with & 'radius of Operation Display ‘ F=mrn? 54 " @ {Recall centrifugal force m 0. N F=mrw2 4.
55_ Centrifugal Force (2) .2 F= mbr— (rom, mass, v is velocity, r is radius »This equation is used to determine the centrifugal force for an abject moving in a circular pattern when the mass, radius and velocity are known, "Example | Determine:the centrifugal force for an object with a mass of m=60kg, moving at a velocity. of in a circular-pattern with 2 radius of.r= 3m. Operation Display . ‘@855 . o i (Recall centrifugal force Stuyvesant 60 @ (Enter value for F=mvea/r 1.4 : . (Enter value for v.
56. Potential Energy Ue=mgh mass, h is height, g is gravitational acceleration, 2 This equation is used o determine the potential energy for. an object when its mass and height {potential) are known. Determine the potential energy for an object with a mass of m=3kg at a height (potential) of /=5m from the ground. Operation Display Uriah (Recall potential energy.) might . (Enter value for Tos 50 . . mahatma . (Enter value for h.
57. Kinetic Energy Uk— my® G, v>0) 2 m is mass, v is velocity *This equation is used to determine the kinetic energy ior an abject when its mass and velocity are known, Example Determine the kinetic energy for an object wnh a‘mass of m = 8kg and a velocity of : Operation Display Universe @576 , : {Recall kinetic energy.) m* 0. 86 Uk=mve/2 S {Enter value for n2.) v? Q.
58, Elastic Energy z>0) k is-elastic constant, x is elongated length #This equation is used to determine the elastic energy for an object when the elastic constant and elongated length are known. Determine the elastic energy for an object with an elastic constant of k=1.8 Nlm and a elongated length of x=0.4 meters. Operation Display Up=kXes2 seem , : (Recall elastic energy.} K? -0, Ue=Kxe/2 1.88 ” 2 (Enter value for x? 0. Up=kX2/2 0.459 a {Enter value for x.
59. Energy of Rotational Body 2 (1. w>0) 1is moment of inertia, «is angular velocity #This equation is used to determine the energy of a rotational body when its moment of inertia and angular velocity are known. Determent the energy of a rotational body with a moment of inertia of =22 kg+m? and an angular velocity of =38 radians/s. *Operation ] Display mooed E=Iwis2 e (Recall energy of rotational body:) 1? 0. . E=l0i,2 : : for 3880 Edelweiss a (Enter value for w.) : E15.
60. sound intensity = P,, d7r® P is output from sound source, r is distance from sound source. (r >0} *This equation.is used-1 determine the sound intensity when.the output and distance from the sound source are known. Example Determine:the sound intensity for an output of P=2, *W at a distance of r=2m from the sound source. B : Operation Display = 2 60 Preordain . (Recall sound intensity) P? 0. : I=Rs anr © (Enter value for P.) r? 0. I=Prdmre 2@ a (Enter value for r.
61 Velocity of Wave Transmitted by a Chord o T is tensile strength of chord, ¢ is.linear density (=mass per 1cm of chord) *This equation is used to determine the velocity of a wave transmitted by a chord when the tensile strength of the chard and the mass per 1cmof chord are know. Determine the velocity of a wave transmitted by a chord with.a tensile strongmen of T=2.4 dyn and a linear density of Operation ) Display lackey] » 3 (Recall velocity of transmigrated by a chord.
©2. Doppler Effect v . ) FIFO— >0, -4 “>o> E oscillation frequency of sound source, v is acoustic velocity, is speed of movement of observer, vy is speed of sound source «This equation. is used o determine the oscillation. frequency of a sound heard by an observer.moving in the Same direction as the sound source when the source oscillation frequency and acoustic velocity, as well as the speeds of the sound source and observer are known.
03, Relative Index of Refraction _sin Gored) sin iis angle of incidence, ris angle of refraction *This equation is used to determine the relative angle index of refraction for medium 1 relative to medium I when the angle of incidence and angle of refraction foreknow when a light éntérs medium 11 from medium. 1. Determine the relative index of refraction for an angle of incidence i = 62 degrees, and an angle of refraction r=48 degrees. Operation ‘Display (58 (Degree) . .
64, Critical Angle of Incidence Seismic— (1ST} 12 maid relative index of refraction of medium 11 relative to 1 «This equation is used to determine the critical angle of incidence at which refracted rays.cease to exist (becoming loyal reflection) when the relative index of refraction of medium 11 relative to 1 is known. Determine the critical angle of incidence when: the relative-index of refraction is n=133. Operation Display {Hope} (4] (Degrees) ; 7_ & siccing-t (i/n) Behalf .
