Calculator Techniques - New

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MATHEMATICS and CALCULATOR TECHNIQUES

ENGR. REYNILAN L. DIMAL

THE MEMORY VARIABLES MEMORY A B C D E (ES PLUS only) F (ES PLUS only) X Y M

CALCULATOR BUTTONS ALPHA (-) ALPHA O ‘ “ ALPHA hyp ALPHA sin ALPHA cos ALPHA tan ALPHA ) ALPHA S D ALPHA M+

HOW TO CLEAR MEMORY • SHIFT 9 1 = – This means you will automatically go to MODE 1

• SHIFT 9 2 = – All values stored in the memory variables will be erased

• SHIFT 9 3 = – This means you will automatically go to MODE 1 and all values stored in the memory variables will be erased.

MODE 1 : GENERAL CALCULATIONS

HOW TO CONVERT BETWEEN DEGREES, RADIANS AND GRADIANS Convert237.6150 to DMS (DegreeMin Sec)

DISPLAY: 237.615O 237036'54"

BASICS

HOW TO CONVERT BETWEEN DEGREES, RADIANS AND GRADIANS Convert210 47'12"todecimaldegrees.

DISPLAY: 210 470120 21.7866666 7

BASICS

HOW TO CONVERT BETWEEN DEGREES, RADIANS AND GRADIANS Convert1200 to radians.

DISPLAY: 1200 2  3

BASICS

HOW TO CONVERT BETWEEN DEGREES, RADIANS AND GRADIANS π Convert radians to degrees. 2

DISPLAY:



r

2 90 BASICS

PAST CE BOARD EXAM Whatis 1200 in centesimalsystem? ENTER

DISPLAY: 0

120 400 3 BASICS

HOW TO GET THE POLAR AND RECTANGULAR COORDINATE OF A POINT IN THE CARTESIAN PLANE

PAST CE BOARD EXAM Find thepolarcoordinateof thepoint(4, - 6).

DISPLAY: Pol(4,6) r  7.211102551 ,  56.30993247 BASICS

HOW TO GET THE POLAR AND RECTANGULAR COORDINATE OF A POINT IN THE CARTESIAN PLANE

PAST ECE BOARD EXAM Find the value of cos if the terminalside containsthepointP(-3,-4) Solution :

BASICS

HOW TO GET THE POLAR AND RECTANGULAR COORDINATE OF A POINT IN THE CARTESIAN PLANE

PAST ECE BOARD EXAM DISPLAY: Pol(3,4) r  5,  126.8698976 NOT E: r is storedautomatically toX and to Y.

DISPLAY : cos(Y ) 3  5

BASICS

PAST ECE BOARD EXAM Find therectangular coordinateof a point whose polarcoordinateis (3,1200 ).

DISPLAY: Rec(3,120) X  1.5, Y  2.59807621

BASICS

HOW TO SOLVE COMBINATION AND PERMUTATION PROBLEMS. PAST ECE BOARD EXAM How many triangles are formedby 10 distinct pointsno threeof which are collinear? Solution :

T henumber of trianglesthatcan be formedfrom 10 non collinearpointsis 10C3. DISP LAY: 10C 3 120

BASICS

PAST ECE BOARD EXAM In how manydifferentways can thejudges choose the winner and thefirst runner up fromamongthe 10 finalistsin a student essay contest? Solution : T hereare10 finaliststaken2 at a time. Note: order is importanthere DISP LAY: 10P 2 90 BASICS

HOW TO EVALUATE FACTORIAL NUMBERS

18. Find the value of 10!

DISP LAY: 10! 3628800

BASICS

PAST EE BOARD EXAM How manydifferentpermutations can be made from thelettersMISSISSIP PI?

Solution : Number of M  1; I's  4; P 's  2; S' s  4; Number of Lett ers 11. Note: T henumber of differentpermutations is : 11! 1!4!2!2! BASICS

PAST EE BOARD EXAM

DISP LAY: 11! 1! x 4! x2!x4! 34650

BASICS

HOW TO EVALUATE FUNCTIONS 11. Evaluatef( 6 ) if f(x)  3x 4  3x 2-5x  6

BASICS

HOW TO EVALUATE FUNCTIONS 12. Evaluatef( 4,3 ) if f(x, y)  4x3 y 2  3x 2 y-2xy2  y 3

BASICS

PAST ME BOARD EXAM Find theremainderwhen 3x4  2x3 - 4x2  x  4 is divided by x  2. Solution: f(x)  3x 4  2 x3-4 x 2  x  4 , remainder f(-2 )

BASICS

HOW TO EVALUATE FUNCTIONS 13. Is (x  3 ) a factorof x6  6x5  8x 4-6x3-9x 2?

