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<Example 2>

Let the acetic acid concentration be

(= 0.1 mol / ), and the hydrogen ion

concentration be

(1) Solve the following quadratic equation to find the hydrogen ion concentration

- (

)

= 0

where

= 2.75 x 10

-5

[mol / ] (ionization equilibrium constant of acetic acid)

= 1.0 x 10

-14

[mol / ] (ionic product of water)

(2) Use the result of (1) to find the pH (= - log

) of acetic acid.

Save constants

(1)

pH = - log

(

>0)

2.75

Operation

1.0

0.1

Display

Polynomial equation

(This example is for EL-W516T only.)

(NORMAL)

Содержание EL-W516T

Страница 1: ...SCIENTIFIC CALCULATOR OPERATION GUIDE SCIENTIFIC CALCULATOR OPERATION GUIDE EL W535TG W516T ...

Страница 2: ...t switch Display pattern 5 Display format and decimal setting function 5 6 Exponent display 6 Angular unit 7 10 to the power of x common logarithm logarithm of x to base a 18 e to the power of x natural logarithm 22 Exponential logarithmic 19 21 Permutations combinations 24 26 Power and radical root 15 17 Factorials 23 Time calculation 27 Fractional calculations 28 Memory calculations 29 Last answ...

Страница 3: ...tion 53 56 Simultaneous calculation 50 52 Complex calculation 57 58 Hyperbolic functions 39 42 Coordinate conversion 43 Statistics functions 59 Data input for 1 variable statistics 59 ANS keys for 1 variable statistics 60 61 Data correction 62 Data input for 2 variable statistics 63 ANS keys for 2 variable statistics 64 66 x d dx x i Matrix calculation 67 68 dx DATA INS D STAT ...

Страница 4: ...bove the ON C key STAT mode Mode 1 mode for performing 1 or 2 variable statistical calculations To select the sub mode press the corresponding number key after HOME key Pressing this key will return to NORMAL mode Single variable statistic calculation Linear regression calculation Quadratic regression calculation Euler Exponential regression calculation Logarithmic regression calculation Power reg...

Страница 5: ... mantissa 2 digit exponent Fixed decimal point format FIX is displayed Displays the fractional part of the calculation result according to the specified number of decimal places Scientific notation SCI is displayed Frequently used in science to handle extremely small or large numbers Engineering scientific notation ENG is displayed Convenient for converting between different units 2 RESET SWITCH R...

Страница 6: ...tering the zeros one by one is a great deal of work and it s easy to make mistakes In such cases the numerical values are divided into mantissa and exponent portions displayed and calculated What is the number of electrons flowing in a conductor when the electrical charge across a given cross section is 0 32 coulombs The charge on a single electron 1 6 x 10 19 coulombs Improper fractions Decimal n...

Страница 7: ...s 360 Radians RAD is shown at the top of the display Radians are different from degrees and express angles based on the circumfer ence of a circle 180 is equivalent to π radians Therefore the angular mea sure of a circle is 2π radians Grads GRAD is shown at the top of the display Grads are a unit of angular measure used in Europe particularly in France An angle of 90 degrees is equivalent to 100 g...

Страница 8: ...stics Values stored in memory are not erased These arrow keys are useful for Multi Line playback which lets you scroll through calculation steps one by one Turns the calculator off These keys are useful for editing equations The key moves the cursor to the left and the key moves the cursor to the right The key deletes the symbol number at the left of the cursor and the key deletes the symbol numbe...

Страница 9: ...ound the sun in a circular orbit how many kilometers will it travel in a year Circumference equals diameter x π therefore 1 496 x 108 x 2 x π The average distance between the earth and the sun being 1 496 x 108 km Enters π 3 14159 The constant π used frequently in function calculations is the ratio of the circumference of a circle to its diameter Enters the minus symbol The subtraction key is not ...

Страница 10: ...with R Int R Int minimum value maximum value For example if you enter 1 99 a random integer from 1 to 99 will be generated To generate the next random integer press Generates random numbers Random numbers are three decimal place values between 0 000 and 0 999 Using this function enables the user to obtain unbiased sampling data derived from random values generated by the calculator APPLICATIONS Bu...

