Sharp WriteView EL-W531X Operation Manual Download

Page: 61 / 75

(1) Solve the following simultaneous equations.

= 9

+ 2

= 8

= 3

(2) Use the result of (1) to find the following value.

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)

0 (2-VLE)

6 (EQUATION)

Operation

0 (NORMAL)

Simultaneous Calculation

Display

Summary of Contents for WriteView EL-W531X

Page 1: ...SCIENTIFIC CALCULATOR OPERATION GUIDE SCIENTIFIC CALCULATOR OPERATION GUIDE Write View ...

Page 2: ...play pattern 4 Display format and decimal setting function 4 5 Exponent display 5 Angular unit 6 10 to the power of x common logarithm logarithm of x to base a 17 e to the power of x natural logarithm 21 Exponential logarithmic 18 20 Permutations combinations 24 26 Matrix calculation 27 31 Power and radical root 14 16 Factorials 22 23 Time calculation 32 Fractional calculations 33 Memory calculati...

Page 3: ...0 72 ANS keys for 2 variable statistics 73 Binary pental octal decimal and hexadecimal operations N base 49 Hyperbolic 44 46 Differentiation calculation 50 51 Integration calculation 52 54 Polynomial equation 55 58 Simultaneous calculation 59 61 Complex calculation 62 63 Hyperbolic functions 47 Coordinate conversion 48 B X x dx C B d dx x i ...

Page 4: ...ion calculation EXP Exponential regression calculation 2nd function ALPHA keys Pressing these keys will enable the functions written in orange 2nd F or green ALPHA above the calculator buttons This calculator can operate in three different modes as follows Normal mode Mode 0 normal mode for performing normal arithmetic and function calculations ON C OFF key Direct function Power on Power off 2nd f...

Page 5: ...r left part of the display Format Indicator Note If more 0 s zeros than needed are displayed when the ON C key is pressed check whether or not the calculator is set to a Special Display Format Floating decimal point format 1 2 N1 N2 is displayed Valid values beyond the maximum range are displayed in the form of 10 digit mantissa 2 digit exponent Fixed decimal point format FIX is displayed Displays...

Page 6: ...sed in scientific calculations but entering 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 cou lombs The charge on a single electron 1 6 x 10 19...

Page 7: ...adians 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 grads Th...

Page 8: ... the last answer ANS and statistics Values stored in memory in normal mode 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 th...

Page 9: ...w 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 Pressing π automatically enters the value for 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 ...

Page 10: ...ndom coin number press Random Integer An integer between 0 and 99 can be generated randomly by pressing 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 Using line mode is preferable sinc...

Page 11: ...l places than that which appears on the display By using 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...

Page 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 ...

Page 13: ...25 20 125 15 125 5 For calculating percentages Four methods 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 ...

Page 14: ...y 2 2 2 2 4 16 2 4 Calculates the inverse of the value on the display Squares the value on the display Cubes the value on the display Calculates exponential values Calculates the square root of the value on the display Calculates the cube root of the value on the display Calculates the xth root of y ...

Page 15: ...a constant that is determined by the material of the shaft and is taken to be 20 N mm2 Function for EL W531X EL W535X EL W531XH EL W531XG EL W531 Operation Display 16 9550 20 14 Power and Radical root d 16T 3 Use instead of Function for EL W506X EL W516X EL W506 ...

Page 16: ...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 1 O...

Page 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 2 400 x 12 2 3 400 x 12 2 12 400 x 12 2 3 2 440 Operation Display Power and Radical root Example 3 ...

Page 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 ...

Page 19: ... 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 18 Exponential Logarithmic Example 1 3 4 8 8 13 1 5 ...

Page 20: ...e 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 19 Q p1V1In p2 p1 p2 p1 log p1V1 0 434 Exponential Logarithmic ...

Page 21: ...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 Function for EL W506X EL W516X EL W506 Function for EL W531X EL W535X EL W531XH EL W531XG EL W531 Use instead of ...

Page 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 ...

Page 23: ...nteger n multiplied by all the lesser positive integers from 1 to n 1 is indicated by n and called the factorial of n c f n 1 x 2 x 3 x xn APPLICATIONS Used in statistics and mathematics In statistics this function is used in calculations involving combinations and permutations ...

