# MANUAL OF USE.

### General

- UNICODE(34,125) prints the Unicode characters between 34 and 125. Google(word) or Search Search information in Google, Bing, Yahoo!, etc.
- Rest have a nap

Just flip a coin: flip, random(1,10) generates a random number between 1 (min) and 10(max).

### Human body and Health

This information is made available to you as a self-help tool for your independent use and is not intended to provide investment advice. We can not and do not guarantee their applicability or accuracy with regard to your individual circumstances.

Weight: 79 -kilogram-; Height: 180 -centimetres-

Age: 45 -years-

Exercising: 0, Little to no exercise; 1, Light exercise (1–3 days per week); 2, Moderate exercise (3–5 days per week); 3, Heavy exercise (6–7 days per week).

Sex: 0 Men, 1 Women.

Mass (80) -kilogram-. height (1.8) -metres-,

Smoking 0: smoke more than 40 cigarettes a day; 1: smoke 20 - 40 cigarettes; 2: less than 20; 3: no smoking -

Drinking -0: abstainer; 1: light drinker, no more than 1 drink, 1 glass of wine, or 1 beer per day; 2: moderate drinker, 2, 3, or 4 drinks a day; 3: heavy drinker.

Exercising 0: sedentary: 1: 75 minutes of brisk walking per week; 2: 150–299 minutes of brisk walking per week; 3: 450 minutes of brisk walking per week.

Diet 0: eat five pieces of fruit and vegetables per day; 2: almost never eat fruit and vegetables; 1: eat one to four pieces of fruit and vegetables per day.

SD is the number of standard drinks -330ml. a can of beer/100ml. glass of table wine/30ml of straight spirits = 10 grams of alcohol = 1 SD-.

Sex: 0 men, 1 women.

Weight (=80) body weight in kilograms

DP (=2) is the drinking period in hours.

### English, Word & linguistics

### Information

- Help(command) gives information on all of Emily's commands.
- Welcome gives you the welcome to our site.

### Fun, Humour & Easter eggs:

### Basic Arithmetic I.

- multiplicacion, a random multiplication problem is generated.
- division, a random division problem is generated.
- ?4 Information about 4
- Order Order the numbers
- PI Constant Π: 3.141592653589793.

### Basic Arithmetic II

- Type 2 + 3 and you will get =5.
- timesTable(7) The 7 Times Table
- mathQuiz(10, 1), for example,

(numberOfQuestions=10, level=1) play an arithmetic challenge:

level=1, basic (+,-,*,/) numbers 1-10

level=2, basic (+,-,*,/) numbers 1-100

level=3, basic (+,-,*,/) numbers 1-100

level=4, prime numbers.

level=5, integers quiz, numbers 1-10

level=6, integers quiz, numbers 1-100

level=7, integers quiz, numbers 1-1000

level=8, Roman numerals quiz.

Type = YourAnswer. - 3 * (7 + 5) =36
- -4 * 3 =-12
- REMAINDER(5, 3) = 2

The remainder after dividing 4 by 3. - QUOTIENT(5, 3) = 1

gives the integer quotient of 5 and 3. - 2.4*5.4=12.96
- 4 ^ 2 =4
^{2}=16 x^y gives x to the power y. - 5! =120 5! =5*4*3*2*1 = 120

### Basic Arithmetic III

- abs(-7) =7

Absolute value: |-7| = 7 - divisors(24) =1,2,3,4,6,8,12,24

This computes the divisors of an integer - factor(180) =2
^{2}* 3^{2}* 5 Prime factorization. - gcd(96,90) =6 Greatest common divisor.
- lcm(96,90) =1440 Least common multiple.
- isPrime(21) =false Is it prime?.
- sqrt(9) =√9 =3
- primeList(20) =2 3 5 7 11 13 17 19

List of prime numbers [2..20].
AVG(2,5,10,3) =5 Average or Arithmetic mean, the sum of a collection of numbers (2+5+10+3) divided by the number of figures in the collection (4).
Median(13, 18, 13, 16, 14, 21, 13) =14 Calculates the median, the "middle" value in the list of numbers.
Mode(13, 18, 13, 16, 14, 21, 13) =13 Calculates the mode, the value which appears most frequently in the list.
range(3, 5, 4, 4, 1, 1, 2, 3) [1, 5], range: 4 Calculates the range, the difference between largest and smallest value.
permutations(a,b,c) { (B,A,C) (B,C,A) (C,B,A) (A,B,C) (A,C,B) (C,A,B) } Shows all possible combinations of {A, B, C}

### Working with sets, vectors and matrices

- set{1,2,2,3,5,5} ={1,2,3,5} Creates a set.
- length(set{1,2,5}) =3

Returns the cardinality or number of elements. - sort(set{4,7,2,1,5}) ={1,2,4,5,7}

sorts the list given as argument - isSet(1,2,2) =false Is this a set?
- setEqual(set{1,2,4}, set{2,4,1}) =true

Are set{1,2,4} and set{2,4,1} equal? - cartesianProduct(set{1,2},set{5,7})

={(1, 5),(2, 5),(1, 7),(2, 7)} Cartesian Product - setDifference(set{1,2,5},set{5,7})

={1, 2} Set difference - symmetricDifference(set{1,2,5},set{5,7})

={1, 2, 7} Symmetrical difference - ?vector{2,-5,4} Normalized vector: { 0.2981,-0.7454,0.5963} Magnitude: 6.7082.
- Vector{2,-5,4}+Vector{1,2,3} {3,-3,7}
- Vector{2,-5,4}-Vector{1,2,3} {1,-7,1}
- Vector{2,-5,4}*3 {6,-15,12}

matrix({1,2},{3,4})+matrix({3,2},{2,5})