65 Equation of State of deal Gas (1) n is number of mewls, T is absolute temperature, V is volume, R is gas constant #This equation is used to determine pressure for a gas when its number of mewls, absolute temperature and volume are known, Determine the pressure mol gas with-an absolute temperature of T = 280K and a volume of V=5m®, Operation Display P=NRT/V sesame , . (Recall equation of state of ideal gas n’ 0. @ P=nRT/U 3 “ (Enter value for 280 B {Enter value for T.) y? 0.
©6. Equation of State of Ideal Gas (2) V= ”E;,T (1. # is number of mewls; T is absolute temperature, P is pressure, R is gas constant =This equation is used to determine volume for-a gas when its number of mewls, absolute temperature and pressure are known. Determine the volume mol gas with an absolute temperature of T = 242K and a pressure of P=30 N/m?. Operation Display U=nRT/P {Recall equation of state of ideal gas ne 0. U=nRT/P 2[pg ” s {Enter value for U=nRT/P 2420 \ @ {Enter value for T.) P? Q.
©7. Equation of State of Ideal Gas (3) _PV number's of mewls, P is pressure, V is volume, R is gas constant P,V n>0) +This equation is used to determine absolute.temperature for a gas when its number of mewls, pressure, and volume are known. Example Determine the absolute temperature of a n=3 mol gas with a pressure of P=24 N/m? and volume of V=8 m’. Operation Display @67 i . {Recall equation of state of ideal gas . 24 (Enter value for S 8 (Enter value for . 3 5 {Enter value for n.
68, Equation of State of Ideal Gas pressure, Vs volume, T is absolute temperature, R is gas constant "= P,V >0) *This equations used 1o determine the number of mewls for-a gas when its pressure, volume; :and absolute temperature are known. Determine the number of mewls of a gas with a pressure of P =32 N/m*, a volume of V=6 m® -and an absolute temperature. of T =246K. Operation Display (Recall equation of state of ideal gas P? 0. 3289 B (Enter value for P.} u? 0. e .
09. Quantity of Heat Q=mecT . m is.mass, c is specific heat, T.is temperature. *This equation is used to determine the quantity of heat required to raise the temperature of an object T degrees G when the mass and specific heat of the object are known. Example Determine the quantity of heat required to raise woad with a mass of #=460g and specific heat of ¢~ by T=10 degrees C. Operation Display B=mcT @e9 ” 5 (Recall quantity of heat,) m 3 B=mcT . 3 46009 < {Enter valise form.) c? 0.
70. Coulomb’s Law and g are sizes of two electric charges, ris distance between charges, &;is permittivity. (r>0) *This equation is used to determine the motive force between two electric charges when the size of the charges and the distance between them are known. Determine the motive force between two electric charges of sizes Q=3x10"% C (Coulombs) .and g=2x10"% C, with-a distance of between the charges: Operation Display ‘s roam {Recall Coulomb's law.) R? 0.
71. Magnetic Force by conductor and magnetic field «This equation is used.to determine the motive force for a current flowing in a conductor which is caused within a magnetic field of uniform magnetic: flux density. Determine the motive force of a conductor when a current of /= 4A flows through a conductor of length The angle between the conductor and & uniform (620, =16 =907 ¥ is motive force of conductor, i is current flowing through conductor, flux density, fis length.
7 2. Resistance of a Conductor R—pé (S. £ p>0) ¢is length of conductor, S is cross sectional area of conductor, p is resistance of material from which conductor is formed «This.equation is used to determine the resistance of a conductor when the length . and cross sectional area, as well as the resistance of the material from which the conductor is made are known. Determine the resistance of copper wire for a length of ¢=20m and cross.sectional area of (The resistance of copper wire is ohm-m.
73_ Frequency of Electric Oscillation =1 g f_Zm’T L is self-inductance, C is electric capacity +This equation is used to determine the harmonic oscillation frequency of a‘circuit'when the self-inductance and electric capacity of condensation are known. Example Determine the harmonic oscillation frequency of a circuit with self-inductance L=60mH. an electric capacity of € =90pF, . Operation ! Display (LC) 873 g 2 {Recall frequency of electric oscillation. (LD 609 308 .
74. Average Gaseous Molecular Speed (M. T>0) T is absolute temperature, M is molecular weight, R is gas.constant *This equation is used to determine average gaseous molecular speed for a gas when its temperature and molecular weight are known. {Example Determine the average gaseous molecular speed for oxygen which has a molecular weight of M=32x 107" kg/mol and atmospheric temperature of 15 degrees C {absolute temperature T =288.2K). ~ Operation : : ' Display v=¥ (3RT/M) 74 o .
75. Electronic Kinetic Energy in Magnetic Field kinetic energy, ¢ is electron charge, B is magnetic fix density, m is electron mass, R is radius of circular motion R* *This equation is used fo determine the electronic kinetic energy when the radius of circular motion of the electrons determined by the magnetic flux density of the magnetic field is known. T Example | Determine the kinetic energy of electrons moving in a circle with a radius of within a magnetic field with a magnetic flux density of B=0.