Страница 11: ...g this function internal calculations will be performed using only the displayed value FIX mode TAB 1 normal calculation Rounded calculation MDF internally 0 5555 internally 0 5555 internally 0 6 APPLICATIONS Frequently used in scientific and technical fields as well as business when performing chained calculations In W VIEW mode press to show the answer in decimal In W VIEW mode press to show the...

Страница 12: ...cation and division Used to specify calculations in which certain operations have precedence You can make addition and subtraction operations have precedence over multiplication and division by enclosing them in parentheses Finds the result in the same way as a standard calculator Basic Arithmetic Keys Parentheses ...

Страница 13: ...ds of calculating percentages are presented as follows 1 125 increased by 10 137 5 2 125 reduced by 20 100 3 15 of 125 18 75 4 When 125 equals 5 of X X equals 2500 NOTE In EL W516T when is specified immediately after a value the value is treated as a percentage is specified by ...

Страница 14: ...uare Root Cube Root xth Root 2 2 2 2 4 16 2 4 Calculates the inverse of the value Squares the value Cubes the value Calculates the xth power of the value Calculates the square root of the value Calculates the cube root of the value Calculates the xth root of the value ...

Страница 15: ...Example 1 Design a shaft that bears a torque T 9 550 Nm is a constant that is determined by the material of the shaft and is taken to be 20 N mm2 Operation Display 16 9550 20 Power and Radical root d 16T 3 ...

Страница 16: ...at an annual interest rate of 5 and the interest is compounded annually 2 When a principal of 300 000 is deposited for five years and the interest is compounded annually the final amount is 339 422 The annual interest rate r is given by the equation below Find the annual interest rate r 1 2 x r 100 1 y a 5 1 339422 300000 y 400000 1 5 100 3 r 100 5 100 300000 y a 1 r 100 x 400000 1 3 100 5 339422 ...

Страница 17: ...ulate the frequencies of the notes in 1 to 3 1 C of A A B B C 2 C of A G F E D C 3 A one octave higher 1 2 12 2 440 3 12 3 12 2 440 12 3 2 2 440 x 12 2 3 440 x 12 2 12 440 x 12 2 3 2 440 Operation Display Power and Radical root Example 3 ...

Страница 18: ...wer of x Common Logarithm Logarithm of x to Base a Calculates the value of 10 raised to the xth power Calculates the logarithm the exponent of the power to which 10 must be raised to equal the given value Calculates the logarithm of x to power a 3 45 ...

Страница 19: ...rgy when the magnitude increases by N holds 1 When the magnitude increases by 1 by what factor does the energy increase 2 When the magnitude increases by 2 by what factor does the energy increase 3 The amount of energy in 20 000 tons of TNT is 8 x 10 13 joules When this energy is converted to a magnitude holds Find the magnitude M 101 5N E E Exponential Logarithmic Example 1 3 4 8 8 13 1 5 ...

Страница 20: ...mple 2 Air is held inside a cylinder of volume V1 0 01 m3 at a pressure P1 1 000 000 Pa at 27 C with a piston Find the quantity of thermal energy Q needed to expand the air at constant temperature to a pressure of P2 101 000 Pa Q p1V1In p2 p1 p2 p1 log p1V1 0 434 Exponential Logarithmic ...

Страница 21: ...d the pH of hydrochloric acid HCl at a concentration of 1 0 x 10 8 mol L pH 7 neutral pH 7 acidic pH 7 alkaline pH log10 2 a a2 4x10 14 a 1 0 10 14 8 4 2 Example 3 Enter the value of a Calculate the pH Exponential Logarithmic ...

Страница 22: ...ion Display e to the Power of x Natural Logarithm Calculates powers based on the constant e 2 718281828 Computes the value of the natural logarithm the exponent of the power to which e must be raised to equal the given value ...