Conclusion:Since f(-3) 0, then x 3 is a factorof x 6  6 x 5  8 x 4 -6 x 3-9 x 2 BASICS

PAST ECE BOARD EXAM Find theremainderwhen 4 y3  18y 2  8 y  4 is divided by 2 y  3. Concept: Set thedivisor tozero and solvefor y. ENTER : DISP LAY: 2Y  3  0, Y - 1.5

ENTER : DISP LAY: 4Y 3  18Y 2  8Y - 4 11 Answer : T heremainderis 11 ADVANCE

HOW TO USE THE ∑ SIGN Find the sum. 1  2  3  ...  20

DISP LAY: 20

x

x1

210 BASICS

HOW TO SOLVE LINEAR EQUATIONS SOLVE 4(3  x)  5(4  x)

BASICS

HOW TO SOLVE LINEAR EQUATIONS x 3 x 1 x2 SOLVE   1 12 6 9

BASICS

HOW TO SOLVE A SPECIFIC VARIABLE D ( 2 X  2Y ), X  4, D  2, and A  9, 7 what is the valueof Y ? If A 

BASICS

PAST ECE BOARD EXAM When 3 is m ultipliedby 5 less thana num ber, the result is 9 less than5 tim esthe num ber. Find 7 less than5 tim esthe num ber.

BASICS

PAST ECE BOARD EXAM

BASICS

HOW TO USE MULTILINE FUNCTION

PAST EE BOARD EXAM Find thearea of a trianglewhose sides are 6m,8m,12m.

Solution : Using Heron's Formula: A  s(s - a)(s- b)(s - c) abc s 2

ENTER :

BASICS

HOW TO USE MULTILINE FUNCTION

PAST EE BOARD EXAM DISP LAY: ABC X : X(X - A)(X- B)(X - C) 2

ENTER : DISP LAY: X

ABC 2 13

DISP LAY: X ( X  A)( X  B)( X  C ) 455 BASICS

HOW TO SOLVE TRIGONOMETRIC EQUATIONS Solve 5tan x - 3  2tan x : 0  x  360 ENTER :

DISPLAY:

ENTER :

5 tan x- 3  2 tan x X 30 L-R 

0

Answer : X  300 and 2100

DISPLAY: 5 tan x- 3  2 tan x X 210 L-R 

0

BASICS

HOW TO USE LOGARITHMIC EQUATIONS

PAST ME BOARD EXAM Solve for xin log2 x  log2 (x  5)  10

ENTER :

DISPLAY: log2 x  log2 (x  5)  10 X L-R 

29.5975076 9 0 BASICS

HOW TO USE LOGARITHMIC EQUATIONS

PAST ECE BOARD EXAM 3log x

Solve for xin x

 100x

DISPLAY: x 3log x  100x X L-R 

10 0 BASICS

HOW TO GET THE DERIVATIVE AT A POINT Find thederivativeof x3  3x 2 when x  3.

ENTER : DISP LAY: d ( X 3  3X 2 ) dx x 3 45 BASICS

PAST ECE BOARD EXAM x2 Differentiate theequation y  x 1 x2  2x x a. b. c.2 x 2 ( x  1) ( x  1)

2x2 d. ( x  1)

T echnique: Differentiate y at any valueof x, say x  2 and comparethis value to the value of thechoiceswhen same value of x is substituted.