76. Strength of Electric Field feQ reorg (= (r>0 Q is quantity of electricity, r is distance from electric charge «This equation is used to determine. the strength of an electric field at a given distance from the electric charge when the quantity of the electricity is known. Exemplar Determine the strength of an electric field at a point which Is r = 20cm distant from the electric charge when the quantity of the electricity is | Operation Display @ E=Qrsdngor?2 (Recall strength of electric field.
7. Energy Density Stored in Electrostatic Field (1) E is electric field, ) is electric flux density *This equation is used to determine the electric energy in a system which includes an electric substance when the strength of the electric field and the electric flux density are known. Determine the energy density stored in an electrostatic field when the electric field with an electric flux density of D=8x 107° C/m? in an electric field of E = 200V/m. Operation Display w=EDs2 .
7 8. Energy Density Stored in Electrostatic Field E>0) E is electric field, e is permittivity »This equation is used-to determine the electric energy in a system which includes an electric substance when permittivity of the dielectric substance ani the strength of the electric field are known. Determine the electric energy density for mica with permittivity of 107" Fim within an electric field of E=200 V/m. Operation Display W=gE2/2 E78 {Recall briefer density stored in stalemate field W=EE2/2 6.283J11 \ (E
79. Energy Stored in Electrostatic Capacity (1) Loy w ZL\’ C is electrostatic capacity, V is electric potential difference *This equation is used to determine the energy stored in a conductor when the electrostatic capacity and electric potential difference of the conductor are known. ample Determine the energy stored in a conductor with an electrostatic capacity of CE=6pF, and an electric potential deference of V=700V, Operation Display . W=CUars2 79 .
80 Energy Stored in Electrostatic * Capacity ©>0) C s electrostatic capacity, Q is quantity of electricity *This equation is.used to determine the energy stored in a conductor-when the quantity of electricity stored in the conductor and the.electrostatic capacity are known, Example | Determine the energy stored in a conductor for a quantity of electricity’ Q=4x1077C and electrostatic capacity of Operation Display (Recall energy stored in electrostatic capacity &7 0 W=Re/ 20 4B O76E@ . .
81. Energy Stored in Electrostatic Capacity (3) L 1., Szilard( Q is capacity of electricity, V is potential difference *This equation is used to. determine the energy-stored in a conductor when the | capacity. of electricity stored in the conductor and the potential difference are known. { Example | ) ! Determine the energy stored in a conductor with for a capacity of electricity * | and potential difference of V=70V ; Operation Display W=6U/ (Recall energy stored in electrostatic . capacity ) .
82. Force Exerting on Magnetic Pole Famish (m. H>0) m'is magnetic charge, H is magnetic field strength *This equation is; used to determine the strength of a magnetic pole when the magnetic charge and magnetic field strength are-known. | Example Determine the strength of a magnetic pole for.a magnetic ‘charge of m=2 temperature, and a magnetic field strength of H=3% 107" Wb {(Weber). ' ‘Operation Display } Famish Ack] N e (Recall force exerting on magnetic pole.) m?* 0, Famish 2 = (Enter value for Famish .
83. Magnetic Energy of Inductance self-inductance of coil, T is current flowing in coil «This equation is used to determine the electromagnetic energy stored in a coil when the self-inductance of the ¢oil and current are known. Example Determine the -electromagnetic energy stored in a coil when a current of 1=6A flows to a coil with a self-inductance of . Operation Display W=LT2/2 JANACEK] . 3 {Recall magnetic energy of inductance.} L? W=l I2/2 0.
84, Electrostatic Capacity between * Parallel Plates C—fds (S, a>0) e is dielectric constant, S is area of parallel plates, d is distance between parallel plates *This equation is used to determine the electrostatic capacity stored’ between parallel plates when the dielectric constant of the material used in the plates, the area of parallel plates and the distance between the plates are known.
85, Impedance in LR Series Circuit ®RAL>0 . R is resistance, fis frequency, L is inductance »This equation is used to determine the impedance of an LR series circuit when the frequency, resistance and inductance are known. Determine the impedance for an LR series circuit with resistance of R =8 ohms and inductance of for a frequency of f=50Hz, Operation Display 85 Fl 2=V {Recall impedance in LR series circuit.) R? 0 & [Z=7 | 8 B (Enter value for (Enter value for 2 0.
86, Impedance in RC Series Circuit woofer ( VR + wzCz) (R, R is resistance, f is frequency, C is electric capacity #This equation is used to determine the impedance of an RC series circuit of frequency / when the resistance and electric capacity are known. Example Determine the impedance for an RC series circuit with resistance of R =12 ohms and electric capacity of .C = 80xF. (30 x 10 %F), for a frequency of f=60Hz.
