In the early days, one orange, 3 oranges, ..etc. any of the natural numbers, the negatives of these numbers, or zero. natural numbers (a positive integer). Root, Radix, Radicals. Real Number VS. Imaginary (complex) Number.
Related searches for natural numbers (a positive integer)
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any of the natural numbers, the negatives of these numbers, or zero
natural numbers (a positive integer)
Root, Radix, Radicals
Real Number VS. Imaginary (complex) Number
Ninth-century Arab writers called one of the equal factors of a number a root, and their medieval translators used the Latin word radix (“root,” adjective “radical”).
Real number = integer-part + fractional-part
Surds: an irrational root such as √3
lacking sense : IRRATIONAL; absurd
4 + 2i
all have to be either -2 or +2
Radicals become easier if you think of them in terms of indices. Think instead of
Rational Numbers VS. Irrational Number
100.3; 1/6 = .16666; 2/7 = .285714285714
Number that can’t be expressed as p/q. Not a quotient of two integers
2½ = 1.4142135623730950488016887242097….
Approximating irrational number by rational numbers: number theory
How do you represent large multiples such as 2x2x2x2 takes too much space to print 2x2x2x2 = 24 the birth of exponential notation (base, exponent or index (indices))
Now we need a set of rules to figure out what things such as is 22 x 23 Or 23 x 32
Properties of exponents
Logarithms: Math based on the exponents themselves, invented in the early 17th century to speed up calculations. Also from the result of the study of arithmetic and geometric series.
(study tip: the exponent is the logarithm).
8 x 9 = 4 x 2 x 9 = 4 x 18 18 – 4 = 14
1 x 25 = 1 x 5 x 5 5 + 5 = 10
16 x 1 = 4 x 4 4 + 4 = 8
Page 30 example 12, 13
1 x 12 = 3 x 4 3 + 4 = 7
2 x 15 = 2 x 3 x 5 = 6 x 5 6 - 5 = 1
Page 39 example 6
Page 42 – Example 10
Combine the numerator terms
On the 2nd day You climbed 4 miles vertically
On the 2nd day, You covered 3 miles horizontally
3rd day end point
2nd day start point
How far did we walk ?
Equation of a straight line
Now that we know there is a right-triangle, how far did we walk ?
We were only given points A and B. Using A and B we could simply figure out point C. Point C is same height as point A but it is (10 – 4) or 6 units away from A
We can find AB using the Pythagoras’ theorem
Mid-point of line segment AB
x and y are variables -- various points along the line
Slope of a line joining points (0,c) and (x,y)
x can’t be 0
Point (0,c) lies on y axis
Set y = 0 to find the x-intercept
Set x = 0 to find the y-intercept
When m = 0
no incline, line is parallel to x-axis. No x intercept
y = c
M can’t be 0
y = c
No gradient (undefined), straight up, perpendicular to the x axis. No y intercept. Parallel to y axis. x = k.
c is y-intercept
Ex: (1,2), (-1,2), (5,2)…
Example: given gradient, and a point on the line, find the line’s equation
Slope of the line is given
The lines passes through (2,1)
Try this: (-2,3); m = -1 y = -x + 1
Example: given two points on a line, find the line’s equation
Step2: once m is known, use the same equation and one of the points to find the equation
Step1: given two points, it is easy to find m
Try this: (3,4), (-1,2) 2y = x + 5