ENTER : DISP LAY: d  x2    dx  x  1  x  2 0.8888888889 ADVANCE

PAST ECE BOARD EXAM Note: Compareit tothechoicesas thevalueof x is being substituted.

x2  2x a) Substitute x  2 2 ( x  1)

ENTER : DISP LAY:

T he valuesof therest of thechoiceswhen x  2 are summarizedas follows:

x2  2x ( x  1) 2 x 2 b.  0.8888888889 ( x  1) x 2 3

c.2 xx2  4

x2 4 d .  ( x  1) x 2 3

x2  2x Answer : a. ( x  1) 2

ADVANCE

HOW TO INTEGRATE 2

Evaluate ( x  3x  1)dx 5

1

ENTER : DISPLAY: 2

x

5

 3x  1 dx

1

16 BASICS

MODE 2 : COMPLEX NUMBER CALCULATIONS

HOW TO SOLVE COMPLEX NUMBERS For thecomplexnumber z  3 - 4i a. Find theabsolute value. b. Find theargument.

DISPLAY: 3  4i  r 5  53.13010235 0

Answer : T heabsolute valueis 5 and theargumentis 53.13 BASICS

HOW TO SOLVE COMPLEX NUMBERS Given : (2 - 3i)(5 2i), find theproduct.

ENTER :

DISP LAY: (2  3i )(5  2i ) 16  11i

BASICS

HOW TO SOLVE COMPLEX NUMBERS 4  2i Simplify : 5 - 2i ENTER :

DISPLAY: 4  3i 5  2i 14 23  i 29 29 BASICS

HOW TO GET THE COMPONENT OF A FORCE AND RESULTANT OF FORCES Find thex and y componentsof theforceF  300N370 ENTER :

DISPLAY: 300370 239.590635 180.5445069i Answer : T hex componentis 239.5N and they componentis 180.54N.

BASICS

HOW TO GET THE COMPONENT OF A FORCE AND RESULTANT OF FORCES Find the x and y componentsof theforce F  800lbs with angle400 at III Quadrant. Solution: Expresstheforceas F  800(180 40)  8002200

ENTER : DISPLAY: 8002200  612.8355545 5142300877 i Answer : T he x componentis - 612.84lbsand the y componentis - 514.23lbs.

BASICS

HOW TO GET THE COMPONENT OF A FORCE AND RESULTANT OF FORCES Find theresultuntof theforces,F1  350Nat 600 and F2  400Nwith an of angle1400. Solution : T heresultantis thesum of thecomplex numbers35060  400140

ENTER :

DISPLAY:

Answer : T hemagnitudeof the

resultantis 575.43Nwith 103.200 350600  4001400 575.4315683103.2017875 with the x - axis(counterclockwise) BASICS

PAST EE/ECE BOARD EXAM Simplify the expression i1997  i1999 wherei is an imaginarynumber. T echnique: Divide theexponentsto 4 and get theremainder.

ENTER : DISP LAY:

ENTER :

1997 4 DISP LAY: 1 499 4

1999 4 499

Not e:1/4 corresponds t o i (i1  i) 2/4 corresponds t o - 1 (i2  i) 3/4 corresponds t o - i (i3  - i) whole number (0 remainder)

3 4

ENTER : DISPLAY: i i 0 (Answer)

corresponds t o1 (i4  1) ADVANCE

PAST CE/ECE BOARD EXAM Find thevalueof (1  i)5 wherei is an imaginarynumber? T echnique: Rewriteas (1  i)3 (1  i)2

ENTER : ENTER : DISPLAY: (1  i)3 (1  i) 2  4  4i

ADVANCE

MODE 3 : STATISTICAL AND REGRESSION CALCULATIONS

HOW TO FIND THE MEAN AND STANDARD DEVIATION Five light bulbs burned out afterlasting867, 859,840,852,and 888hrs. Find themean. DISP LAY:

DISP LAY: x 861.2

1 2 3 4 5

x 867 859 840 852 888 BASICS

PAST ME BOARD EXAM Given thefollowingstatistical data,determine thestandarddeviation. Data:112 132 144 156 164 176 183 197 ENTER DISP LAY: x 1

112

2 3 4

132 144 156

5 6 7

164 176 183

8

197

DISPLAY:

x 26.21545346 BASICS

HOW TO GET THE MEAN, VARIANCE AND STANDARD DEVIATION OF GROUPED DATA DISP LAY: x 1 62 2 3 4 5 6 7

FREQ 2

65 68 71

5 12 15

74 77 80

8 5 3

BASICS

HOW TO GET THE MEAN, VARIANCE AND STANDARD DEVIATION OF GROUPED DATA DISP LAY: n 50 DISPLAY: x 70.94 DISPLAY: sx 4.391132065

DISPLAY: Ans2 19.28204082 BASICS

HOW TO FIND AREAS IN THE NORMAL CURVE

P(a)meansarea fromz  -  to z  a R(a) meansarea fromz  a to z    Q(a) meansarea fromz  0 to z  a

BASICS

HOW TO FIND AREAS IN THE NORMAL CURVE Find thearea under thenormalcurve to theleft of z  1.64.