Страница 23: ...om 1 to n 1 is indicated by n and called the factorial of n cf n 1 x 2 x 3 x x n APPLICATIONS Used in statistics and mathematics In statistics this function is used in calculations involving combinations and permutations Operation Display Example 2 How many arrangements exist of cards of three colors red blue and yellow 3 3 x 2 x 1 6 3 ...

Страница 24: ...CBA The calculation equation is 3 P3 3 x 2 x 1 6 ways This function finds the number of ways of selecting r objects from a set of n objects For example from the three letters ABC there are three ways we can extract groups of two different letters AB AC and CB The calculation equation is 3 C2 APPLICATIONS Used in statistics probability calculations and in simulation hypotheses in fields such as med...

Страница 25: ...he cards are there 2 When three cards are selected from five cards numbered 1 to 5 how many ways of selecting the cards are possible 5P3 5 x 4 x 3 Let the number of ways of selecting the cards be C There are 3 possible orderings of the cards and thus when ordered in a row Therefore C is 1 5 3 Permutations Combinations This is written as 5C3 C x 3 5P3 C 5P3 3 ...

Страница 26: ...ng cards Ways of selecting two cards to make a pair Ways of selecting the number 13 possibilities from 1 to 13 King Ways of selecting the suit Two suits selected from four 4C2 Hence Ways of selecting five cards 52C5 The probability of drawing one pair is 13 x 4C2 x 12C3 x 43 52C5 Ways of selecting remaining three cards Ways of selecting the number Three types are selected from 13 1 types 13 1 C3 W...

Страница 27: ...rees minutes seconds Convert 24 28 35 24 degrees 28 minutes 35 seconds to decimal notation Then convert 24 476 to sexagesimal notation Inputs values in sexagesimal notation degrees minutes seconds Convert to decimal notation Repeat last key operation to return to the previous display APPLICATIONS Used in calculations of angles and angular velocity in physics and latitude and longitude in geography...

Страница 28: ...s a mixed fraction 1 2 5 7 Add 3 and and convert to decimal notation Convert to an improper fraction Convert to decimal notation APPLICATIONS There is a wide variety of applications for this function because fractions are such a basic part of mathematics This function is useful for calculations involving electrical circuit resistance 3 1 2 7 ...

Страница 29: ...6 510 2 750 110 26510 2750 Memory Calculations Stores displayed values in memories A F X Y M Recalls values stored in A F X Y M Temporary memories Independent memory Adds the displayed value to the value in the independent memory M Subtracts the displayed value from the value in the independent memory M 0 Enter 0 for M ...

Страница 30: ...30 Example y 4 x and x 2 3 Operation Display 2 3 4 Last Answer Memory Recalls the last answer calculated by pressing Solve for x first and then solve for y using x ...

Страница 31: ...ined Functions Recall a function that was defined by the user APPLICATIONS Functions that you have previously defined including those using common 2nd Function buttons can be stored in D1 D3 for later use thus saving time on keystrokes 26 ...

Страница 32: ...32 Example Operation Absolute Value Returns an absolute value Display 3 4 ...

Страница 33: ...e Calculates the tangent of an angle The angle from a point 15 meters from a building to the highest floor of the building is 45 How tall is the building 45 15 1 5 View point APPLICATIONS Trigonometric functions are useful in mathematics and various engineering calculations They are often used in astronomical observations civil engineering and in calculations involving electrical circuits as well ...

Страница 34: ...ength of the side of the following triangle Angle setting DEG 30 20 A B B C C A a x y 2 17 b a 20 sin 30 b 20 cos 30 x tan17 2 y sin17 2 Operation Display DRG DEG Trigonometric Functions NOTE In EL W516T Use instead of SET UP ...

Страница 35: ...35 20 30 20 17 2 30 17 2 Trigonometric Functions ...

Страница 36: ...ow Find the instantaneous value of the AC voltage at time t 2 000 2 002 2 004 2 008 2 012 2 016 Angle setting rad RAD Operation Display DRG RAD 2 2 2 100 2 000 60 Root mean square value Ve 100 V Frequency f 60 Hz V 2Vesin 2 ft V Trigonometric Functions NOTE In EL W516T Use instead of SET UP ...