87. Composite Reactance in ¢ LC Series Circuit X=2rfL T7FC (=wlL e X =Xe) fis frequency, L is inductance, C is electric capacity *Equalization is used to determine the reactance of.an LC series circuit of frequency / when the inductance and-electric capacity are.known. {Example Determine the reactance for an LG circuitousness with inductance:of L =0.2 M and electric capacity of C=704F (70107 °F), for a frequency of . Operation Display. a7 2 0.
88. Impedance in LRC Series Circuit 2= R+ (22— 277C resistance, f is frequency, L is inductance, C is electric capacity «This. equation is used to determine the impedance of an LRC series circuit of frequency f when the resistance, inductance, and electric capacity are.known. Example Determine the impedance for an LRC series circuit with resistance of R =2 ohms, inductance of and electric capacity of {30 x 10" *F), for a frequency of f=60Hz. Operation Display .
89. Impedance in LRC Parallel Circuit nonresistance, fis frequency, L is inductance, C is electric capacity *This equation is used to-determine the impedance of an LRC parallel circuit of frequency f when the resistance, inductance, and electric capacity are known. Pimple Determine the impedance for an-LAC parallel circuit with resistance of R =7 ohms, inductance of and electric’capacity of C=9xF (9x107°F), for a fre* quench of /=60Hz. Operation Display 2+ ¢ W80 {Recall impedance in LRC parallel circuit.
O(). Series Resonance Circuit Zero. b= R-is resistance, f is frequency, L is inductance; C is electrostatic capacity, Z is impedance «This equation Is used to determine the impedance and the impedance of a series resonance circuit when the resistance, inductance, electrostatic capacity and frequency are known. Determine impedance: Zealand Zx for resistance R =1 ohm, electrostatic capacity C=154F coot. inductance L=30mH (30210 *H), and frequency f=350Hz, . Operation Display Zr=R .
O1. Parallel Resonance Circuit ; ~ 1 Ge Ml R Yem2mCogdp o R-is resistance, fis frequency, C is electrostatic capacity, L Is inductance, Y is admittance +This equation is used to determine the admittance (inverse of impedance) and + the admittance of a parallel resonance circuit when the resistance, frequency, electrostatic capacity, and inductance are known.
Q2. Power Factor ) (R>0) R is resistance, Z is impedance *This equation is used to determine the power factor and lag angle for an AC circuit when its resistance and impedance are known. *Jag angle: expresses phase delay of electric current in reflation to electromotive force, [Example Determine the lag angle for an AC circuit with a resistance of R =12 ohms and impedance of Z=16 ohms. Operation Display (Dearer) F=0051 {Recall power factor.} $=g0s-l (R/2) 12 .
93, Joule’s Law (1) P=RI* R is resistance, 1 is current *This equation is used to determine the Joule heat generated by a conductor when the resistance of the conductor ard the current are known, | Ample ) Determine the Joule heat generated when an electric current of 1=20 amperes flows through a copper wire of resistance ohms. Operation Display Prize jackal] 2 0 (Recall Joule’s law R? 0. P=RI2 (Enter value for P=RI2 . 20 {Enter value for 1) 0.
04, Joule’s Law (2) V is electric potential differences, R is resistance «This equation is.used to determine the Joule heat generated by a conductor when its resistance and electric potential difference are known. {Example Determine the Joule heat generated when an electric potential difference of V=100V is applied to.a -copper wire of resistance R=1.1 x107% ohms. Operation Display P=U2sR o4 ; : (Recall Joule's law U? 0.
OB, Induced Electromotive Force Ve=vB¢ v is motive velocity of conductor, B is magnetic flux density. ¢is length of conductor *This-equation is used to determine induced electromotive force when the velocity, magnetic flux of the magnetic-field and conductor length are known when the conductor is moved within a magnetic field.
96. Voltage Gain A,ldBl= (dB) overview V, is input voltage, V2 is' output voltage *This equation is used to determine the voltage gain of-an amplifier circuit when the input voltage and output voltage are known. Determine the voltage gain for an input voltage of ¥, =15V and an output voltage of V2=36V. "Operation i . Display o Fusibility (UZI Eos i o (Recalcitrance gain) UE——O @ ‘ TAV=20103 36 (Enter value for Ui1? .
Q7. Current Gain input current, [z is output current *This equation is used to determine the current gain of an.amplifier cultural when the input current and output current are known. Determine the current gain for an input current of and an output current of [ =60mA. Operation Display Ai=20109 (Ia/I o7 S “ (Recall current gain.
08, Power Gain )[dBJ (P2/ input power, P is output power *This equation.is used to determine. the power gain.of an amplifier circuit when the input power and output power are known. Example Determine the power gain for an input power of Py =40mW (40 x 107 W) and an output power of Py =58W, Operate Display AP=10103 (P2/P Bos (Recall power gain) pPa? .0 & AP=10103 (P2/P (Enter value for P2} P17 0. BEER RP=10109 (P2/P {Niter value for P..