ENTER :

DISP LAY: P (1.64) 0.9495 BASICS

HOW TO FIND AREAS IN THE NORMAL CURVE Find thearea beneatha standardnormalcurve between z  0 and thepoint- 1.58.

ENTER :

DISPLAY: Q(-1.58) 0.44295 BASICS

HOW TO FIND AREAS IN THE NORMAL CURVE Find theprobability thata normaldistribution random variable will be within z  1 standarddeviationof themean.

Solution : We are lookingfor thearea fromz  -1 to z  1.

ENTER :

DISPLAY: Q(-1) Q(1) 0.68268 BASICS

HOW TO FIND AREAS IN THE NORMAL CURVE Find theprobability thata normallydistributed random variable will lie more than1.5 standarddeviationabove themean.

Solution : Weare lookingfor thearea fromz  1.5 to z  .

ENTER :

DISP LAY: R(1.5) 0.066807 BASICS

HOW TO SOLVE LINEAR REGRESSION PROBLEMS

BASICS

HOW TO SOLVE LINEAR REGRESSION PROBLEMS ENTER :

DISP LAY:

DISP LAY: A 3.1359045 DISP LAY: B 0.40449955 409

1 2 3 4

x 20 18 16 14

y 12 10 11 6

5 6 7 8

10 8 6 4

7 8 4 6

9 10

2 0

5 2

BASICS

HOW TO SOLVE LINEAR REGRESSION PROBLEMS T herefore: T heregressionequationsis Y  A  BX Y  3.1359045 0.40449954 09X b. To determine the correlatio n coefficien t : DISPLAY: r 0.8854825905

c. T o predict the valueof Y when X  23: DISPLAY: 23y 12.43939394

BASICS

HOW TO GET THE EQUATION OF A LINE GIVEN 2 POINTS

PAST ECE BOARD EXAM Find theequationof theline thatpasses through (2,5)and (-3,8). DISPLAY: ENTER : 1 2

DISPLAY: A 31 5

x

y

2 3

5 8

DISP LAY: B 3

5

BASICS

HOW TO GET THE EQUATION OF A LINE GIVEN 2 POINTS

PAST ECE BOARD EXAM T herefore: theequat ionof theline is : Y  A  BX 31 3 Y  X 5 5 or : 5Y  31 3 X 3 X  5Y  31

BASICS

HOW TO GET A POINT ON THE LINE GIVEN TWO POINTS If a line passes through(4,1)and (3,-7)and (x, y) is on theline,what is the value of x in (x,4)and the value of y in (-5,y)?

DISP LAY: 4 xˆ

Answer : When x  4, y 

35 8

35 8 BASICS

HOW TO GET A POINT ON THE LINE GIVEN TWO POINTS

DISP LAY: Answer : Wheny  - 5, x  - 71  5 yˆ  71

BASICS

PAST ME BOARD EXAM T heequationof theline thatinterceptsthe x - axis at x  4 and the y - axis at y  - 6 is :

ENTER : DISP LAY:

ENTER : x y 1 4 0 2 0 6

DISP LAY: A -6

ENTER : DISP LAY:

Answer : B 1.5 or 3/2

Y  A  BX Y  - 6  3/2X which can be rewrit t enas : 3X - 2Y - 12  0 ADVANCE

PAST CE/ECE BOARD EXAM Find the30th termof thearithmeticprogression 4, 7,10...

ENTER : DISPLAY: x

y

1 1 4 2 2 7

ENTER : DISPLAY: ˆ 30 Y 91

ADVANCE

PAST CE/ECE BOARD EXAM Whatis thesum of theprogression 4, 9,14...up to the20th term?

ENTER : DISPLAY:

ENTER : x

y

DISPLAY:

1 1 4 2 2 9

A DISPLAY: 1 Ans  A 1

ENTER : DISPLAY:

ENTER :

ENTER : B DISP LAY: 5 Ans  B 5 ADVANCE

PAST CE/ECE BOARD EXAM Whatis thesum of theprogression 4, 9,14...up to the20th term?