Страница 37: ...37 4 8 12 16 Trigonometric Functions ...

Страница 38: ...three sides are sin 1 cos 1 and tan 1 Their relations are arc sine Determines an angle based on the ratio b a of two sides of a right triangle arc cosine Determines an angle based on the ratio c a for two sides of a right triangle arc tangent Determines an angle based on the ratio b c for two sides of a right triangle At what angle should an airplane climb in order to climb 80 meters in 100 meters...

Страница 39: ...ned by using natural exponents in trigonometric functions Arc hyperbolic functions are defined by using natural logarithms in trigonometric functions APPLICATIONS Hyperbolic and arc hyperbolic functions are very useful in electrical engineering and physics ...

Страница 40: ...the catenary factor and determines the shape of the curve D acosh 2a a b L 2asinh 2a b Operation Display 0 846 0 846 0 846 2 2 Example 1 The curve that forms when a rope hangs from two fixed points is called a catenary and the sag D of the rope can be expressed using a hyperbolic function 0 846 0 846 2 2 2 Catenary b width between fixed points Sag D Hyperbolic Functions ...

Страница 41: ...ter Atanh BX use the characters A B and X to enter DEG mode Answer Operation Display Example 2 A drop of rain falls against an air resistance proportional to the square of the fall velocity The velocity v at time t seconds after the start of the fall is given by the following equation B X 6 82tanh 1 44x dx 99 01718518 15 0 x 0 1 2 5 10 15 v 0 6 0950185 6 777153851 6 819992397 6 82 6 82 Hyperbolic ...

Страница 42: ...ation calculation For example 4 Enter the value of B 3 Enter the value of A 5 Enter the value of X 6 The answer is obtained Repeat 2 to 6 If 6 82 appears press only the key 6 82 If 1 44 appears press only the key 1 44 1 Hyperbolic Functions ALGB ...

Страница 43: ... polar coordinates x y r Converts polar coordinates to rectangular coordinates r x y θ Splits data used for dual variable data input Determine the polar coordinates r when the rectangular coordinates of Point P are x 7 y 3 θ APPLICATIONS Coordinate conversion is often used in mathematics and engineering espe cially for impedance calculations in electronics and electrical engineering ...

Страница 44: ...n the calculator can carry out the logical operations AND OR NOT NEG XOR and XNOR on binary pental octal and hexadecimal numbers Conversion is performed on the displayed value when these keys are pressed Operation Display Example 1 HEX 1AC BIN PEN OCT DEC 1011 AND 101 BIN DEC Example 2 Operation Display 1AC 1011 101 Converts to the binary system BIN appears Converts to the pental system PEN appear...

Страница 45: ...360 D 48 Price elasticity of demand A value that indicates how sensitive demand is to changes of price P dP D dD D P dP dD Price elasticity of demand Rate of demand change Rate of price change Operation Display 48 24 360 360 25920 d dx x Find the following value when P 360 and D 48 x 360 24 x 25920 D P d dx This example is for EL W516T only ...

Страница 46: ...s given by the equation Find the slope of the tangent AB at point B 1 2 3 2 on the semicircle x dx 2 1 d Operation Display 1 1 2 d dx x x2 1 y x2 1 A O 120 1 B 1 2 3 2 Differentiation calculation This example is for EL W516T only d dx x ...

Страница 47: ...00 and the equilibrium output be 2000 1 Find the consumer surplus of the overall market 2 Find the producer surplus of the overall market 3 Find the total surplus of the overall market 3000 10x 2000 dx Operation Display 100 10 3000 2000 0 x 2 100 20 2000 x 100 0 2000 20x dx 100 0 3000 10x 20x dx 100 0 This example is for EL W516T only dx x dx 0 dx ...

Страница 48: ...48 3 10 20 3000 x Integration calculation dx x x 100 0 dx ...