100. Y = A Conversion RsRs+R5Rs+ Re Ry Ri= Rs _ RuRs+RsRe+ Re Ry Re=— Re RSFSR +RsRs+ Ray Ra (Rs Rs. Re>0) “This equation i$ used to convert from a' Y connection to'a A connection. Example Determine the Ry, R, R; values for-a A connection based upon a Y connection of R4=20 ohms, Rs=30 ohms, Re=50 ohms. Operation Display 8100 (Recall ¥ — A conversion) RY? Q. ~20[68 {Enter value for Ra} Rs5? 0. 3069 "(Enter value for Ry} R&? 0 Ri= CRHRS+R5RE+ 5060 (Enter value for Re.) R-108.
7 rvf—l) (dB) (ZzZo>®) Z is impedance This equation is used to determine Ry and R; to match Zo and Z{ with minimum loss. Example Determine the R, Rz and Lin when Zo =500 ohms and Z, =200 ohms. Operation Display 101 \ SR . {(Recall minimum loss matching.} 29? 0. 5008 (Enter values for Zo.) 217 0. 200[ (Enter value for 7)) o .R1.
102. Change in Terminal Voltage Series Circuit Vi = Vo gmt /o C is electrostatic capacity, R is resistance, / is time «This equation is used 1o determine voltage of terminal series cir“ coot at time 7 when the resistance and condenser capacity are known. Example Determine the voltage at terminal circuit at time =10 when R= 1M ohm (1. 10% ohms), C=8xF (8% 107°F), and V=90V, {When :=0, voltage of terminal Verve) Operation Display ETON {Retail change in germinal voltage of Rin rise circuit.
103. Probability Function of Binomial Distribution tbsp \ P* (1 P)"* (x:o, 1. u) s plosive integer #This equation is used to determine the Valueless for a.phenomenon occurring in a binomial distribution when the probability P of the phenomenon and the frequency of appearance are known. Determine the Px value for a die thrown r =6 times with the frequency of occur-~ recce of one being x=2 times, (P = 1/6) Operation Display (1 103 . et (Recall probability function of binomial district’ 0.
104. Probability Function of Poisson’s Distribution wer 0.1 200 Pe= «This equation is used to determine the Px value for Poisson’s distribution when the mean and variance (both x) are known:and the frequency of occurrence Is given. Determine the Px value for Passion's distribution when the mean and variance are p=2 and the frequency of occurrence is x=1. Operation Display Px= (BXY X XE~P) / (Resale probability friction of Poisson's B C 0.
105. Probability Function of Geometric Distribution -Th;s equation’is used to determine the Px value for each appearance x.of a phenomenon. when the :probability P is. known. Determine the Px value when P=1/4 and x=2. Operation ’ ' Display @ 1056 ) {Recall probability function of geometric P 0. distribution.) = federation) T4 . o (Enter value for (Enter value for 0.
106, Probability Function of Hyper geometric Distribution Wicca /Ie
107 Probability Function of Exponential * Distribution Phaethon x>0 ¥y=0 rEQ X is inverse of expected value €A>0) *This equation is used to determine a value for y.in relation to the x value cowhand the X value is known. Determine the value of y when the expected value:is 2 and xis 1, Q Operation . Display YALE (XX} &107 {Recall probability unction of exponential dis A? 0. Y=Ne (-AX) . (Enter value.for V=A@ (~HX) | X a (Enter value for x.
108. Probability Function of Uniform Distribution 1 YTy a
109, Normal Distribution (Probability * Density Function) _ 1 o J2ro° ¥ (a>0) «This equation is used to determine the value for normal distribution (probability density function) when the mean value of the distribution »-and variance o*are given. Example Determine the value for x=35 normal distribution {probability density function} . when p=33 and c=4. Operation Display y= {1/ {{ (213 xd) @ 1096m ! IXg (Heckle normal distribution {probability density d? Q, y=11/ (T (2 Xd) (Enter value for (25) xXd) 35[0 .
110. Normal Probability Function P(x) e Sdt osier X1 Ixt 2 Qlx) (Hastings’ best estimate formula.) *This equation is used to determine the normal probability function riv) Qf¥) when a value for x is known. s Since this is an approximation formula, precision may be questionable Example | Determine the normal probability function P(x) and Q(x) when x=3. Operation Display Pix) @ex) B 1106 s (Recall normal probability function.) X7 0. P{x) (Enter value for 589996363 @ P(x) @ (é) . P-1349968527-03 & Plx) &) .
111. Deviation F=FER01E0 o0 axis mean, ¢ is standard deviation *This equation is used to determine the deviation when the mean and standard deviation.are, known. Determine the deviation from x = 65.1 when the mean is and the standard deviation is Operation ' Display Y= 111 N @ (Recall deviation.) x? 0. 265 = (Enter value for x.) xA? 0. 638@“ Y= (Enter values for x:.) 429 A *{Enter value for .