ENTER :

DISP LAY: 20

 A  BX x 1

1030

ADVANCE

PAST CE BOARD EXAM

T he4th termof theGP is 216and the6th termis 1944.Find the8th term.

ENTER : DISPLAY: x 1 4 2 6

y 216 1944

ENTER : DISPLAY: ˆ 8Y 17496 ADVANCE

MODE 4 : SPECIFIC NUMBER SYSTEMS CALCULATIONS

HOW TO DO BASE NUMBER CALCULATIONS Convert23410 to binary(base 2). ENTER : DISP LAY: 234 Dec 234

ENTER : Thus: 23410  111010102

DISPLAY: 234 Bin 0000000011 101010

BASICS

HOW TO DO BASE NUMBER CALCULATIONS Convert123410 to HEXADECIMAL system. ENTER : ENTER : DISPLAY: 1234 Hex 000004D2

Thus:123410  000004D216 BASICS

HOW TO DO BASE NUMBER CALCULATIONS ConvertABC1216 toOCTALsystem. ENTER : ENTER : DISP LAY: ABC12 Oct 0000253602 2

Thus: ABC1216  00002536022 8 BASICS

HOW TO DO BASE NUMBER CALCULATIONS Evaluate(AB16 )(3F16 ). ENTER : ENTER : DISPLAY: AB x 3F Hex 00002A15

BASICS

HOW TO DO BASE NUMBER CALCULATIONS Evaluate112  4510  AB216  778. (in base 10)

Solution : Convert all values to base 10. For 112

Result : 3

For AB216

Result : 2738

For 778

Result : 63

Add : 3  45  2738 63 Answer : 2849 BASICS

HOW TO DO BASE NUMBER CALCULATIONS Find thelogical AND ( 1012 and1102 ) ENTER :

DISP LAY: 101and110 Bin 0000000000 000100

BASICS

HOW TO DO BASE NUMBER CALCULATIONS Find thelogical XOR ( 1012 and1102 ) ENTER :

DISP LAY: 101xor11 Bin 0000000000 000110

BASICS

MODE 5 : EQUATION SOLUTION

HOW TO SOLVE EQUATIONS IN 2 UNKNOWNS SOLVE 2 x  7 y  4 x  2y 1

BASICS

PAST ME BOARD EXAM In 5 years, Ana' s agewill betwice as the ageof her friend Jun. Five years ago, she was three tim esas old as his friend. Find their presentages.

BASICS

PAST ME BOARD EXAM

BASICS

PAST EE BOARD EXAM A man has 2 investments one paying3% annualinterest and theotherat 4% interest.T he totalincomefrom theinvestments is P1700.If theinterestrates were interchanged, the totalincomewould be P1800. Find theamountof each investment.

BASICS

PAST EE BOARD EXAM

BASICS

PAST ECE BOARD EXAM 2000kg of st eelcont aining8% nickelis t o be made by mixingst eelcont aining14% nickel wit h anot hercont aining6% nickel.How much of each is needed? Solution: Let : X  amountof steelcontaining14% nickel Y  amountof steelcontaining6% nickel

BASICS

PAST ECE BOARD EXAM

BASICS

HOW TO SOLVE QUADRATIC EQUATIONS Solve thequadraticequation6x  7 x  5  0 2

BASICS

HOW TO SOLVE QUADRATIC EQUATIONS Find the values of xin x2  2x  5  0

BASICS

HOW TO SOLVE QUADRATIC EQUATIONS Solve thequadraticequation5x 2  2x  9  0

NOT E: T hisis theadvantageof CASIO ES PLUS over theOLD ES - It can give irrationalroots

BASICS

HOW TO SOLVE EQUATIONS IN 3 UNKNOWNS Find the values of x, y and zif: 3x - 3 y - z  4 x  9 y  2 z  16 x - y  6 z  14