Страница 49: ...ay 1 1 x2 1 y x 2 1 y O 1 dx The fan shaped curve at left is given by the equation Find the area of the fan shape with radius 1 and central angle 90 x2 1 1 dx 0 Integration calculation dx x This example is for EL W516T only 0 dx x ...

Страница 50: ... the quantities produced of each product are x and y the sales K can be expressed as K 3x 2y The following relations hold for the quantities in stock 3x y 9 x 2y 8 x 0 y 0 Based on these conditions find the values of x and y that maximize sales K The conditions can be graphed as shown above The sales K is a maximum where the line K 3x 2y passes through the intersection point P of lines 3x y 9 and ...

Страница 51: ...lt of 1 to find the following value Equation mode Set the mode to Equation Set the mode to Normal Simultaneous linear equations in two unknowns Enter the coefficients a1 3 b1 1 c1 9 a2 1 b2 2 c2 8 1 2 Operation 3 1 9 1 2 8 3 2 2 3 Simultaneous Calculation Display EQUATION NORMAL 2 VLE ...

Страница 52: ...ce Number of C 2x y Number of H 5x x 2z Number of O x 6 2y z As such the following simultaneous equations are obtained 2x y 0 6x 2z 0 x 2y z 6 Solving these gives x 1 y 2 z 3 and the chemical reaction formula is C2H5OH 3O2 2CO2 3H2O Equation mode Simultaneous linear equations in three unknowns Enter the coefficients Set the mode to Equation a1 2 b1 1 c1 0 d1 0 a2 6 b2 0 c2 2 d2 0 a3 1 b3 2 c3 1 d3...

Страница 53: ...the following quadratic equation to find the hydrogen ion concentration x x2 cx Kw 0 where Kw 1 0 x 10 14 mol ionic product of water 2 Use the result of 1 to find the pH log x of hydrochloric acid Save constants 1 pH log x x 0 1 0 14 NORMAL Operation 1 0 8 B C Polynomial equation Display This example is for EL W516T only ...

Страница 54: ...54 Set the mode to Equation Quadratic equation EQUATION QUAD 0 000000105 Solve the equation enter coefficients a b c 1 C B Set the mode to Normal NORMAL 2 Polynomial equation ...

Страница 55: ...hydrogen ion concentration x x3 Kax2 cKa Kw x KaKw 0 where Ka 2 75 x 10 5 mol ionization equilibrium constant of acetic acid Kw 1 0 x 10 14 mol ionic product of water 2 Use the result of 1 to find the pH log x of acetic acid Save constants 1 pH log x x 0 2 75 5 Operation 1 0 0 1 14 B C Display Polynomial equation This example is for EL W516T only NORMAL ...

Страница 56: ...56 Set the mode to Equation Cubic equation 0 001644619 Solve the equation enter coefficients a b c d 1 C B B Set the mode to Normal 2 Polynomial equation EQUATION CUBIC NORMAL ...

Страница 57: ...ircuit Circuit impedance Value of polar coordinate r Complex mode Rectangular coordinates Angle units RAD Polar coordinates COMPLEX DRG RAD Operation 1 2 1 250 50 20 6 i Example 1 Let R 250 C 20 x 10 6 and f 50 If the complex number Z 1 1 R 2 fCi find the value of the complex number Z and the values of r Display Complex Calculation This example is for EL W516T only i SET UP ...

Страница 58: ... and the voltage Circuit impedance Value of polar coordinate r rectangular coordinates Angle units DEG Polar coordinates DEG Operation 120 3 2 2 60 1 6 4 60 i i Phase difference Polar coordinate Let R 120 L 4 C 3 x 10 6 and f 60 If the complex number Z R 2 fLi 1 2 fCi find the value of the complex number Z and the values of r and Display Complex Calculation Example 2 i This example is for EL W516T...

Страница 59: ...gh primarily used for engineering and mathematics the function is also applied to nearly all other fields including economics and medicine DATA INPUT FOR 1 VARIABLE STATISTICS Close display the input table Splits data used for X and FRQ data input or X Y and FRQ data input Here is a table of examination results Input this data for analysis Insert a line in the input table for data insertion 30 2 1...