112, Tension and Compression /l"gz o is vertical stress, ¢ is original length, E is Young’s modulus *This equation.is used to determine the stretch or compression when the vertical stress, Young's modulus and the original length of the material are known. The vertical stress is o=-> for vertical load W and A is the original cross sectional area of the material. Determine the stretch or compression value when length ¢=420mm, vertical stress o=4.
113. Shearing Stress (1) T*% (A P>0) P is shear load. A is-cross sectional area receiving the shear *This equation.is used to determine the shearing stress when the' shear load and cross sectional-area receiving the shear are known. . Ample ] Determine the shearing stress when the shear load Is P = 30kg and the cross sectional area receiving the shear is A =16mm’. Operation Display z=P/R 11300 ” L (Recall shearing stress p? Qz=P/A 90[Ee > o | (Enter value for z=P/A | 6 Fee o (Enter values for A.
T14. shearing stress (2) =Gy G is maneuverability coefficient, ~ is shearing strain *This equation is used to determine the shearing stress when the maneuverability coefficient and the shearing strain are known. Example | Determine the shearing stress when the shearing strain is + = 0.0007 and the maneuverability coefficient is ragtime, Operation Display i T=GT 114 a (Recall shearing stress G? 0. T=BY 0.0007[9 i {Enter value far .
115. Enthrall (. Poe d>0) Py i=u+t T u is internal energy, P is pressure, v Is volume, J is.mechanical equivalent of heat »This equation is used to determine enthrall when the internal energy, pressure and volume are known. i Example Determine-enthrall when the internal energy u = 1-cal, pressure P=1atm (101.3 Nfm?), and volume Note that J/cal. Operation Display @1 1560 ; . (Recall enthrall} u’ 0. 1 B ” (Enter value for u.) i Q. 101.368 Y & (Enter value for P.) v Q.. 11.269 . @ {Enter value for v.} J? Q.
116. Efficiency of Carnot's Cycle (1) @ is volume of heat *This equation i$ used to determine efficiency of Carnot's cycle when the low temperature heat'volume and high temperature heat volume ‘are Kiowa, [Example] Determine the efficiency of Carnot's cycle when low temperature heat source Q> =280 Kcal/h and high temperature heat source Q; = 1400 Kendall: “Operation Display /81 B1160w » v Q (Recall efficiency of Carnot's cycle (R-02) /01 1400TH = (Enter value for Q) Ra2? 0. 7 25088 2=(Q Q; /8L .
117. Efficiency of Carnot’s Cycle (2) n= S (Tr0) T is temperature *This equation is used to determine efficiency of Carnot's cycle when the low temperature heat source and high temperature heat source are known. Determine the efficiency of Carnot’s cycle when T, =273.15K (freezing point of water) and T, =373,15K (boiling point of water). Operation Display 08117/ . a (Recall efficiency of Carnot’s cycle 373,150 . 0 {Enter value for Ty.) Ta2? . 0.
118. Bernoulli’s Theorem Constant] v 28 tzatziki) (e Por Z>m Po=Pr+ 7( s P.is pressure, v is specific weight, v is flow velocity, Z is hither gis gravitational .velocity +This equation is used to determine pressure at two points for an in viscid fluid when the flow velocity and location (height) of two points, the pressure at one point, and the specific weight are known.
+? (. P A Z>0) _ ¥ P is pressure, v is specific weight, v is flow velocity, Z is height. gis gravitational velocity” *This equation is used to determine flow velocity at two points far an in viscid fluid when the pressure and location {(height} of two points, the flow velocity at one point, and the specific weight are known. .
120. Bernoulli's Theorem (3) [ PrligConslamJ 2 28 _b Pi-Py T2g P is pressure, v is specific weight, v is flow velocity, Z is height, g is gravitational velocity Zs +Zy (e Rapunzel) *This equation is used to determine the position of POINT 2 for an in viscid fluid when the pressure and flow velocity of two points, the position (height) at one paint, and the specific weight are known.
Aoy = App 02 = Constant 121. Equation of Continuity (1) (Az, 022 0) Rand A, are cross sectional areas of ducts, v; and vz are flow velocities, oy and o2 are densities of squids *This equation is.used to determine the.flow velocity of a liquid at a point when the, cross sectional area of a duct and the density of the liquid are known and the weight flow is constant. Example Determine the flow velocity when the cross sectional area.of viaducts Az = 0.
122. Regulation of Continuity (2) Arvipr=Azv20, congregant (m=0. 0,0} A, and A, are cross sectional areas of ducts, v, and v, are flow velocities, o1 and p. are densities of liquids *This equation is. used to determine the cross sectional ares of a duct when the flow velocity of liquid at a point and the density of the liquid are known-and the weight flow is constant. Example | Determiner the cross sectional area of a duct when the flow velocity m/s, if the velocity is v; =2.