BASICS

HOW TO SOLVE EQUATIONS IN 3 UNKNOWNS

BASICS

HOW TO SOLVE CUBIC EQUATIONS Solve thecubic equation x3  2x 2 -5x - 6  0

BASICS

HOW TO SOLVE CUBIC EQUATIONS Solve x - 1  0 3

BASICS

MODE 6 : MATRIX CALCULATIONS

HOW TO SOLVE PROBLEMS INVOLVING MATRICES

PAST ECE BOARD EXAM  3 5  9 1  Simplify 37 1  2 7 1 4 9 8 9

 3 5 Solution : Store 7 1 to MAT A 4 9

ENTER : 9 1  Solution : Store 7 1 to MAT B 8 9

ENTER :

BASICS

HOW TO SOLVE PROBLEMS INVOLVING MATRICES

PAST ECE BOARD EXAM ENTER : DISP LAY: 3 MAT A  2 MAT B

ENTER :

DISP LAY: Ans  27 17  35 5     28 45 BASICS

HOW TO SOLVE PROBLEMS INVOLVING MATRICES  3 2 - 1 Find the transposeof mat rixA if A   3 7 8  - 1 3 2   3 2 - 1 St ore  3 7 8  t o mat rixA. - 1 3 2 

ENTER :

ENTER : DISP LAY: T rn (Mat A) Ent er: Ans  3 3 - 1 2 7 3   - 1 8 2 

BASICS

HOW TO SOLVE PROBLEMS INVOLVING MATRICES  2 1 3 Find t heinverseof mat rixA if A  6 1 4 3 7 2 2 1 St ore 6 1 3 7

3 4 t o mat rixA. 2

ENTER :

ENTER : DISP LAY: Mat A-1 Ans - 0.4 0.2923 0.0153  0  0.076 0.1538    0.6 - 0.169 - 0.061

BASICS

HOW TO COMPUTE THE DETERMINANT OF A 3X3 MATRIX Find thedeterminant :

2 4 -5 2 1 7 8 1 2

ENTER :

DISP LAY: det(Mat A) 228

BASICS

PAST CE BOARD EXAM In a Cartesiancoordinates, the verticesof a triangleare defined by thefollowingpoints(-2,0),(4,0)and (3,3).Whatis thearea? Concept: T hearea of any t riang le wit h vertices (x1 , y1 ), (x 2 , y 2 ) and (x3 , y 3 ) is : x1

A

1 x2 2 x3

y1

2 0 1

1

y2 1 y3 1

A

1 det 4 2 3

0 1 3 1

ENTER : DISP LAY:

ENTER :

-2 0 1 4 0 1 3 3 1 DISP LAY: 0.5det (MatA) 9

ADVANCE

MODE 7 : GENERATING TABLE FROM A FUNCTION

HOW TO TABULATE VALUES OF A FUNCTION T abulatevaluesof f(x)  x 3  2x2  3 from x  0 to x  10 everyunit step. ENTER :

DISP LAY: 1

X 0

2

1

0

3 4

2 3

13 42

5

4

93

6 7

5 6

172 285

8

7

438

9 10

8 9

637 888

11

10

1197

F(X) 3

BASICS

MODE 8 : VECTOR CALCULATIONS

HOW TO DO VECTOR CALCULATIONS Given the2 vectors: A  4i - j  7k and B  3i  5j  9k. a. Find themagnitudeof theresultantof vectorsA and B. b. Find thedot product of vectorA and B. c. Find thecross product of vectorsA and B.

ENTER : DISP LAY: A [ 4

-1

7 ]

ENTER : DISP LAY: B [ 3

5

9 ]

BASICS

HOW TO DO VECTOR CALCULATIONS ENTER : DISPLAY: Abs(VctA VctB) 17.9164728 7

b. ENTER : DISP LAY: Vct A  Vct B 70

c. ENTER : DISPLAY: VctA  VctB Ans [ - 44

- 15

23]

BASICS

HOW TO DO VECTOR CALCULATIONS

PAST ME/CE BOARD EXAM Whatis themagnitudeof the vectorA  4i  2j  7k and give its directioncosine vector. ENTER : ENTER :

T o get themagnitude: ENTER :

BASICS

HOW TO DO VECTOR CALCULATIONS

PAST ME/CE BOARD EXAM DISP LAY: Abs (Vct A) 8.30662386 3 Not e: (T hisis storedin Ans) T o get thedirectioncosine:

DISPLAY: Ans [0.4815 0.2407 0.8427] BASICS

THANK YOU VERY MUCH AND GOD BLESS!!!

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