Sunday, June 10, 2012

some mathematical preliminaries

brackets in mathematics are used for grouping and clarity.
brackets may also be used to indicate multiplication.
brackets are used in functions to declare the independent variable.

powers: positive whole numbers such as 2 3 , which means 2 X 2 X 2 = 8:

(anything) 3 = (anything) X (anythng) X (anything)

(x)3 = x X x X x

(x +4) 5 = (x+4)(x+4)(x+4)(x+4)(x+4)

Note:
Brackets (A) (B) or A X B or AB
all indicate A multiplied by B.

Variables and letters: When we don't know the value of the quantity, we give that quantity a symbol such as x. We may then make general statements about the unknown quantity, x, for example, "For the next 15 weeks, if I save x per week I shall have $4000 to spend on a holiday".  This statement may be expressed as a mathematical equation:

15 X weekly savings = 4000
15 X x = 4000 or 15x = 4000

Now  that the statement has been reduced to mathematical equation, we may solve the equation for the unknown, x:

15x = 4000
15x/15 = 4000 /15 divide both sides of the equation by 15

x = 266.67

Square roots : the square roots of a number is the reverse of squaring:

(2) 2 = 4 -->  sq root 4 = 2

(2.5) 2  = 6.25 --> sq root 6.25 = 2.5

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