Page 24: ...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 23 Factorials ...

Page 25: ...the 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 ...

Page 26: ...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 Ways...

Page 27: ...BA 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 medi...

Page 28: ...ed as follows using a0 and b0 Thus a1 and b1 are The transition matrix is This is equal to matA2 Refer to Example 1 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 ...

Page 29: ... coefficients of the calculation formula of each company s share after 5 years can be found by repeated application of matrix A This is equal to matA3 Refer to Example 1 0 781 0 438 0 219 0 562 A3 a3 0 781a0 0 438b0 b3 0 219a0 0 562b0 The shares of manufacturers A and B after 5 years and 10 years are a2 0 72269a0 0 55462b0 57 b2 0 27731a0 0 44538b0 43 Matrix Calculation ...

Page 30: ...RIX 0 Function for EL W506X EL W516X EL W506 Example 1 Let Find matA2 and matA3 Enter matA Set the mode to Matrix Matrix mode 2 x 2 Matrix 0 Save to matA Enter numeric values matA 0 9 0 2 0 1 0 8 Operation Display 4 MATRIX 4 STORE 2 EDIT 0 9 0 2 0 1 0 8 Matrix Calculation ...

Page 31: ... Enter numeric values 4 STORE 2 EDIT 2 2 1 0 83 0 34 0 17 0 66 Matrix Calculation Let Example 2 0 83 0 34 0 17 0 66 matB c d e f matD 0 781 0 438 0 219 0 562 matC 1 Find matB x matC 2 The calculation result of 1 is Letting a0 10 b0 90 Calculate a5 ca0 db0 b5 ea0 fb0 Function for EL W506X EL W516X EL W506 ...

Page 32: ...alculation 1 MATRIX 1 0 77269 10 0 55462 90 57 6427 Calculate 1 3 1 MATRIX 2 2 Enter matC 2 x 2 Matrix 2 Save to matC Enter numeric values 4 STORE 2 EDIT 2 2 2 0 781 0 438 0 219 0 562 0 27731 10 0 44538 90 42 8573 ...

Page 33: ...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...

Page 34: ...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 ...

Page 35: ...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 ...

Page 36: ... 2 3 4 Last Answer Memory Automatically recalls the last answer calculated by pressing Solve for x first and then solve for y using x Function for EL W506X EL W516X EL W506 Function for EL W531X EL W535X EL W531XH EL W531XG EL W531 Use instead of ...

Page 37: ...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 D4 for later use thus saving time on keystrokes 26 ...

Page 38: ...37 Example Operation Absolute Value Returns an absolute value Display 3 4 ...

Page 39: ... 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 engi neering and in calculations involving electrical circuits as well ...

Page 40: ...f 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 DEG mode Operation Display 0 DRG 0 DEG Trigonometric Functions Function for EL W506X EL W516X EL W506 ...

Page 41: ...40 20 30 20 17 2 30 17 2 Trigonometric Functions Function for EL W531X EL W535X EL W531XH EL W531XG EL W531 Use instead of ...

Page 42: ... 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 0 DRG 1 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 Function for EL W506X EL W516X EL W506 ...

Page 43: ...42 4 8 12 16 Trigonometric Functions Function for EL W531X EL W535X EL W531XH EL W531XG EL W531 Use instead of Use instead of Use instead of ...

Page 44: ...ight triangle The combinations of the 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 ...

Page 45: ...lled 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 ...

Page 46: ...tion of integral v AtanhBt m s Additional note Simulation calculation This function is convenient for repeated calculations using varying values of X 1 Enter 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 ...

Page 47: ...mulation 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 1 ALGB Hyperbolic B X ...

Page 48: ...ed by using natural exponents in trigo nometric functions Arc hyperbolic functions are defined by using natural logarithms in trigono metric functions APPLICATIONS Hyperbolic and arc hyperbolic functions are very useful in electrical engineering and physics ...

Page 49: ... polar coordinates x y r θ Converts polar coordinates to rectangular coordinates r x y Splits data used for dual variable data input Determine the polar coordinates r when the rectangu lar 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 ...

Page 50: ...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...

Page 51: ... 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 Function for EL W506X EL W516X EL W506 ...

Page 52: ...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 x d dx Function for EL W506X EL W516X EL W506 ...