Страница 60: ...a ANS FOR 1 VARIABLE STATISTICS 50 number of input data 69 average value 17 7568613 standard deviation 17 5783958 standard deviation of the population 3450 sum of the data Operation Display DATA Close the input table STAT Calculates Statistical values For examples APPLICATIONS Single variable statistical calculations are used in a broad range of fields including engineering business and economics ...

Страница 61: ... at left were obtained Find the average and standard deviation of the weight Average 96 884 Operation 97 27 No 1 97 27 96 83 96 65 2 3 4 96 90 5 96 77 Weight g 96 83 96 77 Standard deviation 0 209723627 Display DATA DATA Close the input table STAT Display the input table ...

Страница 62: ... cursor position press To delete the entire line where cursor is positioned press Data table 2 X 30 40 40 50 X 30 45 45 45 60 40 2 50 30 DATA CORRECTION Move the cursor to the data that you want to correct enter the numeric value and press INS D 45 3 60 INS D DATA ...

Страница 63: ...e area Determine basic statistical quantities for data X and data Y based on the data table Select two variable statistics mode and linear regression calculation in sub mode The input table is displayed 2010 2011 2012 2013 2014 2015 2016 2017 6 2 7 0 6 8 8 7 7 9 6 5 6 1 8 2 13 9 11 5 7 12 15 7 Year x Average temperature y Date blossoms bloom DATA INPUT FOR 2 VARIABLE STATISTICS ...

Страница 64: ...us data 8 Total count of data 7 175 Average for data x 0 973579551 Standard deviation for data x 0 91070028 Standard deviation of the population for data x 57 4 Sum of data x 418 48 Sum of data x raised to the second power 9 875 Average for data y 3 44082631 Standard deviation for data y 3 2185983 Standard deviation of the population for data y 79 Sum of data y 863 Sum of data y raised to the seco...

Страница 65: ...he force applied to the spring Use linear regression to find the coefficients a and b of the relational expression y a bx and the correlation coefficient r Operation 0 028 0 20 0 073 0 207 Spring extension x m Force F N 0 028 0 073 0 207 0 118 0 16 0 2 0 39 1 0 6 0 77 0 39 1 00 Display DATA DATA Close the input table STAT ...

Страница 66: ...emperature 25 C hot water temperature 92 C Time x S Thermometer temperature C 0 4 8 12 16 20 24 28 32 36 40 25 55 71 79 85 88 90 90 91 91 91 67 37 21 13 7 4 2 2 1 1 1 e Napier s constant e 2 718281828 Display When x and y are in the following relationship use Euler s exponential regression to find the coefficients a and b of the relational expression y aebx and the correlation coefficient r 0 x y ...

Страница 67: ...sed as follows using a0 and b0 Thus a1 and b1 are The transition matrix is This is equal to matA2 Answer 0 9 0 2 0 1 0 8 A 0 83 0 34 0 17 0 66 A2 a1 0 9a0 0 2b0 b1 1 0 9 a0 1 0 2 b0 Expressing a2 and b2 using a0 and b0 gives a2 0 9 0 9a0 0 2b0 0 2 0 1a0 0 8b0 0 9 x 0 9 0 2 x 0 1 a0 0 9 x 0 2 0 2 x 0 8 b0 0 83a0 0 34b0 b2 0 1 0 9a0 0 2b0 0 8 0 1a0 0 8b0 0 1 x 0 9 0 8 x 0 1 a0 0 1 x 0 2 0 8 x 0 8 b0...

Страница 68: ...et the mode to Matrix Matrix mode 2 x 2 Matrix 0 Save to matA Enter numeric values Operation Display MATRIX STORE EDIT 0 9 0 2 0 1 0 8 Matrix Calculation Find the shares of manufacturers A and B after 2 years 0 83 10 0 34 90 0 17 10 0 66 90 A 38 9 B 61 1 ...

Страница 69: ...69 SHARP CORPORATION DEC 2018 18LSC21E1 ...

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