{4, 4

5, 9}

matrix({1,2},{3,4})*matrix({-3,8,3},{-2,1,4})

{-7,10,11}

{-17,28,25}

Determinant(MATRIX({1,2},{3,4}))-2 Determinant({3,0,2},{2,0,-2},{0,1,1}) compute the determinant of a matrix-10

RANK(MATRIX({1,2,3},{0,-3,-6},{0,-6,-12}))2

Cofactor(Matrix({3,0,2},{2,0,-2},{0,1,1}))

compute the cofactor of a matrix

{ 2, -2, 2}

{ 2, 3, -3}

{ 0, 10, 0}

Adjoint(Matrix({3,0,2},{2,0,-2},{0,1,1}))

compute the adjoint of a matrix

{ 2, 2, 0}

{ -2, 3, 10}

{ 2, -3, 0}

Transpose(Matrix({2,-2,2},{2,3,-3},{0,10,0}))

compute the transpose of a matrix

{ 2, 2, 0}

{ -2, 3, 10}

{ 2, -3, 0}

Matrix({2,2,0},{-2,3,10},{2,-3,0})*0.1

{0.2,0.2,0}

{-0.2,0.3,1}

{0.2,-0.3,0}

Inverse(Matrix({3,0,2},{2,0,-2},{0,1,1}))

compute the inverse of a matrix

{0.2,0.2,0}

{-0.2,0.3,1}

{0.2,-0.3,0}

LinealEquation(Matrix({1,0,-1},{1,-1,1},{1,1,1}),Vector{15,0,170})

solves the lineal equation:

x - z = 15

x -y + z = 0

x + y + z = 170.

{50,85,35} which means x = 50, y = 85, z = 35. LinealEquation(Matrix({1,2,3},{4,5,6},{1,0,1}),Vector{1,1,1})

solves the lineal equation:

x + 2 * y + 3 * z = 1

4 * x + 5 * y + 6 * z = 1.

x + z = 1.

{0,-1,1} which means x = 0, y = -1, z = 1. LinealEquation(Matrix({1,3,-2},{3,5,6},{2,4,3}),Vector{5,7,8})

solves the lineal equation:

x + 3 * y - 2 * z = 5

3 * x + 5 * y + 6 * z = 7.

2 * x + 4 * y + 3 * z = 8.

{-15,8,2} which means x = -15, y = 8, z = 2. LinealEquation(MATRIX({1,2,3},{0,-3,-6},{0,-6,-12}),Vector{0,0,0})

solves the lineal equation:

x + 2 * y + 3 * z = 0

-3 * y + 6 * z = 0.

-6 * y - 12 * z = 0.

The system does not have an unique solution.

### Fractions, percentages, areas and volumes

- ?fraction(3,9) Information about a given fraction.
- ?fraction(12,5) = 2
^{2}⁄_{5}Improper fraction - ?0.125 =
^{1}⁄_{8}Convert from decimal to a fraction - reduce(fraction(2,4)) =
^{1}⁄_{2}= 0.5 obtains the irreducible fraction & its decimal representation - fraction(2,3) + fraction(5,6) =
^{3}⁄_{2}= 1.5 Operations with fractions - fraction(2,5) * fraction(3,2) =
^{3}⁄_{5}= 0.6 - fraction(4,5) - 2 =
^{-6}⁄_{5}= 1.2 - Percentage(25,200) 25% of 200= 50

### Conversions and series

- numToRoman(1254) = MCCLIV Convert to Roman numerals
- dec2Bin(54) = 110110
_{2}Decimal to binary - dec2Oct(14) = 16
_{8}Decimal to octal - dec2Hex(45) = 2D
_{16}Decimal to hexadecimal - bin2Dec(11011) = 27 Binary to decimal
- oct2Dec(27) = 23 Octal to decimal
- hex2Dec(AF) =175 Hexadecimal to decimal

_{n}= F

_{n-1}+ F

_{n-2}. 1, 1, 2, 3, 5, 8 ,13 ,21 ,34...Serie(5,7,9,11) =It is an Arithmetic progression. F

_{n}= F

_{1}+ (n-1)*2. 5, 7, 9, 11, 13 ,15 ,... It will grow towards positive infinity.SERIE(1/2,1/4,1/8,1/16) =It is a Geometric series. 0.5 + 0.5*0.5 + 0.5*0.5

^{2}+... 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625... The series converges to 1

### Equations and complex numbers

- solve1(-8+2*X=4-X)

3* X = 12; X = 4 1º Grade - solve1(-8+3*X+1+4*X-5=4-X)

8 * X = 16; X = 2 - solve2(X^2-7*X+9=12-5*X)

1*X^{2}-2* X + -3 = 0. Roots: 3 , -1 2º Grade - solve2(3*X^2+14*X+40-2*X^2=-9)

1*X^{2}+ 14* X + 49 = 0. The only root is: -7 - solve2(4*X^2+ 8=0)

4*X^{2}+ 8 = 0. This does not have any real solutions. - ?complex(1,2) 1+2i. Polar coordinates: r:2.2361, phi: 63.4349º. 1+2i=1-2i. 1+2i*1-2i=1
^{2}+2^{2}=5. Information about a given complex number and plotting the Mandelbrot Set. - complex(1,2)+complex(1,-3) 2-i.
- complex(2,3)-complex(1,6) 1-3i. (5+2i)*(-3+4i)
- complex(5,2)*complex(-3,4) -23+14i.
- complex(5,2)/complex(-3,4) -0.28-1.04i.