Page 53: ... 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 x dx 2 100 20 2000 0 x dx dx 100 0 2000 20x dx 100 0 3000 10x 20x dx 100 0 Function for EL W506X EL W516X EL W506 ...

Page 54: ...53 3 100 10 20 3000 0 x x dx Integration calculation x dx ...

Page 55: ...1 1 0 x x2 1 y x 2 1 y dx 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 x dx Integration calculation Function for EL W506X EL W516X EL W506 ...

Page 56: ...ollowing 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 0 NORMAL Operation 1 0 8 B B C C Polynomial equation Display Function for EL W506X EL W516X EL W506 ...

Page 57: ...56 Set the mode to Equation Quadratic equation 6 EQUATION 2 QUAD 0 000000105 Solve the equation enter coefficients a b c 1 C B Set the mode to Normal 0 NORMAL 2 B C Polynomial equation ...

Page 58: ...en 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 0 NORMAL Operation 1 0 0 1 14 B C Display Polynomial equation C B Function for EL W506X EL W516X EL W506 ...

Page 59: ...58 Set the mode to Equation Cubic equation 6 EQUATION 3 CUBIC 0 001644619 Solve the equation enter coefficients a b c d 1 C B B Set the mode to Normal 0 NORMAL 2 Polynomial equation C B ...

Page 60: ...e 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 x 2...

Page 61: ...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 0 2 VLE 6 EQUATION Operation 0 NORMAL 3 1 9 1 2 8 3 2 2 3 Simultaneous Calculation Display ...

Page 62: ...umber of C 2x y Number of H 5x 1 y Number of O x 3 x 2 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 6 1...

Page 63: ...ircuit Circuit impedance Value of polar coordinate r Complex mode Rectangular coordinates Angle units RAD Polar coordinates 3 CPLX 0 DRG 1 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 i Display Complex Calculation Function for EL W506X EL W516X EL W506 ...

Page 64: ...he current and the voltage Circuit impedance Value of polar coordinate r rectangular coordinats Angle units DEG Polar coordinates 0 DRG 0 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 i Display Complex Calculation Example 2 Function fo...

Page 65: ...alyzing qualities of an event Though primarily used for engineering and mathematics the function is also applied to nearly all other fields including economics and medicine DATA INPUT AND CORRECTION Enters data for statistical calculations Splits data used for dual variable data input Used for dual variable statistical calculations Here is a table of examination results Input this data for analysi...

Page 66: ...x raised to the second power NOTE 1 Sample data refers to data selected randomly from the population 2 Standard deviation of samples is determined by the sample data shift from an average value 3 Standard deviation for the population is standard deviation when the sample data is deemed a population full data Let s check the results based on the previous data ANS KEYS FOR 1 VARIABLE STATISTICS 69 a...

Page 67: ...measured the results at left were obtained Find the average and standard deviation of the weight Average Select Statistics mode 1 STAT 0 SD 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 66 Display ...

Page 68: ...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 cofficient r Select Statistics mode 1 STAT 1 LINE 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 a b r Display ...

Page 69: ...ture difference y C from liquid Room temperature 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 an...

Page 70: ...69 a b r ...

Page 71: ...y Each item is displayed with X Y or F n is the sequential number of the data set Display the data item to modify input the correct value then press Using you can correct the values of the data set all at once When or appears more data items can be browsed by pressing or To delete a data set display an item of the data set to delete then press The data set will be deleted To add a new data set pre...

Page 72: ...variable statistical calculations are used in a broad range of fields including engineering business and economics They are most often applied to analysis in atmospheric observations and physics experiments as well as for quality control in factories ...

Page 73: ...ge temperature for March in that same area Determine basic statistical quantities for data X and data Y based on the data table Select dual variable statistics mode and linear regression calculation in sub mode 1998 1999 2000 2001 2002 2003 2004 2005 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 ...

Page 74: ...sum of the data sample data y raised to the second power Calculates the average value of the data sample data y Calculates the standard deviation for the data sample data y Calculates the standard deviation of a data population sample data y 7 175 Average for data x 0 973579551 Standard deviation for data x 0 91070028 Standard deviation of the population for data x 9 875 Average for data y 3 44082...

Page 75: ... SHARP CORP SEP 13 ...

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