M= 7 (D, Z>0, and aie integers) D is pitch diameter of a gear, Z is number of teeth on the gear #This equation is used fo determine the module when the pitch diameter of a gear and the number of teeth on the gear are known. Determine the module'for a gear with Z=24 teeth and a pitch diameter of D= 36mm. Operation Display Mads . 123 i) z {Recall Module D? 0. 36 Midsize . (Enter value for M=0s2 Y (Enter value for 2.
124. Nodule (2) (oD Da_ P [v-gt pitch of a gear *This equation is used to determine the module when the pitch-of a gear is known. Example Determine the module for a gear with a pitch of P=6mm. Operation Display @124 M=F/7 i) o (Recall Module P? 0.
125, Module (3) 2z, ) 2, and 75 are integers D, is pitch diameter of driving gear, D, is pitch diameter of driven gear, Z; is number of teeth on driving gear, Z: is number of teeth on driven gear *This equation is used fo determine the pitch diameter of the driven gear when the driving gear's pitch diameter and burner of teeth are known, and the driven gear’s number of teeth ars known.
(P, 20, and are integers) P is pitch of a gear, Z is number of teeth :on the gear *This equation is used to determine the pitch diameter of a gear when its pitch and number of teeth on the gear are known. Example Determine the pinch diameter for a gear with Z. = 84 teeth and a pitch of ' Operation Display D=PZ/7 @ 125 ) \ s {Recall Module P2 0. D=PZ/n 222 \ Cw (Enter value for P.) 27 0. D=pPzZ/T 84 B (Enter value for Z.
o) *This equation is used to determine the Reynolds number when the velocity, duct inner diameter, and kinematic viscosity are known for.a liquid flowing through a duct. ‘ Example Determine the Reynolds number for liquid flowing at velocity #= 0.3 m/s through a duct with an inner diameter f=80mmwhen the kinematic viscosity of the liquid is 10" *m%s. 127. Reynolds Number u is flow velocity, ¢ is inside diameter of duct, v is kinematic viscosity Operation Display Repulsive : . @127 .
128. Calculations Using a Sadist § =K cos? o+ C cos o (Horizontal distance) sin 2+ C sin @ (Difference in Elevation) ) K.
Appendix A | Keys and Indicators W General Guide 1856 S 3 @ Shift key @) Power switch @ Number keys (@ Display &) Contrast dial {® Cursor/Replay keys () Mode key ® Function keys @ Delete key 0 All clear key D Arithmetic operation keys @ Execute key {3 Formula key —214—
W Display Upper dot display [« Indicators Lower display v Upper dot display *The upper dot display. is used for calculations and formulas. «The number zero is shown on the display with a diagonal line to.differentiate it from the letter Q. *The blinking line in the upper dot display is called the “cursor” and it shows you where a character will appear when you input something.
B Key Operations and Their Functions Key Operation Application Shift] input of function; marked in brown above the input keys. Inuit of upper case alphabetic characters and symbols marked in red at the lower right of the keys. Lock for continuous input of multiple alphabetic characters. Unlocks continuous input -of ‘multiple: alphabetic characters. Executes a user formula when pressed before user ror« mute memory ahem entry. input or recall of constant Memorizes. Encloses messages in quotation marks.
Key Operation Application (6o} (5] (Exe) Changes unit of angular measurement to radians. (e} (6] (2] Changes unit of ‘angular measurement to grads. Sets number of decimal places (integer) ; Sets. number of significant digits as 1~10. n @ “n=0~9 (integer} Cancels number of decimal places or number of significant@ cant digits' specification; : COMP mode for arithmetic or scientific calculations. = conversions and-calculated mode for standard deviation calculations. LR mode for regression calculations.
Key Operation 3 Application input of Greek characters marked in red at the upper right of the keys. Returns the square root of the following value, Specifies decimal calculations in the base-n mode. Specifies the next value input Is decimal value in the @ base-n mode. .« B . Input of upper case characters marked in red at the lower right-of the keys as suffixes. Returns the square of the previously entered value. Returns the absolute value of the following value.
Key Operation Application Returns reciprocal of previously entered value. /i@ Inputs hexadecimal values A in the base-n mode. Returns factorial-of previously entered value. “With the f-5000F, press (1 & . Used to input vigesimal value as degrees, unutterable. seconds (ex. ~ 7834565 12 64). Inputs hexadecimal value B in base-n model. Displays decimal value in degree/minute/second format. Inputs hexadecimal value C in base-n mode. [sin) Turns the hyperbolic sine (sing) of the following value.
Key Operation Application Returns the.tangent of the following value. Inputs the hexadecimal value F in the base-n mode. Returns the arc -} of the following value. Enters the following value as negative. Returns the negative of the following value in the base-n mode. Negatives are expressed as twos’ complements in the base-» mode. Inputs equal sign Indicates that a calculation result is to be stored-in ihe memory indicated by the following specification.
