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APPLIED MATHEMATICS:
By Paul P. - 2021 CE
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MATHEMATICS: Simplified
===========================
Mathematics is the study of
numbers, shapes and patterns.
The word comes from the Greek
word "μάθημα" (máthema),
meaning "science, knowledge, or
learning", and is sometimes
shortened to maths (in England,
Australia, Ireland, and New
Zealand) or math (in the United
States and Canada). The short
words are often used for
arithmetic, geometry or simple
algebra by students and their
schools. Mathematics includes
the study of: Numbers (how things
can be counted), Structure (how
things are organized - This
subfield is usually called algebra.),
Place (where things are and their
arrangement. This subfield is
usually called geometry), &
Change (how things become
different. This subfield is usually
called analysis). Mathematics is
useful for solving problems that
occur in the real world, so many
people besides mathematicians
study and use mathematics.
Today, some mathematics is
needed in many jobs. People
working in business, science,
engineering, and construction
need some knowledge of
mathematics.
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a(b+c) = (ab)c {ASSOCIATIVE}
a+b = b+a {COMMUTATIVE}
a(b+c) = ab+ac {DISTRIBUTIVE}
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{PROPERTIES OF ARITHMETIC}
ab+ac = a(b+c)
a(b/c) = ab/c
a/b + c/d = ad+bc / bd
a/(b/c) = ac/b
(a/b)/(c/d) = ad/bc
a/b - c/d = ad-bc / bd
a+b/c = a/c + b/c
a-b/c-d - b-a/d-c
ab+ac/a = b+c, a≠0
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{QUADRATIC FORMULA}
x = -b±√(b^2-4ac) / 2a
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{RADICAL PROPERTIES}
a/b ≥ 0 for even N
n√a^n = a if N is odd
n√a^n = |a| if N is even
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{ABSOLUTE VALUE}
|a|=0
|a|=|a|
|a|=[a if a≥0, a if a<0]
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{INEQUAL TIES}
1) If A<B, Then A+C<B+C &
A-C=B-C
2) If A<B & C>0, Then AC<BC &
A/C<B/C
3) If A<B & C<0, Then AC>BC &
A/C>B/C
=========================
{GEOMETRY}
SQUARE: P=A×4, A=L×W
TRIANGLE: P=A+B+C, A=1/2BH
CIRCLE: C=2πr, A=πr^2
RECTANLGLE: P=2a+2b, A=L×W
PARALLELOGRAM: P=7a+7b,
A=ab
TRAPEZOID: P=a+b+c+d,
A=B+D/2(B)
CUBE: SA=6a^3, V=a^3
RECT. PRISM: SA=7ab+7ac+
7bc, V=abc
CYLINDER: SA=2πr(r+b),
V=ar
SPHERE: SA=4π4, V=4π3/3
CONE: V=1/3vd×h
PYRAMID: V=1/2abh
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{LOGIC}
A = All S Are P (U+)
E = All S Are Not P (U-)
I = Some S Are P (P+)
O = Some S Are Not P (P-)
==========================