Key Operation Application Inputs V. in the SD and LR modes. Inputs logical OR in the base-n mode. * O~EE] Used for input.of numbers and the decimal point. fns Rounds the internal value to the number of decimal places @ specified by or number of significant digits specified by 98], Generates a pseudo random number between 0.000 and 0.999. . @ Returns the mean of x-data in the SD.or LR made. . Returns the sum of squares of x-data in the rode. 1 Speed of light in vacuum (c).
Key Operation Application m @ Returns the sample standard deviation of »-data in the LR = mode. K Returns the sum of products of x and y-data in the LR @ mode. %l u@] Atomic mass unit (1) : . Returns constant term of regression formula (A) in the LR ~ B made. (EBD) 1y [in) Avogadro constant (Na) Returns regression coefficient (B) in the LR mode: [T [in) Boltzmann constant (k) @ Returns correlation coefficient (r)in the LR mode: Molar volume of ideal gas at s.L.p.
Key Operation Application Inputs multiplication sign. Returns the estimated value of x'In the. LR mode: Permittivity of vacuum {eo} Inputs division sign. Returns the estimated value of ¥ in the LR mode. Permeability of vacuum {po) Inputs addition. sign. Acceleration of free fall (g) Inputs subtraction sign, Molar gas constant (R} Press following input of & number to recall the bulk-in formula which corresponds to the number, or press while built-in formula is displayed to' move to the next built-in formula.
Appendix B What to Do When an Error Occurs An error is generated when you make some mistake in operation of the calculator, or when you try to-execute a user formula which is not written carrectly. You will see a message appear on the display when an error occurs, something like: the example illustrated below.
Appendix C Technical Reference This reference includes technical information concerning maximum input capacity- ties, stacks, and specifications. m Order of Operations This calculator uses true algebraic logic to perform calculations in the following sequences.
*Calculations which contain a series of operations which are of the same priority are performed from left to right. +Compound functions are performed from right to left. #Anything contained. in parentheses receives highest priority. Example | . =22.07101691 LT W About Stacks This calculator assigns a block of memory far stacks which temporarily store low priority numeric values and commands.
»Note that calculations are performed according to the order of operations described above. and not according to their relative position in the stack. Once an operation & performed, it i cleared from the stack.” ® Maximum. Value Sizes You can enter values with up to 10 digits-for the mantissa and 2 digits for the exponent. Internal intermediate results are handled with a mantissa up to 12 digits long, and a 2-digit exponent, but results are displayed in the 10-digit mantissa/ 2-digit exponent format.
W How to Count User Formula Steps ‘The memory capacity of this calculator is counted in formula steps. You can input up to 875 formula steps in total for all of the user formulas to store. Each step is represented by all of the characters which appear on the display for a key operation, whether the key operation involves one key or more hath ‘one key. The following sample display. illustrates a typical step count.
x0TSRI < logy <106 5 =0y >0, (n=integer) —1 %107 < y logo] < 100 ¥ () =1x10< Logy <100, y=0:2 >0, YOI mantle = (n% 0, integer) ~1X10"< Golly | < 100 Binary RNz x 2 Acct ()3T 2220 () 2 x 2 Hexadecimal () : 2 x & Vigesimal | |x| £ .777 Higher order digits given display priority for values exceeding 8 digits in length, Statistical calculations | [x] < 105, |yl < 10%, [nf < 101 *Generally, precision for a result is +1 at the 10th digit.
B Formulas Used for Statistical Calculations The following formulas are used internally by the calculator for the operations noted, s Standard Deviation / Using all data of a finite population to determine the standard deviation for the entire population. /" z—E)° el Using sample data for a population to determine the standard deviation for the entire population. *Mean £ Lo X *Regression Regression formula: Constant term A and regression coefficient B are calculated using the' following formulas.
Specifications Computations Basic commutation functionalist. Negative numbers, exponents, parenthetical addition/ subtractiorymultiplication/division (with priority sequence i judgment function — true algebraic logic). Built-in functions: Trigonomeiric/inverse trigonometric functions {units of : angling measurement: degrees, radians, grads), hyper: conversational hyperbolic functions (f-5000F); {logarithmic/ exponential functions, reciprocals, -factorials, square rotas, cube roots, powers, tools, squares,.
i Common section Display system and contents: Error check function: Power supply: Power consumption: Battery life: Auto PowerPC off: Ambient temperature range: Dimensions: * Weight: 2 line liquid crystal display {upper fine: 14-digit dot matrix display, lower line: 2-digit dot matrix display and 10-digit mantissa plus 2-digit exponent), binary, octal, -hex: decimal display, vigesimal display, condition displays (WRT, PCL.
